In fact, it is common for investors, funds, market studies, or special reports on impact investing to make a systematic reference to the SDGs. In Figure 5.10 on page 325, we have already seen that the BlueOrchard Microfinance Fund has five SDGs. Another example is the impact report of the 13 funds managed by Triodos Investment Management, one of the largest and most prominent impact investors in the world. All 13 reports<fnref n="30" /> make extensive use of the SDGs. So do the reports produced by Phenix Capital, one of the leading data providers in impact investing. Below, we highlight the five most important SDGs considered by German impact investors.

<figure><img src="image_160.png" /><figcaption>Figure 5.17: Investors’ view of the top 5 SDGs in Germany</figcaption></figure>

Source: Bundesinitiative Impact Investing (2022) (see Footnote 10 on page 304).

The SDGs are not only the responsibility of countries, but also of all stakeholders in society, including businesses. The challenges addressed by the SDGs are global and interconnected, affecting everyone and requiring cooperation across all sectors. For example, challenges such as **SDG 5** on gender equality and **SDG 13** on climate action are particularly relevant to businesses, as they are critical components of sustainable finance and ESG rating systems. In addition, other challenges directly affect companies, particularly those related to the economy. Goals such as **SDG 8** on decent work and economic growth, **SDG 9** on industry, innovation and infrastructure, and **SDG 12** on responsible consumption and production are essential to business operations. Businesses therefore have a strategic role to play, alongside governments and civil society, in achieving the SDGs (Schramade, 2017; Mio et al., 2020). To conduct business in alignment with the SDGs, companies and governments need investors and financial support. The investment needed to achieve the SDGs is substantial, necessitating the creation of specialized financial channels and investment vehicles. In particular, foreign direct investment (FDI) is generally insufficient (Zhan and Santos-Paulino, 2021). This concerns both horizontal FDI, when a company invests in the same type of business in a foreign country as it does in its home country, and vertical FDI, when a company invests in a different stage of production in the same industry, either upstream or downstream. Blended finance or public-private financing mechanisms are another approach to contribute to the SDGs (Sachs et al., 2019). However, the leverage between private and public capital seems to be insufficient:

> "Each $1 of MDB and DFI invested mobilises on average $0.75 of private finance for developing countries, but this falls to $0.37 for low-income countries. Expectations that blended finance can bridge the SDG financing gap are unrealistic: 'billions to billions' is more plausible than 'billions to trillions'." (Attridge and Engen, 2019, page 11).

Impact investing is a third approach to contributing to the SDGs, but we need to distinguish between two types of use of the SDG landmark:

* The SDGs are used to channel the capital, and the real motivation is to finance economic growth and improve the social situation in poor countries. In this case, the SDGs are really at the heart of the investment. This is the case with many microfinance funds, for example.

<footnote n="30">³⁰The impact reports can be found at www.triodos-im.com/impact-report/2023.</footnote>
* The SDGs are more often used to indicate that the investment is related to this framework, but the motivation is not necessarily to finance economic growth and improve social conditions in poor countries. For example, many climate impact funds invest in green bonds in developed countries. The SDG logos are then used, such as **SDG 7** on affordable and clean energy, **SDG 11** on sustainable cities and communities, and **SDG 13** on climate action.

Therefore, references to the SDGs do not always imply impact investing, but impact investing is generally presented within an SDG framework.

### 5.2.3 SDG funds

The concept of an SDG investment fund does not exist in a standardized form, as there are different ways to use the SDG framework. However, we must acknowledge that many funds refer to SDGs, and it is common to hear a fund described as an SDG fund, similar to how some funds are labeled as ESG funds or climate funds. As with the latter two examples, there is no clear definition of what constitutes an SDG fund, although the term has been adopted by the European regulator (Balitzky and Mosson, 2024). In fact, there is no official or regulatory definition. An SDG fund is simply an investment fund that aims to align its portfolio with the SDGs. By adopting this definition, the door is open to interpretations of what an SDG fund is and is not. Again, by using the term SDG in its name, an investment is considered to be an SDG fund. For example, we can point to some public-private partnerships, such as the UN Joint SDG Fund and the Danish SDG Investment Fund. There are also private investment vehicles. Robeco, for example, has 10 SDG funds<fnref n="31" />: (1) Euro SDG Credits (pioneering SDG framework for credit portfolios), (2) Euro SDG Short Duration Bonds (applying Robeco's proprietary SDG framework across the euro bond market with a short maturity), (3) Global SDG Credits (select companies that contribute positively to the SDGs while aiming to outperform over the full credit cycle), (4) Global SDG Engagement Equities (actively targeting impact and financial returns), (5) Global SDG Equities (actively contributing towards meeting the SDGs), (6) QI Global SDG and Climate Beta Equities (systematically investing for global equity returns with significant sustainability improvements), (7) QI Global SDG and Climate Conservative Equities (systematically investing in low volatility stocks and a high sustainability profile), (8) QI Global SDG and Climate Multi-Factor Credits (systematic approach to credits with significant sustainability improvements), (9) SDG Credit Income (targeting a consistent level of income by investing in companies that contribute to the SDGs) and (10) SDG High Yield Bonds (benefiting from a long-term quality approach pays off in high yield bonds).

The ESMA report uses a general definition:

> "SDG funds are funds stating to contribute towards achieving the SDGs." (Balitzky and Mosson, 2024, pages 4-5).

To identify SDG funds, Balitzky and Mosson (2024) first look at all funds domiciled in the EEA that mention the SDGs in their regulatory communications. Using NLP techniques, they find SDG-related terms in the fund's legal name, strategy (from the Morningstar prospectus), and KIID/KID. After a manual screening, the authors identify a sample of 289 SDG funds. They find that the size of SDG funds reaches €74 bn in September 2023, but the increase is mainly due to the launch of many SDG funds between September 2020 and October 2021. Since then, we observe a stagnation or decline in the SDG fund market. The authors construct a sample of non-SDG funds and compare the characteristics of the two samples in terms of exposure to the UN Global Compact, PAI metrics, and SDG scores. Balitzky and Mosson (2024, page 3) conclude that their results show that "SDG

<footnote n="31">³¹Source: www.robeco.com/en-int/glossary/sustainable-investing/sdg-funds.</footnote>
funds do not significantly differ from non-SDG counterparts or ESG peers regarding their alignment with the United Nations SDGs.” An important comparison concerns the SDG index of SDG and non-SDG funds. For each SDG dimension, the authors then calculate the weighted average SDG score of countries, with the weights proportional to the sovereign debt invested by the funds. The overall SDG score is 74 for SDG funds, compared to 64 for non-SDG funds. This means that SDG funds are more aligned than non-SDG funds. However, the authors note that this relatively better performance does not hold systematically across all SDG dimensions. Figure 5.18 shows the average SDG score per SDG dimension. In the case of **SDG 12** (responsible consumption and production) and **SDG 13** (climate action), non-SDG funds outperform SDG funds.

<figure><img src="image_161.png" /><figcaption>Figure 5.18: Sovereign performance per SDG</figcaption></figure>

Source: Balitzky and Mosson (2024, Chart 10, page 12).

The previous comparison exercise raises the question of how to calculate the alignment of an SDG fund. Let $\mathbb{I}_i$ be the SDG index of country i and $w_{i,j}$ be the weight of country i in fund j. The SDG index for fund j is then the weighted average given below:

$$ \mathbb{I}_j = \sum_{i=1}^{n} w_{i,j} \mathbb{I}_i \qquad (5.2) $$

It is generally assumed that the SDG index $\mathbb{I}_j$ measures the level of SDG alignment of fund j. Therefore, we can introduce a preference ordering:

$$ j \succ j' \Leftrightarrow \mathbb{I}_j \geq \mathbb{I}_{j'} \qquad (5.3) $$

This means that fund j is more aligned than fund $j'$ if and only if fund j has a better SDG index. The previous analysis can be done at the global level or for some SDG dimensions.
**Example 20** We consider three SDG funds that hold sovereign debt or have country exposures, as described in Table 5.11. Amounts are in millions of dollars. For example, SDG Fund #1 has $25.9 million of exposure to Bangladesh, $10.3 million to Honduras, and $19.7 million to Haiti. SDG Fund #2 invests primarily in developed countries, while SDG Fund #3 combines investments in both developed and developing countries. For each country, we provide the SDG and spillover indexes calculated by Sachs et al. (2024).

<table><caption>Table 5.11: SDG data and country exposures for three SDG funds (Example 20)</caption><thead><tr><th>Country</th><th>SDG index</th><th>Spillover index</th><th>Fund #1</th><th>Fund #2</th><th>Fund #3</th></tr></thead><tbody><tr><td>Denmark</td><td>85.00</td><td>58.10</td><td></td><td>100.1</td><td>65.8</td></tr><tr><td>France</td><td>82.76</td><td>62.49</td><td></td><td>356.8</td><td>25.6</td></tr><tr><td>Australia</td><td>76.88</td><td>66.80</td><td></td><td>211.3</td><td></td></tr><tr><td>Morocco</td><td>70.85</td><td>94.70</td><td></td><td></td><td>56.5</td></tr><tr><td>Bangladesh</td><td>64.35</td><td>96.98</td><td>25.9</td><td></td><td></td></tr><tr><td>Honduras</td><td>62.00</td><td>93.05</td><td>10.3</td><td></td><td></td></tr><tr><td>Nigeria</td><td>54.58</td><td>96.55</td><td></td><td></td><td>12.3</td></tr><tr><td>Haiti</td><td>52.68</td><td>94.43</td><td>19.7</td><td></td><td></td></tr></tbody></table>

The SDG index for Fund #1 is equal to:

$$ \mathbb{I}_{1}^{\text{SDG}} = \frac{25.9 \times 64.35 + 10.3 \times 62.00 + 19.7 \times 52.68}{25.9 + 10.3 + 19.7} = 59.80 $$

For the spillover index, we get:

$$ \mathbb{I}_{1}^{\text{Spillover}} = \frac{25.9 \times 96.98 + 10.3 \times 93.05 + 19.7 \times 94.43}{25.9 + 10.3 + 19.7} = 95.36 $$

Finally, the results for the three SDG funds are:

<table><thead><tr><th>Score</th><th>Fund #1</th><th>Fund #2</th><th>Fund #3</th></tr></thead><tbody><tr><td>II<sup>SDG</sup><sub>j</sub></td><td>59.80</td><td>81.24</td><td>77.32</td></tr><tr><td>II<sup>Spillover</sup><sub>j</sub></td><td>95.36</td><td>63.20</td><td>74.66</td></tr></tbody></table>

We obtain the following ranking:

$$ \mathbb{I}_{2}^{\text{SDG}} \geq \mathbb{I}_{3}^{\text{SDG}} \geq \mathbb{I}_{1}^{\text{SDG}} \Rightarrow \text{Fund}_2 > \text{Fund}_3 > \text{Fund}_1 $$

This means that Fund #2 is the most SDG-aligned of the three SDG funds. However, this result is completely absurd. In reality, it is more impactful to invest in countries like Bangladesh, Honduras, and Haiti than it is to invest in Denmark, France, and Australia. In other words, SDG alignment is not the right metric for impact investing. For example, investing in a country with an SDG index of 100% would result in zero SDG impact, as the country cannot further improve its SDG score because all sustainable development goals have already been achieved. Conversely, investing in a poor country with a low SDG score can have a significant impact. Thus, effective impact investing targets low SDG scores, not high ones. Therefore, the preference ordering defined in Equation (5.3) is completely wrong. If we look at the spillover index instead of the SDG index, Fund #1 has a better score. All these results raise the question of the SDG investor's utility function. Going back to the ESMA study, the fact that SDG funds have a higher SDG index score than non-SDG funds (74 vs. 64) is not necessarily a positive conclusion.
As mentioned above, the SDGs were created and defined for countries, not for companies. For example, we don't know how a company can contribute to indicator 1.2.2 (proportion of population living in multidimensional poverty) of SDG 1 (end poverty in all its forms everywhere). Nevertheless, several ESG rating agencies have developed scores for corporate SDG alignment since 2020:

* In September 2020, MSCI introduced the MSCI SDG Alignment Tool, designed to offer investors a comprehensive view of a company's overall contribution — both positive and negative — towards achieving each of the 17 SDGs.

* In March 2021, Factset announced the launch of the Truvalue Labs SDG Monitor, which allows investors to see the alignment of companies around the world with the SDGs in real time.

* Sustainalytics' impact metrics is a set of company-level metrics that provide investors with useful measures of companies' environmental and social impact. The metrics are aligned to Sustainalytics' proprietary impact framework and the UN SDGs.

* ISS developed the SDG Impact Rating to provide a comprehensive and detailed view of a company's overall SDG impact, as well as across all 17 SDGs, and to better understand the issuer's performance relative to its industry peers.

* In August 2021, Moody's launched SDG Alignment Screening, a data solution to help investors integrate the SDGs into SDG-aligned investment strategies, funds, indexes and reporting.

* Etc.

These SDG ratings and scores are used by asset owners and managers to create SDG funds, SDG investment strategies, etc. For example, on January 9, 2024, S&P Dow Jones Indices announced the launch of two new sustainability indexes: the S&P 500 SDG Index and the S&P Global LargeMid-Cap SDG Index. The S&P 500 SDG Index tracks large-cap US equities, while the S&P Global LargeMidCap SDG Index tracks a broad range of market capitalizations across developed and emerging markets. S&P Dow Jones Indices worked with Impact Cubed to develop these indices, using their methodology to evaluate companies based on their revenue-generating activities and community engagement<fnref n="32" />.

To illustrate corporate SDG alignment, we consider the MSCI approach (MSCI, 2024), which is among the most widely used by professionals. The MSCI SDG alignment methodology assesses each company's alignment with the 17 SDGs using a numerical score (−10 to 10) and a categorical assessment (strongly aligned to strongly misaligned). It does not provide an aggregate company-level score. The evaluation includes:

1. SDG net alignment score and assessment: overall alignment with each SDG;

2. SDG product alignment score and assessment: alignment of the company's products and services with each SDG;

3. SDG operational alignment score and assessment: alignment of the company's operations with each SDG.

<footnote n="32">³²The methodology behind the construction of the S&P SDG Indices, as well as the underlying data used, can be found at www.spglobal.com/spdji/en/education/article/introducing-the-sp-sustainable-development-goals-indices.</footnote>
<figure><img src="image_162.png" /><figcaption>Figure 5.19: Example of the SDG net alignment assessment of a food retail company (MSCI)</figcaption></figure>

Source: MSCI (2024, Exhibit 3, page 7).
Each company then receives a total of 51 scores and 51 corresponding assessments (17 net alignment + 17 product alignment + 17 operational alignment). The assessment is based on the score $\mathbf{S}$, categorized as: strongly aligned if $\mathbf{S} > 5$, aligned if $2 < \mathbf{S} \le 5$, neutral if $-2 < \mathbf{S} \le 2$, misaligned if $-10 < \mathbf{S} \le -2$, and strongly misaligned if $\mathbf{S} = -10$. For example, if the SDG product alignment score for a company is $\mathbf{S} = 6$, then the company is considered strongly aligned for the product dimension. The SDG net alignment score is the average of its SDG product alignment score and SDG operational alignment score, unless one of the two scores is $-10$, in which case the net alignment score is $-10$:

$$ \mathbf{S}^{\text{net}} = \begin{cases} \frac{\mathbf{S}^{\text{product}} + \mathbf{S}^{\text{operational}}}{2} & \text{if } \min(\mathbf{S}^{\text{product}}, \mathbf{S}^{\text{operational}}) > -10 \\ -10 & \text{if } \min(\mathbf{S}^{\text{product}}, \mathbf{S}^{\text{operational}}) = -10 \end{cases} $$

Criteria for a score of $-10$ in product or operational alignment are generating more than 50% of revenue from products/services with negative SDG impacts, or involvement in significant (red flag) controversies related to an SDG. Figure 5.19 shows an example of the SDG net alignment assessment of a food retailer, which can be found in MSCI (2024).

<table><caption>Table 5.12: SDG product alignment score aggregation</caption><thead><tr><th>Product alignment</th><th>Score contribution</th></tr></thead><tbody><tr><td rowspan="5">Positive alignment (% of revenue)</td><td>&gt; 50%</td><td>+10</td></tr><tr><td>25 - 50%</td><td>+7</td></tr><tr><td>10 - 25%</td><td>+5</td></tr><tr><td>5 - 10%</td><td>+3</td></tr><tr><td>0 - 5%</td><td>+1</td></tr><tr><td rowspan="5">Negative alignment (% of revenue)</td><td>0 - 5%</td><td>-1</td></tr><tr><td>5 - 10%</td><td>-3</td></tr><tr><td>10 - 25%</td><td>-5</td></tr><tr><td>25 - 50%</td><td>-7</td></tr><tr><td>&gt; 50%</td><td>-10</td></tr></tbody></table>

Source: MSCI (2024, Exhibit 4, page 9).

To calculate the SDG product alignment score, MSCI (2024) determines the percentage of revenue that is positively aligned with the SDG and the percentage of revenue that is negatively aligned with the SDG. For each of the SDGs, they define a list of products and services with positive and negative impacts. For example, in the case of **SDG 13** (climate action), revenue from services with positive impacts comes from alternative energy, including hydropower, demand-side management, smart grid, and turbine manufacturing for alternative energy and hydropower, while revenue from services with negative impacts comes from electricity generation from fossil fuels, oil and gas exploration and production, or coal mining, and fossil fuel turbines. Then they use the score aggregation method shown in Table 5.12. For example, if a utility company has 55% of its revenue from solar power generation, 20% of its revenue from coal power generation, and 25% of its revenue from water management, it has a positive alignment of 55% and a negative alignment of 20% with respect to **SDG 13**. The product alignment score for this company is $10 - 3 = 7$. Because this score is greater than 5, this company is considered to be strongly aligned with **SDG 13**. If the revenue split is not 55%/20%/25%, but 20%/55%/25%, the score is not $3 - 10 = -7$, but $-10$, because the positive impact cannot offset the negative impact. This means that a company with a negative impact score of $-10$ has a global score of $-10$ and is considered strongly misaligned.
<table><caption>Table 5.13: SDG operational alignment score aggregation</caption><thead><tr><th></th><th>Operational alignment</th><th>Score contribution</th></tr></thead><tbody><tr><td rowspan="4">Positive impact</td><td>Policies aligned with the SDG</td><td>+1 each</td></tr><tr><td>Initiatives aligned with the SDG</td><td>+1 each</td></tr><tr><td>Targets aligned with the SDG</td><td>+1 each</td></tr><tr><td>Involvement in operations with adverse impact</td><td>-1 each</td></tr><tr><td rowspan="8">Negative impact</td><td>Any red flag controversies</td><td>-10</td></tr><tr><td>3 or more orange flag controversies</td><td>-7</td></tr><tr><td>7 or more yellow flag controversies</td><td>-7</td></tr><tr><td>1 or 2 orange flag controversies</td><td>-5</td></tr><tr><td>5 or 6 yellow flag controversies</td><td>-5</td></tr><tr><td>3 or 4 yellow flag controversies</td><td>-3</td></tr><tr><td>1 or 2 yellow flag controversies</td><td>-1</td></tr><tr><td rowspan="2">Performance metrics</td><td>Improving trend</td><td>+2</td></tr><tr><td>Worsening trend</td><td>-2</td></tr></tbody></table>

Source: MSCI (2024, Exhibit 5, page 12).

The assessment of SDG positive and negative operational impacts is based on evidence from publicly disclosed company data. Each aligned policy, practice or target gains 1 point. Each engagement in operations with negative impacts loses 1 point. In addition, controversies contribute to the SDG negative operational impact score, which ranges from 0 to -10 based on the frequency and severity of incidents. This score uses the MSCI ESG controversy methodology to categorize controversies as red, orange, and yellow flags. Finally, the SDG operational alignment score takes into account a company's performance metrics, which are either positive or negative depending on the trend over the past three years. These performance metrics include energy consumption, carbon emissions, female employment, and employee injury rates. The method of aggregating the scores is shown in Table 5.13. Consider the case of **SDG 5** (gender equality). The metrics indicating positive impact include programs for workforce diversity and diversity policies, a percentage of women in the workforce, executive management, and senior management all exceeding 20%, a percentage of women on the board exceeding 30%, and a minimum of one woman sits on the board. Metrics indicating negative impact involve controversies related to labor (such as gender discrimination, gender harassment, forced labor in operations or supply chains, and employee or labor discrimination in operations or supply chains) and customer discrimination. Finally, performance metrics include the trend in the growth of the percentage of women employees in the workforce over the past three years and the trend in the growth of the percentage of women in senior management.

The presentation of the MSCI approach highlights that corporate SDG alignment is based on two main components: revenue breakdown and controversies. Other SDG methodologies also rely on these two components. Notably, the country dimension is completely absent from these methodologies. For example, companies are considered aligned with **SDG 2** (zero hunger) if their revenue comes from nutrition and sustainable agriculture. This concept of **SDG 2** for corporate alignment differs significantly from the broader **SDG 2** objectives. A company operating in a wealthy country with 100% of its revenues from sustainable agriculture is seen as strongly aligned with **SDG 2**. However, its actual contribution to the UN SDGs is negligible. Therefore, we must be cautious with corporate SDG alignment as it is easy to fall into SDG washing (Heras-Saizarbitoria et al., 2022). While the use of SDG logos is helpful for visualizing the SDG themes behind impact investing, it is dangerous to take this further because companies are not countries.
## 5.3 The market of impact investing

In the following analysis, we examine the impact investing market from two perspectives. First, we assess the size of the market by analyzing statistics on assets under management. Second, we examine the different products that make up the impact investing market, including specialized investment vehicles such as social impact bonds, blended finance structured funds, and specialized investment funds such as blue and microfinance funds.

### 5.3.1 Market size

#### Total size

Estimating the size of the impact investing market is challenging due to the large proportion of direct investments, particularly those made by charities or philanthropic investors. However, we have three specialized sources that can provide an approximation of the size of the market. In October 2022, the GIIN estimated that more than 3000 public and private organizations were managing $1.164 trillion in impact investing AUM globally as of December 2021 (Hand et al., 2022). In a subset of 1289 organizations, the average impact investment portfolio is $485 million, while the median is $62.5 million. This shows that a few large organizations manage high AUM in impact investing, implying that most organizations have relatively small allocations to impact investing. The geographic breakdown of impact AUM is 55% in Europe, 37% in North America, 3% in Africa, 2.5% in Asia and 1% in Latin America.

A second source for estimating the size of the market is the impact investing reports published by PitchBook (2023, 2024). There are several statistics available in the Excel file provided by PitchBook. To understand the different metrics, consider the following identity:

Cumulative capital raised + Mark-to-market + Termination value = Dry powder + Remaining value

where cumulative capital raised is the total amount of money committed by investors to the funds, mark-to-market reflects any appreciation or depreciation of the investments based on their current market price, termination value is the value realized from exited investments<fnref n="33" />, dry powder is the uninvested portion of the capital raised (the capital available for future investments), and remaining value is the current value of the investments still held by the funds, including the mark-to-market value of those investments. We can simplify this equation because the right side is equal to the current assets under management:

$$Dry powder + Remaining value = Current AUM$$

Figure 5.20 shows the assets under management per year and their decomposition between dry powder and remaining value. As of June 30, 2023, the AUM is $885 billion, with a significant portion, 26%, not yet deployed and classified as dry powder. Fundraising activity can be measured in two ways: the number of funds launched and the capital raised during the year. These metrics are given in Figure 5.21, while the cumulative statistics since 2007 are shown in Figure 5.22. Between 2007 and 2023, 2292 impact investing funds have been launched, raising a total of $1.05 trillion in capital. Of this capital, 47.2% has been raised in North America, 34.6% in Europe, 11.1% in Asia, and 7.1% in the rest of the world. Table 5.14 shows the breakdown of fundraising activity by strategy since 2007. While private equity and venture capital dominate the traditional ESG investing market in alternative assets, real assets account for two-thirds of the capital raised in impact investing for

<footnote n="33">³³This is the cash or other value received when investments are sold or otherwise exited.</footnote>
<figure><img src="image_163.png" /><figcaption>Figure 5.20: Size of the impact investing market (AUM in $ bn, PitchBook impact database)</figcaption></figure>

Source: PitchBook (2023, page 5), https://pitchbook.com & Author's calculations.

both public and private assets. According to the PitchBook database, most impact investments are made in private markets. In addition to the 67% allocated to real assets, private equity represents 21.5% of the capital raised, and real estate accounts for 3.9%. Furthermore, a significant portion of the debt strategy also pertains to private markets (Table 5.14).

<table><caption>Table 5.14: Strategy representation of impact investing (as of December 2023, PitchBook impact database)</caption><thead><tr><td>Strategy</td><td>Fund count</td><td>Capital raised</td></tr></thead><tbody><tr><td>Private equity (buyout)</td><td>21.90%</td><td>14.49%</td></tr><tr><td>Venture capital</td><td>40.18%</td><td>7.03%</td></tr><tr><td>(Private) debt</td><td>7.16%</td><td>6.26%</td></tr><tr><td>Real estate</td><td>5.80%</td><td>3.93%</td></tr><tr><td>Real assets*</td><td>20.55%</td><td>66.96%</td></tr><tr><td>Other</td><td>4.41%</td><td>1.33%</td></tr></tbody></table>

*Real assets = infrastructure & natural resources.

Source: PitchBook (2023), https://pitchbook.com & Author's calculations.

**Remark 49** We observe a high dispersion in fund size. For example, the median fund size is $147.9 million in Europe, $63.8 million in North America, and $70.0 million in the rest of the world, while the average fund size is $633.0 million, $563.7 million, and $468.7 million, respectively. This high skew is mainly due to the large size of infrastructure funds. The dispersion is highest in Europe, where the top 10% of funds start at $1.6 billion, while the bottom 10% is $16.9 million.
<figure><img src="image_164.png" /><figcaption>Figure 5.21: Fundraising activity (PitchBook impact database)</figcaption></figure>

Source: PitchBook (2023, page 5), https://pitchbook.com & Author's calculations.

<figure><img src="image_165.png" /><figcaption>Figure 5.22: Cumulative fundraising (PitchBook impact database)</figcaption></figure>

Source: PitchBook (2023, page 5), https://pitchbook.com & Author's calculations.
The third specialized source is the Phenix impact database, developed by the Phenix Capital Group. According to Phenix Capital (2024a), €589 billion has been allocated to more than 2600 impact investing funds, which are managed by approximately 1100 asset managers. The distribution of assets under management by strategy differs from the PitchBook database. In fact, we have the following breakdown: 48% private equity (buyout and venture capital), 22% real assets (including real estate), 13% private debt, 3% public debt, 9% public equity, and 4% other. Figure 5.23 shows the evolution of the capital raised between 2014 and 2023. We observe a significant increase in the rate of capital growth until 2020, followed by a notable slowdown starting in 2021. This deceleration is also reflected in the PitchBook impact database. Interestingly, this phenomenon coincides with a period of intense discussion and popularization of impact investing among asset managers.

<figure><img src="image_166.png" /><figcaption>Figure 5.23: Cumulative capital raised in € bn (Phenix impact database)</figcaption></figure>

Source: Phenix Capital (2024a, page 16).

One interesting piece of information from the impact reports published by Phenix is the SDGs targeted by impact funds. Figure 5.24 shows Phenix's mapping of the SDGs to the themes commonly used by impact investing practitioners. This enables Phenix to count the number of funds targeting each SDG. The results are shown in Table 5.15. For instance, across all investment funds, **SDG 7** (affordable and clean energy) is the most targeted goal, followed by **SDG 9** (industry, innovation and infrastructure) and **SDG 3** (good health and well-being). This ranking varies significantly by asset class. In private equity, impact funds predominantly target **SDG 3** (good health and well-being) and **SDG 2** (zero hunger), while in private debt, they focus on **SDG 1** (no poverty) and **SDG 5** (gender equality). This is because private equity impact funds invest primarily in the healthcare and food sectors, whereas private debt impact funds are dominated by microfinance funds. In the case of real assets, the two most targeted goals are **SDG 7** (affordable and clean energy) and **SDG 11** (sustainable cities and communities) because of the importance of infrastructure in this asset class.
<figure><img src="image_167.png" /><figcaption>Figure 5.24: Phenix Capital Group's mapping of the SDGs to the themes commonly used by impact investing practitioners</figcaption></figure>

Source: www.phenixcapitalgroup.com/sustainable-development-goals-impact-investing-themes.

<table><caption>Table 5.15: Most targeted SDGs (Phenix impact database)</caption><thead><tr><th>Rank</th><th>All Funds</th><th>Private Equity</th><th>Private Debt</th><th>Real Assets</th><th>Public Equity</th><th>Public Debt</th></tr></thead><tbody><tr><td>1</td><td>SDG 7</td><td>SDG 3</td><td>SDG 1</td><td>SDG 7</td><td>SDG 7</td><td>SDG 11</td></tr><tr><td>2</td><td>SDG 9</td><td>SDG 2</td><td>SDG 5</td><td>SDG 11</td><td>SDG 3</td><td>SDG 7</td></tr><tr><td>3</td><td>SDG 3</td><td>SDG 9</td><td>SDG 7</td><td>SDG 15</td><td>SDG 9</td><td>SDG 13</td></tr><tr><td>4</td><td>SDG 2</td><td>SDG 7</td><td>SDG 2</td><td>SDG 2</td><td>SDG 12</td><td>SDG 12</td></tr><tr><td>5</td><td>SDG 11</td><td>SDG 12</td><td>SDG 8</td><td>SDG 12</td><td>SDG 11</td><td>SDG 14</td></tr></tbody></table>

Source: Phenix Capital (2024a).
The situation in public markets differs from that in private markets. While there are some similarities between public and private equities, the same is not true for public and private debt. For example, public equity impact funds primarily target **SDG 7** (affordable and clean energy) and **SDG 3** (good health and well-being), which are also major goals for private equity impact funds. However, only one SDG (affordable and clean energy) is common among the top five SDGs targeted by both public equity impact funds and private equity impact funds.

**Remark 50** These three specialized data sources provide three different pictures of the impact investing market. However, there are some similarities between them. First, the GIIN report is primarily based on data from Phenix Capital Group and Pitchbook. Second, while the size of the market differs from provider to provider (especially GIIN vs. Phenix), the three databases show the same trend in terms of capital growth. The growth of impact investing is more important through 2020 than from 2021.

## Regional size

In addition to these global reports, there are also regionally focused impact investing reports. Here are a few examples:

1. *Estimating and Describing the UK Impact Investing Market*, published by EY and the Impact Investing Institute in March 2022;

2. *The African Investing for Impact Barometer*, published by RisCura in April 2022;

3. *Impact Investing in Germany 2022*, published by Bundesinitiative Impact Investing in October 2022;

4. *Accelerating Impact: Main Takeaways from the First Harmonised European Impact Investment Market Sizing Exercise*, published by EVPA in December 2022;

5. *Overview of the French Impact Investment Market 2023*, published by FAIR in November 2023;

6. *2023 in Retrospect: India Impact Investment Trends*, published by Impact Investors Council in May 2024;

7. *Impact Investing in Africa: A 2024 Analytical Map*, published by FERDI in June 2024;

Below we report the size estimated by each study for the corresponding region:

<table><thead><tr><th>Study</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>Region</td><td>UK</td><td>Africa</td><td>Germany</td><td>Europe</td><td>France</td><td>India</td><td>Africa</td></tr><tr><td>Reporting year</td><td>2020</td><td>2021</td><td>2022</td><td>2022</td><td>2022</td><td>2023</td><td>2024</td></tr><tr><td>AUM (in bn)</td><td>£58</td><td>$72.6</td><td>€38.9</td><td>€80</td><td>€14.8</td><td>$2.9</td><td>$25</td></tr></tbody></table>

These figures fall significantly short of the $1.164 trillion in impact investing assets under management (AUM) estimated by the GIIN (Hand et al., 2022). According to the EVPA, the size of the impact investing market in Europe is around €80 billion, while the GIIN estimates it to be over $500 billion globally. One reason for the discrepancy is that a significant portion of the AUM in the GIIN study corresponds to publicly traded assets. Another factor is that most assets are self-reported. However, it is reasonable to conclude that the true size of the impact investing market is probably less than $500 billion and certainly not more than $1 trillion.
### 5.3.2 Market products

Another way to gain a clearer understanding of the impact investing market is to examine specific investment products. This approach can shed light on why there are such significant discrepancies in market size estimates, particularly when listed assets are included. In fact, the question of market size is closely related to the distinction made at the beginning of this chapter: investing WITH impact versus investing FOR impact. The analysis of specific products will help to clarify this distinction.

#### Social impact bonds

There is no single definition of social impact bonds (SIB), as they come in many different forms. Depending on the country and structure, they may also be referred to as pay-for-success bonds, social outcomes contracts (SOC), pay-for-benefit bonds, payment-by-results (PBR) instruments, development impact bonds, or simply impact bonds. However, they share certain common characteristics, most notably that they belong to the category of outcome-based financial contracts in which investors provide up-front capital to finance social programs and are repaid only if the desired outcomes are achieved. Typically, social impact bonds work through a partnership between the public sector, private investors, and service providers to address social issues such as homelessness, education, criminal justice, and public health. There are two major types of impact bonds. Domestic impact bonds are those where the outcome payer is the government representing the citizen target group. In contrast, development impact bonds (DIB) involve an external organization, such as an aid agency, as the outcome payer rather than the government.

In 2009, UK Prime Minister Gordon Brown committed the government to developing social outcomes contracts. At the same time, Social Finance, a London-based charity, developed the concept of social impact bonds and defined the SIB mechanism as follows:

> "Social Impact Bonds are based on a commitment from government to use a proportion of the savings that result from improved social outcomes to reward non-government investors that fund the early intervention activities. Social Impact Bonds are based on a contract negotiated with government that includes clear definitions of the success metric — for example, the 1 year reoffending rate for short-sentence offenders in a specified geographic area; the target population — for example, offenders aged over 18 leaving prison after a sentence of less than 12 months and returning to a specified geographic area; the value of success — the amount returned to investors for a given improvement in the social outcome, generally a proportion of the related savings to government. In order to effectively incentivise investors this needs to be tailored to each situation. For example, the value of success may increase as the reoffending rate falls in recognition of the fact that more difficult target groups require more expensive interventions. Once the contract is in place, investment is raised from non-government investors. This investment is used to finance a range of interventions to improve the target social outcome over the contract period (around 5 years). If the interventions are successful and the social outcomes improve, government pays investors a reward based on the pre-agreed payment schedule." (Social Finance, 2009, page 3).

Social Finance proposed using the SIB mechanism to reduce recidivism. In the 2000s, approximately 40 000 adults in the UK left prison each year after serving sentences of less than 12 months. These prison placements cost the taxpayer over £213 million annually. Despite this, adults serving short sentences received no formal support to help them successfully reintegrate into the community,
resulting in 73% of these offenders reoffending within two years of release. Social Finance's approach aimed to provide support that would reduce reoffending rates, lower costs for the government and society, and use these savings to finance the interventions, with returns paid to investors. In 2010, the project was approved and the first SIB pilot was implemented in HM Prison Peterborough. From September 2010 to June 2014, approximately 2000 offenders released from prison received one year of individualized care and support from a variety of organizations to assist with housing, employment, and, if necessary, drug and alcohol treatment. With a budget of £5 million, the program aimed to reduce recidivism by 7.5%. It was funded by private investors and Social Finance, who were reimbursed by the Ministry of Justice and the Big Lottery Fund. The program ultimately exceeded expectations, achieving a 9% reduction in reoffending. It's a story that's been told around the world<fnref n="34" /> and the subject of numerous works on SIBs.

Box 5.4: Outcomes-based contracting

Outcomes-based contracting (OBC) shifts the focus of public service contracting from activities and inputs to achieving measurable outcomes that positively impact service users. Traditional models, such as fee-for-service, pay providers for delivering specified services. In contrast, OBC links payments to the achievement of specific outcomes, incentivizing service providers to deliver results that improve the lives of users. OBC is a subset of results-based financing (RBF), of which impact bonds are a prominent example, in which private investors provide up-front capital for service delivery and are repaid only if the desired outcomes are achieved. The theoretical benefits of OBC include incentivizing positive behavior, managing risk by transferring responsibility to providers or investors, and potentially reducing the cost of public services while increasing their effectiveness. However, evidence on the effectiveness of OBC remains limited and sometimes contradictory, as most evaluations focus on service outcomes rather than the contracting mechanism itself.

Source: https://golab.bsg.ox.ac.uk/the-basics/outcomes-based-contracting.

Since the pilot in 2010, approximately 300 impact bonds have been launched globally. In August 2012, the first impact bond outside the UK was introduced in New York City, targeting a reduction in reoffending. By 2013, the first social impact bonds were launched in Australia, Germany, and the Netherlands. In 2014, Belgium and Canada saw their first SIBs, followed by Austria, India, Israel, Finland, Portugal, and Switzerland in 2015. Additionally, in February 2015, the first development impact bond was announced to support sustainable cocoa and coffee production within the indigenous Asháninka community in Peru. In 2016, the UK government and the University of Oxford established the Government Outcomes Lab (GO Lab), a research and policy center dedicated to exploring how governments can work with the private and social sectors to improve social outcomes. In particular, the GO Lab developed the impact bond dataset INDIGO<fnref n="35" />, which serves as the primary source of information on social impact bonds (SIBs). As of July 2024, the INDIGO dataset contains 321 projects (or impact bonds), 37 funds, and 1645 organizations. One project corresponds to one impact bond. For example, project INDIGO-POJ-0001 is the Proyecta Tu Futuro (Plan Your Future, Buenos Aires Youth Employability SIB), which aims to reduce youth unemployment in the city of Buenos Aires<fnref n="36" />. A fund is a basket of social projects. For example, fund INDIGO-FUND-0001 is

<footnote n="34">³⁴A fuller description of the Peterborough Prison SIB pilot, including the investment and payment structure, can be found in Disley et al. (2011, 2016).</footnote>

<footnote n="35">³⁵The direct link to the dataset is https://golab.bsg.ox.ac.uk/knowledge-bank/indigo.</footnote>

<footnote n="36">³⁶The project focuses on vulnerable unemployed young citizens and vulnerable young citizens who have not com-</footnote>
the Youth Engagement Fund launched by the United Kingdom<fnref n="37" />. An organization is a stakeholder in an impact bond or fund. The GO Lab distinguishes three types of organizations, both of which participate to achieve better outcomes for the target group:

* Outcome payers are the commissioners. They identify social problems, specify payable outcomes that must be achieved to address those problems, and pay for the outcomes that are achieved.

* Service providers work with the target population to achieve the outcomes specified by the outcome payer and receive payments based on the achievement of specified outcomes.

* Investors provide upfront funding to the service provider to finance the project and are repaid based on the achievement of specified outcomes.

For example, organization INDIGO-ORG-0001 is Sheffield Futures, which is a youth charity. For a given impact bond or fund, we have the list of organizations participating in the project. For example, there are 14 organizations participating in the Buenos Aires Youth Employability SIB<fnref n="38" />.

According to the INDIGO database, there are 296 social impact bonds (SIBs) with a total capital raised exceeding $760 million. The median size of these bonds is relatively small, at $1.2 million. Approximately 2.6 million people benefit from these impact projects, although the median number of service users is only 500. This suggests that most social impact bonds are highly targeted to specific groups. Around 40% of SIBs have matured and been completed, while 60% are still active. In terms of policy areas, employment and training is the most common focus, followed by health and wellbeing, child and family welfare, and homelessness. The SIB market is led by the UK, followed by the US, Portugal, Japan, and the Netherlands. However, the market's growth has slowed in recent years, particularly after the COVID-19 crisis, as illustrated by the number of social impact bonds initiated each year, shown in Table 5.16.

<table><caption>Table 5.16: Number of social impact bonds per start year</caption><thead><tr><th>Year</th><th>#</th><th>Year</th><th>#</th><th>Year</th><th>#</th></tr></thead><tbody><tr><td>2010</td><td>1</td><td>2015</td><td>24</td><td>2020</td><td>35</td></tr><tr><td>2011</td><td>1</td><td>2016</td><td>26</td><td>2021</td><td>22</td></tr><tr><td>2012</td><td>13</td><td>2017</td><td>41</td><td>2022</td><td>14</td></tr><tr><td>2013</td><td>7</td><td>2018</td><td>47</td><td>2023</td><td>9</td></tr><tr><td>2014</td><td>9</td><td>2019</td><td>36</td><td>2024</td><td>1</td></tr></tbody></table>

Source: https://golab.bsg.ox.ac.uk/knowledge-bank/indigo/impact-bond-dataset-v2.

**Remark 51** There are few resources devoted to the theoretical aspects of SIB design, except for the work of Chowdhry et al. (2019).

pleted high school. The intervention will provide weekly workshops on soft skills training, employment support, orientation and placement in companies. The intervention aims to help the participant to find and keep a job and to graduate from high school (if the participant has not yet graduated).

<footnote n="37">³⁷The Youth Engagement Fund aims to support disadvantaged young people to participate and succeed in education or training in order to improve their employability, reduce their long-term dependency on benefits, and reduce their likelihood of offending. The UK government aims to provide funding through social impact bonds and will only pay out if projects deliver positive outcomes.</footnote>

<footnote n="38">³⁸They are Social Finance UK, AMIA, Fundacion Forge, Fundacion Pescar, Fundacion Reciduca, Acruz Partners, Beccar Varela Law Firm, Fundacion Alimentaris, Government of the City of Buenos Aires, Banco Ciudad de Buenos Aires, Banco Galicia, IRSA Propiedades Comerciales, Organizacion Roman, and the Inter-American Development Bank.</footnote>
## Blue funds

A blue bond works similarly to a green or social bond, but with a specific focus on ocean and sea protection. Blue bonds are typically issued by governments, supranational organizations or development banks to support initiatives and finance projects that promote the conservation and sustainable use of ocean and water resources. In September 2023, ICMA, together with ADB, IFC, UNEP FI and UN Global Compact, developed a global practitioner's guide for bonds to finance the sustainable blue economy (SBE). It is a preliminary version of the Blue Bond Principles. According to this guide, funds raised through blue bonds are typically used to support eight typical activities (ICMA, 2023, Table 1, pages 6-7):

1. Coastal climate adaptation and resilience (climate change adaptation): Projects that support ecological and community resilience and adaptation to climate change including using nature-based solutions;

2. Marine ecosystem management, conservation, and restoration (terrestrial and aquatic biodiversity): Projects that manage, conserve, and restore the health of coastal and marine ecosystems<fnref n="39" />;

3. Sustainable coastal and marine tourism: Projects that improve the environmental sustainability of coastal and marine tourism

4. Sustainable marine value chains (environmentally sustainable management of living natural resources and land use): Projects that improve the environmental sustainability of marine value chains:

(a) Sustainable marine fisheries management

(b) Sustainable aquaculture operations (algae, bivalves, fish, and seagrass)

(c) Seafood supply chain sustainability

5. Marine renewable energy (renewable energy): Projects that increase contribution of marine and offshore renewable energy to energy mix and renewable energy projects that support other SBE sectors while safeguarding the marine environment. These include offshore wind (both fixed and floating installations), wave, tidal, floating solar and ocean thermal energy conversion;

6. Marine pollution (pollution prevention and control/sustainable water and wastewater management/circular economy adapted products, production technologies and processes): Projects that prevent, control, and reduce waste from entering the coastal and marine environments<fnref n="40" />:

(a) Wastewater management

(b) Solid waste management

(c) Resource efficiency and circular economy (waste prevention and reduction)

(d) Non-point source pollution management

7. Sustainable ports (clean transportation): Projects that increase environmental performance and sustainability of port functions and infrastructure;

<footnote n="39">³⁹Projects must be within the marine environment or within 100 km of the coast.</footnote>

<footnote n="40">⁴⁰For wastewater management, projects must be within 100 km of the coast. For solid waste management, projects must be within 50 km of the coast or a river that drains to the ocean. For non-point source pollution management, projects must be within 200 km of the coast or within 50 km of rivers (and their tributaries) that flow to the ocean.</footnote>
8. Sustainable marine transport (clean transportation): Projects that involve increasing environmental performance and sustainability of maritime transportation.

Blue bonds are a key component of blue finance, a broad term for investments aimed at supporting projects that protect oceans and improve water management. Other instruments in blue finance include blue loans and blue funds. More broadly, blue finance aligns with the concept of the blue economy, a term introduced by Belgian economist Gunter Pauli<fnref n="41" />. In 2015, Hoegh-Guldberg et al. (2015) estimated that the value of blue economy assets, including energy production, mining, tourism, maritime transportation, aquaculture, fisheries, and more, is more than $24 trillion<fnref n="42" />. These assets generate annual revenues of approximately $2.5 trillion. If considered as a national economy, the blue economy would rank as the world's seventh largest, surpassing both Brazil and Italy in GDP, just behind the United Kingdom. However, the blue economy faces significant risks as natural assets deteriorate, including declines in fisheries, habitats, and marine species. This has driven the emergence of the sustainable blue economy and the growth of blue finance.

In 2018, Seychelles became the first country to issue a blue bond, known as the Seychelles blue bond. The World Bank assisted in developing this 10-year bond, which raised $15 million<fnref n="43" /> with the goal of expanding marine protected areas, enhancing governance of priority fisheries, and fostering the development of Seychelles' blue economy through the financing of sustainable fishing practices and marine conservation initiatives. The Seychelles blue bond is partially guaranteed by a $5 million guarantee from the World Bank and further supported by a $5 million concessional loan from the Global Environment Facility (GEF) which will partially cover interest payments for the bond. The Seychelles blue bond is an example of a use of proceeds (UOP) bond, a common term in green bond terminology. However, blue bond issuance can also take other forms. One such form is a debt-for-nature (DFN) swap, a financial arrangement in which a portion of a country's debt is forgiven or reduced in exchange for commitments to invest in marine conservation and sustainable management. In 2023, Ecuador completed the world's largest debt-for-nature swap (the Galapagos blue bond). Although it did not significantly reduce the government's overall debt, it allows Ecuador to direct savings toward conservation efforts in the Galapagos Islands. Credit Suisse led the transaction, facilitating a buyback of approximately $656 million in external bonds. The deal was supported by a blue bond, rated Aa2 by Moody's due to a $85 million guarantee from the Inter-American Development Bank<fnref n="44" />. While the transaction reduced Ecuador's debt by approximately 1.6%, it is expected to generate $323 million for Galapagos marine conservation through 2041. Because the blue bond market is new, it is less mature than the green or social bond markets:

> "Between 2018 and 2022, 26 blue bond transactions took place, amounting to a total value of $5 billion, with a 92% CAGR between those years. Currently, blue bonds represent less than 0.5% of the sustainable debt market. The use of proceeds has mostly focused on waste management, biodiversity, and sustainable fisheries, but also ranges across other areas of the sustainable blue economy. Only two-thirds of blue bond issuers report on impact metrics, providing further opportunity to add detail and rigor. We draw comparisons to the more mature green bond market and conclude that a lack of standardized definitions, metrics, and expertise by issuers and investors are significant barriers to the blue bond market." (Bosmans and de Mariz, 2023, page 1).

<footnote n="41">⁴¹See his book on the blue economy (Pauli, 2010).</footnote>

<footnote n="42">⁴²This estimate includes $6.9 trillion in direct ocean output, $5.2 trillion from shipping lanes, $7.8 trillion from productive coastlines, and $4.3 trillion from carbon absorption assets.</footnote>

<footnote n="43">⁴³The investors were Calvert Impact Capital, Nuveen, and Prudential Financial.</footnote>

<footnote n="44">⁴⁴The Aa2 rating of the Galapagos blue bond is 16 notches above Ecuador's sovereign rating. The blue bond offers a coupon of 5.645% compared to the 17% to 26% yield on Ecuadorian government bonds.</footnote>
As of July 2024, there are 41 blue bonds in circulation, 17 of which were issued in 2023. A key challenge for the growth of this market is that it primarily involves small island developing states, which often require technical assistance to issue blue bonds, implement projects and establish credibility with investors (Thompson, 2022; March et al., 2023). Table 5.17 provides examples of blue bonds. It is important to note that blue bonds are issued not only by governments and multilateral development banks but also by corporations, such as Mowi, a seafood company, and Ørsted, an energy company.

<table><caption>Table 5.17: Some examples of blue bonds</caption><thead><tr><td>Year</td><td>Type</td><td>Amount (in $ mn)</td><td>Bond name</td></tr></thead><tbody><tr><td>2018</td><td>UOP</td><td>15</td><td>Seychelles blue bond</td></tr><tr><td>2018</td><td>DFN</td><td>21</td><td>Seychelles debt-for-nature swap</td></tr><tr><td>2019</td><td>UOP</td><td>220</td><td>Nordic-Baltic blue bond I (Nordic Investment Bank)</td></tr><tr><td>2020</td><td>UOP</td><td>220</td><td>MOWI green bond</td></tr><tr><td>2020</td><td>UOP</td><td>150</td><td>Nordic-Baltic blue bond II (Nordic Investment Bank)</td></tr><tr><td>2020</td><td>UOP</td><td>940</td><td>Bank of China blue bond</td></tr><tr><td>2021</td><td>UOP</td><td>300</td><td>ADB Australia/NZ blue bond</td></tr><tr><td>2021</td><td>DFN</td><td>365</td><td>Belize debt-for-nature swap</td></tr><tr><td>2022</td><td>UOP</td><td>385</td><td>Bahamas blue bond</td></tr><tr><td>2022</td><td>DFN</td><td>150</td><td>Barbados debt-for-nature swap</td></tr><tr><td>2023</td><td>UOP</td><td>3.5</td><td>Cabo Verde marine & ocean-based blue bond (International Investment Bank)</td></tr><tr><td>2023</td><td>DFN</td><td>656</td><td>Galapagos debt-for-nature swap (Ecuador)</td></tr><tr><td>2023</td><td>UOP</td><td>150</td><td>Indonesia blue bond (Republic of Indonesia)</td></tr><tr><td>2023</td><td>UOP</td><td>100</td><td>Ørsted blue bond</td></tr><tr><td>2023</td><td>UOP</td><td>50</td><td>Bank of Ayudhya blue bond (Thailand)</td></tr><tr><td>2023</td><td>DFN</td><td>500</td><td>Gabon debt-for-nature swap</td></tr></tbody></table>

Source: Author's research.

Blue funds are investment funds that focus on the blue economy. While they can invest in blue bonds, this market remains relatively small. As a result, they also allocate capital to other securities, such as public and private equities or private debt instruments. The Phenix impact database currently has 164 blue funds, representing less than 6% of the impact funds. However, we observe a high growth over the last ten years (Figure 5.25). The fund distribution is as follows: 50% private equity vehicles, 23.8% public debt funds and 15.9% public equity funds (Phenix Capital, 2024c, page 14). The primary investors in blue funds are foundations (20%), corporations (17%), and family offices (16%), with pension funds representing less than 10% of the investor base.

When we map these funds to the SDGs, we find that there are only 18 funds that focus solely on **SDG 14** (life below water). In most cases, these blue funds also target other additional SDGs, such as **SDG 6** (clean water and sanitation) and **SDG 7** (affordable and clean energy). The total capital raised by blue funds is estimated to be €45 billion, while the total capacity for new investments over the next few years is approximately €13 billion (Phenix Capital, 2024c, page 10). These amounts fall far short of the $174.52 billion per year needed for ocean health (Johansen and Vestvik, 2020).

**Remark 52** More recently, Ocean 14 Capital raised €200 mn for its first **SDG 14** fund while Denmark's Navigare Capital is targeting $650 mn for its sustainable shipping fund. In November 2023, T Rowe Price and the IFC announced a partnership to launch a blue fund with a target size of $425 mn.
<figure><img src="image_168.png" /><figcaption>Figure 5.25: Cumulative number of funds targeting the blue ocean economy</figcaption></figure>

Source: Phenix Capital (2024c, page 11) & Author's calculations.

## Structured blended finance funds

Blended finance was previously introduced on page 309. It's an investment strategy that combines public<fnref n="45" /> or philanthropic and private capital to fund projects in emerging and frontier markets. But blended finance goes beyond simple co-investment. Consider a mutual fund with both public institutions and private investors, such as pension funds or insurance companies. This fund may look like blended finance, but it's not. In this case, public and private investors have equal status, and the fund could exist without public participation. True blended finance involves situations where the investment product would not be possible without public involvement. Therefore, the participation of public investors is essential to the product's creation, with a clear distinction between the roles of public and private investors. A key feature of blended finance is its ability to catalyze and leverage private investment by addressing projects that are too risky to be financed by private capital alone. Due to issues such as asymmetric information, moral hazard, and low returns relative to the risks taken, many sustainable projects struggle to attract private investors. Blended finance helps overcome these barriers by ensuring that the risk sharing between private and public investors is not equal. The core idea is that public institutions assume a significant portion of the risk to encourage private capital participation. This differentiated risk-sharing is achieved through structured products, which are central to blended finance. For example, Convergence, the global network for blended finance network, defines it as follows:

> "Blended finance is a structuring approach that allows organizations with different objectives to invest alongside each other while achieving their own objectives (whether

<footnote n="45">⁴⁵In this section, we use the term public investor in a broader sense to include, for example, development finance institutions (DFIs) and multilateral development banks (MDBs).</footnote>
financial return, social impact, or a blend of both). The main investment barriers for private investors addressed by blended finance are (i) high perceived and real risk and (ii) poor returns for the risk relative to comparable investments. Blended finance creates investable opportunities in developing countries which leads to more development impact. Blended finance is not an investment approach, instrument, or end solution. It is also different from impact investing. Impact investing is an investment approach, and impact investors often participate in blended finance structures." (Convergence, 2024, https://www.convergence.finance/blended-finance).

Blended finance differs from impact investing for two main reasons. First, impact investing is a broader concept that encompasses a wider range of investment strategies and cannot be reduced to blended finance alone. Second, private investors do not always fit the criteria for impact investing, as they may not be willing to take the same level of risk or prioritize impact as public investors. However, it's important to note that many blended finance deals do indeed qualify as impact investments because of their explicit focus on achieving positive social or environmental outcomes. Therefore, when assessing the nature of a blended finance transaction, it's important to distinguish between the specific deal or project and the motivations of the individual investors involved.

Blended finance belongs to the family of structured finance (structured products, securitization, tranching, credit enhancement). According to Convergence (2024, page 12), there are four main typical blended finance structures:

* Concessional capital

Public or philanthropic investors provide funds at below-market rates within the capital structure to reduce the overall cost of capital or to provide an additional layer of protection for private investors. The goal is to change the risk/return profile of the investment.

* Credit enhancing

Public or philanthropic investors provide credit enhancement through guarantees or insurance against specific risks, such as political instability or natural disasters. The purpose of credit enhancing is to reduce the perceived risk of an investment, making it more attractive to private investors.

* Technical assistance facility (TAF)

Transaction is associated with a grant-funded technical assistance facility that can be utilized pre- or post-investment to strengthen commercial viability and developmental impact. The purpose is to transfer knowledge to the owners of the project in order to make it successful. In practice, a technical assistance facility refers to a dedicated pool of human and capital resources that provide expertise, training, and advisory services to support the successful implementation of projects in developing markets.

* Design-stage grants

Transaction design or preparation is funded by grants (including project preparation or design-stage grants). Therefore, they correspond to non-repayable funds provided in the early stages of a project to support its planning, structuring and preparation, or to cover the initial costs of project design to ensure that the project is viable and sustainable.

The distinction between the first two categories is somewhat arbitrary. Both categories aim to mitigate investment risk<fnref n="46" /> or modify the risk-return profile. Within these categories, blended finance

<footnote n="46">⁴⁶For example, credit enhancement can be used to obtain a better credit rating.</footnote>
Box 5.5: Tranching technique and collateralized debt obligation

A collateralized debt obligation (CDO) is a pay-through ABS structure whose securities are bonds linked to a series of tranches. In the example below, there are 4 types of bonds, whose return depends on the loss of the corresponding tranche (equity, mezzanine, senior and super senior). Each tranche is characterized by an attachment point A and a detachment point D. In our example, we have:

<table><thead><tr><th>Tranche</th><th>Equity</th><th>Mezzanine</th><th>Senior</th><th>Super senior</th></tr></thead><tbody><tr><td>A</td><td>0%</td><td>15%</td><td>25%</td><td>35%</td></tr><tr><td>D</td><td>15%</td><td>25%</td><td>35%</td><td>100%</td></tr></tbody></table>

The protection buyer of the tranche [A, D] pays the protection seller a coupon rate on the outstanding principal amount of the tranche. In return, the protection buyer receives the protection leg, which is the loss on the tranche. However, the losses are subject to a payment priority, which is as follows:

* The equity tranche is the most risky security, which means that the first losses will hit this tranche alone until the cumulative loss reaches the detachment point;

* When the portfolio loss is greater than the detachment point of the equity tranche, the equity tranche ceases to exist and the protection seller of the mezzanine tranche will pay the next losses to the protection buyer of the mezzanine tranche;

* The protection buyer of a tranche pays the coupon from the inception of the CDO until the death of the tranche, i.e., when the cumulative loss is greater than the detachment point of the tranche;

<figure><img src="image_169.png" /><figcaption>Figure 5.A: Structure of a collateralized debt obligation</figcaption></figure>

Source: Roncalli (2020a, pages 155-156).
can offer concessional loans, use tranching techniques to create a junior/mezzanine/senior liability structure, propose subordinated loans, provide junior equity, and offer first-loss guarantees. Similarly, the difference between the last two categories is somewhat arbitrary. Both categories focus on ensuring the success of the project. For example, public organizations may provide technical experts to assist with project development or financial experts to assess the project's potential to attract private investors.

Certainly, the most best-known blended finance products are based on the tranching technique that has gained popularity through credit securitization, asset-backed securities, and collateralized debt obligations (see Box 5.5). The concept of tranching involves creating multiple risk/return profiles from a single collateral pool of assets. In the case of a portfolio of defaultable loans, the senior tranche would offer a lower return compared to the equity tranche because the credit risk of the senior tranche is lower than that of the equity tranche. When applied to blended finance, the collateral pool could consist of a portfolio of projects, a basket of green bonds, or a set of credit loans. An example of a tranched product is the European Energy Efficiency fund (eeef), a Luxembourg-based alternative investment fund focused on financing energy efficiency, small-scale renewable energy and clean urban transport projects<fnref n="47" />. These projects typically involve municipalities, public authorities and public-private partnerships. The eeef provides a range of financial instruments, including equity, debt and mezzanine financing, and may use concessional capital. A summary of the eeef investment structure is shown in Figure 5.26.

<figure><img src="image_170.png" /><figcaption>Figure 5.26: The eeef investment structure</figcaption></figure>

Source: Eurosif (2021, Figure 7, page 26).

Another example of a tranching product is the AP EGO fund (Amundi Planet Emerging Green One), a joint creation of Amundi and the IFC (Bolton et al., 2020). The fund invests in emerging market (EM) green bonds in both primary and secondary markets and is structured as a CDO fund,

<footnote n="47">⁴⁷The fund's website is www.eeef.lu.</footnote>
with the IFC providing credit enhancement to mitigate specific investor risks. The senior tranche accounts for 90% of the fund's portfolio, with the remaining 10% split between the first-loss junior tranche (6.25%) and the mezzanine tranche (3.75%). The AP EGO fund is currently the largest EM green bond fund. This innovative fund aims to address two key challenges that have prevented financiers from scaling up infrastructure investment in emerging markets: first, how to mitigate sovereign credit risk in these regions, and second, how to generate sufficient supply of EM green bonds to meet demand from institutional investors in developed markets.

Let us see how a tranching product of blended finance works. To do this, we use part of the mathematical framework for pricing a CDO tranche (Roncalli, 2020a, page 157). Given an investment portfolio of n bonds, the cumulative loss of the portfolio at time t is equal to:

$$L_t = \sum_{i=1}^{n} N_i \cdot (1 - \mathcal{R}_i) \cdot \mathbf{1}\{\tau_i \le t\}$$

where $N_i$, $\mathcal{R}_i$ and $\tau_i$ are the nominal amount, the recovery rate and the default time of bond i. The loss of tranche [A, D] is given by:

$$L_t^{[A,D]} = (L_t - A) \cdot \mathbf{1}\{A \le L_t \le D\} + (D - A) \cdot \mathbf{1}\{L_t > D\}$$

where A and D are the attachment and detachment points expressed in $. The outstanding notional amount of the tranche is therefore:

$$N_t^{[A,D]} = (D - A) - L_t^{[A,D]}$$

This notional amount is then reduced by the loss of the tranche. At inception date $t = 0$, $N_t^{[A,D]}$ is equal to the tranche thickness $D - A$. At the fixing date $t$, we have:

$$N_t^{[A,D]} = \begin{cases} D - A & \text{if } L_t \le A \\ D - L_t & \text{if } A \le L_t \le D \\ 0 & \text{if } L_t > D \end{cases}$$

We now define the income of each tranche. The gain between two fixing dates $t-1$ and $t$ is equal to:

$$\Delta\Pi_t = \sum_{i=1}^{n} c_i \cdot N_i \cdot \mathbf{1}\{\tau_i > t\}$$

where $c_i$ is the (fixed) coupon paid by bond i between $t-1$ and $t$. The cumulative profit generated by the portfolio at time $t$ is then equal to $\Pi_t = \Pi_{t-1} + \Delta\Pi_t$ where $\Pi_0 = 0$. At this stage, we need to define the revenue sharing policy between the different tranches:

$$\Delta\Pi_t^{[A,D]} = \varphi^{[A,D]} (\Delta\Pi_t)$$

In general, the gain for tranche [A, D] depends on the total income $\Delta\Pi_t$ of the portfolio and the pricing formula $\varphi^{[A,D]}$. The cumulative profit of tranche [A, D] is then $\Pi_t^{[A,D]} = \Pi_{t-1}^{[A,D]} + \Delta\Pi_t^{[A,D]}$ where $\Pi_0^{[A,D]} = 0$. We deduce that the cumulative return of the tranche is equal to:

$$R_t^{[A,D]} = \frac{\Pi_t^{[A,D]} - L_t^{[A,D]}}{D - A}$$

This is the difference between the income and the loss of the tranche. Finally, the average return is $\bar{R}_t^{[A,D]} = \frac{1}{t} R_t^{[A,D]}$.
**Example 21** Consider a simple blended finance fund where the junior and senior tranches account for 20% and 80% of the investment, respectively. The total fund size is $500 million, invested equally in 100 emerging market (EM) green bonds. We assume that these green bonds are homogeneous, each paying an annual coupon of 10%. The recovery rate is set to zero. To define the income distribution policy, the senior tranche receives an annual coupon of 4% until the junior tranche is exhausted, while the junior tranche receives the remaining income generated by the bond portfolio. Finally, the maturity of the fund is set at ten years.

Let us apply the previous mathematical framework to this example. For the junior tranche, the attachment and detachment points are 0 and $100 mn. For the senior tranche, the attachment and detachment points are $100 mn and $500 mn. We have $N_i = $5 mn, $\mathcal{R}_i = 0$ and $c_i = 10\%$. Let $n_t^\tau = \sum_{i=1}^n 1 \{\tau_i \le t\}$ be the cumulative number of defaults. We deduce that$^{48}$:

$$
\left\{
\begin{aligned}
L_t &= \sum_{i=1}^{100} 5 \times (1-0) \times 1 \{\tau_i \le t\} = 5n_t^\tau \\
L_t^{(\text{junior})} &= \min(5n_t^\tau, 100) \\
L_t^{(\text{senior})} &= \max(5n_t^\tau - 100, 0)
\end{aligned}
\right.
$$

The outstanding notional amount of the junior tranche is:

$$
N_t^{(\text{junior})} = 100 - L_t^{(\text{junior})} = \max(100 - 5n_t^\tau, 0)
$$

For the senior tranche, we get:

$$
N_t^{(\text{senior})} = 400 - L_t^{(\text{senior})} = \min(500 - 5n_t^\tau, 400)
$$

The income generated by the bond portfolio is:

$$
\Delta\Pi_t = \sum_{i=1}^{100} 10\% \times 5 \times 1 \{\tau_i > t\} = 0.5 (100 - n_t^\tau)
$$

The maximum annual income is $50 mn. If there are 20 defaults, $\Delta\Pi_t = \$40 mn$ is sufficient to pay the guaranteed income for the senior tranche, which is equal to $400 \times 4\% = \$16 mn$. We deduce that:

$$
\Delta\Pi_t^{(\text{senior})} = \varphi^{(\text{senior})}(\Delta\Pi_t) = 16 \times 1 \{n_t^\tau \le 20\} + \Delta\Pi_t \times 1 \{n_t^\tau > 20\}
$$

and:

$$
\Delta\Pi_t^{(\text{junior})} = \varphi^{(\text{junior})}(\Delta\Pi_t) = \Delta\Pi_t - \Delta\Pi_t^{(\text{senior})} = (\Delta\Pi_t - 16) \times 1 \{n_t^\tau \le 20\}
$$

We have all the formulas to perform a simulation of the blended finance fund.

Table 5.18 shows the results for three different scenarios. In the first scenario, the number of annual defaults over the ten-year period is 0, 1, 1, 0, 2, 1, 0, 1, 1, and 1. In this low-risk scenario, the total performance of the fund over the ten-year period is 8.80%. The junior tranche returns 28% and the senior tranche returns 4%. However, this scenario is considered unrealistic due to the low number of defaults relative to the 10% coupon level. The second scenario is more realistic, with an average annual default rate of 4.10%. In this scenario, the junior tranche pays 1.00% while the senior tranche pays 3.92%. The third scenario shows that the senior tranche can exceed a return of 4%. This is because the junior tranche is exhausted after four years, leaving the senior tranche exposed to credit risk from the fourth year onward. However, because fewer defaults occur between years four and ten, the senior tranche benefits from the high yield of green bonds and the lower default rate. As a result, the senior tranche achieves a return of 5.14% over the life of the fund.
<table><caption>Table 5.18: Simulation of the blended finance fund</caption><thead><tr><th>t</th><th>n<sub>t</sub><sup>T</sup></th><th>L<sub>t</sub></th><th>L<sub>t</sub><sup>(junior)</sup></th><th>L<sub>t</sub><sup>(senior)</sup></th><th>ΔΠ<sub>t</sub></th><th>ΔΠ<sub>t</sub><sup>(junior)</sup></th><th>ΔΠ<sub>t</sub><sup>(senior)</sup></th><th>Π<sub>t</sub></th><th>Π<sub>t</sub><sup>(junior)</sup></th><th>Π<sub>t</sub><sup>(senior)</sup></th><th>R&#773;<sub>t</sub></th><th>R&#773;<sub>t</sub><sup>(junior)</sup></th><th>R&#773;<sub>t</sub><sup>(senior)</sup></th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>50.0</td><td>34.0</td><td>16.0</td><td>50.0</td><td>34.0</td><td>16.0</td><td>10.00%</td><td>34.00%</td><td>4.00%</td></tr><tr><td>2</td><td>1</td><td>5.0</td><td>5.0</td><td>0.0</td><td>49.5</td><td>33.5</td><td>16.0</td><td>99.5</td><td>67.5</td><td>32.0</td><td>9.45%</td><td>31.25%</td><td>4.00%</td></tr><tr><td>3</td><td>2</td><td>10.0</td><td>10.0</td><td>0.0</td><td>49.0</td><td>33.0</td><td>16.0</td><td>148.5</td><td>100.5</td><td>48.0</td><td>9.23%</td><td>30.17%</td><td>4.00%</td></tr><tr><td>4</td><td>2</td><td>10.0</td><td>10.0</td><td>0.0</td><td>49.0</td><td>33.0</td><td>16.0</td><td>197.5</td><td>133.5</td><td>64.0</td><td>9.38%</td><td>30.88%</td><td>4.00%</td></tr><tr><td>5</td><td>4</td><td>20.0</td><td>20.0</td><td>0.0</td><td>48.0</td><td>32.0</td><td>16.0</td><td>245.5</td><td>165.5</td><td>80.0</td><td>9.02%</td><td>29.10%</td><td>4.00%</td></tr><tr><td>6</td><td>5</td><td>25.0</td><td>25.0</td><td>0.0</td><td>47.5</td><td>31.5</td><td>16.0</td><td>293.0</td><td>197.0</td><td>96.0</td><td>8.93%</td><td>28.67%</td><td>4.00%</td></tr><tr><td>7</td><td>5</td><td>25.0</td><td>25.0</td><td>0.0</td><td>47.5</td><td>31.5</td><td>16.0</td><td>340.5</td><td>228.5</td><td>112.0</td><td>9.01%</td><td>29.07%</td><td>4.00%</td></tr><tr><td>8</td><td>6</td><td>30.0</td><td>30.0</td><td>0.0</td><td>47.0</td><td>31.0</td><td>16.0</td><td>387.5</td><td>259.5</td><td>128.0</td><td>8.94%</td><td>28.69%</td><td>4.00%</td></tr><tr><td>9</td><td>7</td><td>35.0</td><td>35.0</td><td>0.0</td><td>46.5</td><td>30.5</td><td>16.0</td><td>434.0</td><td>290.0</td><td>144.0</td><td>8.87%</td><td>28.33%</td><td>4.00%</td></tr><tr><td>10</td><td>8</td><td>40.0</td><td>40.0</td><td>0.0</td><td>46.0</td><td>30.0</td><td>16.0</td><td>480.0</td><td>320.0</td><td>160.0</td><td>8.80%</td><td>28.00%</td><td>4.00%</td></tr><tr><td>1</td><td>6</td><td>30.0</td><td>30.0</td><td>0.0</td><td>47.0</td><td>31.0</td><td>16.0</td><td>47.0</td><td>31.0</td><td>16.0</td><td>3.40%</td><td>1.00%</td><td>4.00%</td></tr><tr><td>2</td><td>10</td><td>50.0</td><td>50.0</td><td>0.0</td><td>45.0</td><td>29.0</td><td>16.0</td><td>92.0</td><td>60.0</td><td>32.0</td><td>4.20%</td><td>5.00%</td><td>4.00%</td></tr><tr><td>3</td><td>16</td><td>80.0</td><td>80.0</td><td>0.0</td><td>42.0</td><td>26.0</td><td>16.0</td><td>134.0</td><td>86.0</td><td>48.0</td><td>3.60%</td><td>2.00%</td><td>4.00%</td></tr><tr><td>4</td><td>20</td><td>100.0</td><td>100.0</td><td>0.0</td><td>40.0</td><td>24.0</td><td>16.0</td><td>174.0</td><td>110.0</td><td>64.0</td><td>3.70%</td><td>2.50%</td><td>4.00%</td></tr><tr><td>5</td><td>25</td><td>125.0</td><td>100.0</td><td>25.0</td><td>37.5</td><td>0.0</td><td>37.5</td><td>211.5</td><td>110.0</td><td>101.5</td><td>3.46%</td><td>2.00%</td><td>3.82%</td></tr><tr><td>6</td><td>30</td><td>150.0</td><td>100.0</td><td>50.0</td><td>35.0</td><td>0.0</td><td>35.0</td><td>246.5</td><td>110.0</td><td>136.5</td><td>3.22%</td><td>1.67%</td><td>3.60%</td></tr><tr><td>7</td><td>32</td><td>160.0</td><td>100.0</td><td>60.0</td><td>34.0</td><td>0.0</td><td>34.0</td><td>280.5</td><td>110.0</td><td>170.5</td><td>3.44%</td><td>1.43%</td><td>3.95%</td></tr><tr><td>8</td><td>36</td><td>180.0</td><td>100.0</td><td>80.0</td><td>32.0</td><td>0.0</td><td>32.0</td><td>312.5</td><td>110.0</td><td>202.5</td><td>3.31%</td><td>1.25%</td><td>3.83%</td></tr><tr><td>9</td><td>40</td><td>200.0</td><td>100.0</td><td>100.0</td><td>30.0</td><td>0.0</td><td>30.0</td><td>342.5</td><td>110.0</td><td>232.5</td><td>3.17%</td><td>1.11%</td><td>3.68%</td></tr><tr><td>10</td><td>41</td><td>205.0</td><td>100.0</td><td>105.0</td><td>29.5</td><td>0.0</td><td>29.5</td><td>372.0</td><td>110.0</td><td>262.0</td><td>3.34%</td><td>1.00%</td><td>3.92%</td></tr><tr><td>1</td><td>4</td><td>20.0</td><td>20.0</td><td>0.0</td><td>48.0</td><td>32.0</td><td>16.0</td><td>48.0</td><td>32.0</td><td>16.0</td><td>5.60%</td><td>12.00%</td><td>4.00%</td></tr><tr><td>2</td><td>7</td><td>35.0</td><td>35.0</td><td>0.0</td><td>46.5</td><td>30.5</td><td>16.0</td><td>94.5</td><td>62.5</td><td>32.0</td><td>5.95%</td><td>13.75%</td><td>4.00%</td></tr><tr><td>3</td><td>10</td><td>50.0</td><td>50.0</td><td>0.0</td><td>45.0</td><td>29.0</td><td>16.0</td><td>139.5</td><td>91.5</td><td>48.0</td><td>5.97%</td><td>13.83%</td><td>4.00%</td></tr><tr><td>4</td><td>20</td><td>100.0</td><td>100.0</td><td>0.0</td><td>40.0</td><td>24.0</td><td>16.0</td><td>179.5</td><td>115.5</td><td>64.0</td><td>3.98%</td><td>3.88%</td><td>4.00%</td></tr><tr><td>5</td><td>24</td><td>120.0</td><td>100.0</td><td>20.0</td><td>38.0</td><td>0.0</td><td>38.0</td><td>217.5</td><td>115.5</td><td>102.0</td><td>3.90%</td><td>3.10%</td><td>4.10%</td></tr><tr><td>6</td><td>27</td><td>135.0</td><td>100.0</td><td>35.0</td><td>36.5</td><td>0.0</td><td>36.5</td><td>254.0</td><td>115.5</td><td>138.5</td><td>3.97%</td><td>2.58%</td><td>4.31%</td></tr><tr><td>7</td><td>29</td><td>145.0</td><td>100.0</td><td>45.0</td><td>35.5</td><td>0.0</td><td>35.5</td><td>289.5</td><td>115.5</td><td>174.0</td><td>4.13%</td><td>2.21%</td><td>4.61%</td></tr><tr><td>8</td><td>30</td><td>150.0</td><td>100.0</td><td>50.0</td><td>35.0</td><td>0.0</td><td>35.0</td><td>324.5</td><td>115.5</td><td>209.0</td><td>4.36%</td><td>1.94%</td><td>4.97%</td></tr><tr><td>9</td><td>33</td><td>165.0</td><td>100.0</td><td>65.0</td><td>33.5</td><td>0.0</td><td>33.5</td><td>358.0</td><td>115.5</td><td>242.5</td><td>4.29%</td><td>1.72%</td><td>4.93%</td></tr><tr><td>10</td><td>34</td><td>170.0</td><td>100.0</td><td>70.0</td><td>33.0</td><td>0.0</td><td>33.0</td><td>391.0</td><td>115.5</td><td>275.5</td><td>4.42%</td><td>1.55%</td><td>5.14%</td></tr></tbody></table>
<figure><img src="image_171.png" /><figcaption>Figure 5.27: Probability density function of the average returns $\bar{R}_{10}$, $\bar{R}_{10}^{(\text{junior})}$ and $\bar{R}_{10}^{(\text{senior})}$ (in %)</figcaption></figure>

In practice, the fund manager performs Monte Carlo simulations to calibrate the income-sharing policy and to discuss with public and private investors the risk/return profile of each tranche. Assuming exponential default times with an intensity of 300 bps and correlated by a Gaussian copula with uniform correlation $\rho$, Figure 5.27 illustrates the results of 20 000 Monte Carlo simulations<fnref n="49" />. For the overall portfolio, an expected average return of 5.9% is observed, independent of $\rho$. However, the probability distribution of returns is significantly affected by $\rho$. In particular, the density function of $\bar{R}_t$ is left-skewed when $\rho = 50\%$. The expected average return of the junior tranche is 10.7% when $\rho = 0\%$ and increases to 16.8% when $\rho = 50\%$. While a high correlation between default times improves the junior tranche's performance, it also increases its risk since the probability of a negative return becomes more significant<fnref n="50" />. Conversely, the expected average return of the senior tranche decreases from 4.7% to 3.2% as $\rho$ increases from 0% to 50%. This indicates that a higher correlation between default times can negatively impact the performance of the senior tranche.

<table><thead><tr><th></th><th>Portfolio</th><th>Junior</th><th>Senior</th></tr></thead><tbody><tr><td>ρ = 0%</td><td>0.0%</td><td>0.3%</td><td>0.0%</td></tr><tr><td>ρ = 50%</td><td>11.4%</td><td>19.1%</td><td>8.7%</td></tr></tbody></table>

<footnote n="48">⁴⁸In the following we use the following properties: $\min(a, b) \pm c = \min(a \pm c, b \pm c)$, $\max(a, b) \pm c = \max(a \pm c, b \pm c)$, $-\min(a, b) = \max(-a, -b)$ and $-\max(a, b) = \min(-a, -b)$. We deduce that $a - \min(b, c) = a + \max(-b, -c) = \max(a - b, a - c)$ and $a - \max(b, c) = a + \min(-b, -c) = \min(a - b, a - c)$.</footnote>

<footnote n="49">⁴⁹In this Monte Carlo exercise, the default times $(\tau_1, \dots, \tau_n)$ are simulated with the following algorithm. First we simulate the Gaussian vector $(x_1, \dots, x_n)$ with $x_i = \sqrt{\rho}\varepsilon_0 + \sqrt{1-\rho}\varepsilon_i$ where $(\varepsilon_0, \varepsilon_1, \dots, \varepsilon_n)$ are $n + 1$ independent normal random variates $N(0, 1)$. The simulated values of the Gaussian copula are then $(u_1, \dots, u_n)$ with $u_i = \Phi(x_i)$. Finally, the simulated default times are generated using the inverse of the probability integral transform: $\tau_i = -\ln(1 - u_i) / \lambda_i$ where $\lambda_i = 300$ bps is the intensity parameter of the exponential distribution.</footnote>

<footnote n="50">⁵⁰Below is the probability of observing negative performance:</footnote>
<figure><img src="image_172.png" /><figcaption>Figure 5.28: Growth of blended finance activities</figcaption></figure>

Source: Convergence (2024), www.convergence.finance/blended-finance & Author's calculations.

Convergence (2024) reports that blended finance has mobilized $230 billion for sustainable development in developing countries by June 2024 (Figure 5.28). This figure represents 1200 transactions with a median deal size of $64 million. While most transactions (70%) are concessional loans, enhancing credit and technical assistance account for 25% each. Geographically, sub-Saharan Africa dominates the market with 50% of transactions, followed by Asia (27%) and Latin America (17%). However, the market is skewed towards smaller deals, with 35% of transactions under $25 million and only 15% exceeding $250 million. In terms of sectors, energy, financial services, and agriculture each account for more than 20% of blended finance transactions. In terms of investors, Convergence (2024) notes that 65% of blended finance investors are from the private sector, but the majority have only participated in one blended finance transaction. The public and philanthropic sectors represent 19% and 16% of investors, respectively. The most active public investors are the International Finance Corporation (IFC), the Netherlands Development Finance Company (FMO), the US International Development Finance Corporation (DFC), the US Agency for International Development (USAID), and the European Investment Bank (EIB), while the top philanthropic investors include the Shell Foundation, the Bill & Melinda Gates Foundation, the Omidyar Network, Oikocredit, and the Rockefeller Foundation.

## Microfinance funds

The most emblematic product in the impact investing universe is undoubtedly the microfinance fund. A microfinance fund is a financial vehicle that provides capital and other financial services to low-income individuals and businesses, often in developing countries. The goal of microfinance funds is to help these groups access financial resources that they might not otherwise be able to
obtain from traditional banks due to a lack of credit history, collateral or debt market structure. As a result, microfinance funds typically provide microloans, which are small amounts of capital. They focus on amounts in the thousands rather than millions of dollars.

<figure><img src="image_173.png" /><figcaption>Figure 5.29: SDGs targeted by microfinance</figcaption></figure>

Microfinance funds are part of the microfinance ecosystem, which is a complex and large financial system that includes traditional banks<fnref n="51" />, microfinance institutions (MFIs), non-banking financial companies, philanthropic investors, etc. Microfinance has an important role to play in advancing several of the SDGs. The key SDGs targeted by microfinance are:

* **SDG 1** No Poverty

Microfinance can help individuals and businesses escape poverty by giving them access to credit, savings and other financial services. This can enable them to start or grow their businesses, increase their incomes, create jobs and improve their livelihoods.

* **SDG 2** Zero Hunger

Microfinance can support smallholder farmers and food producers by providing them with loans to purchase seeds, fertilizers and equipment. This can help them increase agricultural productivity and food security. This is particularly important in rural areas where hunger is more prevalent.

* **SDG 5** Gender Equality

Microfinance institutions often focus on women, who are disproportionately affected by poverty and exclusion from financial systems. This can help them start their own businesses, become financially independent, and participate more fully in the economy.

* **SDG 8** Decent Work and Economic Growth

Microfinance can promote decent work and economic growth by providing individuals and businesses with the financial resources they need to create jobs and generate income. This can contribute to economic development and improved living standards.

* **SDG 10** Reduced Inequality

Microfinance can help reduce inequalities by providing financial services to marginalized groups, including the poor, women and rural communities, who often lack access to traditional banking services.

According to the World Bank's Global Financial Inclusion (Global Findex) Database 2021, approximately 1.4 billion adults worldwide remain unbanked or excluded from formal banking services<fnref n="52" />. The majority of the unbanked population is concentrated in developing regions, particularly in sub-Saharan Africa, South Asia, and parts of Latin America and Southeast Asia. Two segments of the

<footnote n="51">⁵¹For example, the reader can consult the 2024 Microfinance Social Performance Report, supported by BNP Paribas, available at https://group.bnpparibas/uploads/file/2024_bnp_paribas_microfinance social report.pdf.</footnote>

<footnote n="52">⁵²Source: www.worldbank.org/en/publication/globalfindex.</footnote>
population are particularly affected. Women and people living in rural areas are more likely to be unbanked than men and people living in urban areas. This explains the importance of SDG 5 and SDG 10 in microfinance.

According to the *MicroFinance Global Strategic Business Report*, the global microfinance market was valued at approximately $224.6 billion in 2023. Projections indicate substantial growth, reaching $506.0 billion by 2030, with an annual growth rate of 12.3% during this period. These estimates are slightly higher than those reported by ATLAS, which valued the total market at $182.7 billion in 2022, serving 173 million borrowers<fnref n="53" />. Based on these figures, the average microfinance loan size in ATLAS's data was approximately $1050. Data on microfinance funds is more difficult to obtain. However, we can use the classification of private debt funds in the Phenix impact database to assess this market:

> "Private debt, also known as private credit, are loans made to companies that are not provided by banks or public markets. These private market investments can range in size and scale and be implemented in different forms, such as direct lending<fnref n="54" />, mezzanine finance<fnref n="55" />, and microcredit<fnref n="56" />." (Phenix Capital, 2023, pages 6 & 31).

As explained by Phenix Capital (2024d, page 6), the private debt sector is often too small to qualify for loans from banks or public markets, but too large for microfinance organizations. As a result, the average loan size in microfinance funds is higher than in MFIs.

<table><caption>Table 5.19: Frequency of private debt funds per targeted region</caption><thead><tr><th>Region</th><th>Africa</th><th>Asia</th><th>Latam</th><th>Europe</th><th>Middle East</th><th>North America</th><th>Oceania</th></tr></thead><tbody><tr><th>Frequency (in %)</th><td>30.7</td><td>23.9</td><td>20.8%</td><td>19.5</td><td>4.1</td><td>13.7</td><td>1.8</td></tr></tbody></table>

Source: Phenix Capital (2024d, page 12) & Author's calculations.

According to Phenix Capital (2024d), the estimated size of the private debt impact fund market is € 50 billion, with 394 funds managed by 218 asset managers. Of these funds, 70% are focused on emerging markets. Africa accounts for more than 30% of fund investments, followed by Asia, Latin America and Europe with approximately 20% each. A key difference between developed and emerging markets lies in the types of impact metrics used by private debt impact funds. Funds investing in developed markets prioritize E metrics more, allocating 70% to them and 30% to S metrics. In contrast, funds investing in emerging markets emphasize social metrics more, with a breakdown of 57% S metrics and 43% E metrics. Foundations, philanthropic investors, and development finance institutions are the primary sources of funding for private debt impact funds. Microfinance asset managers are specialized and distinct from the traditional asset management industry. Leading examples include BlueOrchard Finance (Switzerland), ResponsAbility Investments AG (Switzerland), Triodos Investment Management (Netherlands), Symbiotics (Switzerland), Oikocredit (Sweden), Incofin IM (Belgium), Developing World Markets (United States), Finance in Motion (Germany), Triple Jump (Netherlands), MicroVest Capital Management (United States) and Regmifa (Regional MSME Investment Fund for Sub-Saharan Africa).

<footnote n="53">⁵³Source: www.atlasdata.org & Impact Finance Barometer 2023 (www.convergences.org/publications).</footnote>

<footnote n="54">⁵⁴A specialised form of private debt, in which loans are made to middle-market companies. It is the private debt strategy with lower risk, achieved by using collateral.</footnote>

<footnote n="55">⁵⁵A specialised form of financing in which loans are subordinated to banks, with no collateral. It is the most equity-like form of private debt.</footnote>

<footnote n="56">⁵⁶A common form of microfinance, characterised by small loans to individuals or small companies.</footnote>
5.4 An example with the biodiversity risk

Biodiversity has become an important issue in the ESG financial community in recent years. For example, the SFDR's mandatory principal adverse impact indicator on biodiversity (PAI 7) requires companies to disclose activities that negatively impact biodiversity sensitive areas<fnref n="57" />, the sixth economic objective of the EU green taxonomy is the protection and restoration of biodiversity and ecosystems<fnref n="58" /> while the ESRS E4 category of the CSRD is named biodiversity and ecosystems<fnref n="59" />. In this context, where biodiversity is an important issue in sustainable finance regulations, it was obvious that investors wanted to develop biodiversity products or manage investments with respect to biodiversity risks and they have done so. And this is certainly just the beginning. When we talk about biodiversity, the two words that come to mind are risk and impact. It's easy to take the shortcut that an investment that takes biodiversity into account is an investment with impact, but does that mean it falls into the category of impact investing? Generally not, because there is a significant difference between investing in assets that carry biodiversity risks and investing with the goal of having a positive impact on biodiversity. To understand this distinction between investing with impact and investing for impact, it is important to first define what biodiversity really means<fnref n="60" />.

Box 5.6: Edward O. Wilson

Edward O. Wilson (1929–2021) was a renowned American biologist, naturalist, ecologist, and entomologist. He is widely regarded as one of the greatest natural scientists of our time and is often referred to as the father of biodiversity. He received his B.S. and M.S. in biology from the University of Alabama and his Ph.D. in biology from Harvard University in 1955. The author of more than 400 scientific articles from 1950 to 2005, he has written numerous influential books, including *The Theory of Island Biogeography* (1967), *Sociobiology* (1975), *On Human Nature* (1979), and *The Diversity of Life* (1992), which have had a profound impact on the fields of biology and ecology. In 1988, he co-edited the first book on biodiversity with Frances Peter.

Figure 5.B: Cover of the book *Tales from the Ant World*

<figure><img src="image_174.png" /></figure>

<footnote n="57">⁵⁷See Section 1.4.3 on page 36 and Table 1.8 on page 38.</footnote>

<footnote n="58">⁵⁸See Section 1.4.1 on page 33.</footnote>

<footnote n="59">⁵⁹See Section 1.4.5 on page 39.</footnote>

<footnote n="60">⁶⁰This section is based on the textbook *Biodiversity: An Introduction* written by Kevin Gaston and John Spicer and the scientific book *Conservation Biology for All* edited by Navjot Sodhi and Paul Ehrlich. *Essentials of Conservation Biology* by Richard Primack is another reference book, but it is more advanced and technical.</footnote>
5.4.1 Definition

We have already talked about biodiversity in Chapter 2, between the pages 62 and 65. Biodiversity, or
biological diversity, refers to the variety and variability of life on Earth in all its many manifestations.
According to Gaston and Spicer (2004), it is a broad, unifying concept that encompasses all forms,
levels, and combinations of natural variation at all levels of biological organization. For example,
it includes genetic diversity within species, the diversity of species in different habitats, and the
diversity of ecosystems themselves. In other words, biodiversity encompasses all living organisms,
from the smallest bacteria to the largest mammals, and the complex relationships and interactions
among them. In addition, biodiversity is essential to the health of ecosystems, providing critical
services such as air and water purification, crop pollination, climate regulation and food production.

**Remark 53** In the scientific world, biodiversity is generally associated with conservation biology, the scientific discipline dedicated to understanding and preserving biodiversity and protecting ecosystems. This field emerged in response to the rapid loss of biodiversity due to human activities such as habitat destruction, pollution, and climate change. Biodiversity and conservation biology are therefore closely related, which is why many master's programs use both the term biodiversity and conservation biology.

Key components of biodiversity

There are several ways to assess and measure biodiversity. In general, we consider three building
blocks:

1. Genetic diversity

This refers to the variety of genes within a species, such as different varieties of rice. Genetic diversity is essential for the survival and adaptability of species, allowing them to evolve in response to changing conditions.

2. Organismal (or species) diversity

This refers to the variety of species in a given area or ecosystem. It includes the number of different species (species richness), the relative abundance of each species (species evenness), and variation in the distribution of species in space (beta diversity or species density). A greater number of species indicates greater biodiversity and generally contributes to more resilient ecosystems that are able to maintain their functionality after environmental changes.

3. Ecological (or ecosystem) diversity

This refers to the variety of ecosystems in a region, including different habitats, biological
communities, and ecological processes. Ecosystem diversity includes forests, grasslands, wet-
lands, deserts, marine environments, etc. This element is essential for maintaining the range
of ecological processes that support life, such as nutrient cycling, energy flow, and climate
regulation.

In Table 5.21 we reproduce the different elements of the three building blocks, which are organized in nested hierarchies with higher and lower order elements (Gaston, 2010, pages 27-32). Some elements are specific to a given building block, e.g., nucleotides belong to the genetic diversity cluster, while other elements may be shared by two or three building blocks, e.g., individuals belong to both the genetic diversity and species diversity clusters. In addition to these three building blocks, we can consider other dimensions of biodiversity, such as functional diversity<fnref n="61" /> or temporal diversity<fnref n="62" />.

<footnote n="61">⁶¹Functional diversity refers to the range of different functions or roles that species play within an ecosystem.</footnote>

<footnote n="62">⁶²Temporal diversity refers to changes in biodiversity over time, including seasonal variations, successional changes in ecosystems, and long-term evolutionary processes.</footnote>
<table><caption>Table 5.20: Elements of biodiversity</caption><thead><tr><th>Ecological diversity</th><th>Genetic diversity</th><th>Organismal diversity</th></tr></thead><tbody><tr><td>Biogeographic realms</td><td></td><td>Domains or Kingdoms</td></tr><tr><td>Biomes</td><td></td><td>Phyla</td></tr><tr><td>Provinces</td><td></td><td>Families</td></tr><tr><td>Ecoregions</td><td></td><td>Genera</td></tr><tr><td>Ecosystems</td><td></td><td>Species</td></tr><tr><td>Habitats</td><td></td><td>Subspecies</td></tr><tr><td>Populations</td><td>Populations</td><td>Populations</td></tr><tr><td></td><td>Individuals</td><td>Individuals</td></tr><tr><td></td><td>Chromosomes</td><td></td></tr><tr><td></td><td>Genes</td><td></td></tr><tr><td></td><td>Nucleotides</td><td></td></tr></tbody></table>

Source: Heywood (1995) & Gaston (2010, Table 2.1, page 27).

**Genetic diversity** Genetic (or genomic) diversity can be assessed at different structural levels: nucleotides, genes, or chromosomes. Thus, we can measure genetic diversity by nucleotide<fnref n="63" /> differences, allelic diversity (average number of alleles per locus), gene diversity or polymorphism (proportion of polymorphic loci<fnref n="64" /> across the genome), and heterozygosity<fnref n="65" />.

<figure><img src="image_175.png" /><figcaption>Figure 5.30: Nucleotides, genes, and chromosomes</figcaption></figure>

Source: blog.myheritage.com/2018/02/dna-basics-chapter-3-dna-expression.

<footnote n="63">⁶³For example, adenine (A), cytosine (C), guanine (G), and thymine (T) are the four types of nucleotides that make up DNA.</footnote>

<footnote n="64">⁶⁴At a polymorphic locus, two or more different alleles exist within a population. For example, the ABO blood group system is determined by a polymorphic locus on chromosome 9, where multiple alleles (A, B, and O) exist, resulting in different blood types. The four basic ABO phenotypes are A, B, AB, and O.</footnote>

<footnote n="65">⁶⁵If an individual has two identical alleles at a given locus, they are said to be homozygous for that gene. If they have two different alleles, they are heterozygous.</footnote>
Box 5.7: Ploidy and the number of chromosomes

Ploidy is the number of sets of chromosomes in the nucleus of a cell. Ploidy varies from species to species and can even vary within the same species. A haploid cell has only one set of chromosomes, while cells with two, three, four, etc. complete sets of chromosomes are called diploid, triploid, tetraploid, and so on. The haploid number of chromosomes is called *n*, while 2*n* and *kn* are the diploid and k-ploid numbers of chromosomes, respectively. For example, humans are diploid because human cells contain two copies of each chromosome. Since humans have two copies of 23 chromosomes, the haploid number of chromosomes is *n* = 23, while the diploid number of chromosomes is 2*n* = 46. The total number of chromosomes is *kn*, where *k* is the ploidy of the cell. In the case of humans, the total number of chromosomes is then 46. Most organisms on Earth are diploid, so the reported number of chromosomes is generally the diploid number. There are some exceptions. For example, Mycoplasma, Escherichia coli (E. coli), and most bacteria are haploid organisms. Human gametes (sperm in males and egg in females) are also haploid because they are reproductive cells that contain half the number of chromosomes. This means that the number of chromosomes in the sperm or egg is *n* = 23, not 2*n* = 46. In honey bees, the diploid queen has 32 chromosomes (2*n* = 32). The drones (male bees) are entirely derived from the queen (they are formed from unfertilized eggs), which means that the haploid drones have 16 chromosomes (*n* = 16). Female worker bees, on the other hand, are derived from the mother and a father, so they are diploid organisms with 32 chromosomes (2*n* = 32). A common example of a polyploid organism is the potato:

> "Common cultivated potato varieties include tetraploid (4*n* = 48) with a basic chromosome number of 12, while there are cultivated species at the diploid (2*n* = 24) to pentaploid (5*n* = 60) levels. The triploid and pentaploid cultivated species are grown only on highland plateaus and slopes of the Andes, but diploid cultivated species are grown more widely and also used for breeding tetraploid varieties." (Watanabe, 2015, page 53).

To measure genetic diversity, we can look at the number of genes. However, we must be careful because genes can be divided into several categories based on their functions. For example, we generally distinguish between protein-coding genes, which encode instructions for the synthesis of proteins; non-coding genes, which produce RNA molecules that do not encode proteins but play an essential role in regulating gene expression and cellular processes; and pseudogenes, which are inactive copies of protein-coding genes. A more complex measure is genome size, also called C-value. The C-value is the amount of DNA contained in a haploid set of chromosomes. It is typically measured in picograms (pg) or base pairs (bp). A base pair is the basic unit of DNA sequence and corresponds to two nucleotides that combine to form the DNA double helix. The conversion between C-value and base pairs uses the following correspondence: 1 picogram is equal to 978 Mbp (million base pairs). For example, Gaston (2010, page 28) reports that the genome size of eukaryotic organisms (animals, plants, fungi, and many unicellular organisms) varies enormously, with C-values ranging from 0.0023 pg (or 2.25 million base pairs) for the parasitic microsporidium *Encephalitozoon intestinalis* to 1 400 pg (or 1.369 trillion base pairs) for the free-living amoeba *Chaos chaos*.

For a given organism, the number of genes and the C-value may vary from one measurement to another. They depend on the sample, the measurement instrument, the data size, etc. Therefore, most numbers are revised over time as data collection becomes more complete. Consider the human genome. Twenty years ago, Taft and Mattick (2003) wrote: "*Until recently, the estimated number of*
protein-coding genes in the human genome was predicted to range from as low as 40 000 to as high as 120 000. However, it is now apparent that humans have no more than 30 000 protein-coding genes, similar to other vertebrates such as the mouse and pufferfish". An important step in the sequencing of the human genome was taken in 2001 with the publication *The Sequence of the Human Genome* by Venter *et al.* (2001) in Science. They estimated 2.91 billion base pairs and 26 588 protein-coding genes. Since 2001, we have made great progress in sequencing the human genome, and the most recent published papers converge on some common numbers. Nurk *et al.* (2022) performed a new sequencing of the human genome and compared it to the previous reference studies performed by Schneider *et al.* (2017). Here are the results:

<table><thead><tr><th>Statistics</th><th>GRCH38</th><th>T2T-CHM13</th></tr></thead><tbody><tr><td>Base pairs (Gbp)</td><td>2.92</td><td>3.05</td></tr><tr><td>Number of genes</td><td>60 090</td><td>63 494</td></tr><tr><td>Number of protein-coding genes</td><td>19 890</td><td>19 969</td></tr><tr><td>% of repeats</td><td>51.89</td><td>53.94</td></tr></tbody></table>

where GRCH38 is the genomic database used by Schneider *et al.* (2017) and T2T-CHM13 is the genomic database used by Nurk *et al.* (2022). We can conclude that the human genome has 3 billion base pairs and the number of genes is 20 000. For many other organisms, the uncertainty in the number of base pairs and genes is more important because there are not enough resources (human and capital) to sequence their genomes with sophisticated instruments. Therefore, we may prefer to use the third metric of genetic diversity, the number of chromosomes, which is a more stable measure. For example, humans have exactly 46 chromosomes<fnref n="66" />, while a mouse has exactly 40 chromosomes.

<table><caption>Table 5.21: Genetic diversity of some organisms</caption><thead><tr><th>Organism</th><th>C-value (in pg)</th><th>Base pairs (in Mbp)</th><th>Genes (×10<sup>3</sup>)</th><th>Chromosomes (2n or kn)</th></tr></thead><tbody><tr><td>Mycoplasma (bacterium)</td><td></td><td>0.580</td><td>0.45 – 0.70</td><td>1*</td></tr><tr><td>Haemophilus influenzae (bacterium)</td><td></td><td>1.8</td><td>1.750</td><td>1*</td></tr><tr><td>Escherichia coli (bacterium)</td><td></td><td>4.6</td><td>4 – 5</td><td>1*</td></tr><tr><td>Drosophila melanogaster (fruit fly)</td><td>0.17</td><td>180</td><td>13 – 17</td><td>8</td></tr><tr><td>Arabidopsis thaliana (mustard plant)</td><td>0.14</td><td>135</td><td>27</td><td>10</td></tr><tr><td>Caenorhabditis elegans (nematode)</td><td>0.10</td><td>100</td><td>21</td><td>12</td></tr><tr><td>Saccharomyces cerevisiae (yeast)</td><td>0.02</td><td>12</td><td>6</td><td>16</td></tr><tr><td>Zea mays (corn)</td><td>2.30</td><td>2 300</td><td>32 – 40</td><td>20</td></tr><tr><td>Oryza sativa (rice)</td><td>0.40</td><td>430</td><td>32 – 50</td><td>24</td></tr><tr><td>Mus musculus (mouse)</td><td>2.60</td><td>2 700</td><td>20 – 25</td><td>40</td></tr><tr><td>Rattus norvegicus (brown rat)</td><td>2.75</td><td>2 700</td><td>20 – 25</td><td>42</td></tr><tr><td>Homo sapiens (human)</td><td>3.20</td><td>3 050</td><td>20</td><td>46</td></tr><tr><td>Solanum tuberosum (tetraploid potato)</td><td>3.50</td><td>3 400</td><td>39 – 45</td><td>48*</td></tr><tr><td>Fragaria ananassa (octoploid strawberry)</td><td>2.50</td><td>2 500</td><td>35 – 45</td><td>56*</td></tr><tr><td>Canis lupus familiaris (dog)</td><td>2.80</td><td>2 800</td><td>20</td><td>78</td></tr><tr><td>Agrodiaetus shahrami (butterfly)</td><td>0.75</td><td>750</td><td>12 – 14</td><td>100 – 268*</td></tr><tr><td>Ophioglossum reticulatum (polyploid fern)</td><td>6.25</td><td>6 200</td><td>30 – 50</td><td>1 440*</td></tr></tbody></table>

Source: Author's research.

<footnote n="66">⁶⁶This is not always true. Some humans have 47 chromosomes (trisomy), while others have 45 chromosomes (monosomy).</footnote>
Table 5.21 shows the genetic diversity of some organisms. The first column gives the scientific name of the organism and indicates the family. Then we have the C-value calculated in pg, the genome size expressed in million base pairs, and the number of (protein-coding) genes. The last column is the number of chromosomes. The symbol * indicates that the cells are not diploid. The fern *Ophioglossum reticulatum* is the organism with the highest number of chromosomes. Interestingly, the number of chromosomes in butterflies can vary greatly from species to species. Most butterfly species have between 28 and 100 chromosomes. For example, common butterflies such as the Monarch (*Danaus plexippus*) have 30 chromosomes. Some species may have as few as 20 chromosomes or as many as 268 chromosomes, such as some *Agrodiaetus* butterflies.

<figure><img src="image_176.png" /><figcaption>Figure 5.31: Blue Morpho butterfly</figcaption></figure>

Source: www.color-meanings.com/colorful-butterflies.

**Species diversity** Organismal diversity can be assessed at different levels, but the most common is species diversity. Individuals represent the first level. They are grouped into populations, which form the second level of organismal diversity. Individuals and populations are also the two last levels of genetic diversity. Finally, populations are grouped into species. Defining a species is not straightforward (De Queiroz, 2007). In common language, species refer to a group of organisms that share certain physical or morphological characteristics. For example, we might say that butterflies form a species. However, this is not true from a biological standpoint. According to *Nature*<sup>67</sup>, “*a biological species is a group of organisms that can reproduce with one another in nature and produce fertile offspring. Species are defined by the fact that they are reproductively isolated from other groups, meaning that organisms within one species cannot successfully reproduce with those of another species.*” For example, butterflies belong to families, not species. Some well-known butterfly species include the Monarch (*Danaus plexippus*) and the Blue Morpho (*Morpho menelaus*). Phylogenetics is another widely used approach to classifying organisms into species. A phylogenetic species is defined as the smallest group of organisms that share a common ancestor and can be distinguished by unique genetic or physical characteristics. Species are then grouped into genera (singular: genus), genera are assembled into families, families into phyla, and so on, progressing through higher taxonomic levels. The principal ranks in modern biological taxonomies are domain, kingdom, phylum (or division), class, order, family, genus, and species. For example, humans are classified as *Homo sapiens*, a species within the genus *Homo*. The *Homo* genus includes *Homo sapiens*

<footnote n="67"><sup>67</sup>Source: https://www.nature.com/scitable/definition/species-312.</footnote>
(the only surviving species today) and several extinct species, such as *Homo neanderthalensis*, *Homo erectus*, and *Homo habilis*. *Homo* belongs to the *Hominidae* family, also known as the great apes. This family also includes chimpanzees, bonobos, and gorillas. Humans are further classified into the *Primates* order, the *Mammalia* class, the *Chordata* phylum, the *Animalia* kingdom, and the *Eukarya* domain. Readers can explore the species taxonomic tree on specialized websites<fnref n="68" />.

In 1988, Robert May published a landmark article in *Science: How Many Species are There on Earth?* This article does not answer the question in the title. Why not? Because he didn't have enough information at the time to make a confident estimate. May (1988) preferred to review the different kinds of information scientists need to produce an answer that isn't just a guess. Thirty-five years later, can we give an accurate answer? In fact, not as many scientific articles suggest:

> "In 2010, Robert May pointed out an embarrassing truth about modern science<fnref n="69" />. Even as we invest huge amounts of time, money, and effort to find life on other planets, we still do not know how much life (i.e., how many species) is on our own. Although 'do not know' might sound like hyperbole, estimates have ranged wildly, from 2 million to 3 trillion." (Wiens, 2023, page 1).

The current reference paper on this topic is Mora et al. (2011), who estimated 8.7 million (±1.3 million standard error) eukaryotic species worldwide, of which 2.2 million (±0.18 million SE) are marine. The decomposition of their estimates is shown in Table 5.22. This result contrasts with the 1.5 or 2 million of species catalogued in current databases, suggesting that many species remain to be discovered. However, these figures continue to be challenged by new research, most of which puts the number of species on Earth at around 11 million, not excluding the possibility that there are at least one billion species on Earth (Larsen et al., 2017).

<table><caption>Table 5.22: Currently catalogued and predicted total number of species on Earth and in the ocean</caption><thead><tr><th rowspan="2">Species</th><th colspan="3">Earth</th><th colspan="3">Ocean</th></tr><tr><th>Catalogued</th><th>Predicted</th><th>± SE</th><th>Catalogued</th><th>Predicted</th><th>± SE</th></tr></thead><tbody><tr><td>Eukaryotes</td><td>1 233 500</td><td>8 740 000</td><td>1 300 000</td><td>193 756</td><td>2 210 000</td><td>182 000</td></tr><tr><td>Animalia</td><td>953 434</td><td>7 770 000</td><td>958 000</td><td>171 082</td><td>2 150 000</td><td>145 000</td></tr><tr><td>Chromista</td><td>13 033</td><td>27 500</td><td>30 500</td><td>4 859</td><td>7 400</td><td>9 640</td></tr><tr><td>Fungi</td><td>43 271</td><td>611 000</td><td>297 000</td><td>1 097</td><td>5 320</td><td>11 100</td></tr><tr><td>Plantae</td><td>215 644</td><td>298 000</td><td>8 200</td><td>8 600</td><td>16 600</td><td>9 130</td></tr><tr><td>Protozoa</td><td>8 118</td><td>36 400</td><td>6 690</td><td>8 118</td><td>36 400</td><td>6 690</td></tr><tr><td>Prokaryotes</td><td>10 860</td><td>10 100</td><td>3 630</td><td>653</td><td>1 320</td><td>436</td></tr><tr><td>Archaea</td><td>502</td><td>455</td><td>160</td><td>1</td><td>1</td><td>0</td></tr><tr><td>Bacteria</td><td>10 358</td><td>9 680</td><td>3 470</td><td>652</td><td>1 320</td><td>436</td></tr><tr><td>Total</td><td>1 244 360</td><td>8 750 000</td><td>1 300 000</td><td>194 409</td><td>2 210 000</td><td>182 000</td></tr></tbody></table>

Source: Mora et al. (2011, Table 2, page 5).

<footnote n="68">⁶⁸The two most popular are www.ncbi.nlm.nih.gov/taxonomy, developed by the NCBI (National Center for Biotechnology Information), and www.fws.gov/explore-taxonomic-tree, provided by the FWS (US Fish & Wildlife Service).</footnote>

<footnote n="69">⁶⁹Here is the abstract of Robert May's paper:</footnote>

<footnote>> "If some alien version of the Starship Enterprise visited Earth, what might be the visitors' first question? I think it would be: How many distinct life forms — species — does your planet have? Embarrassingly, our best-guess answer would be in the range of 5 to 10 million eukaryotes (never mind the viruses and bacteria), but we could defend numbers exceeding 100 million, or as low as 3 million." (May, 2010, page 41).</footnote>
<table><caption>Table 5.23: Exploring the taxonomy classification tree</caption><thead><tr><th>Kingdom</th><th>Phylum</th><th>Class</th><th>Order</th><th>Family</th><th>Genus</th><th>Species</th><th>Vernacular name</th></tr></thead><tbody><tr><td rowspan="10">Animalia</td><td>34</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Arthropoda</td><td></td><td>Insecta</td><td>43</td><td>1 738</td><td>89 273</td><td>994 767</td><td>Insects</td></tr><tr><td>Arthropoda</td><td></td><td>Insecta</td><td>Lepidoptera</td><td>Nymphalidae</td><td>Morpho</td><td>Morpho menelaus</td><td>Blue morphos</td></tr><tr><td>Chordata</td><td></td><td>Mammalia</td><td>Carnivora</td><td>Phocidae</td><td>14</td><td>19</td><td>True seals</td></tr><tr><td>Chordata</td><td></td><td>Mammalia</td><td>Carnivora</td><td>Phocidae</td><td>Phoca</td><td>Phoca largha</td><td>Large seals</td></tr><tr><td>Chordata</td><td></td><td>Mammalia</td><td>Carnivora</td><td>Phocidae</td><td>Phoca</td><td>Phoca vitulina</td><td>Common seals</td></tr><tr><td>Chordata</td><td></td><td>Mammalia</td><td>Primates</td><td>16</td><td>83</td><td>528</td><td>Primates</td></tr><tr><td>Chordata</td><td></td><td>Mammalia</td><td>Primates</td><td>Hominidae</td><td>Homo</td><td>Homo sapiens</td><td>Humans</td></tr><tr><td>Mollusca</td><td></td><td></td><td>Gastropoda</td><td>Helicidae</td><td>Helix</td><td>Helix pomatia</td><td>Escargots</td></tr><tr><td rowspan="10">Archaea</td><td>2</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>29</td><td>Crenarchaeota</td><td>Thermoprotei</td><td>Thermoproteales</td><td>Thermoproteaceae</td><td>1 996</td><td>Bacillus anthracis</td><td>B. anthracis</td></tr><tr><td>51</td><td>Firmicutes</td><td>Bacilli</td><td>Bacillales</td><td>Bacillaceae</td><td>297</td><td>Bacillus</td><td>B. coli</td></tr><tr><td>58</td><td>Pseudomonadota</td><td>Gammaproteobacteria</td><td>Enterobacteriales</td><td>Enterobacteriaceae</td><td>1 101</td><td>Escherichia</td><td>Escherichia coli</td></tr><tr><td>13</td><td></td><td></td><td>200</td><td></td><td>7 248</td><td>61 900</td><td></td></tr><tr><td>5</td><td>Foraminifera</td><td></td><td>22</td><td></td><td>4016</td><td>49 654</td><td></td></tr><tr><td>61</td><td></td><td></td><td>274</td><td>1 086</td><td>12 778</td><td>155 869</td><td></td></tr><tr><td>12</td><td></td><td></td><td>23</td><td>148</td><td>1 875</td><td>40 825</td><td></td></tr><tr><td>9</td><td>Basidiomycota</td><td>Agaricomycetes</td><td>Agaricales</td><td>Amanitaceae</td><td>Amanita</td><td>Amanita phalloides</td><td>Death caps</td></tr><tr><td>9</td><td>Basidiomycota</td><td>Agaricomycetes</td><td>Boletales</td><td>Boletaceae</td><td>Boletus</td><td>Boletus edulis</td><td>Ceps</td></tr><tr><td>44</td><td></td><td></td><td>256</td><td>1 079</td><td>21 463</td><td>385 774</td><td>Plants</td></tr><tr><td>9</td><td>Tracheophyta</td><td>Liliopsida</td><td>Liliales</td><td>Liliaceae</td><td>Tulipa L.</td><td>96</td><td>Tulips</td></tr><tr><td>9</td><td>Tracheophyta</td><td>Magnoliopsida</td><td>Fabales</td><td>Fabaceae</td><td>Phaseolus</td><td>Phaseolus vulgaris</td><td>Common bean</td></tr><tr><td>9</td><td>Tracheophyta</td><td>Magnoliopsida</td><td>Rosales</td><td>Rosaceae</td><td>110</td><td>8 147</td><td>Roses</td></tr><tr><td>9</td><td>Tracheophyta</td><td>Magnoliopsida</td><td>Solanales</td><td>Solanaceae</td><td>102</td><td>2 808</td><td></td></tr><tr><td>9</td><td>Tracheophyta</td><td>Magnoliopsida</td><td>Solanales</td><td>Solanaceae</td><td>Capsicum</td><td>Capsicum annuum</td><td>Pimientos</td></tr><tr><td>9</td><td>Tracheophyta</td><td>Magnoliopsida</td><td>Solanales</td><td>Solanaceae</td><td>Solanum</td><td>Solanum lycopersicum</td><td>Tomatos</td></tr><tr><td>9</td><td>Tracheophyta</td><td>Magnoliopsida</td><td>Solanales</td><td>Solanaceae</td><td>Solanum</td><td>Solanum tuberosum</td><td>Potatos</td></tr><tr><td>10</td><td></td><td></td><td>41</td><td></td><td>227</td><td>1 090</td><td></td></tr><tr><td>10</td><td>Choanozoa</td><td>Ichthyosporea</td><td>Eccrinida</td><td>Amoebidiidae</td><td>Amoebidium</td><td>Amoebidium parasiticum</td><td>Protozoans</td></tr></tbody></table>

For each taxon we indicate the parent nodes of the tree on the left and the number of taxa on the right. For example, *Insecta* belongs to the phylum *Arthropoda* in the kingdom *Animalia* and includes 43 orders, 1 738 families, 89 273 genera, and 994 767 species.
**Ecological diversity** The third element of biodiversity is ecosystems. Again, there are several levels of ecological diversity. Populations, which are also part of genetic and organismal diversity, are the first level. Populations are grouped into habitats. The other three levels are ecosystems, ecoregions, and provinces. Then we find the biomes, which are large-scale ecosystems characterized by similar climatic conditions, vegetation, and wildlife. We generally distinguish between terrestrial and aquatic biomes. Terrestrial biomes include boreal forests (taiga), chaparral (Mediterranean climate), deserts, savannas, temperate forests, temperate grasslands, tropical rainforests, and tundra. Aquatic biomes include freshwater biomes such as wetlands and marine biomes such as oceans, coral reefs and mangroves. The highest level of ecological diversity corresponds to biogeographic realms, which are the broadest divisions of the Earth's land surface delineated by natural barriers such as oceans, deserts, and mountain ranges. Olson et al. (2001) defined eight realms: Australasia, Antarctic, Afrotropic, Indo-Malaya, Nearctic, Neotropic, Oceania and Palearctic.

<figure><img src="image_177.png" /><figcaption>Figure 5.32: The 867 terrestrial ecoregions of Olson et al. (2001)</figcaption></figure>

Source: Olson et al. (2001, Figure 2, page 935).

In general, ecoregions are the most common level at which ecological diversity is assessed. The World Wide Fund for Nature (WWF) describes them as biogeographic units, which are “defined as relatively large units of land or water containing a distinct assemblage of natural communities sharing a large majority of species, dynamics, and environmental conditions.” Most current world ecoregion maps<fnref n="70" /> are based on the seminal work of Olson et al. (2001), who defined 867 distinct ecoregions (Figure 5.32). Among these ecosystems, Olson and Dinerstein (2002) identified 238 priority ecoregions for protection (142 terrestrial, 53 freshwater, and 43 marine). This research has been used extensively by the WWF and the International Union for Conservation of Nature (IUCN) to define protected areas<fnref n="71" />. The 2001 study was recently updated by Dinerstein et al. (2017), which

<footnote n="70">⁷⁰See, for example, the maps available at https://ecoregionsSpot.com and https://www.oneearth.org/bioregions.</footnote>

<footnote n="71">⁷¹IUCN has developed a system of protected area management categories to define, record and classify the wide variety of specific goals and concerns in categorizing protected areas and their objectives. The six categories are: strict nature reserve and wilderness area (Cat. I), national park (Cat. II), natural monument or feature (Cat. III), habitat or species management area (Cat. IV), protected landscape or seascape (Cat. V), and protected area with</footnote>
now has a list of 846 terrestrial ecoregions. A more recent study used a different mapping approach and identified 431 global ecosystems (Sayre et al., 2020). By conducting a global gap analysis of the representation of these ecosystems in protected areas, the authors showed that most natural and semi-natural ecosystems are inadequately protected, with protection rates of less than 20%.

## Biodiversity loss (and gain)

Regardless of the element of biodiversity (genetic, organismal or ecological), most figures show that the loss of biodiversity is significant and has accelerated over the past 50 years. However, such a message is not really clear. Indeed, we can first ask ourselves what biodiversity loss is, how it is measured, and is the current figure really significant? For example, the second chapter of Gaston and Spicer (2004) is devoted to the temporal dynamics of biodiversity and illustrates that biodiversity has fluctuated over geological time scales, such as millions of years. This long-term perspective shows that changes in biodiversity are a natural part of Earth's history and makes it difficult to understand whether current trends represent an exceptional crisis or a continuation of these natural cycles.

<figure><img src="image_178.png" /><figcaption>Figure 5.33: Genus diversity during the Phanerozoic era</figcaption></figure>

Source: Rohde and Muller (2005, Figure 1, page 208) & Supplementary Tables (www.nature.com/articles/nature03339).

The evolution of biodiversity over time is typically represented by a Sepkoski curve, which plots the number of genera over time. Although this is a simple metric, it is difficult to calculate due to

<footnote>sustainable use of natural resources (Cat. VI). For example, in France, Les Landes de Gascogne is managed under IUCN category VI of protected areas, while Le Parc du Mercantour is managed under IUCN category II. Readers can explore protected areas and other effective area-based conservation measures (OECMs) at www.protectedplanet.net.</footnote>
the complexity of data collection. Joseph John Sepkoski devoted much of his career to building a database of marine animal families and genera. This dataset, used extensively in numerous publications, was released in 2002 after Sepkoski's death (Sepkoski, 2002). Figure 5.33 shows the Sepkoski curve generated by Rohde and Muller (2005). The three series shown are: the total number of known genera of marine animals from Sepkoski's catalog<sup>72</sup>, the total number of well-defined genera (i.e., known genera excluding those with single occurrences or poorly dated records), and the long-term trend estimated using a third-order polynomial fitted to the data. First, we observe that the number of genera has fluctuated continuously throughout the Phanerozoic. About 500 million years ago, the number of genera was estimated at 370 000, while today it exceeds 5 million. Second, the increase in the number of genera was not linear. Genus diversity increased about 400 million years ago, then declined until about 200 million years ago, after which it increased dramatically. In the present era, genus diversity is higher than at any time in Earth's history. Finally, while the long-term trend is clear, there are numerous discontinuities with a frequency of about one million years. In particular, we observe several sharp declines known as extinction events or mass extinctions.

**Speciation, extinction and the birth-death model** The number of species on Earth results from a balance between two evolutionary processes: speciation (the formation of new species) and extinction<sup>73</sup>. When speciation rates exceed extinction rates, the number of species increases. Conversely, when extinction rates exceed speciation rates, the number of species decreases. Both processes can occur naturally or be influenced by external factors. In fact, the processes of birth and death apply not only to individuals and populations, but also to higher levels of biological classification, such as species. For example, *Homo sapiens* appeared about 300 000 years ago, while *Australopithecus* disappeared about 1.9 million years ago. Similarly, dinosaurs became extinct about 65 million years ago, illustrating that species extinction is a natural process that can occur without human intervention. Thus, we generally recognize that each species and subspecies has a finite lifespan:

> "Like all species, plants, mammals, and birds have been subject to extinction as a fundamental part of evolution. Indeed, only about 2-4% of all the species that have ever lived during the 600 million years of the fossil record still survive today. Looking at the fossil record, it can be said that invertebrate species and mammals have had an average life span of 5-10 and 1-2 million years, respectively." (Mace, 1998).

Even as some species disappear, new species continue to appear. This process of species formation is called speciation or diversification (Gaston and Spicer, 2004, Section 2.3.2, page 31). Speciation most often occurs when populations of the same species become geographically isolated. Over time, these populations evolve independently, accumulating genetic changes that can eventually lead to the emergence of distinct species. As these genetic differences increase, individuals from the two populations may no longer be able to interbreed or produce fertile offspring. A classic example of this phenomenon is donkeys and horses. Both belong to the same family (*Equidae*) and genus (*Equus*), but are classified as separate species. Donkeys (*Equus africanus asinus*) are a subspecies of the African wild ass (*Equus africanus*), while domestic horses (*Equus ferus caballus*) are a subspecies of the wild horse (*Equus ferus*). Although donkeys and horses can interbreed, their offspring are usually sterile<sup>74</sup>, meaning they cannot reproduce. This sterility occurs because donkeys have 62

<footnote n="72"><sup>72</sup>The Sepkoski database can be found at https://strata.geology.wisc.edu/jack.</footnote>

<footnote n="73"><sup>73</sup>Extinction refers to the complete disappearance of a species from the Earth, while extirpation refers to the disappearance of a species from a particular region, but the species continues to exist in other regions.</footnote>

<footnote n="74"><sup>74</sup>The offspring of a female horse and a male donkey is a mule, while the offspring of a male horse and a female donkey is a hinny.</footnote>
<figure><img src="image_179.png" /><figcaption>Figure 5.34: Rates of origination and extinction during the Phanerozoic era</figcaption></figure>

Source: Rohde and Muller (2005) & Author's calculations.

<figure><img src="image_180.png" /><figcaption>Figure 5.35: Net diversification rate during the Phanerozoic era</figcaption></figure>

Source: Rohde and Muller (2005) & Author's calculations.
chromosomes while horses have 64, resulting in offspring with 63 chromosomes. In fact, donkeys, horses and zebras share a common ancestor, but diverged for various reasons. According to Carbone et al. (2006), zebras and donkeys split about 0.9 million years ago, while their common ancestor diverged from the horse about 2 million years ago.

The number of species $N(t)$ at time $t+1$ can be expressed as:

$$N(t+1) = N(t) + \Delta N^{+}(t+1) - \Delta N^{-}(t+1)$$

where $\Delta N^{+}(t+1)$ and $\Delta N^{-}(t+1)$ are the number of new species and extinct species between $t$ and $t+1$. In continuous time, this equation becomes:

$$\frac{dN(t)}{dt} = \frac{dN^{+}(t)}{dt} - \frac{dN^{-}(t)}{dt}$$

Dividing both sides by $N(t)$ gives:

$$\underbrace{\frac{dN(t)}{N(t) dt}}_{\delta(t)} = \underbrace{\frac{dN^{+}(t)}{N(t) dt}}_{\lambda(t)} - \underbrace{\frac{dN^{-}(t)}{N(t) dt}}_{\mu(t)}$$

The growth rate $\delta(t)$ is the difference between the origination (or speciation) rate $\lambda(t)$ and the extinction rate $\mu(t)$:

$$\delta(t) = \lambda(t) - \mu(t) \qquad (5.4)$$

$\delta(t)$ is also called the net diversification rate. Here, $\lambda(t)$, $\mu(t)$ and $\delta(t)$ are assumed to be instantaneous rates. Given two dates $t_1$ and $t_2$, we can compute the cumulative rates $\lambda(t_1, t_2) = \int_{t_1}^{t_2} \lambda(t) dt$, $\mu(t_1, t_2) = \int_{t_1}^{t_2} \mu(t) dt$, and $\delta(t_1, t_2) = \int_{t_1}^{t_2} \delta(t) dt$. We derive the average rate by dividing the cumulative rate by the time interval. For example, the average net diversification rate is equal to:

$$\bar{\delta}(t_1, t_2) = \frac{\delta(t_1, t_2)}{t_2 - t_1} = \frac{1}{t_2 - t_1} \int_{t_1}^{t_2} \delta(t) dt$$

In Figures 5.34 and 5.35, we report the origination, extinction, and net diversification rates calculated by Rohde and Muller (2005) from the Sepkoski database. For example, the range of the net diversification rate $\delta(t_1, t_2)$ is between -49% and +66%. However, these numbers are difficult to compare because they represent time periods ranging from one million years to seven million years.

The previous remark indicates that we need to normalize the extinction (and other) rates. These rates can be expressed as a percentage per decade, century, or millennium. For long-term trends based on fossil records, we typically express them as a percentage per million years. For example, if the extinction rate $\mu$ is constant and equals 1% per century, this is equivalent to an extinction rate of:

$$\mu = \frac{1\%}{1 \text{ century}} = \frac{1\%}{100 \text{ years}} = 0.01\% \text{ per year}$$

If we assume that the speciation rate is zero, then the number of surviving species follows an exponential survival function:

$$S(t) = \frac{N(t)}{N_0} = e^{-\mu t} \qquad (5.5)$$

We deduce that the lifespan (or average lifetime) of species is the inverse of the extinction rate:

$$\tau = \frac{1}{\mu}$$
For example, if the extinction rate of a genus is 0.1% per millennium, we obtain:

$$ \tau = \frac{1000 \text{ years}}{0.1\%} = 10^6 \text{ years (or 1 million years)} $$

The lifespan of this genus is then one million years. Pimm et al. (1995) introduced a new metric $\eta$ for assessing extinction rates. They use the number of extinctions (E) per million species per year (MSY) or E/MSY. The relationship between $\eta$, $\mu$ and $\tau$ is then:

$$ \eta = 10^6 \mu = \frac{10^6}{\tau} $$

For example, if $\mu$ is 0.1% per millennium, we get:

$$ \eta = \frac{0.1\%}{10^3 \text{ years}} \times 10^6 = \frac{10^{-3}}{10^3 \text{ years}} \times 10^6 = 1 \text{ E/MSY} $$

If there are 1 million species, the number of extinctions per year would be one. Because scientists use these three metrics $\eta$, $\mu$, and $\tau$ interchangeably to assess extinction rates, it is crucial to understand their definitions and how to convert one metric to another.

**Remark 54** We consider the previous example where the extinction rate of a genus equals 1% per century or 0.01% per year. We get:

$$ \mu = \frac{1\%}{1 \text{ century}} = \frac{1\%}{10^2 \text{ years}} \times \frac{10^6}{10^6} = 10000\% \text{ per million years} $$

This example shows that we must be careful with conversion formulas because they ignore the compound effect. Using Equation 5.5, we deduce that$^{75}$:

$$ \mu^* = -\frac{1}{t} \ln \left( \frac{N(t)}{N_0} \right) = -\frac{1}{t} \ln \left( 1 - \frac{N_0 - N(t)}{N_0} \right) = -\frac{1}{t} \ln \left( 1 - \frac{N^+(t)}{N_0} \right) $$

where $N^+(t)$ is the number of extinctions between 0 and $t$. This formula was proposed by Spalding and Hull (2021) to calculate the extinction rate for long timescales.

**Example 22** We consider three datasets with different species:

<table><thead><tr><th>Species</th><th>N<sub>0</sub></th><th>&Delta;N<sup>+</sup></th><th>&Delta;N<sup>-</sup></th><th>&Delta;t</th></tr></thead><tbody><tr><td>Birds</td><td>5 000</td><td>7</td><td>5</td><td>10 years</td></tr><tr><td>Insects</td><td>75 000</td><td>25</td><td>50</td><td>3 centuries</td></tr><tr><td>Plants</td><td>10<sup>6</sup></td><td>30 &times; 10<sup>3</sup></td><td>15 &times; 10<sup>3</sup></td><td>1 millennium</td></tr></tbody></table>

where $N_0$ is the number of species at the beginning of the period, and $\Delta N^+$ and $\Delta N^-$ are the number of new and dead species during the period $\Delta t$.

The calculated values of $\lambda$, $\mu$, and $\delta$ are shown in the table below. For example, the net diversification rate for the bird species is 0.004% per year, or 4% per millennium. In this example, it is better to use a longer time unit (millennium instead of year) because of the magnitude of the rates.

<table><thead><tr><th>Species</th><th>&lambda;</th><th>&mu;</th><th>&delta;</th><th>&lambda;</th><th>&mu;</th><th>&delta;</th></tr><tr><td></td><td colspan="3" style="text-align: center;">(in % per year)</td><td colspan="3" style="text-align: center;">(in % per millennium)</td></tr></thead><tbody><tr><td>Birds</td><td>0.01400</td><td>0.01000</td><td>0.00400</td><td>14.00</td><td>10.00</td><td>4.00</td></tr><tr><td>Insects</td><td>0.00011</td><td>0.00022</td><td>-0.00011</td><td>0.11</td><td>0.22</td><td>-0.11</td></tr><tr><td>Plants</td><td>0.00300</td><td>0.00150</td><td>0.00150</td><td>3.00</td><td>1.50</td><td>1.50</td></tr></tbody></table>

<footnote>$^{75}$To distinguish the logarithmic approach from the arithmetic approach, we use the symbol $\mu^*$ instead of $\mu$. We also define $\tau^* = 1/\mu^*$ and $\eta^* = 10^6\mu^* = 10^6/\tau^*$.</footnote>
We now focus on the extinction rate and calculate this metric with different units. $\mu(0, \Delta t)$ is the cumulative extinction rate. For the bird and plant species, it is equal to:

$$ \mu_{\text{bird}}(0, \Delta t) = \frac{5}{5\,000} = 0.1\% $$

and:

$$ \mu_{\text{plant}}(0, \Delta t) = \frac{15 \times 10^3}{10^6} = 1.5\% $$

These two rates cannot be directly compared because the time periods over which the extinction rate is assessed are very different (10 years versus 1 millennium). Therefore, it is important to normalize. The extinction rate $\mu$ is then expressed in % per year. We can also calculate the extinction rate $\mu^*$ using the previous logarithmic formula. These two extinction rates can then be converted in lifetime (expressed in years) and E/MSY. Numerical results are given below:

<table><thead><tr><th>Species</th><th>μ (0, Δt)<br>(in %)</th><th>μ<br>(in % per year)</th><th>μ<sup>*</sup></th><th>τ<br>(in years)</th><th>τ<sup>*</sup></th><th>η<br>(in E/MSY)</th><th>η<sup>*</sup></th></tr></thead><tbody><tr><td>Birds</td><td>0.10000</td><td>0.01000</td><td>0.01401</td><td>10 000</td><td>7 138</td><td>100.0</td><td>140.1</td></tr><tr><td>Insects</td><td>0.06667</td><td>0.00022</td><td>0.00011</td><td>450 000</td><td>899 850</td><td>2.2</td><td>1.1</td></tr><tr><td>Plants</td><td>1.50000</td><td>0.00150</td><td>0.00305</td><td>66 667</td><td>32 831</td><td>15.0</td><td>30.5</td></tr></tbody></table>

Several observations can be made. First, the figures for $\mu(0, \Delta t)$ cannot be compared directly due to their lack of normalization. We observe extinction rates of 0.1%, 0.07% and 1.5% for birds, insects, and plants, respectively, but these values correspond to different time periods: ten years, three centuries, and one millennium. Second, the results obtained using the arithmetic approach differ from those using the logarithmic approach. Finally, the lifetime and E/MSY figures are probably the easiest to interpret. For example, among one million species, we observe 100, 2.2, and 15 extinctions per year for birds, insects, and plants.

**Background extension rate** The background extension rate is the normal or typical extension rate that has occurred over the past 500 million years. By normal, we mean the long-term rate at which species would go extinct in the absence of human presence. Thus, most estimates use data up to 1500 AD. In a brief communication, Simpson (1952) estimated the average duration of a species to be between 0.5 and 5 million years. This was one of the first publications on the subject. For marine invertebrates, Valentine (1970) estimated the average lifetime to be between 5 and 10 million years. The publication of Van Valen (1973) marked a turning point and generated considerable controversy. In this influential paper, the author introduced the concept of Van Valen's Law, which states that extinction rates within a given taxonomic group remain constant over time. To explain this pattern, he proposed the Red Queen hypothesis, which suggests that species must constantly evolve to keep up with competitors and predators. This ongoing evolutionary arms race results in a constant extinction rate. Van Valen (1973, Table 1) calculated the background extinction rate for 20 families, 38 genera, and 3 species. His results satisfy the following coherent inequalities:

$$ \tau_{\text{family}} \geq \tau_{\text{genus}} \geq \tau_{\text{species}} $$

We report some of his estimates<fnref n="76" /> in Table 5.24. The work of Pimm et al. (1995) was a major milestone in the study of background extinction rates. Based on an analysis of 11 studies, they estimated

<footnote n="76">⁷⁶Van Valen (1973) used the macarthur (ma) measure to define the lifespan of species. One macarthur is the rate of extinction given a half-life of 500 years. Since the figures reported by Van Valen are expressed in micromacarthurs ($\mu$ma), we estimate the lifespan in million years using the following formula: $\tau = 500/(\mu \ln 2)$ where $\mu$ is the extinction rate in $\mu$ma.</footnote>
<table><caption>Table 5.24: Estimates of the background extension rate $\bar{\eta}$</caption><thead><tr><th>Taxonomy</th><th>τ (in myr)</th><th>η (in E/MSY)</th><th>Source</th></tr></thead><tbody><tr><td>All species</td><td>1 – 10</td><td>0.10 – 1.00</td><td>Pimm et al. (1995)</td></tr><tr><td>All species</td><td>1.0</td><td>0.10</td><td>De Vos et al. (2015)</td></tr><tr><td>All fossil groups</td><td>0.5 – 5</td><td>0.20 – 2.00</td><td>Simpson (1952)</td></tr><tr><td>Marine fossil groups</td><td>7.4 – 20</td><td>0.05 – 0.13</td><td>Raup and Sepkoski (1982)</td></tr><tr><td>Marine invertebrates</td><td>5 – 10</td><td>0.10 – 0.20</td><td>Valentine (1970)</td></tr><tr><td>Cetacea (genus)</td><td>3.61</td><td>0.277</td><td>Van Valen (1973)</td></tr><tr><td>Devonian & Cenozoic bivalves</td><td>6.5 – 9.7</td><td>0.10 – 0.15</td><td>Valentine (1970)</td></tr><tr><td>Silurian graptolites</td><td>2.0 – 3.0</td><td>0.33 – 0.50</td><td>Rickards (1977)</td></tr><tr><td>Diatoms</td><td>8.02</td><td>0.125</td><td>Van Valen (1973)</td></tr><tr><td>Dinoflagellata</td><td>13.12</td><td>0.076</td><td>Van Valen (1973)</td></tr><tr><td>Foraminifera (planktonic)</td><td>7.21</td><td>0.139</td><td>Van Valen (1973)</td></tr><tr><td>Foraminifera (genus)</td><td>24.04</td><td>0.042</td><td>Van Valen (1973)</td></tr><tr><td>Foraminifera (family)</td><td>72.13</td><td>0.014</td><td>Van Valen (1973)</td></tr><tr><td>Arthropods</td><td>1.07 – 11.11</td><td>0.090 – 0.934</td><td>De Vos et al. (2015)</td></tr><tr><td>Chordates</td><td>1.71 – 15.63</td><td>0.064 – 0.586</td><td>De Vos et al. (2015)</td></tr><tr><td>Mammals</td><td>0.56</td><td>1.800</td><td>Barnosky et al. (2011)</td></tr><tr><td>Mammals & birds</td><td>0.55 – 4.80</td><td>0.208 – 1.818</td><td>Loehle and Eschenbach (2012)</td></tr><tr><td>Mammals</td><td>9.80 – 43.48</td><td>0.023 – 0.102</td><td>De Vos et al. (2015)</td></tr><tr><td>Mammals</td><td>0.50</td><td>2.000</td><td>Ceballos et al. (2015)</td></tr><tr><td>Mollusca</td><td>0.60 – 7.41</td><td>0.135 – 1.672</td><td>De Vos et al. (2015)</td></tr><tr><td>Primates (genus)</td><td>3.28</td><td>0.305</td><td>Van Valen (1973)</td></tr><tr><td>Reptilia (family)</td><td>24.05</td><td>0.042</td><td>Van Valen (1973)</td></tr><tr><td>Plants</td><td>2.84 – 18.87</td><td>0.053 – 0.352</td><td>De Vos et al. (2015)</td></tr><tr><td>Plants</td><td>7.69 – 20.00</td><td>0.050 – 0.130</td><td>Gray (2019)</td></tr></tbody></table>

the background rate $\bar{\eta}$ to be between 0.1 and 1 E/MSY. Since then, the 1 E/MSY benchmark has been widely adopted in many mass extinction studies. However, it's important to note that this benchmark can vary depending on the specific species or taxonomic group being considered. For example, Barnosky et al. (2011) proposed a benchmark of 1.8 E/MSY for mammals. De Vos et al. (2015) conducted a comprehensive study across different taxa (arthropods, chordates, mammals, mollusca, and plants) and suggested that the lower bound of the Pimm et al. (1995) estimate is a more appropriate benchmark, namely $\bar{\eta} = 0.1$ E/MSY.

**Mass extinction** A mass extinction is a widespread and rapid decline in Earth's biodiversity (genetic or species diversity), during which a substantial proportion of the planet's species disappear over a relatively short period of time — typically thousands to millions of years, which is short on the geologic time scale. The characterization of an extinction event is then determined using calculated extinction rates. Mathematically, we have:

$$[t_1, t_2] \text{ is an extinction event period} \Leftrightarrow \mu(t_1, t_2) \ge \mu^* \text{ and } \bar{\eta}(t_1, t_2) \gg \bar{\eta} \quad (5.6)$$

where $\mu(t_1, t_2)$ is the (total) extinction rate expressed in % during the period $[t_1, t_2]$, $\bar{\eta}(t_1, t_2)$ is the mean extinction rate expressed in E/MSY, $\mu^*$ is a threshold value and $\bar{\eta}$ is the background rate. For example, $\mu^* = 30\%$ means that 30% of species must disappear between times $t_1$ and $t_2$ for the period $[t_1, t_2]$ to be characterized as an extension event. Although there is no consensus on the threshold,
scientists generally use a minimum of 30% for species and 15% for families to characterize a mass extinction.

Using fossil data records, Raup and Sepkoski (1982) demonstrated that four mass extinctions in the marine realm — occurring in the late Ordovician, Permian, Triassic, and Cretaceous periods — had extinction rates that were statistically significantly higher than background rate levels. However, this was not the case for a fifth extinction event in the Devonian. Benton (1995) used a new database that included both marine and continental fossil records and examined 22 extinction events. His results showed that extinction rates can be very different for marine and continental organisms. The study of Bambach (2006) identifies eighteen extinctions and comes to the same conclusion:

> "A review of different methods of tabulating data from the Sepkoski database reveals 18 intervals during the Phanerozoic have peaks of both magnitude and rate of extinction that appear in each tabulating scheme. These intervals all fit Sepkoski's definition of mass extinction. However, they vary widely in timing and effect of extinction, demonstrating that mass extinctions are not a homogeneous group of events." (Bambach, 2006, page 127).

For this reason, paleontologists often use a scale to categorize mass extinction events, distinguishing between<sup>77</sup>:

* Small extinction events: Relatively minor events that do not drastically alter biodiversity;

* Pulse events: More pronounced extinctions that can significantly impact certain taxonomic groups;

* The 'Big Five' extinctions: The five major mass extinctions in Earth's history that resulted in a significant loss of biodiversity.

The Big Five extinctions are those identified by Raup and Sepkoski (1982). For each event, we report below some figures<sup>78</sup> on the total extinction rate<sup>79</sup> and the possible causes:

1. Ordovician-Silurian mass extinction — LOME (445–443 Myr BP)
About 27% of all families, 57% of all genera and 85% of all species became extinct. It is generally assumed that the cause is climate change (global cooling) and volcanic activity, which affect the chemistry of the atmosphere and oceans and CO₂ sequestration.

<footnote n="77"><sup>77</sup>For more informations and illustrations, the reader can consult Chapter 7 of Primack (2014) for detailed information on extinction with a lot of numbers and examples.</footnote>

<footnote n="78"><sup>78</sup>Following the terminology of Algeo and Shen (2024), we use the following abbreviations for the five major mass extinctions: LOME for Late Ordovician, LDME for Late Devonian, EPME for end-Permian, ETME for end-Triassic and ECME for end-Cretaceous mass extinctions. Other commonly used abbreviations include: O-S for Ordovician-Silurian, L-D for Late Devonian, P-T for Permian-Triassic, T-J for Triassic-Jurassic, K-Pg for Cretaceous-Paleogene (previously called K-T for Cretaceous-Tertiary) extinctions. It's important to note that a mass extinction period can be characterized by multiple extinction events. According to Benton (1995), the Big Five extinctions can be further broken down as follows: 1 event for LOME (Ashgillian), 2 events for LDME (Givetian-Frasnian & Famennian), 3 events for EMPE (Ufimian, Kazanian-Tatarian & Tatarian), 3 events for ETME (Carnian, Norian-Rhaetian & Rhaetian) and 2 events for ECME (Cenomanian & Maastrichtian).</footnote>

<footnote n="79"><sup>79</sup>These figures come from the Wikipedia page (https://en.wikipedia.org/wiki/Extinction_event) and are based on the book of Benton (2015). These estimates should be treated with caution, as they may vary from study to study. For example, Barnosky et al. (2011) estimated extinction rates for genera and species to be 57% and 86% for LOME, 35% and 75% for LDME, 56% and 96% for EPME, 47% and 80% for ETME, and 40% and 76% for ECME, respectively. However, we observe that the order of magnitude is the same in most studies.</footnote>
2. Late Devonian mass extinction — LDME (372–359 Myr BP)
About 19% of all families, 35-50% of all genera and 75% of all species became extinct. The cause is generally thought to be climate change (global cooling followed by global warming) and the removal of global CO2.

3. Permian-Triassic extinction or ‘*The Great Dying*’ — EPME (252–251 Myr BP)
About 57% of marine families, 84% of marine genera, 81% of all marine species and 90% of terrestrial vertebrate species became extinct. The cause is generally thought to be climate change (global warming) and volcanic activity (massive volcanic eruptions in Siberia).

4. Triassic-Jurassic extinction — ETME (200–201 Myr BP)
About 23% of all families, 48% of all genera (20% of marine families and 55% of marine genera) and 70-75% of all species became extinct. It is generally thought to be caused by volcanic activity (massive volcanic eruptions in the Central Atlantic Magmatic Province) and sea level changes.

5. Cretaceous-Paleogene extinction — ECME (66 Myr BP)
About 17% of all families, 47% of all genera and 75% of all species became extinct. The Cretaceous extinction is marked by the disappearance of the Dinausores. It is generally assumed that the cause is an asteroid impact followed by widespread environmental disruption, including tsunamis, forest fires, and climate change.

We find that the causes, while diverse, are related to a small number of natural phenomena:

> "Every mass extinction has both an ultimate cause, i.e., the trigger that leads to various climato-environmental changes, and one or more proximate cause(s), i.e., the specific climato-environmental changes that result in elevated biotic mortality. With regard to ultimate causes, strong cases can be made that bolide (i.e., meteor) impacts, large igneous province eruptions and bioevolutionary events have each triggered one or more of the Phanerozoic Big Five mass extinctions, and that tectono-oceanic changes have triggered some second-order extinction events. [...] With regard to proximate mechanisms, most extinctions are related to either carbon-release or carbon-burial processes, the former being associated with climatic warming, ocean acidification, reduced marine productivity and lower carbonate δ¹³C values, and the latter with climatic cooling, increased marine productivity and higher carbonate δ¹³C values." (Algeo and Shen, 2024, page 1).

The leading hypothesis for the fifth mass extinction is the impact of a large asteroid that struck the Earth near the Yucatán Peninsula in Mexico, forming the Chicxulub crater (Schulte et al., 2010). The asteroid, estimated to be 10 to 15 kilometers in diameter, released an immense amount of energy, equivalent to billions of nuclear bombs. This catastrophic impact caused massive earthquakes, tsunamis, and forest fires. In addition, the impact likely caused a ‘nuclear winter’ as a massive plume of debris and vaporized rock was ejected into the atmosphere and spread globally. This debris blocked sunlight, leading to a drastic cooling of the planet, reduced photosynthesis, and a collapse of food chains. While the asteroid impact hypothesis is widely accepted, other factors such as climate change and volcanic activity may also have contributed to the Cretaceous-Paleogene mass extinction. Interestingly, this extinction paved the way for the rise of mammals, including humans, as it wiped out the dinosaurs that had previously dominated the planet. As shown in Figure 5.34 on page 376, biodiversity tends to rebound significantly after each mass extinction. Although biodiversity loss is generally followed by strong gains, this recovery occurs on the paleontological timescale of millions of years.
Box 5.8: IUCN Red List of Threatened Species

Founded in 1964, the International Union for Conservation of Nature (IUCN) is responsible for maintaining and updating the IUCN Red List of Threatened Species. It is now considered the world's most comprehensive source of information on the global extinction status of animals, fungi and plants. They correspond to three kingdoms in organismal diversity or modern biological taxonomy, the other two being protista (single-celled eukaryota) and monera (single-celled prokaryota). IUCN (2012) assesses the risk status of a species according to the following A-E criteria: (A) population size reduction (population decline measured over the longer of 10 years or 3 generations, trend), (B) geographic range (extent of occurrence, area of occupancy), (C) small population size and decline (number of mature individuals, trend), (D) very small or restricted population (number of mature individuals, number of locations), and (E) quantitative analysis (probability of extinction). The Red List divides then species into nine categories:

* **Not Evaluated (NE) & Data Deficient (DD)**

A taxon is NE if it has not yet been evaluated against the criteria. NE species are not published in the IUCN Red List. A taxon is DD if there is insufficient information to make a direct or indirect assessment of its risk of extinction based on its distribution and/or population status. A taxon in this category may be well studied and its biology well understood, but adequate data on abundance and/or distribution are lacking.

* **Least Concern (LC) & Near Threatened (NT)**

A taxon is LC if it has been assessed against the Red List criteria and is not considered CR, EN, VU or NT. A taxon is NT if it has been evaluated against the criteria, but does not currently qualify as CR, EN, or VU, but is close to or is likely to qualify for a threatened category in the near future.

* **Vulnerable (VU), Endangered (EN) & Critically Endangered (CR)**

A taxon is VU (EN or CR, respectively) if the best available evidence indicates that it meets any of the criteria A to E for VU and is therefore considered to be at high (very high or extremely high, respectively) risk of extinction in the wild.

* **Extinct in the Wild (EW)**

A taxon is EW if it is known to survive only in cultivation, captivity, or as a naturalized population (or populations) far outside its historical range. A taxon is presumed to be EW if exhaustive surveys in known and/or expected habitats at appropriate times (diurnal, seasonal, annual) throughout its historical range have failed to record an individual. Surveys should be conducted over a period of time appropriate to the life cycle and life form of the taxon.

* **Extinct (EX)**

A taxon is EX when there is no reasonable doubt that the last individual has died. A taxon is presumed EX when exhaustive surveys in known and/or expected habitat at appropriate times (diurnal, seasonal, annual) throughout its historical range have failed to record an individual. Surveys should be conducted over a period of time appropriate to the life cycle and life form of the taxon.
The Holocene extinction, the Anthropocene extinction or the sixth mass extinction?

At the October 1991 symposium *The Visions of a Sustainable World* at Caltech, Edward O. Wilson warned that “we are now in the midst of a sixth extinction spasm, the greatest since the one that closed the age of the dinosaurs 66 million years ago.” In 1995, Richard Leakey published the book *The Sixth Extinction*, which popularized the term in the scientific community (Leakey and Lewin, 1995). Since then, numerous research papers have been published (Pimm and Brooks, 2000; Wake and Vredenburg, 2008; Barnosky et al., 2011; Dirzo et al., 2014; Ceballos et al., 2015; Cowie et al., 2022). However, it was Elizabeth Kolbert’s book *The Sixth Extinction: An Unnatural History*, which won the Pulitzer Prize in 2015, that introduced the term to the general public (Kolbert, 2014).

There is no doubt that the extinction rate observed since 1500 AD is largely higher than the background rate, as demonstrated by Pimm *et al.* (1995, page 347) (“recent extinction rates are 100 to 1000 times their pre-human levels in well-known, but taxonomically diverse groups from widely different environments”), and De Vos *et al.* (2015, page 452) (“current extinction rates are 1000 times higher than natural background rates of extinction and future rates are likely to be 10 000 times higher”). This is true for both terrestrial and marine extinctions (Ceballos *et al.*, 2017; Del Monte-Luna *et al.*, 2023). This is why we can speak of a Holocene extinction. There is also no doubt that this extinction event is due to humans, leading to the concept of Anthropocene extinction or defaunation (Dirzo *et al.*, 2014). However, it is still difficult to definitively classify our current epoch as the sixth mass extinction. While we meet the criterion for the elevated background extinction rate based on relation (5.6), we have yet to confirm the condition $\mu(t_1, t_2) \ge \mu^*$. Therefore, there is no scientific research that claims that more than 75% of all marine and terrestrial vertebrate species have become extinct in the last five centuries or in the last 10 000 years. We do not really know. Moreover, a mass extinction is usually followed by a period of intense species origination. Therefore, it is difficult to say that the sixth mass extinction has already occurred (Barnosky *et al.*, 2011). The majority of scientists prefer to argue that “we are either entering or in the midst of the sixth great mass extinction” (Wake and Vredenburg, 2008).

Why are we talking about the sixth mass extinction? Because the number of species that have become extinct in the last few centuries is so large, these extinctions are due to human activities, and we do not expect these extinctions to stop in the next few years with population growth and deforestation. The trends are dramatic and we are clearly facing a biodiversity crisis. These facts are extensively documented in the research cited above, as well as in the monumental 1148-page report by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES, 2019).

The stylized facts about current extinction rates are based on the IUCN Red List of Threatened Species (Box 5.8). As of September 2024, the current Red List database contains 163 040 species whose extinction risk has been assessed. For each species, we can obtain the assessment report by using the search query https://www.iucnredlist.org/search. For example, the figures for the snow leopard are available at www.iucnredlist.org/species/22732/50664030. We learned that the snow leopard species (*Panthera uncia*) was assessed in November 2016. Panthera uncia is currently listed as VU (Vulnerable), whereas in 2008 it was listed as EN (Endangered). Much more information can be found in its assessment card<fnref n="80" />.

<footnote n="80">⁸⁰The snow leopard belongs to the following taxonomic classification tree: Animalia (kingdom), Chordata (phylum), Mammalia (class), Carnivora (order), Felidae (family), Panthera (genus), and Panthera uncia (species). The number of mature individuals is estimated to be between 2 710 and 3 386, with a decreasing population trend. It is found in Asia, including Afghanistan, Bhutan, China, India, Kazakhstan, Kyrgyzstan, Mongolia, Nepal, Pakistan, the Russian Federation, Tajikistan, and Uzbekistan. The Panthera uncia inhabits altitudes between 500 and 5 800 meters. Its home range is estimated to be about 2.8 million km² and its generation length is approximately 7.54 years. Additionally, a list of threats and conservation actions has been documented.</footnote>
<figure><img src="image_181.png" /><figcaption>Figure 5.36: Number of extinct species since 1500 AD</figcaption></figure>

Source: IUCN (2024a), www.iucnredlist.org & Author's calculations.

Among the 163 040 species evaluated, 908 are extinct, with the following distribution: 85.6% from Animalia and 14.4% from Plantae (Table 5.25). This corresponds to an extinction rate of 0.56%. Most of these extinct species belong to four phyla: Chordata, Mollusca, Arthropoda, and Tracheophyta (Figure 5.36). Within the Chordata phylum, the class Aves (birds) is the most represented, followed by Mammalia, Actinopterygii (ray-finned fishes), Amphibia, and Reptilia. In the Mollusca phylum, most extinct species are in the class Gastropoda, with the remainder in Bivalvia. In the Tracheophyta phylum, the class Magnoliopsida is the most dominant. Some examples of extinct species are the Dodo, the Splendid Poisson Frog, the Floreana Giant Tortoise, the St Helena Olive, the Stringwood and the Galapagos Amaranth.

Table 5.25 shows the breakdown of the 163 040 evaluated species according to the IUCN Red List categories. There are 81 species classified as Extinct in the Wild (EW), with a balanced distribution between Animalia and Plantae. Examples of EW species include the Spix's Macaw, the Polynesian Tree Snail, the Golden Skiffia, the Yellow Fatu, the Superb Cyanea, and Wood's Cycad. A similar distribution between Animalia and Plantae is observed for Critically Endangered (CE) species, but their number is much larger, totaling 10 031 species. Examples include the Hainan Gibbon, the Golden Line Fish, the Gomera Stick Grasshopper, the Didymous Chamomile, the French Grass, and the Hawaiian Gardenia.

According to IUCN (2024b), the number of threatened species (TH) is defined as follows:

$$TH = EW + CR + EN + VU$$

It is usually expressed in %:

$$TH (\%) = \frac{TH}{TOT - EX - DD} = \frac{EW + CR + EN + VU}{TOT - EX - DD}$$
<table><caption>Table 5.25: Statistics of the IUCN Red List database</caption><thead><tr><th>Kingdom</th><th>Animalia</th><th>Chromistra</th><th>Fungi</th><th>Plantae</th><th>Total</th></tr></thead><tbody><tr><td>Extinct</td><td>777</td><td></td><td></td><td>131</td><td>908</td></tr><tr><td>Extinct in the Wild</td><td>36</td><td></td><td></td><td>45</td><td>81</td></tr><tr><td>Critically Endangered</td><td>4 067</td><td>4</td><td>45</td><td>5 915</td><td>10 031</td></tr><tr><td>Endangered</td><td>6 426</td><td>1</td><td>105</td><td>11 477</td><td>18 009</td></tr><tr><td>Vulnerable</td><td>7 165</td><td>1</td><td>178</td><td>9 937</td><td>17 281</td></tr><tr><td>Conservation Dependent</td><td>18</td><td></td><td></td><td>114</td><td>132</td></tr><tr><td>Near Threatened</td><td>5 149</td><td></td><td>66</td><td>4 203</td><td>9 418</td></tr><tr><td>Least Concern</td><td>51 689</td><td></td><td>240</td><td>33 373</td><td>85 302</td></tr><tr><td>Data Deficient</td><td>15 895</td><td>12</td><td>160</td><td>5 811</td><td>21 878</td></tr><tr><td>Total</td><td>91 222</td><td>18</td><td>794</td><td>71 006</td><td>163 040</td></tr></tbody></table>

Source: IUCN (2024a), www.iucnredlist.org & Author's calculations.

<table><caption>Table 5.26: Number of species assessed and number of threatened species by major group of organisms</caption><thead><tr><th>Taxon</th><th>Clade</th><th>Number of species</th><th colspan="2">Evaluated species</th><th colspan="2">Threatened species</th></tr><tr><th></th><th></th><th></th><th>#</th><th>%</th><th>#</th><th>%</th></tr></thead><tbody><tr><td rowspan="6">Vertebrates</td><td>Mammals</td><td>6 701</td><td>5 983</td><td>89.3%</td><td>1 338</td><td>22.4%</td></tr><tr><td>Birds</td><td>11 195</td><td>11 195</td><td>100.0%</td><td>1 354</td><td>12.1%</td></tr><tr><td>Reptiles</td><td>12 162</td><td>10 309</td><td>84.8%</td><td>1 844</td><td>17.9%</td></tr><tr><td>Amphibians</td><td>8 744</td><td>8 011</td><td>91.6%</td><td>2 873</td><td>35.9%</td></tr><tr><td>Fishes</td><td>36 863</td><td>27 972</td><td>75.9%</td><td>3 927</td><td>14.0%</td></tr><tr><td>Subtotal</td><td>75 665</td><td>63 470</td><td>83.9%</td><td>11 336</td><td>17.9%</td></tr><tr><td rowspan="10">Invertebrates</td><td>Insects</td><td>1 053 578</td><td>12 718</td><td>1.2%</td><td>2 415</td><td>19.0%</td></tr><tr><td>Molluscs</td><td>86 859</td><td>9 111</td><td>10.5%</td><td>2 451</td><td>26.9%</td></tr><tr><td>Crustaceans</td><td>90 531</td><td>3 213</td><td>3.5%</td><td>747</td><td>23.2%</td></tr><tr><td>Corals</td><td>5 623</td><td>831</td><td>14.8%</td><td>252</td><td>30.3%</td></tr><tr><td>Arachnids</td><td>95 894</td><td>774</td><td>0.8%</td><td>272</td><td>35.1%</td></tr><tr><td>Velvet Worms</td><td>222</td><td>11</td><td>5.0%</td><td>9</td><td>81.8%</td></tr><tr><td>Horseshoe Crabs</td><td>4</td><td>4</td><td>100.0%</td><td>2</td><td>50.0%</td></tr><tr><td>Others</td><td>157 543</td><td>1 090</td><td>0.7%</td><td>174</td><td>16.0%</td></tr><tr><td>Subtotal</td><td>1 490 254</td><td>27 752</td><td>1.9%</td><td>6 322</td><td>22.8%</td></tr><tr><td rowspan="7">Plants</td><td>Mosses</td><td>21 925</td><td>327</td><td>1.5%</td><td>181</td><td>55.4%</td></tr><tr><td>Ferns and Allies</td><td>11 800</td><td>821</td><td>7.0%</td><td>321</td><td>39.1%</td></tr><tr><td>Gymnosperms</td><td>1 113</td><td>1 059</td><td>95.1%</td><td>451</td><td>42.6%</td></tr><tr><td>Flowering Plants</td><td>369 000</td><td>68 704</td><td>18.6%</td><td>26 367</td><td>38.4%</td></tr><tr><td>Green Algae</td><td>13 960</td><td>17</td><td>0.1%</td><td>0</td><td>0.0%</td></tr><tr><td>Red Algae</td><td>7 523</td><td>78</td><td>1.0%</td><td>9</td><td>11.5%</td></tr><tr><td>Subtotal</td><td>425 321</td><td>71 006</td><td>16.7%</td><td>27 329</td><td>38.5%</td></tr><tr><td rowspan="3">Fungi</td><td>Mushrooms, etc.</td><td>156 313</td><td>794</td><td>0.5%</td><td>328</td><td>41.3%</td></tr><tr><td>Brown Algae</td><td>4 683</td><td>18</td><td>0.4%</td><td>6</td><td>33.3%</td></tr><tr><td>Subtotal</td><td>160 996</td><td>812</td><td>0.5%</td><td>334</td><td>41.1%</td></tr><tr><td colspan="2">Total</td><td>2 152 236</td><td>163 040</td><td>7.6%</td><td>45 321</td><td>27.8%</td></tr></tbody></table>

Source: IUCN (2024b, Table 1a), www.iucnredlist.org & Author's calculations.
where TOT is the total number of species assessed<fnref n="81" />. We deduce that:

$$TH = 81 + 10031 + 18009 + 17281 = 45402$$

In Table 5.26 we reproduce the calculations that can be found in IUCN (2024b, Table 1a). In this case, the number of threatened species does not include the EW category, which means that:

$$TH^* = 10031 + 18009 + 17281 = 45321$$

The percentage of threatened species is 27.8%. Excluding the clades with low population numbers, we conclude that two categories are particularly threatened: Amphibians and flowering plants with a threat rate of 35.9% and 38.4% respectively. Figure 5.37 shows the evolution of the number of threatened species over time. Over the past 24 years, the number of threatened species has increased by 310%, which corresponds to an annual growth rate of 6.1%. This graph is widely cited and can be found in numerous publications on the current biodiversity crisis. However, caution is needed. A significant part of this trend is due to the fact that the database has become more comprehensive over time. For instance, the IUCN Red List aims to assess 260 000 species and reassess 142 000 of those already assessed by 2030. Naturally, the number of threatened species will rise as the database's coverage increases. For this reason, we have included the proportion of threatened species in Figure 5.38. Since 2010, this proportion has remained stable at around 30%.

However, the previous observation could not hide the fact that the current biodiversity crisis is real and serious, and that we may be in a sixth mass extinction period. There are so many facts that demonstrate this critical situation (Barnosky et al., 2011; Ceballos et al., 2015; Cowie et al., 2022). A major challenge in addressing the current biodiversity crisis is the concept of ‘extinction debt’ (Kuussaari et al., 2009; Figueiredo et al., 2019). This refers to the delayed extinction of species following environmental changes such as habitat loss, fragmentation or degradation. Despite these threats, species may persist for years, decades, or even centuries before succumbing to extinction. This lag creates a debt, where species are essentially doomed, but survive temporarily in their environment. Therefore, extension debt is related to habitat loss and relaxation time:

> “The idea that species can initially survive habitat change but later become extinct without any further habitat modification has a long history. It was first conceptualized in island biogeography (MacArthur and Wilson, 1967) and further elaborated by Jared Diamond, who introduced the term relaxation time as the delay of expected extinctions after habitat loss. According to theoretical predictions and supporting empirical data, the relaxation time increases with increasing patch area and with decreasing isolation. A second root stems from metapopulation modeling. Tilman et al. (1994) introduced the term extinction debt and considered the order of extinctions in relation to competitive dominance [...] The concept of extinction debt is related to relaxation time but specifies the number or proportion of extant species predicted to become extinct as the species community reaches a new equilibrium after an environmental perturbation.” (Kuussaari et al., 2009, page 565).

$$LB (\%) \leq TH (\%) \leq UB (\%)$$

where:

$$LB (\%) = \frac{TH}{TOT - EX} = \frac{EW + CR + EN + VU}{TOT - EX}$$

and:

$$UB (\%) = \frac{TH}{TOT - EX} = \frac{EW + CR + EN + VU + DD}{TOT - EX}$$

<footnote n="81">⁸¹Sometimes the IUCN gives a lower and an upper bound for the estimated percentage of threatened species:</footnote>
<figure><img src="image_182.png" /><figcaption>Figure 5.37: Number of species in the threatened categories (CR, EN, and VU)</figcaption></figure>

Source: IUCN (2024b, Tables 1.b & 2), www.iucnredlist.org & Author's calculations.

<figure><img src="image_183.png" /><figcaption>Figure 5.38: Percentage of species in the threatened categories (CR, EN, and VU)</figcaption></figure>

Source: IUCN (2024b, Tables 1.b & 2), www.iucnredlist.org & Author's calculations.
The issue of habitat loss is explored on page 432, while the issue of relaxation time<fnref n="82" /> can be described as follows. Kuussaari et al. (2009, Glossary, page 564) defined the equilibrium (or stable) state in an ecological community when the number of species does not change because the local extinction rate is equal to the local origination rate. The relaxation time scale is then the time to reach a new equilibrium. Assessing the extinction debt for a given species involves estimating whether the species will eventually go extinct and, if so, determining the likely time of extinction. Kuussaari et al. (2009, Box 1, page 567) outline five main approaches for evaluating extinction debt:

* Detection of extinction debt using past and present habitat characteristics;

* Estimating extinction debt by comparing present-day stable and unstable landscapes;

* Estimating extinction debt based on past and present species richness and habitat characteristics;

* Tracking extinction debt based on time series data;

* Evaluating extinction debt for single species using empirical population data and spatially explicit modeling.

The survey of empirical studies on extinction debt by Kuussaari et al. (2009, Table 1, page 568) found inconsistencies across these approaches. For instance, studies using the first approach typically conclude that amphibians are subject to extinction debts, while studies using the second approach often suggest that amphibians are not subject to extinction debts. However, empirical evidence consistently suggests that forest birds, primates, wood-living fungi, and forest beetles are likely to have extinction debts.

In Halley et al. (2016b), it is assumed that the remaining habitat area is reduced from $A_0$ to $A$, leading to a corresponding decline in species richness to a new value $S(t)$ at time $t$. The equation governing species loss is given by:

$$ \frac{dS(t)}{dt} = \lambda(t) - \mu(t) S(t) \qquad (5.7) $$

where $\lambda(t)$ is the origination rate and $\mu(t)$ is the extinction date. The remaining habitat contains a (constant) number $N(t)$ of individuals, which is proportional to the area $A$ and the density $\rho$ of individuals per unit area: $N(t) = \rho A$. Let $n(t) = N(t)/S(t)$ be the average population size per species. At time $t=0$, we have $n = N_0/S_0 = \rho A/S_0$ where $S(0) = S_0$ is the initial species richness. The authors further assumed that the extinction rate is described by:

$$ \mu(t) = kn(t)^{-\alpha} = k \left( \frac{S(t)}{N(t)} \right)^{\alpha} $$

Therefore, Equation (5.7) becomes:

$$ \frac{dS(t)}{dt} = \lambda(t) - k \left( \frac{S(t)}{\rho A} \right)^{\alpha} S(t) = \lambda(t) - \frac{k}{n^{\alpha} S_{0}^{\alpha}} S(t)^{\alpha+1} \qquad (5.8) $$

The numerical solution can be easily found when the origination rate $\lambda(t)$ is specified. In the case of extinction debt, we can assume that $\lambda(t) = 0$ and the solution is<fnref n="83" />:

$$ S(t) = S_0 \left( 1 + \frac{k\alpha}{n^{\alpha}} t \right)^{-1/\alpha} \qquad (5.9) $$

<footnote n="82">⁸²The concept of relaxation time is used extensively in equilibrium temperature modeling (see pages 671 and 683) and bifurcation theory (see page 692).</footnote>

<footnote n="83">⁸³This is derived from the known solution of the differential equation $x'(t) = -bx(t)^{\alpha+1}$ with initial condition $x(0) = x_0$, which is $x(t) = (abt + x_0^{-\alpha})^{-1/\alpha}$.</footnote>
Figure 5.39 shows the evolution of the relative species richness for various values of $\alpha$ with fixed parameters $A = 500$, $k = 0.20$, $\rho = 0.90$ and $S_0 = 100$. As the value of $\alpha$ approaches 0, the solution converges to the exponential model, which assumes species richness is independent of population size. In this case we have $S(t) = S_0 e^{-kt}$. When $\alpha$ approaches 1, we obtain the neutral model, where species richness remains constant over time: $S(t) = S_0$. In the other cases $\alpha \in (0, 1)$, the extinction curve follows a hyperbolic trajectory. To understand the effect of time, Halley et al. (2016b) examine the case $\alpha = 0.5$ and show that the extinction debt is inversely proportional to the square of time:

$$S(t) = \frac{S_0}{\left(1 + \frac{k}{2\sqrt{n}}t\right)^2} \sim \frac{2S_0}{k^2} t^{-2}$$

Extinction debt is typically quantified by the relaxation time $\tau$, which represents the time required for species richness to decrease by half. Solving the equation $S(t) = S_0/2$ gives the following solution:

$$S_0 \left(1 + \frac{k\alpha}{n^\alpha}\tau\right)^{-1/\alpha} = \frac{S_0}{2} \Leftrightarrow \tau = (2^\alpha - 1) \frac{n^\alpha}{k\alpha} \propto n^\alpha$$

In the previous example, $\tau$ is equal to 4.2, 8.8 and 18.6, respectively.

<figure><img src="image_184.png" /><figcaption>Figure 5.39: Relative species richness and relaxation time</figcaption></figure>

The previous analysis assumes no speciation, which means that the equilibrium species richness $\bar{S} = \lim_{t \to \infty} S(t)$ ultimately approaches zero. To get a more realistic model, we now introduce a constant origination rate: $\lambda(t) = \lambda$. The equilibrium state $\bar{S}$ is reached when the rate of change in species richness becomes zero:

$$\frac{dS(t)}{dt} = 0 \Leftrightarrow \lambda - \frac{k}{n^\alpha S_0^\alpha} \bar{S}^{\alpha+1} = 0 \Leftrightarrow \bar{S} = \left( \frac{\lambda n^\alpha S_0^\alpha}{k} \right)^{1/(\alpha+1)}$$
This is the value of the steady state after the reduction of the area to A. Before reducing the area, the steady state $\bar{S}_0$ satisfies the following equation:

$$ \lambda - \frac{k}{n_0^\alpha \bar{S}_0^\alpha} \bar{S}_0^{\alpha+1} = 0 \Leftrightarrow \bar{S}_0 = \left( \frac{\lambda (\rho A_0)^\alpha}{k} \right)^{1/(\alpha+1)} $$

because the original habitat area was $A_0$ and $n_0 = \rho A_0 / \bar{S}_0$. In Figure 5.40 we illustrate the transition from one steady state to another. We use the following parameters: $A_0 = 1000$, $A = 500$, $k = 0.10$, $\alpha = 0.5$, $\rho = 10$ and $\lambda = 5\%$. Initially, at time $t = -1000$ years, we consider two starting values for species richness: $S(-1000) = 15$ and $S(-1000) = 12$. Both trajectories converge to the steady state value $\bar{S}_0 = 13.572$. At time $t = 0$, we reduce the available habitat by 50%, causing the species richness to shift to a new steady state $\bar{S}_0 = 10.772$. However, it takes time, and the transition between the two equilibria is not instantaneous. It is gradual, resulting in what is known as an extinction debt. The key challenge is to determine whether we are in the early or late stages of this extinction debt process.

<figure><img src="image_185.png" /><figcaption>Figure 5.40: Extinction debt and steady state</figcaption></figure>

**Remark 55** The modeling of extinction debt, particularly in relation to the current biodiversity crisis, has generated extensive research. Notable contributions include the work of Tilman et al. (1994), Hanski and Ovaskainen (2002, 2003), and more recently, Spalding and Hull (2021) with the pulse event model (Box 5.9).
Box 5.9: The Spalding-Hull pulse model

Spalding and Hull (2021) extended the constant birth-death model by introducing extinction pulses:

$$ \mu^{(\text{pulse})}(t) = \mu_0 - \sum_{k=1}^{n^{(\text{pulse})}} \omega_k^{(\text{pulse})} \ln(1 - A_k^{(\text{pulse})}) f_k(t - t_k^{(\text{pulse})}) $$

where $\mu_0$ is the background rate, $n^{(\text{pulse})}$ is the number of pulses, $\omega_k^{(\text{pulse})}$, $A_k^{(\text{pulse})}$ and $t_k^{(\text{pulse})}$ are the scaling factor, the fraction of species removed and the date of the $k^{\text{th}}$ extinction pulse event, and $f_k(x)$ is the probability density function. For example, Spalding and Hull (2021) used the Gaussian single pulse model:

$$ \mu^{(\text{pulse})}(t) = \mu_0 - \omega^{(\text{pulse})} \frac{\ln(1 - A^{(\text{pulse})})}{\sigma\sqrt{2\pi}} \exp\left(-\frac{1}{2}\left(\frac{t - t^{(\text{pulse})}}{\sigma}\right)^2\right) $$

where $\sigma$ is the standard deviation controlling the pulse duration. We deduce that:

$$ \begin{aligned} \mathcal{E}(t) &= \frac{1}{\Delta t} \int_{t}^{t+\Delta t} \mu^{(\text{pulse})}(s) \, ds \\ &= \mu_0(s) - \frac{\omega^{(\text{pulse})} \ln(1 - A^{(\text{pulse})})}{\Delta t} \left( \Phi\left(\frac{t + \Delta t - t^{(\text{pulse})}}{\sigma}\right) - \Phi\left(\frac{t - t^{(\text{pulse})}}{\sigma}\right) \right) \end{aligned} $$

Using the following parameters: $\mu_0 = 0.1$ E/MSY, $\omega = 10^5$, $A^{(\text{pulse})} = 30\%$, $\sigma = 120$ years, and $t^{(\text{pulse})} = 2100$ years AD, we obtain the results given in Figure 5.C.

<figure><img src="image_186.png" /><figcaption>Figure 5.C: Illustration of the Spalding-Hull pulse model</figcaption></figure>
## Biodiversity hotspot

A biodiversity hotspot is a region of the world that is both rich in plant and animal species and highly threatened by human activities. Specifically, it is characterized by the following two criteria:

* Exceptional levels of endemism: The region must have at least 1500 species of vascular plants that are endemic, meaning that they are found nowhere else on Earth;

* High levels of habitat loss: The region must have lost at least 70% of its original natural vegetation, typically due to human activities such as deforestation, agriculture, or urbanization.

The term biodiversity hotspot was coined by Norman Myers, who identified 10 geographic regions as conservation priorities (Myers, 1988). This list has been updated twice by Norman Myers: 18 hotspots in 1990 and 25 hotspots in 2000 (Myers, 1990; Myers et al., 2000). New publications have updated this list several times (Mittermeier et al., 2011). The last update is done by Noss et al. (2015), who included the North American Coastal Plain. Today we recognize 36 biodiversity hotspots (Figure 5.41).

<figure><img src="image_187.png" /><figcaption>Figure 5.41: The 36 biodiversity hotspots</figcaption></figure>

The 25 original biodiversity hotspots identified by Myers et al. (2000) are in green, while the added eleven regions are in blue. The 36 regions are (1) Tropical Andes, (2) Mesoamerica, (3) Caribbean Islands, (4) Atlantic Forest, (5) Tumbes-Chocó-Magdalena, (6) Cerrado, (7) Chilean Winter Rainfall-Valdivian Forests, (8) California Floristic Province, (9) Madagascar and the Indian Ocean Islands, (10) Coastal Forests of Eastern Africa, (11) Guinean Forests of West Africa, (12) Cape Floristic Region, (13) Succulent Karoo, (14) Mediterranean Basin, (15) Caucasus, (16) Sundaland, Indonesia and Nicobar islands of India, (17) Wallacea of Indonesia, (18) Philippines, (19) Indo-Burma, Bangladesh, India and Myanmar, (20) Mountains of Southwest China, (21) Western Ghats and Sri Lanka, (22) Southwest Australia, (23) New Caledonia, (24) New Zealand, (25) Polynesia-Micronesia, (26) Madrean pine-oak woodlands, (27) Maputaland-Pondoland-Albany, (28) Eastern Afromontane, (29) Horn of Africa, (30) Irano-Anatolian, (31) Mountains of Central Asia, (32) Eastern Himalaya, (33) Japan, (34) East Melanesian Islands, (35) Eastern Australian temperate forests, and (36) North American Coastal Plain.

Source: upload.wikimedia.org/wikipedia/commons/9/93/Biodiversity_Hotspots.svg.
These biodiversity hotspots cover only 2.5% of the Earth's land surface, but support more than half of the world's endemic plant species. As shown in Figure 5.41, many of these hotspots are concentrated around the tropics. Biodiversity is unevenly distributed across the Earth's surface, a pattern known as the biodiversity gradient. This concept refers to the variation in species diversity across geographic regions, often along specific environmental gradients. The most common example is the latitudinal biodiversity gradient, which describes how species richness generally increases as one moves from the poles toward the equator (Willig et al., 2003). As noted by Gaston and Spicer (2004, Section 3.4, pages 71-85), it is hard to explain this phenomenon<sup>84</sup>, understand the causes and draw general conclusions.

In fact, biodiversity hotspots are often characterized by a high extinction debt because they frequently host species that are on a delayed extinction pathway due to past habitat destruction. These regions are at high risk of losing species in the future, even if no additional habitat loss occurs. The existence of an extinction debt makes conservation efforts in hotspots particularly urgent, as many species may already be committed to extinction. Fragmentation and isolation in these areas exacerbate the problem by weakening the long-term survival chances of species. Therefore, unless immediate action is taken, biodiversity hotspots may face significant hidden biodiversity loss and a substantial extinction debt.

## 5.4.2 Ecosystem functions and services

### Definition

Ecosystem functions are natural processes, such as nutrient cycling, while ecosystem services are the benefits humans derive from these processes, such as food:

> "In our increasingly technological society, people give little thought to how dependent they are on the proper functioning of ecosystems and the crucial services for humanity that flow from them. Ecosystem services are "the conditions and processes through which natural ecosystems, and the species that make them up, sustain and fulfill human life" (Daily, 1997, page 3); in other words, "the set of ecosystem functions that are useful to humans" (Kremen, 2005, page 468). Although people have been long aware that natural ecosystems help support human societies, the explicit recognition of "ecosystem services" is relatively recent (Mooney and Ehrlich, 1997)." (Sekercioglu, 2010, page 45).

Sekercioglu (2010) classified ecosystem services into 6 categories: (1) climate and biogeochemical cycles (climate stability, air purification, UV protection), (2) regulation of the hydrological cycle (drought mitigation, flood mitigation, water purification), (3) soils and erosion (detoxification and decomposition of wastes, soil formation and soil fertility), (4) biodiversity and ecosystem function (ecosystem goods), (5) mobile linkages (pollination, seed dispersal), and (7) nature's remedies for emerging diseases (medicine, pest control). For his part, Gaston and Spicer (2004, Chapter 4) made the distinction between direct-use and indirect-use values of ecosystem services. The direct-use

<footnote n="84"><sup>84</sup>Gaston and Spicer (2004, pages 72 and 73) highlights four key features of the latitudinal biodiversity gradient:</footnote>

<footnote>* Persistence: The latitudinal gradient has been a consistent feature throughout much of Earth's history;</footnote>

<footnote>* Equatorial Peak: The peak of biodiversity often occurs slightly off-center from the equator;</footnote>

<footnote>* Asymmetry: The gradient often shows an asymmetric pattern, with a steeper increase from northern regions toward the equator and a more gradual decrease from the equator to southern regions;</footnote>

<footnote>* Steepness variation: The steepness of the gradient can vary considerably among taxonomic groups. For example, butterflies are more tropical than birds.</footnote>
value describes the role of biological resources in consumption or production and mainly concerns
commodities such as food, medicine and industrial materials. This category also includes biolog-
ical control, recreational use (e.g., hunting and fishing), and ecotourism. Indirect-use values are
more related to ecosystem functions such as atmospheric regulation, climate regulation, hydrolog-
ical regulation, nutrient cycling, pest control, photosynthesis, pollination, and soil formation and
maintenance.

One of the first classifications of ecosystem services was developed by Millennium Ecosystem Assessment (2005, Table 1, page 7 & Box 3.1, page 50). They distinguished 4 families: supporting, provisioning, regulating and cultural services. However, they emphasized the main role of supporting ecosystem services (nutrient cycling, soil formation, primary production), which is essential for the other three ecosystem services<fnref n="85" />. In other words, without supporting ecosystem services, there is no life. The major report of IPBES (2019, Glossary, page 1031) adopted a different classification based on three categories: material (corresponding to provisioning services), regulating (corresponding to the merger of supporting and regulating services), non material (corresponding to cultural services). This three-category system has also been adopted by ENCORE (2024) and TNFD (2023, page 28), which distinguish between (1) provisioning, (2) regulation and maintenance, and (3) cultural services. However, the categorization between the last three systems changes relatively when we consider the Level 2 system<fnref n="86" />. Below is a list of the different ecosystem services described in the 4 classification systems:

1. Aesthetic and cultural services

* Aesthetic, symbolic and spiritual values (nature inspires creativity, provides spiritual connections, and contributes to cultural identity)

* Cultural and spiritual significance (many ecosystems have deep cultural, historical or spiritual significance for local communities and indigenous peoples)

* Educational, scientific and research services (biodiversity provides opportunities for scientific study and learning)

* Recreational opportunities and tourism (forests, parks and other natural areas provide opportunities for recreation and tourism)

* Visual amenity services (non-material benefits that contribute to well-being, emotional satisfaction, and cultural enrichment)

2. Provisioning services

* Energy (natural processes by which ecosystems produce energy such as biomass, solar energy capture, and fossil fuels)

* Food and feed (agriculture, biomass supply, fisheries, plants, animals, seafood, and livestock)

* Genetic resources (biodiversity provides genetic material essential for breeding crops and livestock, and developing new technologies)

<footnote n="85">⁸⁵Provisioning services include food, freshwater, timber, wood, fiber, fuel, and genetic resources; regulating services include the regulation of climate, floods, disease, water quality, and waste management; and cultural services include recreation, aesthetic enjoyment, education, and spiritual fulfillment.</footnote>

<footnote n="86">⁸⁶In the case of ENCORE, the classification system is described in the two CSV files of the 2024 zipped database: ENCORE knowledge base/Encore files/02. Ecosystem services definition.csv and ENCORE knowledge base/Encore files/08. Ecosystem services and ecosystem components.csv. A comparison of the three systems (IPBES, ENCORE and TNFD) can be found in NGFS (2024, Table 1, page 45).</footnote>
* Medicinal and biochemical resources (many medicines and pharmaceutical products are derived from natural compounds found in biodiversity)

* Raw materials (timber, fuel wood, minerals, fibers, and other natural resources)

* Water supply (clean water for drinking, irrigation, and industrial use)

### 3. Regulating services

* Air quality regulation (ecosystems filter pollutants from the air, improving air quality)

* Climate regulation (forests absorb carbon dioxide and help regulate global temperatures)

* Waste detoxification and decomposition (natural decomposition of organic matter, natural ability to detoxify harmful chemicals and pollutants)

* Erosion control (vegetation helps stabilize soils, reducing erosion and preventing landslides)

* Hazard and extreme event regulation (flood, storm, rainfall)

* Pest and disease control (natural predators and parasites help regulate populations of harmful organisms)

* Pollination and seed dispersal (bees, birds, insects, and other pollinators allow many plants to reproduce)

* Water purification (freshwater, wetlands, and forests filter pollutants from water)

### 4. Supporting services

* Habitat creation and maintenance (habitats are the natural environments in which organisms live, grow, and reproduce; they form the basis of ecosystems by providing the resources necessary for species to thrive)

* Nutrient cycling (the movement of nutrients through ecosystems, essential for plant growth and productivity)

* Photosynthesis (plants convert solar energy into chemical energy, producing oxygen and forming the base of the food chain)

* Primary production (the production of organic material by plants and algae forms the foundation of ecosystems)

* Soil formation and fertility (the breakdown of rocks and organic matter to create soil)

* Water cycle regulation (ecosystems play an important role in regulating the water cycle, from evaporation to precipitation)

Rather than examining all of these ecosystem services, we focus on two of them (pollination and food) to illustrate the importance of ecosystem functions. We also develop the concept of natural capital, which is essential for valuing these ecosystem services.

#### Natural capital

Ecosystem services are derived from natural capital, which can be defined as the world's stock of natural assets, including geology, soil, air, water, and all living things. The concept of natural capital in biodiversity is generally attributed to David Pearce, an environmental economist, with his work on the economics of sustainable development (Pearce, 1988). However, the concept itself draws on earlier ideas in ecological economics<fnref n="87" />. For example, the underlying idea of natural capital can be

<footnote n="87">⁸⁷For a historical perspective on natural capital in economics, the reader can refer to Åkerman (2003) and Missemer (2018).</footnote>
found in the extension of input-output models<sup>88</sup> proposed by Daly (1968), who argued that biology and economics are not two separate sciences but need to be integrated:

> "The purpose of this essay is to bring together some of the more salient similarities between biology and economics and to argue that, far from being superficial, these analogies are profoundly rooted in the fact that the ultimate subject matter of biology and economics is one, viz., the life process." (Daly, 1968, page 392).

However, the concept was really popularized by Robert Costanza in 1997 and his seminal paper on the valuation of ecosystem services and natural capital (Costanza et al., 1997). The definition of natural capital has remained largely consistent since Pearce (1988), for whom natural capital is "the set of all environmental assets". Costanza and Daly (1992) used the stock-flow model to define capital as a stock that provides a flow of valuable goods or services into the future. In this context, natural capital and natural income are simply the stock and flow components, respectively, of natural resources. Today, natural capital is broadly recognized as the stock of environmental assets and ecosystem services that provide goods and services to humans and life. The challenge, once this definition is accepted, is to determine the full extent of these assets and services and to value them accurately.

<table><caption>Table 5.27: Total value of annual ecosystem services in 1997 (1995 price levels)</caption><thead><tr><th>Biome</th><th>Area<br>(in ha ×10<sup>6</sup>)</th><th>Value<br>(in $/ha/yr)</th><th>Total value<br>(in $bn/yr)</th><th>Breakdown<br>(in %)</th></tr></thead><tbody><tr><td>Marine</td><td>36 302</td><td>577</td><td>20 949</td><td>63.0</td></tr><tr><td>Open ocean</td><td>33 200</td><td>252</td><td>8 381</td><td>25.2</td></tr><tr><td>Coastal</td><td>3 102</td><td>4 052</td><td>12 568</td><td>37.8</td></tr><tr><td>Terrestrial</td><td>15 323</td><td>804</td><td>12 319</td><td>37.0</td></tr><tr><td>Forest</td><td>4 855</td><td>969</td><td>4 706</td><td>14.1</td></tr><tr><td>Grassland & meadow</td><td>3 898</td><td>232</td><td>906</td><td>2.7</td></tr><tr><td>Wetland</td><td>330</td><td>14 785</td><td>4 879</td><td>14.7</td></tr><tr><td>Lake & river</td><td>200</td><td>8 498</td><td>1 700</td><td>5.1</td></tr><tr><td>Desert</td><td>1 925</td><td></td><td></td><td></td></tr><tr><td>Tundra</td><td>743</td><td></td><td></td><td></td></tr><tr><td>Ice & rock</td><td>1 640</td><td></td><td></td><td></td></tr><tr><td>Cropland</td><td>1 400</td><td>92</td><td>128</td><td>0.4</td></tr><tr><td>Urban</td><td>332</td><td></td><td></td><td></td></tr><tr><td>Total</td><td>51 625</td><td></td><td>33 268</td><td>100.0</td></tr></tbody></table>

Source: Costanza et al. (1997, Table 2, page 256) & Author's calculations.

The publication of Costanza et al. (1997) marked a milestone in the valuation of natural capital. They estimated that the value of ecosystem services was in the range of $16–$54 trillion per year, with an average of $33 tn/yr in 1995. Given that world GDP was $28 trillion per year, ecosystems would represent 1.2 times the economic value created by humans (Pearce, 1998). The positive reception of the paper published in *Nature* was largely supported by the scientific community, although we can find some criticism of the methodology, the total figure of $33 tn/yr and the applicability to environmental policy. However, the impact of the paper has been profound, leading to further research on ecosystem service valuation.

<footnote n="88"><sup>88</sup>See Section 8.4.2 on page 819.</footnote>