role. But it's not just a matter of choosing one ecosystem service over another. Instead, we see a global deterioration of ecosystem services when examining the ecological footprint and the Earth's biocapacity. The ecological footprint, introduced by Wackernagel and Rees (1996), measures the rate at which we consume resources and produce waste compared to the rate at which nature can regenerate those resources and absorb waste. This metric balances the demand for ecosystem services against their supply. On the demand side, the ecological footprint assesses the use of productive land areas, and quantifies the ecological assets required by a population or product to produce the resources it consumes and to absorb its wastes. On the supply side, biocapacity measures the productivity of ecological assets (such as cropland, grazing land, forests, fisheries, and built-up areas). Both metrics are expressed in global hectares, either for a region or per capita, allowing for meaningful comparisons across regions.

<figure><img src="image_48.png" /><figcaption>Figure 19: Global ecological footprint and biocapacity (in global hectares per capita)</figcaption></figure>

Source: https://data.footprintnetwork.org & Author's calculations.

Figure 19 shows the global ecological footprint when considering the various ecological assets. If the ecological footprint exceeds biocapacity, the region has a biocapacity deficit (red area); otherwise, it has a biocapacity reserve (green area). Before 1970, global biocapacity was greater than the ecological footprint, but since then, a biocapacity deficit has emerged. This shift has occurred because, while the per capita ecological footprint has remained relatively constant, the per capita biocapacity has declined, as the Earth's resources are finite. There are significant regional differences. South America's biocapacity balance has declined over time but remains positive, while Europe has experienced a biocapacity deficit for many years. If we focus specifically on the ecosystem service of cropland (Figure 20), we see different regional trends. In Asia, Europe, and South America, both demand and supply per capita have increased. However, the biocapacity balance remains positive in South America, is negative but significantly reduced in Europe, and is negative and increasing in Asia. In North America, the biocapacity reserve has remained roughly constant since 2000.
<figure><img src="image_49.png" /><figcaption>Figure 20: Cropland ecological footprint and biocapacity (in global hectares per capita)</figcaption></figure>

Source: https://data.footprintnetwork.org & Author's calculations.

In addition to food diversity, a second important dimension of food security is the Earth's capacity to feed the planet, or 8.2 billion people. The FAO uses several measures to assess food insecurity. One of the main metrics is the prevalence of (severe/moderate) food insecurity. Let X and R be the random variables for energy intake and energy requirement, respectively, with a joint probability distribution F (x, r). Sukhatme (1961, Equation 1, page 466) defines the prevalence of undernourishment as the probability that intake is less than requirement:

$$ \text{PoU} = \text{Pr}\{X < R\} = \iint \mathbb{1}\{x < r\} \cdot d\mathbf{F}(x, r) = \iint_{x<r} f(x, r) \, dx \, dr \quad (13) $$

where f (x, r) is the bivariate density function of (X, R). The non-parametric estimator of PoU is the empirical frequency:

$$ \text{PoU} = \frac{1}{n} \sum_{i=1}^{n} \mathbb{1}\{x_i < r_i\} $$

where n denotes the population size and (xᵢ, rᵢ) are the observed intake and requirement values for individual i. Another approach assumes a parametric density function f (x, r; θ), estimates the vector of parameters θ, and calculates PoU = ∬_{x<r} f (x, r; θ) dx dr. Both statistical methods require a sample (xᵢ, rᵢ) of energy intake and requirement values. However, in practice, determining an individual's exact energy requirement is challenging. Therefore, the FAO approximates the prevalence of undernourishment as follows:

$$ \text{PoU} = \text{Pr}\{X < r_L\} = \int_{x<r_L} f_x(x) \, dx = \mathbf{F}_x(r_L) \quad (14) $$
where $F_x(x)$ is the cumulative distribution function of energy intake, often called dietary energy consumption (DEC), and $r_L$ is a cut-off point representing the minimum requirement, also known as the minimum dietary energy requirement (MDER)$^{49}$. The univariate approach is valid when applied to a homogenous group such that $\sigma(R) \approx 0$. Therefore PoU is calculated at the group level (e.g., sex × age) and then aggregated across the different groups in a population. It is commonly accepted that $X \sim \mathcal{LN}(\mu_x, \sigma_x^2)$. The calibration of the parameters $\mu_x$ and $\sigma_x$ is done by matching the first two statistical moments of X. Let $\mu(X)$ and $CV(X) = \sigma(X)/\mu(X)$ be the empirical mean$^{50}$ and the coefficient of variation of X, respectively. Since we have $\mu(X) = \exp(\mu_x + \frac{1}{2}\sigma_x^2)$ and $CV^2(X) = \exp(\sigma_x^2) - 1$, we deduce that:

$$ \left\{ \begin{array}{l} \mu_x = \ln \mu(X) - \frac{1}{2} \ln (CV^2(X) + 1) \\ \sigma_x = \sqrt{\ln (CV^2(X) + 1)} \end{array} \right. $$

According to FAO (2024a), the minimum energy requirement $m_i$ by sex and age group is calculated by estimating the basal metabolic rate (BMR) and multiplying it by the ideal weight for a healthy person in that sex/age group. These ideal weights are derived from the body mass index (BMI) reference tables published by the World Health Organization (WHO). The minimum energy requirement is then adjusted using a physical activity level (PAL) coefficient. Finally, the cut-off point is obtained as the weighted average of the minimum energy requirements: $r_L = \sum_{i=1}^{n} f_i m_i$ where $f_i$ is the frequency of individuals in sex/age group i within the population.

**Remark 6** While the estimation of $\mu(X)$ is simply the empirical mean, the estimation of $CV(X)$ is more complex. According to Naiken (2002), the coefficient of variation is assumed to have two components:

$$ CV^2(X) = CV^2(X | Y) + CV^2(X | R) $$

where $CV(X | Y)$ is the coefficient of variation of X due to income dispersion and $CV(X | R)$ is the coefficient of variation of X due to energy requirement. In general, $CV(X | R)$ is assumed to be constant and equal to 20%.

**Example 2** We assume$^{51}$ that the average dietary energy consumption (ADEC) $\mu(X)$ is 2589 kcal/capita/day, the coefficient of variation $CV(X)$ is 0.27, the minimum dietary energy requirement (MDER) $r_L$ is 1803 kcal/capita/day and the average dietary energy requirement (ADER) is 2333 kcal/capita/day.

We first calibrate the log-normal distribution of the dietary energy consumption. The estimated values of the parameters are:

$$ \sigma_x = \sqrt{\ln(0.27^2 + 1)} = 0.2653 $$

$$ \mu(X) = \frac{1}{365} \left( \frac{1}{N} \sum_{i=1}^{m} Q_i C_i \right) $$

<footnote>$^{49}$This approximation is suggested in Sukhatme (1961, Equation 4, page 473). See also Exercise A.1 on page 230 for a comparison between the bivariate and univariate distribution approaches.</footnote>

<footnote>$^{50}$The mean dietary energy consumption is given by:</footnote>

<footnote>where $Q_i$ is the amount (in kg) of food product i consumed annually by the population, $C_i$ is the energy density (in Calories/kg) of food product i, and N is the population size. The term $\sum_{i=1}^{m} Q_i C_i$ represents the total calories consumed by the population in one year, while $\mu(X)$ is the average number of calories per capita per day. We recall that food available for human consumption is equal to the total food supply (production + imports – exports – changes in stocks) minus animal feed minus seeds minus other non-human uses minus waste.</footnote>

<footnote>$^{51}$These figures are those obtained from the FAO in the case of India in 2022.</footnote>
and:

$$ \mu_x = \ln(2589) - \frac{0.2653^2}{2} = 7.8238 $$

We can then deduce that the prevalence of undernourishment is 10.91%:

$$ \text{PoU} = \text{Pr}\{X < 1803\} = \Phi\left(\frac{\ln(1803) - 7.8238}{0.2653}\right) = 0.1091 $$

Figure 21 shows the probability distribution of the dietary energy consumption X, the MDER and the prevalence of undernourishment. We also report the values of ADER and ADEC, which measure the average dietary energy requirement and consumption. In this case, we observe that ADER < ADEC, which is the normal situation.

<figure><img src="image_50.png" /><figcaption>Figure 21: Dietary energy consumption and prevalence of undernourishment (India, 2022)</figcaption></figure>

Source: www.fao.org/faostat/en/#data/FS & Author's calculations.

Figure 22 shows the evolution of several statistics from 2000 to 2022. The first panel compares ADEC, ADER and MDER. As expected, the average and minimum dietary energy requirements are relatively stable. On average, ADER is equal to 2360 kcal/capita/year, while MDER is equal to 1820 kcal/capita/year. On the contrary, the average dietary energy consumption is increasing over time at the global level. It is now close to 3000 kcal/capita/year. However, these global figures hide some large differences between countries, as some countries have experienced large declines in recent years. In fact, we observe that the prevalence of undernourishment has decreased from 2000 to 2019, but it is increasing since 2020. As a result, the number of undernourished people is currently around 730 million. Figure 23 highlights this wide variability across countries. Average dietary energy consumption ranges from 1834 Calories per capita per day in Somalia to 3912 Calories in the USA. Somalia also has the highest prevalence of undernourishment, at 51% in 2022. The suite of
<figure><img src="image_51.png" /><figcaption>Figure 22: Prevalence of undernourishment and number of undernourished people (World)</figcaption></figure>

Source: www.fao.org/faostat/en/#data/FS & Author's calculations.

<figure><img src="image_52.png" /><figcaption>Figure 23: Histogram of food insecurity indicators (country level, 2022)</figcaption></figure>

Source: www.fao.org/faostat/en/#data/FS & Author's calculations.
food security indicators on the FAOSTAT website includes many other statistics on food insecurity. For example, the bottom panels of Figure 23 show the prevalence of severe food insecurity in the total population and the prevalence of obesity in adults (18 years and older). Other indicators are presented in table 21 for the different regions of the world.

<table><caption>Table 21: Food security indicators by region (2022)</caption><thead><tr><th>Indicator</th><th>Africa</th><th>Asia</th><th>Europe</th><th>North America</th><th>Oceania</th><th>South America</th><th>World</th></tr></thead><tbody><tr><td>MDER (kcal/capita/day)</td><td>1736</td><td>1831.0</td><td>1931</td><td>1962</td><td>1871</td><td>1856</td><td>1832</td></tr><tr><td>ADER (kcal/capita/day)</td><td>2237</td><td>2369.0</td><td>2505</td><td>2554</td><td>2424</td><td>2403</td><td>2370</td></tr><tr><td>ADEC (kcal/capita/day)</td><td>2578</td><td>2917.0</td><td>3467</td><td>3882</td><td>3104</td><td>3104</td><td>2971</td></tr><tr><td>Prevalence of undernourishment</td><td>19.9</td><td>8.2</td><td></td><td></td><td>7.1</td><td>6.6</td><td>9.1</td></tr><tr><td>People undernourished (million)</td><td>284.1</td><td>386.5</td><td></td><td></td><td>3.2</td><td>43.9</td><td>723.8</td></tr><tr><td>Severe food insecurity</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Total population</td><td>21.7</td><td>9.7</td><td>1.8</td><td>0.9</td><td>9.3</td><td>11.0</td><td>10.8</td></tr><tr><td>Rural adult population</td><td>23.5</td><td>10.4</td><td>1.7</td><td>0.8</td><td>2.8</td><td>13.5</td><td>12.2</td></tr><tr><td>Town adult population</td><td>22.2</td><td>10.9</td><td>1.9</td><td>0.7</td><td>4.0</td><td>12.9</td><td>11.5</td></tr><tr><td>Urban adult population</td><td>19.8</td><td>8.3</td><td>1.8</td><td>1.2</td><td>3.0</td><td>9.6</td><td>9.3</td></tr><tr><td>Male adult population</td><td>20.8</td><td>8.6</td><td>1.7</td><td>0.7</td><td>8.5</td><td>9.6</td><td>9.1</td></tr><tr><td>Female adult population</td><td>21.3</td><td>9.9</td><td>1.9</td><td>1.2</td><td>8.3</td><td>12.0</td><td>10.2</td></tr><tr><td>Total population (million)</td><td>309.0</td><td>459.2</td><td>13.3</td><td>3.5</td><td>4.2</td><td>72.5</td><td>861.7</td></tr><tr><td>Male adults (million)</td><td>87.9</td><td>157.2</td><td>6.4</td><td>1.0</td><td>1.5</td><td>23.7</td><td>277.7</td></tr><tr><td>Female adults (million)</td><td>92.0</td><td>177.6</td><td>7.8</td><td>1.9</td><td>1.4</td><td>31.2</td><td>311.9</td></tr><tr><td>Water services</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Safely managed drinking water</td><td>33.0</td><td>76.0</td><td>93.0</td><td>97.0</td><td></td><td>75.0</td><td>73.0</td></tr><tr><td>Basic drinking water</td><td>66.0</td><td>95.0</td><td>98.0</td><td>100.0</td><td></td><td>98.0</td><td>91.0</td></tr><tr><td>Sanitation services</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Safely managed sanitation</td><td>26.0</td><td>59.0</td><td>79.0</td><td>96.0</td><td>73.0</td><td>49.0</td><td>57.0</td></tr><tr><td>Basic sanitation</td><td>36.0</td><td>86.0</td><td>97.0</td><td>100.0</td><td>80.0</td><td>90.0</td><td>81.0</td></tr><tr><td>Children under 5 years</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Affected by wasting</td><td>5.8</td><td>9.3</td><td></td><td>0.2</td><td></td><td>1.4</td><td>6.8</td></tr><tr><td>Who are stunted</td><td>30.0</td><td>22.3</td><td>4.0</td><td>3.6</td><td>22.0</td><td>11.5</td><td>22.3</td></tr><tr><td>Who are overweight</td><td>4.9</td><td>5.1</td><td>7.3</td><td>8.2</td><td>16.8</td><td>8.6</td><td>5.6</td></tr><tr><td>Affected by wasting (million)</td><td>12.2</td><td>31.6</td><td></td><td></td><td></td><td>0.7</td><td>45.0</td></tr><tr><td>Who are stunted (million)</td><td>63.1</td><td>76.6</td><td>1.4</td><td>0.7</td><td>0.8</td><td>5.7</td><td>148.1</td></tr><tr><td>Who are overweight (million)</td><td>10.2</td><td>17.7</td><td>2.6</td><td>1.7</td><td>0.6</td><td>4.2</td><td>37.0</td></tr><tr><td>Obesity</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Adult population</td><td>16.2</td><td>10.4</td><td>21.4</td><td>40.3</td><td>29.5</td><td>29.9</td><td>15.8</td></tr><tr><td>Adult population (million)</td><td>123.9</td><td>353.9</td><td>129.0</td><td>119.2</td><td>9.6</td><td>141.4</td><td>880.7</td></tr></tbody></table>

All statistics are expressed in %, except those whose units are indicated.

Source: www.fao.org/faostat/en/#data/FS & Author's calculations.

**Remark 7** As discussed in Roncalli (2025, Section 2.1.1), food security encompasses many dimensions and issues. Here, we focus on two critical aspects: genetic diversity and the capacity to feed the global population. In a fragmented world, a third important dimension is each country's dependence on external sources for its food supply.
## 3 Biodiversity threats and risks

Primack (2014) categorizes different threats to biodiversity into three main clusters: (1) extinction, (2) habitat destruction, fragmentation, degradation, and global climate change, and (3) overexploitation, invasive species, and disease. Sodhi and Ehrlich (2010) consider a similar list of biodiversity risks but groups them differently: (1) extinction, (2) habitat loss and fragmentation, (3) overexploitation, (4) invasive species, (5) climate change, and (6) fire. In reality, these factors often interact with each other, amplifying their combined effects. Moreover, it is important to distinguish between biodiversity threats and biodiversity risks:

* Biodiversity threats are the specific drivers or causes of biodiversity loss. They are external factors that contribute directly or indirectly to biodiversity loss by impacting species, habitats, and ecosystems. For example, invasive species can severely disrupt an ecosystem and therefore constitute a threat to biodiversity.

* Biodiversity risks refer to the potential consequences of biodiversity loss due to these threats. Specifically, biodiversity risks encompass the likelihood and severity of negative impacts on human life and ecosystem functions. For example, the emergence of new diseases as a result of ecosystem disturbances is a biodiversity risk.

The distinction between biodiversity threats and biodiversity risks is not always clear. For example, habitat loss is a threat because it directly reduces biodiversity and disrupts ecosystems. But it is also a risk because activities such as agriculture and land-use change contribute to further habitat loss. Similarly, pollution can be both a threat and a risk to biodiversity. It is a direct factor in biodiversity loss, but it can also result from that loss. In this context, the boundary between threats and risks to biodiversity can be somewhat artificial. Furthermore, these different threats are often interrelated, and the same is true of risks. In addition, feedback loops can complicate the distinction between the two concepts. For instance, habitat fragmentation may reduce biodiversity, but the resulting loss of biodiversity may in turn exacerbate further habitat fragmentation. According to Wilson (1989), the central cause of biodiversity risk is the destruction of natural ecosystems by human beings. He identified five major threats: habitat destruction, overexploitation, pollution, global climate change and invasion by introduced species. He argued that these five causes are driven by underlying social conditions, in particular increased per capita consumption, rapid population growth and unsound economic policies. Since this seminal paper on biodiversity loss, these key elements have been extensively studied and documented by scientists, showing that the Earth's ecosystems are dominated by humans (Vitousek et al., 1997), and that humans are ultimately the cause of the current biodiversity crisis. Land-use change is undoubtedly the greatest threat (Sala et al., 2000), while the decline in species richness is the most visible risk.

The possibility of a sixth mass extinction (Late Quaternary Mass Extinction or LQME), has been raised before<fnref n="52" />. According to Algeo and Shen (2024), the LQME differs from previous extinctions because it is driven by technological advances, particularly those that have allowed humans to exert widespread influence over the Earth's climate and ecosystems. The extinction process occurred in phases. In the first phase (50 Kyr BP–1750 AD), overhunting and the loss of top predators led to the extinction of many large animal species, especially after human expansion into new regions such as Australasia and the Americas. The first phase is characterized by limited global impacts (less than 1% of species loss) but significant ecosystem impacts. The current phase (1750 AD to present) is driven by habitat loss as humans convert land for agriculture and urbanization, with invasive species and climate change also contributing to species loss. The current phase is characterized by current

<footnote n="52">⁵²See the section on page 27 dedicated to the LQME.</footnote>
<figure><img src="image_53.png" /><figcaption>Figure 24: Stages of the Late Quaternary mass extinction</figcaption></figure>

Stage 1 (from ~ 50 to 0.25 ka), characterized by direct exploitation of species, comprised megafaunal extinctions in (A) Australasia, (B) the Americas and (C) the Indo-Pacific region. Stage 2 (from ~ 0.25 ka to the near future) is dominated by extinctions due to habitat loss. Stages 3 and 4 (future, timeline speculative) will be marked by climate change and ecosystem collapse, respectively, as the dominant proximate causes of extinction, while invasive species will play a supporting role during Stages 2 to 4.

Source: Algeo and Shen (2024, Figure 5, page 11).

losses of 1–2% of total biodiversity, but the extinction rate is about 1000 times the background extinction rate. Algeo and Shen (2024) suggest that the near future phase will be dominated by climate change, which will become the primary driver of biodiversity loss, while they estimate that the final phase could lead to widespread ecosystem collapse. In this case, the final phase could be characterized by a rapid and extensive loss of biodiversity, comparable to Earth’s largest historical extinction events. Figure 24 illustrates this worst-case scenario of the sixth mass extinction.

**Remark 8** *World Economic Forum (2020b) published the New Nature Economy Report to address the growing threats posed by biodiversity loss and the current biodiversity crisis to economies and businesses worldwide. The report emphasizes that biodiversity decline is not only an environmental issue but also a significant economic risk. The report outlines 15 major threats to biodiversity and identifies 15 critical transitions across three socio-economic systems. These threats are linked to issues such as habitat loss, overexploitation, and pollution, which pose not only risks to human welfare but also substantial risks to our economic systems. The proposed transitions aim to reduce nature-related risks while unlocking economic opportunities, potentially generating $10 trillion in economic value and creating 395 million jobs by 2030.*
In 2000, the World Economic Forum issued an alarming report on the impact of business on biodiversity and biodiversity on business (double materiality). This report highlights three key socio-economic systems: (1) food, land and ocean use, (2) infrastructure and the built environment, and (3) energy and extractives. These systems contribute 12%, 40% and 23% of global GDP, respectively, and employ 40%, 18% and 16% of the world's workforce. They also exert the greatest pressure on biodiversity, with 80% of threatened and near-threatened species at risk from activities in these sectors, and 72% affected by the food, land and ocean use sector alone. The WEF estimates that over half of the global GDP (around $44 trillion in economic value) relies heavily or moderately on natural resources. It also identifies 15 major pressing business-related threats to nature:

* Food, land and ocean use: (1) annual and perennial non-timber crops, (2) logging and wood harvesting, (3) livestock farming and ranching, (4) invasive non-native/alien species/diseases, (5) fire and fire suppression, (6) agricultural and forestry effluents, (7a) water management/use*, (8) fishing and aquatic resources;

* Infrastructure and the built environment: (9) housing and urban areas, (10) tourism and recreational areas, (11) domestic and urban wastewater, (12) roads and railroads, (13) commercial and industrial areas, (14) industrial and military effluents;

* Energy and extractives: (15) mining and quarrying, (7b) dams*.

In a similar way, the WEF identities 15 key socio-economic transitions needed to tackle the nature crisis:

* Food, land and ocean use: (1) ecosystem restoration and avoided expansion, (2) productive and regenerative agriculture, (3) healthy and productive ocean, (4) sustainable management of forests, (5) planet-compatible consumption, (6) transparent and sustainable supply chains;

* Infrastructure and the built environment: (7) densification of the urban environment, (8) nature-positive built environment design, (9) planet-compatible urban utilities, (10) nature as infrastructure, (11) nature-positive connecting infrastructure;

* Energy and extractives: (12) circular and resource efficient models, (13) nature-positive metals and minerals extraction, (14) sustainable materials supply chains, (15) nature-positive energy transition.

<footnote>*Dams and water management/use are treated as separate threats because they involve different economic activities.</footnote>
Box 9: New Nature Economy Report II (continued)

The capital investment required to implement these fifteen transitions across the three systems is approximately $2.7 trillion per year, which the following breakdown: 16% for the six transitions related to food, land and ocean use, 64% for the five transitions related to infrastructure and the built environment, and 31% for the four transitions related to energy and extractives. However, implementing these transitions could generate $10 trillion in business opportunities and create approximately 400 million jobs by 2030. Among these, the food, land, and ocean use system is expected to yield the greatest socio-economic benefits.

<table><caption>Table 5.C: Key figures of the New Nature Economy Report II</caption><thead><tr><th>System</th><th>Description</th><th>Share of threatened species impacted</th><th>Threats</th><th>Total business opportunities by 2030</th><th>Total jobs by 2030</th><th>Annualized investment costs (2020-2030)</th></tr></thead><tbody><tr><td></td><td>Food, land and ocean use</td><td>72%</td><td>8</td><td>$3,565 bn</td><td>191 mn</td><td>$440 bn</td></tr><tr><td></td><td>Infrastructure and the built environment</td><td>29%</td><td>6</td><td>$3,015 bn</td><td>117 mn</td><td>$1,430 bn</td></tr><tr><td></td><td>Energy and extractives</td><td>18%</td><td>2</td><td>$3,530 bn</td><td>87 mn</td><td>$840 bn</td></tr><tr><td></td><td>Total<sup>†</sup> of the three socio-economic systems</td><td>79%</td><td>15</td><td>$10,110 bn</td><td>395 mn</td><td>2,710 bn</td></tr></tbody></table>

<figure><img src="image_54.png" /></figure>

<figure><img src="image_55.png" /></figure>

<figure><img src="image_56.png" /></figure>

<figure><img src="image_57.png" /></figure>

<footnote>†Because some species are affected by more than one of the three systems, the percentage of species impacted by all systems is less than the sum of the percentages impacted by each individual system. The total number of threats is also 15 because water management/use and dams are considered as a single threat.</footnote>
<figure><img src="image_58.png" /><figcaption>Figure 25: Habitat loss vs. fragmentation vs. degradation</figcaption></figure>

## 3.1 Habitat loss, fragmentation and degradation

Habitat loss, fragmentation, and degradation is the largest cause of biodiversity loss and the primary threat leading to species extinction. Written in the singular form, this sentence suggests that these three processes are interconnected or form a single, overarching factor. However, it's important to distinguish between them:

* Habitat loss occurs when a natural habitat is completely removed, destroyed, or converted to another use, resulting in the disappearance of species that previously lived there. For example, deforestation — transforming a forest into cropland or an urban area — is a typical case of habitat loss. This process is the most severe form of habitat disruption, because it eliminates the existing living space and is often irreversible.

* Habitat fragmentation occurs when a large, continuous habitat is divided into smaller, isolated patches by human-made structures. Building highways through a forest, for instance, is a typical example of habitat fragmentation. Fragmentation creates habitat islands that may be too small to support the original populations, increasing the risk of species decline or extinction.

* Habitat degradation is the process by which the quality of a habitat is damaged or reduced, making it less suitable for the species that live there. Factors such as pollution, water contamination, water stress, climate change or invasive species often contribute to degradation. In such cases, species may become endangered as their populations decline or suffer from poor health.

In summary, loss is the total elimination of a habitat, fragmentation is the breaking up of a habitat into smaller habitats, and degradation is the decline in habitat quality (Figure 25). The distinction
between these three concepts and the definition of habitat fragmentation were popularized by *Fahrig* (2003). In her research, Lenore Fahrig challenges common perceptions of habitat fragmentation. She argues that while habitat loss typically has detrimental effects on biodiversity, the effects of fragmentation itself<fnref n="53" /> are more nuanced. In particular, fragmentation can sometimes have neutral or even potentially beneficial consequences for some species by creating more diverse landscape configurations that increase habitat heterogeneity and enhance dispersal opportunities (Fahrig, 2017):

> "I found 118 studies reporting 381 significant responses to habitat fragmentation independent of habitat amount. Of these responses, 76% were positive. Most significant fragmentation effects were positive, irrespective of how the authors controlled for habitat amount, the measure of fragmentation, the taxonomic group, the type of response variable, or the degree of specialization or conservation status of the species or species group. [...] Thus, although 24% of significant responses to habitat fragmentation were negative, I found no conditions in which most responses were negative. Authors suggest a wide range of possible explanations for significant positive responses to habitat fragmentation: increased functional connectivity, habitat diversity, positive edge effects, stability of predator-prey/host-parasitoid systems, reduced competition, spreading of risk, and landscape complementation." (Fahrig, 2017, page 1).

This conclusion contrasts sharply with the findings of Haddad et al. (2015), who reported very negative impacts:

> "We conducted an analysis of global forest cover to reveal that 70% of remaining forest is within 1 km of the forest's edge, subject to the degrading effects of fragmentation. A synthesis of fragmentation experiments spanning multiple biomes and scales, five continents, and 35 years demonstrates that habitat fragmentation reduces biodiversity by 13 to 75% and impairs key ecosystem functions by decreasing biomass and altering nutrient cycles." (Haddad et al., 2015, page 1).

These conflicting results have fueled a lively debate in the journal *Biological Conservation*, reflected in two contrasting publications: *Is Habitat Fragmentation Good for Biodiversity?* (Fletcher et al., 2018) and *Is Habitat Fragmentation Bad for Biodiversity?* (Fahrig et al., 2019). To this day, the debate remains open, especially when we consider human pressures and matrix conditions<fnref n="54" /> (Ramírez-Delgado et al., 2022).

### 3.1.1 Theory of island biogeography

This theory (known as TIB) was proposed by MacArthur and Wilson (1967) to explain the factors that influence biodiversity on islands. They emphasised the importance of studying islands because they are less complex and more common than larger ecosystems, meaning that research can be easily replicated. Their theory describes how the size of an island and its distance from the mainland affect the balance between immigration and extinction rates of species. This balance ultimately determines an equilibrium, or the number and types of species an island can support. An illustration is provided in Figure 26. Two key elements characterize the theory of island biogeography. First, the distance from the mainland measures the isolation of the island. Indeed, islands closer to the mainland have more species because they are easier for species to reach, receive colonizers more frequently, and so

<footnote n="53">⁵³We generally speak of fragmentation ‘per se’, i.e., fragmentation independent of habitat loss.</footnote>

<footnote n="54">⁵⁴In the context of biodiversity, the matrix condition refers to the quality and characteristics of the landscape that surrounds habitat patches or fragments. It’s essentially the non-habitat environment that separates discrete areas of suitable habitat.</footnote>
on. Second, the size of the island determines species richness. Larger islands support greater species diversity because they offer more diverse habitats, contain more resources, and so forth. Specifically, MacArthur and Wilson (1967) proposed that the immigration rate<fnref n="55" /> $\lambda(t)$ decreases with the number of species present and the isolation of the island (first panel in Figure 26), while the extinction rate $\mu(t)$ increases with the number of species present but decreases with the size of the island (second panel in Figure 26). Equilibrium occurs when immigration and extinction rates are equal, implying that the net diversification rate is zero: $\delta(t) = \lambda(t) - \mu(t) = 0$ (third panel in Figure 26).

<figure><img src="image_59.png" /><figcaption>Figure 26: Theory of island biogeography</figcaption></figure>

### 3.1.2 Species-area relationship

The previous equilibrium model is often associated with the species-area relationship (SAR). Since extinction dynamics are influenced by the size of an island, an increase in island size shifts the equilibrium point to the right on the immigration-extinction diagram, indicating higher species richness. However, the rate of increase in species richness is generally slower than the rate of increase in area<fnref n="56" /> (fourth panel in Figure 26). This reflects “an ecological version of the law of diminishing returns” (Lomolino, 2001): as area increases, each additional unit of area contributes proportionally less to species diversity. Certainly, the most famous species-area relationship is the power model originally formulated by Arrhenius (1921):

$$S = cA^z \quad (15)$$

where S is species richness, c is a constant, A is the area of the island and z is the slope of the log-log A-S curve. Typical values of z are between 0.15 and 0.35. If the areas of the original and

<footnote n="55">⁵⁵In the theory of island biogeography, the immigration rate corresponds to the origination rate in the birth-death model.</footnote>

<footnote n="56">⁵⁶See Exercise A.2 on page 232 for a mathematical derivation of the species-area relationship from the theory of island biogeography.</footnote>
current habitats are $A_0$ and $A$, respectively, we obtain the following survival function:

$$ \frac{S}{S_0} = \left( \frac{A}{A_0} \right)^z $$

This equation is used by Pimm et al. (1995) to calibrate species loss due to habitat loss:

$$ \mathcal{L}oss_{species} = 1 - (1 - \mathcal{L}oss_{habitat})^z \quad (16) $$

Assuming $z = 0.25$, Pimm et al. (1995, page 349) found that 50% of habitat loss should reduce the number of species by 15.91%, while 90% of habitat loss leads to 43.77% of species loss (Table 22).

<table><caption>Table 22: Species loss $Loss_{species}$</caption><thead><tr><th rowspan="2">z</th><th colspan="6">Loss<sub>habitat</sub></th></tr><tr><th>0.00%</th><th>25.00%</th><th>50.00%</th><th>75.00%</th><th>90.00%</th><th>100.00%</th></tr></thead><tbody><tr><td>0.05</td><td>0.00%</td><td>1.43%</td><td>3.41%</td><td>6.70%</td><td>10.87%</td><td>100.00%</td></tr><tr><td>0.10</td><td>0.00%</td><td>2.84%</td><td>6.70%</td><td>12.94%</td><td>20.57%</td><td>100.00%</td></tr><tr><td>0.25</td><td>0.00%</td><td>6.94%</td><td>15.91%</td><td>29.29%</td><td>43.77%</td><td>100.00%</td></tr><tr><td>0.35</td><td>0.00%</td><td>9.58%</td><td>21.54%</td><td>38.44%</td><td>55.33%</td><td>100.00%</td></tr></tbody></table>

While ecologists are nearly unanimous in accepting the principles of the species-area relationship<sup>57</sup>, they do not always agree on the specific form it should take. An alternative to Equation (15) is the exponential model proposed by Gleason (1922):

$$ S = c + z \ln(A) \quad (17) $$

These two models (power and exponential) were extensively studied in the seminal review by Connor and McCoy (1979). The authors provided a comprehensive and critical analysis of the species-area curve, arguing that many estimated SAR curves could be explained by statistical sampling effects rather than underlying biological mechanisms. Therefore, they emphasized the importance of distinguishing between ecological drivers (e.g., habitat diversity, island biogeography) and statistical drivers (e.g., sampling bias, incomplete sampling, inappropriate statistical methods) of SAR. By examining 100 datasets, they showed that the value of $z$ varies across scales and contexts (e.g., small versus large areas) and concluded that the species-area relationship is not a fixed law but rather a complex, context-dependent pattern. This variation depends on specific ecological settings, taxonomic groups, and geographic regions. In particular, they noted that the parameters $c$ and $z$ estimated for one island or archipelago cannot be reliably applied to another island or archipelago. Furthermore, reducing the species-area relationship to a function of a single variable with two parameters fails to account for several second-order factors, such as elevation, latitude, and the density of small- and large-bodied species. Nevertheless, the search for the best species-area relationship model has continued to fascinate researchers since the publication of Connor and McCoy's paper in 1979. While it is impossible to cite all of the subsequent studies, some have significantly shaped this field. For instance, the default value of $z = 0.25$ for the power model is largely due to the influential

<footnote n="57"><sup>57</sup>The relationship between species and area is considered to be a fundamental ecological principle:</footnote>

<footnote>"It is common, perhaps axiomatic, to refer to the species-area relationship as one of ecology's few laws [...]. According to a very broad consensus of ecologists, the pattern has two principal features: 1) species richness of a given taxon increases with the area sampled, and 2) the rate of increase slows for the larger islands or patches of habitat." (Lomolino, 2001, page 1).</footnote>
book by Rosenzweig (1995). Similarly, Tjørve (2003) made an important contribution by organizing
a comparison of 14 statistical models to identify the best-fitting SAR model. More recently, Dengler
(2009) and Triantis et al. (2012) reviewed 23 and 20 functions, respectively, and concluded that no
single function universally outperforms all others. However, they emphasized that the power model
often provides the best fit and remains a robust choice when it does not. Triantis et al. (2012)
also identified three other simple models that can rival the power model for certain datasets: the
linear model (S = c + zA), the exponential model (S = c + z *ln(A)*), and the Kobayashi model
(S = c *ln(1 + zA)*).

<figure><img src="image_60.png" /><figcaption>Figure 27: Analyzing the species-area relationship in Mediterranean islands</figcaption></figure>

Source: Fattorini et al. (2017, Figure 1), created with www.paintmaps.com.

Let us now examine an empirical application to understand how the species-area relationship
is estimated. For this purpose, we consider the study<fnref n="58" /> by Fattorini et al. (2017). The authors
estimated the SAR curves for two groups of Mediterranean islands: the Tyrrhenian Islands, located
in Italy, and the Aegean Islands, located between Greece and Turkey. In Figure 27, we present
the Tyrrhenian islands with areas larger than 10 km² and the Aegean islands with areas exceeding
100 km². The Tyrrhenian islands are mainly located off the western coast of Italy, near regions such
as Tuscany, Lazio, Campania, Calabria, and Sicily. The dataset includes 47 islands, with the largest
being Elba (223 km²) and the smallest being Scoglietto di Portoferraio (24.9 m²). The Aegean Sea
is known for its multitude of islands, the total number of which is estimated to be around 6,000.
However, the dataset contains only 127 islands, with the largest being Rodos (1,401 km²) and the
smallest being Petallidi (6,000 m²). The results for various taxonomic groups (centipedes, isopods,
land snails, reptiles and tenebrionid beetles) are given in Table 23 and Figure 28. Fattorini et al.
(2017) found that *z* varies between 0.141 and 0.308, while *c* varies between 2.716 and 12.274 species
per km². According to the authors, these results “demonstrate the importance of comparing SARs
either of different groups within the same area, or of the same group in different areas.”

<footnote n="58">⁵⁸The advantage of this study is that the dataset is relatively small, and the results are easily reproducible since the data are freely available on the paper’s webpage: onlinelibrary.wiley.com/doi/abs/10.1111/jbi.12874.</footnote>
<table><caption>Table 23: Estimated values of *c*, *z*, and *S* for different area values *A*</caption><thead><tr><th rowspan="2">Islands</th><th rowspan="2">Species</th><th colspan="2">c, z</th><th colspan="6">Area A (in km²)</th></tr><tr><th>0.01</th><th>0.10</th><th>1</th><th>10</th><th>100</th><th>1000</th></tr></thead><tbody><tr><td rowspan="5">Tyrrhenian</td><td>Centipedes</td><td>6.281</td><td>0.308</td><td>1.52</td><td>3.09</td><td>6.28</td><td>12.77</td><td>25.94</td><td>52.73</td></tr><tr><td>Isopods</td><td>9.226</td><td>0.262</td><td>2.76</td><td>5.05</td><td>9.23</td><td>16.87</td><td>30.83</td><td>56.36</td></tr><tr><td>Land snails</td><td>12.274</td><td>0.225</td><td>4.35</td><td>7.31</td><td>12.27</td><td>20.61</td><td>34.59</td><td>58.08</td></tr><tr><td>Reptiles</td><td>3.357</td><td>0.141</td><td>1.75</td><td>2.43</td><td>3.36</td><td>4.64</td><td>6.43</td><td>8.89</td></tr><tr><td>Tenebrionids</td><td>8.610</td><td>0.270</td><td>2.48</td><td>4.62</td><td>8.61</td><td>16.03</td><td>29.85</td><td>55.59</td></tr><tr><td rowspan="5">Aegean</td><td>Centipedes</td><td>3.864</td><td>0.243</td><td>1.26</td><td>2.21</td><td>3.86</td><td>6.76</td><td>11.83</td><td>20.70</td></tr><tr><td>Isopods</td><td>9.354</td><td>0.203</td><td>3.67</td><td>5.86</td><td>9.35</td><td>14.93</td><td>23.82</td><td>38.02</td></tr><tr><td>Land snails</td><td>9.572</td><td>0.184</td><td>4.10</td><td>6.27</td><td>9.57</td><td>14.62</td><td>22.34</td><td>34.12</td></tr><tr><td>Reptiles</td><td>2.716</td><td>0.278</td><td>0.75</td><td>1.43</td><td>2.72</td><td>5.15</td><td>9.77</td><td>18.53</td></tr><tr><td>Tenebrionids</td><td>4.055</td><td>0.268</td><td>1.18</td><td>2.19</td><td>4.05</td><td>7.52</td><td>13.93</td><td>25.82</td></tr></tbody></table>

Source: Fattorini et al. (2017, Table 1).

<figure><img src="image_61.png" /><figcaption>Figure 28: SAR curves in Tyrrhenian and Aegean islands</figcaption></figure>

Source: Fattorini et al. (2017) & Author's calculations.
**Example 3** Table 24 shows the data used by Fattorini et al. (2017, Appendix S1) to estimate the SAR curve of land snail species in the Tyrrhenian Islands. The area A is expressed in km².

<table><caption>Table 24: Number of species of land snails in the Tyrrhenian islands</caption><thead><tr><th>Island</th><th>A</th><th>S</th><th>Island</th><th>A</th><th>S</th><th>Island</th><th>A</th><th>S</th></tr></thead><tbody><tr><td>Alicudi</td><td>5.000</td><td>11</td><td>Filicudi</td><td>9.000</td><td>20</td><td>Montecristo</td><td>10.430</td><td>18</td></tr><tr><td>Argentarola</td><td>0.012</td><td>4</td><td>Formica di Grosseto</td><td>0.145</td><td>5</td><td>Panarea</td><td>3.380</td><td>22</td></tr><tr><td>Basiluzzo</td><td>0.270</td><td>11</td><td>Giannutri</td><td>2.390</td><td>19</td><td>Pianosa</td><td>10.410</td><td>28</td></tr><tr><td>Capraia</td><td>19.000</td><td>18</td><td>Giglio</td><td>21.000</td><td>35</td><td>Salina</td><td>26.000</td><td>25</td></tr><tr><td>Cerboli</td><td>0.051</td><td>8</td><td>Gorgona</td><td>2.270</td><td>24</td><td>Stromboli</td><td>12.000</td><td>18</td></tr><tr><td>Elba</td><td>223.000</td><td>50</td><td>Lipari</td><td>37.000</td><td>28</td><td>Vulcano</td><td>21.000</td><td>13</td></tr></tbody></table>

Source: Fattorini et al. (2017, Appendix S1).

Since the equation $S = cA^z$ is equivalent to $\ln(S) = \ln(c) + z \ln(A)$, the species-area relationship is generally estimated using the log-log regression model:

$$Y_i = \beta^\top X_i + \varepsilon_i$$

where $i = 1, \dots, n$, $n$ is the number of observations, $S_i$ and $A_i$ are the number of species and the area of the $i^{th}$ observation, $Y_i = \ln(S_i)$, $X_i = (1 \ \ln(A_i))$, $\beta = (\begin{pmatrix} \ln(c) \\ z \end{pmatrix})$ and $\varepsilon_i \sim N(0, \sigma_\varepsilon^2)$ is the noise process. We have:

$$ \begin{aligned} \hat{\beta} &= (X^\top X)^{-1} X^\top Y \\ &= \left( \begin{array}{cc} n & \sum_{i=1}^{n} \ln(A_i) \\ \sum_{i=1}^{n} \ln(A_i) & \sum_{i=1}^{n} \ln^2(A_i) \end{array} \right)^{-1} \left( \begin{array}{c} \sum_{i=1}^{n} \ln(S_i) \\ \sum_{i=1}^{n} \ln(A_i) \ln(S_i) \end{array} \right) \\ &= \left( \begin{array}{cc} 18 & 24.5506 \\ 24.5506 & 141.5006 \end{array} \right)^{-1} \left( \begin{array}{c} 50.6670 \\ 93.3758 \end{array} \right) \\ &= \left( \begin{array}{c} 2.5084 \\ 0.2247 \end{array} \right) \end{aligned} $$

We deduce that $\hat{c} = \exp(\hat{\beta}_1) = 12.285$ and $\hat{z} = \hat{\beta}_2 = 0.225$. In Table 25, we compare the figures presented in the research paper (columns c and z) and our estimates (columns $\hat{\beta}_1$, $\exp(\hat{\beta}_1)$ and $\hat{\beta}_2$). We get the same values for z and very close values for c, the difference being due to rounding.

<table><caption>Table 25: Comparison of SAR values: research paper results vs. our estimates</caption><thead><tr><th rowspan="2">Species</th><th colspan="6">Tyrrhenian islands</th><th colspan="6">Aegean islands</th></tr><tr><th>n</th><th>c</th><th>z</th><th>β̂<sub>1</sub></th><th>e<sup>β̂<sub>1</sub></sup></th><th>β̂<sub>2</sub></th><th>n</th><th>c</th><th>z</th><th>β̂<sub>1</sub></th><th>e<sup>β̂<sub>1</sub></sup></th><th>β̂<sub>2</sub></th></tr></thead><tbody><tr><td>Centipedes</td><td>32</td><td>6.281</td><td>0.308</td><td>1.837</td><td>6.275</td><td>0.308</td><td>43</td><td>3.864</td><td>0.243</td><td>1.352</td><td>3.865</td><td>0.243</td></tr><tr><td>Isopods</td><td>28</td><td>9.226</td><td>0.262</td><td>2.221</td><td>9.216</td><td>0.262</td><td>43</td><td>9.354</td><td>0.203</td><td>2.236</td><td>9.360</td><td>0.203</td></tr><tr><td>Land snails</td><td>18</td><td>12.274</td><td>0.225</td><td>2.508</td><td>12.285</td><td>0.225</td><td>65</td><td>9.572</td><td>0.184</td><td>2.258</td><td>9.567</td><td>0.184</td></tr><tr><td>Reptiles</td><td>28</td><td>3.357</td><td>0.141</td><td>1.212</td><td>3.360</td><td>0.141</td><td>56</td><td>2.716</td><td>0.278</td><td>1.001</td><td>2.720</td><td>0.277</td></tr><tr><td>Tenebrionids</td><td>46</td><td>8.610</td><td>0.270</td><td>2.153</td><td>8.607</td><td>0.270</td><td>32</td><td>4.055</td><td>0.268</td><td>1.417</td><td>4.125</td><td>0.265</td></tr></tbody></table>

Source: Fattorini et al. (2017, Table 1) & Author's calculations.
We have seen how the species-area relationship can be used to measure the effect of habitat loss, i.e., when area A is reduced. Hanski et al. (2013) suggested reformulating Equation (15) to account for habitat fragmentation. Let $\varphi$ be the degree of fragmentation. The authors introduce the function $P(\varphi)$, which measures the fraction of the species that are expected to persist when the degree of fragmentation of A is given by $\varphi$ and assume that $P(\varphi) = e^{-b\varphi}$ where b is a parameter. We have $P(0) = 1$ and $P(\infty) = 0$. We deduce that the species-area relationship becomes:

$$S = cA^zP(\varphi) = cA^z e^{-b\varphi} \quad (18)$$

If the initial area $A_0$ is reduced to A, we have:

$$\frac{S}{S_0} = \left(\frac{A}{A_0}\right)^z e^{-b(\varphi-\varphi_0)}$$

where $\varphi_0$ is the degree of fragmentation of $A_0$. We deduce that:

$$\mathcal{L}oss_{\text{species}} = 1 - (1 - \mathcal{L}oss_{\text{habitat}})^z e^{-b \Delta_{\text{frag}}} \quad (19)$$

where $\Delta_{\text{frag}} = \varphi - \varphi_0$ is the variation in the fragmentation. When $\varphi = \varphi_0$, we retrieve Equation (17).

**Example 4** We assume that $c = 10$, $z = 0.25$ and $b = 0.10$. We consider two initial landscapes, each with an initial area $A_0$ equal to $100 \text{ km}^2$. The first landscape is unfragmented ($\varphi_0 = 0$), while the second landscape is fragmented ($\varphi_0 = 0.50$). Both landscapes experience a habitat loss of 50%. In the first landscape, this habitat reduction is accompanied by habitat fragmentation ($\varphi = 0.50$), while in the second landscape we observe an improvement in habitat quality ($\varphi = 0.25$).

We obtain the following results:

<table><thead><tr><th>Landscape</th><th>#1</th><th>#2</th></tr></thead><tbody><tr><td>$S_0$</td><td>31.6228</td><td>30.0805</td></tr><tr><td>$S$</td><td>25.2946</td><td>25.9349</td></tr><tr><td>$Loss_{\text{species}}$</td><td>20.01%</td><td>13.78%</td></tr></tbody></table>

Normally, the impact of habitat loss alone on the species loss is 0.50$^{0.25}$, or 15.91%. However, the species loss is higher in the first landscape because habitat fragmentation has increased. In contrast, the species loss is lower in the second landscape because the fragmentation has increased.

### 3.1.3 Species distribution, sampling and endemics-area curve

The species-area relationship describes the impact of area size on the number of species. It is a simple two-parameter model and may be limited in its ability to capture the effects of habitat loss on species richness and biodiversity. In particular, it overlooks important aspects of biodiversity such as species evenness and abundance$^{59}$. It also ignores the spatial distribution of species and sampling effects. In this section, we explain these two effects, show how sampling affects the species-area relationship, and define species loss more precisely by introducing the endemics-area relationship.

<footnote>$^{59}$Abundance refers to the total number of individuals per species or in an ecosystem, while evenness is the degree to which individuals are evenly distributed across species.</footnote>
**Species abundance models** We consider a region or community<fnref n="60" /> with *S* species. For each species *i*, the number of individuals is denoted by *n*ᵢ. The species abundance can be described by a traditional frequency distribution table<fnref n="61" />:

<table><thead><tr><th>Species</th><th>1</th><th>2</th><th>...</th><th><i>i</i></th><th>...</th><th><i>S</i></th></tr></thead><tbody><tr><th>Frequency</th><td><i>n</i><sub>1</sub></td><td><i>n</i><sub>2</sub></td><td></td><td><i>n</i><sub><i>i</i></sub></td><td></td><td><i>n</i><sub><i>S</i></sub></td></tr></tbody></table>

Another approach is to calculate the species abundance distribution (SAD), which summarizes the number of species by their abundance (McGill et al., 2007):

<table><thead><tr><th>Number of individuals</th><th>1</th><th>2</th><th>...</th><th><i>j</i></th><th>...</th><th><i>n</i><sup>+</sup></th></tr></thead><tbody><tr><th>Number of species</th><td><i>s</i>(1)</td><td><i>s</i>(2)</td><td></td><td><i>s</i>(<i>j</i>)</td><td></td><td><i>s</i>(<i>n</i><sup>+</sup>)</td></tr></tbody></table>

where *s*(*j*) is the number of species with *j* individuals, and *n*<sup>+</sup> = max *n*ᵢ is the maximum number of individuals found in any single species in the community. Mathematically, we have:

$$s(j) = \sum_{i=1}^{S} 1 \{n_i = j\}$$

The two representations — the frequency table and the species abundance distribution — then convey the same information about the structure of the community. However, it is not possible to retrieve the exact value of *n*ᵢ from the SAD. This is because individual species are not identified in the SAD, unlike in the frequency table, where species are explicitly listed.

**Example 5** We consider a community consisting of 25 species and 407 individuals, distributed across a region of 2 km². The abundances of the 25 species are as follows: 2, 10, 13, 2, 1, 5, 25, 17, 1, 4, 28, 117, 23, 10, 13, 1, 4, 3, 10, 5, 7, 70, 10, 25, 1.

There are four species with only one individual, so *s* (1) = 4. Similarly, *s* (2) = 2 because there are two species with two individuals each. For *s* (3), we have *s* (3) = 1, as only one species has three individuals, and so on. Finally, we get the resulting species abundance distribution:

<table><thead><tr><th><i>j</i></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>7</th><th>10</th><th>13</th><th>17</th><th>23</th><th>25</th><th>28</th><th>70</th><th>117</th></tr></thead><tbody><tr><th><i>s</i>(<i>j</i>)</th><td>4</td><td>2</td><td>1</td><td>2</td><td>2</td><td>1</td><td>4</td><td>2</td><td>1</td><td>1</td><td>2</td><td>1</td><td>1</td><td>1</td></tr></tbody></table>

We confirm that the total abundance is exactly 407 individuals<fnref n="62" />. In practice, the label *j* is omitted when *s*(*j*) = 0 (McGill et al., 2007). However, when the number of species is large, the species abundance distribution can become highly atomic or fragmented, with many values of *s*(*j*) = 1. To address this, it is important to group the number of individuals into classes. We have *s*(*C*<sub>c</sub>) = Σ<sub>j∈(*C*<sub>c</sub>)</sub> *s*(*j*) where *C*<sub>c</sub> represents the *c*<sup>th</sup> grouping class. Here is an example where we group species whose number of individuals is greater than 5:

<table><thead><tr><th><i>C</i><sub>c</sub></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6–10</th><th>11–25</th><th>26–50</th><th>51–100</th><th>100–117</th></tr></thead><tbody><tr><th><i>s</i>(<i>C</i><sub>c</sub>)</th><td>4</td><td>2</td><td>1</td><td>2</td><td>2</td><td>5</td><td>6</td><td>1</td><td>1</td><td>1</td></tr></tbody></table>

$$\sum_{j=1}^{\infty} s(j) \cdot j = \sum_{i=1}^{S} n_i = n$$

<footnote n="60">⁶⁰A community is the total set of species in an ecosystem.</footnote>

<footnote n="61">⁶¹It is called the rank-abundance distribution when $n_i$ are sorted (in ascending or descending order).</footnote>

<footnote n="62">⁶²We have the following property:</footnote>
There are five species with an abundance of 6 to 10 individuals, six species with an abundance of 11 to 25 individuals, and so on. According to McGill et al. (2007, page 996), another way to illustrate the relative abundance and diversity of species within a community is to use a rank-abundance diagram (RAD), which is a graphical representation used in ecology to provide insights into species richness and species evenness. On the x-axis, species are ranked according to their abundance, from most abundant (rank 1) to least abundant (rank S), while on the y-axis, we plot relative abundance, that is the proportion of individuals belonging to each species. Mathematically, we calculate the order statistics of the set {$n_1, \dots, n_S$}:

$$ \underset{\mathcal{R}_S}{n_{1:S}} \le \underset{\mathcal{R}_{S-1}}{n_{2:S}} \le \dots \le \underset{\mathcal{R}_k}{n_{S-k+1:S}} \le \dots \le \underset{\mathcal{R}_1}{n_{S:S}} $$

We then assign the rank $\mathcal{R}_k$ to the order statistic $n_{S-k+1:S}$. The relative abundance $f_k$ associated with $\mathcal{R}_k$ is defined as $f_k = \frac{n_{S-k+1:S}}{n} = \frac{n_i}{n}$ where index i is the solution to the equation $n_i = n_{S-k+1:S}$. By construction we have $f_1 = \frac{\max n_i}{n}$ and $f_S = \frac{\min n_i}{n}$. Looking at the previous example, we get the following rank-abundance distribution:

<table><thead><tr><th>k</th><th>1</th><th>2</th><th>3</th><th>4, 5</th><th>6</th><th>7</th><th>8, 9</th><th>...</th><th>19</th><th>20, 21</th><th>22-25</th></tr></thead><tbody><tr><th>i</th><td>12</td><td>22</td><td>11</td><td>7, 24</td><td>13</td><td>8</td><td>3, 15</td><td></td><td>18</td><td>1,4</td><td>5, 9, 16, 25</td></tr><tr><th>n<sub>i</sub></th><td>117</td><td>70</td><td>28</td><td>25</td><td>23</td><td>17</td><td>13</td><td>...</td><td>3</td><td>2</td><td>1</td></tr><tr><th>f<sub>k</sub> (in %)</th><td>28.75</td><td>17.20</td><td>6.88</td><td>6.14</td><td>5.65</td><td>4.18</td><td>3.19</td><td></td><td>0.74</td><td>0.49</td><td>0.25</td></tr></tbody></table>

Species 12 ranks first and represents 28.75% of the total abundance of the community. It is followed by species 22 and 11, whose relative abundance is 17.20% and 6.88%, respectively.

In 1949–1951, Robert H. Whittaker studied plant community composition in the Siskiyou Mountains to understand variation across environmental gradients. He developed the concept of diversity partitioning. His work, published in 1960, led to extensive data analyses and contributed significantly to the study of community structure (Whittaker, 1960). Since 2022, the data are freely available at https://doi.org/10.6084/m9.fishshare.19661094.v3 (Whittaker et al., 2022). We use the tree data CSV file, which contains 2078 observations with the following information:

* The first column represents the sample number, corresponding to one of the 359 sampling locations;

* The second column lists the species name;

* The third column gives the number of individuals of each species in the sample;

* The fourth column indicates the number of large individuals with a diameter at breast height<fnref n="63" /> (DBH) greater than 30 inches (76.2 cm).

For each species, we pooled the data from the 359 sampling sites. We obtain the abundance of 59 tree species. The five most represented trees are *Lithocarpus densiflorus*, *Quercus chrysolepis*, *Abies concolor*, *Pseudotsuga menziesii* and *Chrysolepis chrysophylla*. Their abundance is 8439, 4207, 4172, 3725 and 1886, respectively. The species abundance distribution is shown in Figures 29 and 30. The species abundance curve is constructed with classes of length 50. Most of these classes have one or two species, except for the first three classes: 22 species for the first class (between 1 and 50 individuals), 7 species for the second class (between 51 and 100 individuals), and 3 species for the third class (between 101 and 150 individuals).

<footnote n="63">⁶³In the United States, DBH refers to the diameter of the tree measured 4.5 feet above the ground.</footnote>
<figure><img src="image_62.png" /><figcaption>Figure 30: Rank-abundance curve (Whittaker plot)</figcaption></figure>

<figure><img src="image_63.png" /></figure>
<figure><img src="image_64.png" /><figcaption>Figure 31: Barro Colorado Island (Panama)</figcaption></figure>

There are many ways to plot a species abundance distribution. The species abundance curve (also called a frequency histogram) and the rank-abundance curve (Whittaker, 1965) are just a few examples. Other methods include the species rarefaction curve, the empirical cumulative distribution function (ECDF), the *k*-dominance plot, and the Robbins curve, among others (Matthews and Whittaker, 2015). Moreover, the axes of these graphs can be linear, but they are often transformed using $log_2$ or $log_{10}$ functions to better display the variability in the shape of the species abundance distribution. One particularly famous plot was proposed by Preston (1948), who popularized the use of a frequency histogram with $log_2$-based classes along the *x*-axis. In this approach, the number of species is grouped into intervals of $2^k$ (e.g., 1, 2, 4, 8, 16, 32, 64, etc.), called octaves. Using Example 5, we obtain the following results<fnref n="64" />:

<table><thead><tr><th>Octave k</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><th>C<sub>k</sub></th><td>1</td><td>2-3</td><td>4-7</td><td>8-15</td><td>16-31</td><td>32-63</td><td>64-127</td></tr><tr><th>s(k)</th><td>4</td><td>3</td><td>5</td><td>6</td><td>5</td><td>0</td><td>2</td></tr></tbody></table>

We now consider another community ecology dataset, the Barro Colorado Island (BCI) data, which was established by the Smithsonian Tropical Research Institute (STRI) and studied to understand the dynamics of tropical forest vegetation. The data contain 50 contiguous 1-ha plots and record tree species identity, spatial coordinates, size measurements, and environmental variables. Periodic censuses have been conducted every five years since 1980 until 2015. Such analysis and data collection has been done in many other regions of the world, especially in South America. In Figure 32 we show the species abundance distribution of the tropical forest tree dataset<fnref n="65" /> compiled by Condit et al. (2002). This dataset includes 100 plots from Barro Colorado Island in Panama, the Yasuni National Park in Ecuador and the Manu Biosphere Reserve in Peru. The histogram shows that many species are found in the first octaves. Preston (1948) proposed that species abundances in

<footnote n="64">⁶⁴The general formula for the range of each octave *k* is $2^{k-1}$ to $2^k - 1$. The first octave contains the species with one individual, the second octave contains the species with two and three individuals, the third octave contains the species with four to seven individuals, and so on.</footnote>

<footnote n="65">⁶⁵The conditwebtable.xls file is available at www.science.org/doi/abs/10.1126/science.1066854.</footnote>
natural communities follow a log-normal distribution. When the logarithm of species abundances forms a bell-shaped curve, this pattern suggests that most species are moderately abundant, with fewer species being either extremely rare or extremely common. In some cases, when the positive skew of the log-normal distribution is very pronounced, the number of species decreases logarithmically with abundance, indicating that most species have only a few individuals. Preston (1948) further concluded that because many species in an ecological community are rare, they are often not observed in traditional ecological surveys<fnref n="66" />. This means that traditional sampling methods tend to underestimate total species richness, because rare species are likely to be missed in small samples.

<figure><img src="image_65.png" /><figcaption>Figure 32: Species abundance distribution of tropical forest trees</figcaption></figure>

Empirical analysis of the number of species has led to the formulation of several probability models of species abundance. In 1932, Isao Motomura developed the resource (or niche) preemption model, which assumes that one species preempts a fraction $\kappa \in (0, 1)$ of the resource, a second species the same fraction $\kappa$ of the remaining resource $(1 - \kappa)$, and so on. Assuming that the abundance of species $i$ is proportional to its share of the resource, i.e., $(1 - \kappa)^{i-1} \kappa$, we obtain the geometric rank-abundance model<fnref n="67" />:

$$n_i = \frac{n\kappa (1 - \kappa)^{i-1}}{1 - (1 - \kappa)^S} \qquad (20)$$

where $S$ is the number of species and $n$ is the total number of individuals. Another approach was proposed by Fisher et al. (1943), who developed a model where the number of species is derived

$$\sum_{i=1}^{S} n_i = \frac{n\kappa}{1 - (1 - \kappa)^S} \sum_{i=1}^{S} (1 - \kappa)^{i-1} = \frac{n\kappa}{1 - (1 - \kappa)^S} \cdot \frac{1 - (1 - \kappa)^S}{1 - (1 - \kappa)} = n$$

<footnote n="66">⁶⁶This concept is often called the ‘invisible fraction’ in ecology.</footnote>

<footnote n="67">⁶⁷The scaling factor ensures that the sum of the individuals equals the total abundance:</footnote>
from the limiting form of the negative binomial distribution $NB(r, p)$, excluding zero observations. They demonstrated that the expected number of species with exactly $j$ individuals is given by:

$$s(j) = \alpha \frac{x^j}{j} \qquad (21)$$

where $x = (1-p)^{-1} p \in (0,1)$, $p$ is the success probability of the negative binomial distribution, and $\alpha$ is a scaling factor that depends on the parameters $r$ and $p$. Since the total expected number of species is $S = \sum_{j=1}^{\infty} s(j) = -\alpha \ln(1-x)$ and the total expected number of individuals is $n = \sum_{j=1}^{\infty} s(j) \cdot j = \sum_{j=1}^{\infty} \alpha x^j = \alpha x / (1-x)$, the parameters of the log-series distribution $LS(\alpha, x)$ can be determined by solving the following system of equations$^{68}$:

$$\left\{ \begin{array}{l} S = \alpha \ln \left( 1 + \frac{n}{\alpha} \right) \\ x = \frac{n}{\alpha + n} \end{array} \right. \qquad (22)$$

In chronological order, the third and fourth important SAD models are the log-normal model of Preston (1948), seen earlier on page 86, and the broken-stick model formulated by MacArthur (1957). In the log-normal model, the probability that a species has $j$ individuals is given by $\text{Pr}\{X = j\}$ where $X \sim LN(\mu, \sigma^2)$. In practice, $j$ is discrete rather than continuous. Considering the disjoint intervals $\left[j - \frac{1}{2}, j + \frac{1}{2}\right]$, we get$^{69}$:

$$s_j = S \frac{\Phi\left(\sigma^{-1}\left(\ln\left(j + \frac{1}{2}\right) - \mu\right)\right) - \Phi\left(\sigma^{-1}\left(\ln\left(j - \frac{1}{2}\right) - \mu\right)\right)}{1 - \Phi\left(\sigma^{-1}\left(\ln\left(\frac{1}{2}\right) - \mu\right)\right)} \qquad (23)$$

By construction we have $\sum_{j=1}^{\infty} s_j = S$. To calibrate $\mu$ and $\sigma$, we can fit the first moment — $\frac{n}{S} = e^{\mu + \frac{1}{2}\sigma^2}$ (or use the discrete version $\sum_{j=1}^{\infty} s_j \cdot j = n$ — or we can estimate $\mu$ and $\sigma$ using the method of maximum likelihood. The broken-stick model assumes that the total resources (or individuals) available in a community are divided randomly among species, leading to a characteristic pattern of abundances. The community is represented as a stick of fixed length, the stick is broken into $S$ segments at $S-1$ randomly chosen points, and the lengths of the resulting segments are proportional to the abundances of the $S$ species — they follow a uniform distribution. The $i^{th}$ largest segment corresponds to a specific harmonic expectation based on the number of breaks. The abundance of the $i^{th}$ species is then given by $n_i = \frac{n}{S} \sum_{k=i}^{S} \frac{1}{k}$. May (1975) demonstrated that the corresponding species abundance distribution is:

$$s(j) = \frac{S}{n}(S-1)\left(1-\frac{j}{n}\right)^{S-2} \qquad (24)$$

<footnote>$^{68}$However, this approach ignores the distribution of the number of individuals ($n_1, n_2, \dots, n_S$). This means that two communities with the same number of species, the same total abundance, but different distributions of individuals among species will have the same species abundance distribution. To overcome this limitation, it is preferable to estimate the parameters $x$ using the maximum likelihood method with the following probability mass function: $\text{Pr}\{N = j\} = -\frac{x^j}{j \ln(1-x)}$ where $N$ is the random variable representing the abundance of a species. Once the parameter $x$ is estimated, the parameter $\alpha$ can be calculated as it serves as a scaling factor to fit the total number of species $S$.</footnote>

<footnote>$^{69}$The normalization factor is needed because the support of the log-normal distribution is $(0, +\infty)$, while in this case we use the support $(\frac{1}{2}, +\infty)$.</footnote>
where $j \in [0, S]$. We verify that the total number of species is exactly equal to $S^{70}$. Figure 22 illustrates the four distributions when the number of species is $S = 15$ and the total abundance is $n = 80$. For the geometric model, the parameter $\kappa$ is set to 0.50. The parameters of the log-series model are determined by solving Equation (), yielding $\alpha = 5.450$ and $x = 0.936$. In the case of the log-normal model, we set $\sigma = 1$, which implies $\mu = \ln(\frac{80}{15}) - 0.5 \times 1^2 = 1.174$. The broken-stick model is already parameterized using $n$ and $S$. The calibration of the parameters can be improved if the rank-abundance distribution ($n_1, \dots, n_S$) or the species abundance distribution ($s(1), \dots, s(n^+)$) is known, by using the method of maximum likelihood. However, this approach is applicable only for the first three models.

<figure><img src="image_66.png" /><figcaption>Figure 33: Species abundance models</figcaption></figure>

**Sampling** The species accumulation curve (SAC) is a graphical representation that illustrates how the number of observed species in a particular environment increases with additional sampling effort. It is also referred to as the species discovery curve or the collector's curve. The x-axis represents the sampling effort, such as the number of samples, individuals, cells, or plots surveyed, while the y-axis represents the cumulative number of species recorded. Let $n_i(s)$ be the number of individuals

$$ \int_{0}^{n} s(j) \, dj = S(S-1) \int_{0}^{n} \left(1 - \frac{j}{n}\right)^{S-2} \frac{dj}{n} $$

Using the change of variable $u = \frac{j}{n}$, we obtain the desired result:

$$ \int_{0}^{n} s(j) \, dj = S(S-1) \int_{0}^{1} (1-u)^{S-2} \, du = S(S-1) \left[ -\frac{(1-u)^{S-1}}{S-1} \right]_{0}^{1} = S $$

<footnote n="70">⁷⁰Specifically, we have:</footnote>
of species i recorded in the s^th^ sample. The SAC function is defined as:

$$SAC(m) = \sum_{i=1}^{S} 1 \left\{ \sum_{s=1}^{m} n_i(s) \geq 1 \right\}$$

where $m \le m_s$ is the number of samples, and $m_s$ is the total number of samples available. SAC(m) counts the number of species present in the m samples. When a sample represents an individual, SAC(m) is the expected number of species among m individuals selected at random. Hurlbert (1971, Equation (13), page 581) shows that^71^:

$$SAC(m) = \sum_{i=1}^{S} \left( 1 - \frac{\binom{n-n_i}{m}}{\binom{n}{m}} \right)$$

where $n_i$ is the abundance (number of individuals) of the i^th^ species and n is the total abundance of the community. In this case, the species accumulation curve is often referred to as the species rarefaction curve. In the Barro Colorado Island census, the database contains 21 457 trees and 225 species, located in 50 1-ha plots. For each plot, the species and the number of individuals per species are recorded. Figure 34 shows the distribution of individual trees across the 50 plots. The species rarefaction curve is given in Figure 35. In addition to the theoretically expected number of species, the 95% confidence interval is also reported.

<figure><img src="image_67.png" /><figcaption>Figure 34: Number of individuals per plot (BCI trees)</figcaption></figure>

More generally, the species accumulation curve is represented as the parametric curve (SAC(1),...,SAC($m_s$)), where the sample set at iteration m is constructed by adding one sample to the set used in the previous iteration $m-1$, selected from the $m_s - m + 1$ remaining samples. Thus, the species accumulation curve is sensitive to the order in which the $m_s$ samples are arranged.

<footnote n="71">⁷¹The binomial coefficient $\binom{n-n_i}{m}$ is zero when $m > n - n_i$.</footnote>
<figure><img src="image_68.png" /><figcaption>Figure 35: Species accumulation curve (BCI trees)</figcaption></figure>

For instance, samples may be ordered by size, either from smallest to largest or vice versa. Alternatively, the historical order of sampling, from first to last, may be considered. Considering the BCI dataset, we discover 77 tree species if we start by sampling the 11th plot, and 109 tree species if the first sample is the 39th plot (Figure 36). To eliminate the sensitivity of the results to the ordering of the samples, we can use a third approach, which consists of generating random permutations of the entire sample set (1, ..., $m_s$), computing the SAC function for each permutation, and performing a Monte Carlo simulation. By repeating this process $r$ times and averaging the resulting curves, a more robust estimate of the species accumulation curve can be obtained. Figure 37 shows the species accumulation curve for trees in the Barro Colorado Island census. The mean curve (in red) is estimated using the Monte Carlo method with 1000 replications. The 99% confidence interval is also shown in green.

The previous estimator of the species accumulation curve has some bias because it does not account for the underestimation of rare species. To address this problem, more sophisticated approaches are often used, in particular the estimators developed by Anne Chao. The *Chao1* estimator is a non-parametric method for estimating species richness from abundance data (Chao, 1984). It uses the frequency of rare species (singletons and doubletons) in the dataset to estimate the likely number of undetected species. The *Chao2* estimator is a variant of *Chao1* designed for use with presence-absence data across multiple samples (Chao, 1987). Instead of focusing on individual counts, it examines how often species are detected in different samples. The formula for this estimator is as follows:

$$S_{\text{Chao2}}(m_s) = S_{\text{obs}}(m_s) + \frac{(m_s - 1)}{m_s} \left( \frac{q_1(q_1 - 1)}{2(q_2 + 1)} \right)$$

where $S_{\text{obs}}(m_s) = \text{SAC}(m_s)$ is the total number of species observed in the set of $m_s$ samples, $q_m$ is the number of species present in exactly $m$ samples — $q_1$ and $q_2$ are then the number of singleton and
<figure><img src="image_69.png" /><figcaption>Figure 37: Species accumulation curve (BCI trees)</figcaption></figure>

<figure><img src="image_70.png" /></figure>
doubleton species. In Figure 37 we have added the *Chaos2* estimator to compare with the traditional empirical estimator. In this case, the number of tree species for the 50 ha patch is estimated to be 237 instead of 225.

The species accumulation curve is widely used to estimate the number of species in a region larger than the sampled area. This approach, known as extrapolation, was popularized by Robert K. Colwell in numerous published research papers (Colwell and Coddington, 1994; Gotelli and Colwell, 2001; Colwell et al., 2004). For example, Cazzolla Gatti et al. (2022) used this method to estimate the number of tree species on Earth. They first fitted a log-series model, then estimated the species accumulation curve, corrected it with the *Chao2* estimator, and finally extrapolated it by considering the lower 95% confidence bound. Their results indicate that there are 73 271 tree species globally, with the following distribution: 11 874 in Africa, 16 262 in Eurasia, 11 129 in North America, 31 110 in South America, and 8 232 in Oceania. Returning to the BCI tree database, we assume that the number of species follows the exponential model: SAC($m$) = $\theta_1(1 - \exp(-\theta_2m^{\theta_3}))$. Using the species accumulation curve, we fit the parameters ($\theta_1, \theta_2, \theta_3$) using the method of non-linear least squares. We find $\hat{\theta}_1 = 241.064$, $\hat{\theta}_2 = 0.562$ and $\hat{\theta}_3 = 0.517$. Since the 50 plots corresponds to 50 hectares, we would need to sample $15.6 \times 100 = 1560$ plots to cover the entire area of Barro Colorado Island, which spans 15.6 km$^2$. We estimate that there are about 241 different tree species$^{72}$, suggesting that 16 species remain to be discovered in the island (Figure 37).

**Species-area relationship vs. endemics-area relationship** We consider a region (or area) A where the total number of species and the number of individuals per species are known exactly to be $S$ and $n_i$. The species-area relationship can be expressed as the equality: SAR($A$) = $S$. Our goal is to determine the expected number of species $S_a$ of a subregion (or subarea) $a$ contained within the larger region $A$. Assuming random placement of individuals within the area, we can show that the species-area relationship becomes$^{73}$:

$$SAR(a) = S_a = S - \sum_{i=1}^{S} \left(1 - \frac{a}{A}\right)^{n_i}$$

where $n_i$ is the number of individuals of species $i$ in region $A$. We define two types of endemism as follows:

* Global endemism: A species is globally endemic to $A$ if it is found exclusively in region $A$ and nowhere else.

* Local endemism: A species is locally endemic to $a$ if it occurs exclusively in subarea $a$ and not in the complementary area $A - a$.

Under the assumption of random placement, the endemics-area relationship (EAR) is$^{74}$:

$$EAR(a) = E_a = \sum_{i=1}^{S} \left(\frac{a}{A}\right)^{n_i}$$

where $E_a$ is the expected number of species endemic to the subregion $a$. In Table 26, we report the expressions for SAR($a$) and EAR($a$) under different models (He and Legendre, 2002; Green and

$$SAC(1560) = \hat{\theta}_1 (1 - \exp(-\hat{\theta}_2 \times 1560^{\hat{\theta}_3})) \approx 241$$

<footnote>$^{72}$We have:</footnote>

<footnote>$^{73}$The proof is given in Question 1 of Exercise A.3 on page 234.</footnote>

<footnote>$^{74}$The proof is given in Question 2 of Exercise A.3 on page 234.</footnote>
<table><caption>Table 26: Species-area and endemics-area relationships for various species abundance models</caption><thead><tr><th>Model</th><th>Specification</th><th>SAR (a)</th><th>EAR (a)</th></tr></thead><tbody><tr><td>Random placement</td><td>n<sub>i</sub> is known</td><td>S<sub>a</sub> = S - &sum;<sub>i=1</sub><sup>S</sup> (1 - <sup>a</sup>&frasl;<sub>A</sub>)<sup>n<sub>i</sub></sup></td><td>E<sub>a</sub> = &sum;<sub>i=1</sub><sup>S</sup> (<sup>a</sup>&frasl;<sub>A</sub>)<sup>n<sub>i</sub></sup></td></tr><tr><td>Most even</td><td>n<sub>i</sub> = <sup>n</sup>&frasl;<sub>S</sub></td><td>S<sub>a</sub> = S (1 - (<sup>a</sup>&frasl;<sub>A</sub>)<sup>S</sup>)</td><td>E<sub>a</sub> = S (<sup>a</sup>&frasl;<sub>A</sub>)<sup>S</sup></td></tr><tr><td>Most uneven</td><td>n<sub>i&lt;S</sub> = 1, n<sub>S</sub> = n - S + 1</td><td>S<sub>a</sub> = 1 + (S - 1) <sup>a</sup>&frasl;<sub>A</sub></td><td>E<sub>a</sub> = (S - 1) <sup>a</sup>&frasl;<sub>A</sub> + (<sup>a</sup>&frasl;<sub>A</sub>)<sup>n-S+1</sup></td></tr><tr><td>Geometric</td><td>n<sub>i</sub> = <sup>n&kappa;(1 - &kappa;)<sup>i-1</sup></sup>&frasl;<sub>1 - (1 - &kappa;)<sup>S</sup></sub></td><td>S<sub>a</sub> = <sup>s</sup>&frasl;<sub>A</sub> + (S - s) &middot; (<sup>a</sup>&frasl;<sub>A</sub>)<sup>n-S</sup></td><td>E<sub>a</sub> = S - s (<sup>a</sup>&frasl;<sub>A</sub>) - (S - s) (<sup>a</sup>&frasl;<sub>A</sub>)<sup>n-S</sup></td></tr><tr><td>Mixed even-uneven</td><td>n<sub>i&le;s</sub> = 1, n<sub>i&gt;s</sub> = <sup>n - s</sup>&frasl;<sub>S - s</sub></td><td>S<sub>a</sub> = S - &sum;<sub>j</sub>s<sub>j</sub>(1 - <sup>a</sup>&frasl;<sub>A</sub>)<sup>j</sup></td><td>E<sub>a</sub> = &sum;<sub>j</sub>s<sub>j</sub>(<sup>a</sup>&frasl;<sub>A</sub>)<sup>j</sup></td></tr><tr><td>Random placement</td><td>s(j) is known</td><td>S<sub>a</sub> = S - &sum;<sub>j</sub>s<sub>j</sub>(1 - <sup>a</sup>&frasl;<sub>A</sub>)<sup>j</sup></td><td>E<sub>a</sub> = &sum;<sub>j</sub>s<sub>j</sub>(<sup>a</sup>&frasl;<sub>A</sub>)<sup>j</sup></td></tr><tr><td>Log-series</td><td>s(j) = &alpha;<sup>x<sub>j</sub></sup>&frasl;<sub>j</sub></td><td>S<sub>a</sub> = &alpha; ln(1 + <sup>x</sup>&frasl;<sub>1 - x</sub><sup>a</sup>&frasl;<sub>A</sub>)</td><td>E<sub>a</sub> = -&alpha; ln(1 - <sup>x</sup>&frasl;<sub>A</sub>)<sup>a</sup></td></tr><tr><td>Broken-stick</td><td>s(j) = <sup>S</sup>&frasl;<sub>n</sub>(S - 1) (1 - <sup>j</sup>&frasl;<sub>n</sub>)<sup>S-2</sup></td><td>S<sub>a</sub> = <sup>S ln(1 - <sup>a</sup>&frasl;<sub>A</sub>)</sup>&frasl;<sub>ln(1 - <sup>a</sup>&frasl;<sub>A</sub>) - <sup>S</sup>&frasl;<sub>n</sub></sub></td><td>E<sub>a</sub> = - <sup>S<sup>2</sup></sup>&frasl;<sub>n ln(<sup>a</sup>&frasl;<sub>A</sub>) - S</sub></td></tr><tr><td>Truncated negative binomial distribution</td><td>s(j) = <sup>&Gamma;(&gamma; + j)</sup>&frasl;<sub>&Gamma;(j + 1)</sub> &Gamma;(&gamma;)</td><td>S<sub>a</sub> = <sup>S</sup>&frasl;<sub>1 - (1 + &phi;)<sup>a</sup>&frasl;<sub>A</sub></sub> &middot; (<sup>a</sup>&frasl;<sub>1 + &phi;</sub>)<sup>-&gamma;</sup></td><td>E<sub>a</sub> = S <sup>(1 + &phi;)(1 - <sup>a</sup>&frasl;<sub>A</sub>)</sup>&frasl;<sub>1 - (1 + &phi;)<sup>-&gamma;</sup></sub></td></tr></tbody></table>

$n_i$ is the number of individuals of species i, $s_j$ is the number of species with j individuals, $\alpha$ and $x$ are the parameters of the log-series model, $\kappa$ is the resource preemption parameter, and $\gamma$ and $\phi$ are the shape and scale parameters of the TNBD model.

Source: He and Legendre (2002, Table 1, page 1187), Green and Ostling (2003, Table 1, page 3091) & Author's calculations.
Ostling, 2003). According to He and Hubbell (2011), the expected number of species lost due to the loss of area a can be calculated as:

$$ \mathcal{L}oss(a | A) = S_A - S_{A-a} = S - \left( S - \sum_{i=1}^{S} \left( 1 - \frac{A-a}{A} \right)^{n_i} \right) = \sum_{i=1}^{S} \left( \frac{a}{A} \right)^{n_i} = E_a $$

Thus, $E_a$ can be interpreted as the number of species lost if habitat area a is destroyed. This gives the following identity:

$$ SAR(A) = SAR(A-a) + EAR(a) $$

which states that the number of species in region A is equal to the sum of the species found in subregion A-a and the species locally endemic in subregion a.

He and Legendre (2002) used the tree dataset from the Pasoh Forest Reserve in Malaysia. The research area consists of a 50-ha plot (500×1000 m), established in 1986 and resurveyed several times between 1990 and 2016. The 1987 survey recorded 335 356 individual stems and 814 tree species. He and Legendre (2002) calibrated several species abundance models<sup>75</sup>. Figure 38 shows the estimated species-area relationship for each model compared to the empirical species-area relationship derived from the recorded data. We observe that the empirical curve lies between the broken-stick and geometric models. The endemics-area relationship is plotted in Figure 39. We restrict the analysis to surface areas larger than 1 ha because EAR(a) ≈ 0 when a ≈ 0. This is not the case for the function SAR(a). As noted by He and Hubbell (2011), there is an asymmetry between the two curves. In fact, it is easier to discover a species quickly when exploring a patch, whereas the extinction of a species requires the destruction of a large proportion of the patch. He and Hubbell (2011) concluded that species-area relationships always overestimate extinction rates due to habitat loss:

> "Here we show that extinction rates estimated from the SAR are all overestimates. [...] These overestimates are due to the false assumption that the sampling problem for extinction is simply the reverse of the sampling problem for the SAR. The area that must be added to find the first individual of a species is in general much smaller than the area that must be removed to eliminate the last individual of a species. Therefore, on average, it takes a much greater loss of area to cause the extinction of a species than it takes to add the species on first encounter, except in the degenerate case of a species having a single individual. [...] Only in a very special and biologically unrealistic case, when all species are randomly and independently distributed in space, is it possible to derive the EAR from the SAR." (He and Hubbell, 2011, page 368).

In this context, the choice of the power-law model can create some bias. Recall that $S_A = cA^z$. We can deduce that $S_{A-a} = c(A-a)^z$ and $E_a = S_A - S_{A-a} = cA^z - c(A-a)^z$. It follows that:

$$ \mathcal{L}oss_{species} = \frac{E_a}{S_A} = 1 - \frac{(A-a)^z}{A^z} = 1 - (1 - \mathcal{L}oss_{habitat})^z \quad (25) $$

We retrieve Equation (16) on page 78. At first glance, it seems that the approach based on the endemics-area relationship is coherent with the species-area relationship. In fact, the issue lies in the calibration of the endemics-area curve, which generally produces a value of z smaller than

<footnote n="75"><sup>75</sup>The estimated parameters are $κ = 0.009927$ for the geometric model, and $α = 100.3014$ and $x = 0.999701$ for the log-series model. The other models are completely determined by the number of individuals ($n = 335 356$) and the number of species ($S = 814$).</footnote>
<figure><img src="image_71.png" /><figcaption>Figure 38: Species-area relationship (Pasoh Forest Reserve)</figcaption></figure>

Source: He and Legendre (2002, Figure 2a, page 1191) & Author's calculations.

<figure><img src="image_72.png" /><figcaption>Figure 39: Endemics-area relationship (Pasoh Forest Reserve)</figcaption></figure>

Source: Green and Ostling (2003, Figure 1a, page 3093) & Author's calculations.
<figure><img src="image_73.png" /><figcaption>Figure 40: Comparison of species-area and endemics-area curves (Barro Colorado Island)</figcaption></figure>

Source: He and Hubbell (2011, Figure S1) & Author's calculations.

the value obtained with the species-area curve. As a result, we deduce that the extinction rate is overestimated:

$$ \mathcal{L}oss_{species} = 1 - (1 - \mathcal{L}oss_{habitat})^{z_{EAR}} \le 1 - (1 - \mathcal{L}oss_{habitat})^{z_{SAR}} $$

To illustrate this bias, He and Hubbell (2011) considered nine datasets, including those from the Barro Colorado Island and the Pasoh Forest, and found that $z_{EAR} \le z_{SAR}$ in all cases. For example, for the Pasoh Forest Reserve, they found $z_{EAR} = 0.0536$ and $z_{SAR} = 0.124$. Figure 40 shows the empirical and theoretical SAR and EAR curves, along with the calibrated power-law models. We verify that $Loss_{species}$ is overestimated when $z_{SAR}$ is used instead of $z_{EAR}$. On page 78 we estimate that 50% of habitat loss should reduce the number of species by 15.91%, while 90% of habitat loss leads to 43.77% of species loss because we use the value $z_{SAR} = 0.25$ suggested by Pimm et al. (1995). If we consider a value of $z_{EAR} = 0.10$, which is the median value obtained by He and Hubbell (2011), 50% of habitat loss should reduce the number of species by 6.70%, while 90% of habitat loss leads to 20.57% of species loss (Table 22, page 78). The numbers are quite different.

**Remark 9** Censuses of tree data are abundant and valuable for studying relationships between habitat and species richness. Many of these datasets (including those from Barro Colorado Island and the Pasoh Forest Reserve) are available at http://ctfs.si.edu/datarequest, the data portal of ForestGEO (Forest Global Earth Observatory). ForestGEO is a global network dedicated to the study of forests and their ecosystems. Hosted by the Smithsonian Institution, it is one of the most comprehensive forest monitoring programs in the world. The network includes 78 forest research sites in the Americas, Africa, Asia, Europe, and Oceania, that monitor the growth and survival of approximately 7 million trees representing nearly 13 000 species.
Box 10: Forest definitions adopted by major international environmental and forestry organizations

* United Nations Food and Agriculture Organization (2000)
  Land with tree crown cover (or equivalent stocking level) of more than 10% and an area of more than 0.5 ha. Trees should be able to reach a minimum height of 5 m at maturity *in situ*.

* United Nations Framework Convention on Climate Change (2002)
  Minimum area of 0.05–1.0 ha of land with tree crown cover (or equivalent stocking level) of more than 10–30% with trees that have the potential to reach a minimum height of 2–5 m at maturity *in situ*.

* United Nations Convention on Biological Diversity
  Land area of more than 0.5 ha, with a tree canopy cover of more than 10%, which is not primarily under agriculture or other specific non-forest land use.

* United Nations Convention to Combat Desertification (2000)
  Dense canopy with multi-layered structure including large trees in the upper story.

* International Union of Forest Research Organizations (2002)
  Land area with a minimum 10% tree crown coverage (or equivalent stocking level), or formerly having such tree cover and that is being naturally or artificially regenerated or that is being afforested.

Source: Chazdon et al. (2016, Box 1, page 542).

### 3.1.4 Forest loss

Among the various types of habitat loss, forests are particularly important because they are biodi- versity hotspots, home to numerous endemic species. These ecosystems provide essential services, including climate regulation, water cycle maintenance, and soil stabilization. In addition, forests are complex, interconnected networks where species are highly interdependent. Loss of forest habitat can trigger trophic cascades, destabilizing entire ecological systems by disrupting some fundamen- tal biological relationships. However, the concept of forest loss is somewhat vague and requires a clear definition of what constitutes a forest and what does not. According to the Oxford English Dictionary, a forest is defined as “*a large area of land that is thickly covered with trees*”, while the Cambridge Dictionary defined it as “*a large area of land covered with trees and plants, usually larger than a wood*”. However, despite its common usage, there is no universally agreed-upon definition of the word forest. The concept of a forest extends far beyond a simple description of tree cover- age and must encompass various dimensions of biodiversity, particularly when aiming to measure ecosystem functions or address key aspects of forest conservation biology (Zalles et al., 2024). For instance, these aspects include forest loss, degradation, afforestation, reforestation, and other related processes. In Box 10, we report the forest definitions of five international organizations collected by Chazdon et al. (2016). While the definition depends on the purpose and the organization, the FAO definition is the most widely used globally. The FAO definition is practical because it uses measurable parameters such as tree height, canopy cover, and area. Here is the latest version used for the 2025 FRA<fnref n="76" />:

<footnote n="76">⁷⁶A forest is defined by the presence of trees and the absence of dominant non-forest land uses. It includes young or regenerating areas that are expected to reach a height of 5 meters and a canopy cover of 10%. Forests also include</footnote>
"Land spanning more than 0.5 hectares with trees higher than 5 meters and a canopy cover of more than 10 percent, or trees able to reach these thresholds in situ. It does not include land that is predominantly under agricultural or urban land use." (FAO, 2023a, Section 1a, page 7).

Another success factor is that data on forest status and trends are easily available thanks to the Global Forest Resources Assessment (FRA), which is collected and published by the FAO every five years<sup>77</sup>.

<figure><img src="image_74.png" /><figcaption>Figure 41: Proportion and distribution of global forest area by climatic domain in 2020</figcaption></figure>

Source: FAO (2020, page 1).

According to FAO (2020), the world has a total forest area of 4.06 billion hectares, which represents 31% of the total land area. This area corresponds to 0.52 ha per person. Tropical forests<sup>78</sup> account for 45% of the world's forests, followed by boreal forests (27%), temperate forests (16%) and subtropical forests (11%), while polar forests account for less than 1% (Figure 41). More than 50% of the world's forests are located in just five countries: Russia, Brazil, Canada, the United States and China. In Table 27, we present the forest area of the top 20 countries, changes by decade, the distribution of the world's forest area in 2020, and the proportion of primary forest<sup>79</sup> in 2020. For instance, Brazil had 589 million hectares of forest in 1990, which decreased to 497 million hectares in 2020. The country experienced forest area losses of 6.42%, 7.17%, and 2.92% between 1990-2000, 2000-2010, and 2010-2020, respectively. In 2020, Brazil accounted for 12.24% of the world's forest area, and 43.53% of its forests were classified as primary forests. Figure 42 shows the percentage of land area covered by forests. Globally, forests cover 31.1% of the total land area, but there are significant differences between countries. Seven countries have more than 90% of their land area covered by forest: Suriname (97.41%), French Guiana (97.36%), Guyana (93.55%), Micronesia

mangroves, shelterbelts, bamboo, palms, and specialty plantations such as rubber and cork oak. Protected areas, forest infrastructure and abandoned shifting cultivation areas with tree regeneration are included. Agricultural tree systems such as orchards, fruit plantations and agroforestry with crops are excluded.

⁷⁷The FRA website is www.fao.org/forest-resources-assessment while the FRA data are available at https://fra-data.fao.org/assessments/fra/2020.

⁷⁸The climatic groups are defined as follows: tropical (all months without frost; in marine areas above 18°C), subtropical (eight months or more above 10°C), temperate (four to eight months above 10°C), boreal (up to three months above 10°C) and polar (all months below 10°C).

⁷⁹Primary forests are old-growth natural forests that have been largely undisturbed by human activity and have retained their original biodiversity and ecological processes.
<table><caption>Table 27: Forest area (top 20 countries and six world regions)</caption><thead><tr><th rowspan="2">Country/region</th><th colspan="4">Value (in million ha)</th><th colspan="3">Variation by decade (in %)</th><th rowspan="2">Geographical distribution in %</th><th rowspan="2">Cumulated</th><th rowspan="2">Primary forest in %</th></tr><tr><th>1990</th><th>2000</th><th>2010</th><th>2020</th><th>2000</th><th>2010</th><th>2020</th></tr></thead><tbody><tr><td>Russia</td><td>809</td><td>809</td><td>815</td><td>815</td><td>0.04</td><td>0.72</td><td>0.02</td><td>20.09</td><td>20.09</td><td>31.30</td></tr><tr><td>Brazil</td><td>589</td><td>551</td><td>512</td><td>497</td><td>-6.42</td><td>-7.17</td><td>-2.92</td><td>12.24</td><td>32.32</td><td>43.53</td></tr><tr><td>Canada</td><td>348</td><td>348</td><td>347</td><td>347</td><td>-0.14</td><td>-0.14</td><td>-0.11</td><td>8.55</td><td>40.87</td><td>59.13</td></tr><tr><td>United States of America</td><td>302</td><td>304</td><td>309</td><td>310</td><td>0.36</td><td>1.71</td><td>0.35</td><td>7.63</td><td>48.50</td><td>24.31</td></tr><tr><td>China</td><td>157</td><td>177</td><td>201</td><td>220</td><td>12.64</td><td>13.34</td><td>9.65</td><td>5.42</td><td>53.92</td><td>5.21</td></tr><tr><td>Australia</td><td>134</td><td>132</td><td>130</td><td>134</td><td>-1.54</td><td>-1.72</td><td>3.44</td><td>3.30</td><td>57.22</td><td></td></tr><tr><td>Congo (DRC)</td><td>151</td><td>144</td><td>137</td><td>126</td><td>-4.47</td><td>-4.68</td><td>-8.03</td><td>3.11</td><td>60.33</td><td>65.59</td></tr><tr><td>Indonesia</td><td>119</td><td>101</td><td>100</td><td>92</td><td>-14.56</td><td>-1.60</td><td>-7.55</td><td>2.27</td><td>62.60</td><td>48.56</td></tr><tr><td>Peru</td><td>76</td><td>75</td><td>74</td><td>72</td><td>-1.51</td><td>-1.66</td><td>-2.32</td><td>1.78</td><td>64.38</td><td></td></tr><tr><td>India</td><td>64</td><td>68</td><td>69</td><td>72</td><td>5.71</td><td>2.82</td><td>3.83</td><td>1.78</td><td>66.16</td><td>21.76</td></tr><tr><td>Angola</td><td>79</td><td>78</td><td>72</td><td>67</td><td>-1.96</td><td>-7.14</td><td>-7.69</td><td>1.64</td><td>67.80</td><td>40.15</td></tr><tr><td>Mexico</td><td>71</td><td>68</td><td>67</td><td>66</td><td>-3.13</td><td>-2.10</td><td>-1.87</td><td>1.62</td><td>69.42</td><td>48.77</td></tr><tr><td>Colombia</td><td>65</td><td>63</td><td>61</td><td>59</td><td>-3.42</td><td>-3.07</td><td>-2.74</td><td>1.46</td><td>70.88</td><td></td></tr><tr><td>Bolivia</td><td>58</td><td>55</td><td>53</td><td>51</td><td>-4.68</td><td>-3.66</td><td>-4.24</td><td>1.25</td><td>72.13</td><td></td></tr><tr><td>Venezuela</td><td>52</td><td>49</td><td>48</td><td>46</td><td>-5.53</td><td>-3.35</td><td>-2.68</td><td>1.14</td><td>73.27</td><td>97.06</td></tr><tr><td>Tanzania</td><td>57</td><td>54</td><td>50</td><td>46</td><td>-6.48</td><td>-6.93</td><td>-8.42</td><td>1.13</td><td>74.40</td><td>62.32</td></tr><tr><td>Zambia</td><td>47</td><td>47</td><td>47</td><td>45</td><td>-0.76</td><td>-0.76</td><td>-4.03</td><td>1.10</td><td>75.50</td><td></td></tr><tr><td>Mozambique</td><td>43</td><td>41</td><td>39</td><td>37</td><td>-5.05</td><td>-5.38</td><td>-5.72</td><td>0.91</td><td>76.40</td><td></td></tr><tr><td>Papua New Guinea</td><td>36</td><td>36</td><td>36</td><td>36</td><td>-0.33</td><td>-0.27</td><td>-0.89</td><td>0.88</td><td>77.29</td><td></td></tr><tr><td>Argentina</td><td>35</td><td>33</td><td>30</td><td>29</td><td>-5.19</td><td>-9.48</td><td>-5.43</td><td>0.70</td><td>77.99</td><td></td></tr><tr><td>Africa</td><td>743</td><td>710</td><td>676</td><td>637</td><td>-4.41</td><td>-4.79</td><td>-5.82</td><td>15.68</td><td>15.68</td><td>19.30</td></tr><tr><td>Asia</td><td>585</td><td>587</td><td>611</td><td>623</td><td>0.34</td><td>4.01</td><td>1.92</td><td>15.34</td><td>31.03</td><td>13.79</td></tr><tr><td>Europe</td><td>994</td><td>1002</td><td>1014</td><td>1017</td><td>0.80</td><td>1.17</td><td>0.34</td><td>25.07</td><td>56.09</td><td>25.22</td></tr><tr><td>North and Central America</td><td>755</td><td>752</td><td>754</td><td>753</td><td>-0.39</td><td>0.24</td><td>-0.20</td><td>18.54</td><td>74.64</td><td>41.62</td></tr><tr><td>Oceania</td><td>185</td><td>183</td><td>181</td><td>185</td><td>-0.89</td><td>-1.26</td><td>2.34</td><td>4.56</td><td>79.20</td><td>1.41</td></tr><tr><td>South America</td><td>974</td><td>923</td><td>870</td><td>844</td><td>-5.24</td><td>-5.69</td><td>-2.98</td><td>20.80</td><td>100.00</td><td>35.38</td></tr><tr><td>World</td><td>4236</td><td>4158</td><td>4106</td><td>4059</td><td>-1.85</td><td>-1.24</td><td>-1.15</td><td>100.00</td><td>200.00</td><td>26.61</td></tr></tbody></table>

Source: FAO (2020), https://fra-data.fao.org/assessments/fra/2020, & Author's calculations.
<figure><img src="image_75.png" /><figcaption>Figure 42: Percentage of land area covered by forest, by country (2020)</figcaption></figure>

Source: Our World in Data, https://ourworldindata.org/forest-area.

<figure><img src="image_76.png" /><figcaption>Figure 43: Distribution of global forest area (2020)</figcaption></figure>

Source: Our World in Data, https://ourworldindata.org/forest-area.
(92.03%), Gabon (91.32%), Solomon Islands (90.14%), and Palau (90.02%). Some of the world's largest countries also have a significant proportion of their land area covered by forest. For example, Russia (49.78%), China (23.34%), the United States (33.87%), Canada (38.15%), and Brazil (59.42%) all have significant forest cover. Conversely, other large countries have relatively low forest cover, such as Argentina (10.44%), Kazakhstan (1.28%), and Algeria (0.82%). Among the largest European countries (those with a land area of more than 20 million hectares), forest cover also varies widely. Most of these countries have at least 30% forest cover, including Belarus (43.19%), Germany (32.73%), Spain (37.17%), Finland (73.74%), France (31.51%), Italy (32.52%), Norway (40.05%), Poland (30.97%), Romania (30.12%) and Sweden (68.69%). However, some countries fall below this threshold, such as Ukraine (16.73%) and the United Kingdom (13.19%).

Table 28 presents some key forest characteristics. Globally, 17% of forests are located in protected areas, representing more than 700 million hectares. Among the six world regions, South America has the highest proportion of forests in protected areas (30.5%), followed by Africa (24.8%). Natural (regenerative) forests account for 92.4% of the global forest area, while 7.2% consists of planted forests. In addition, the majority of the world's forests are publicly owned (71.5%), compared to 21.7% under private ownership, with the remainder classified as unknown. Public ownership predominates in all regions, especially in Europe (88.2%), largely due to Russia, where 100% of forests are publicly owned.

We have seen that the world lost 177 million hectares of forest between 1990 and 2020. Focusing on the period 2015–2020, the annual forest loss was about 5 million hectares. This figure, representing the net change, is the difference between the forest expansion rate and the deforestation rate. In Table 28, we present these two statistics together with the reforestation rate, all expressed in 1000 hectares per year. For some countries, data on forest expansion, deforestation, and reforestation<fnref n="80" /> are missing (e.g., the United States, Australia, Congo, Angola), which introduces bias into the global rates. However, estimates from FAO (2020, page 4) indicate that the annual net loss of 5 million hectares is the result of a deforestation rate of 10 million hectares per year offset by a forest expansion rate of 5 million hectares per year. Although there is a declining trend in forest loss in the short term, the average rate of forest loss has accelerated in the long term. In fact, between the invention of agriculture and the beginning of the Industrial Revolution, we lost 2% of forest area every 5 000 years. Since 1700, as shown in Table 29, this rate has accelerated, especially since 1950.

The GFA dataset is not dedicated to the study of forest loss, although it contains a lot of information on this topic. To obtain information at a higher resolution than regional and country levels, and at a higher frequency than the 5-year period (for example, to obtain statistics on the Amazon rainforest on quarterly basis), other sources of information are available:

* The Global Forest Review (GFR) is an initiative of the World Resources Institute (WRI) that provides data, analysis and insight on the world's forests (https://research.wri.org/gfr/global-forest-review). It serves as a resource for tracking the state of the world's forests, understanding deforestation trends, and evaluating forest conservation efforts. GFR uses many datasets derived from geospatial data and maps.

* Global Forest Watch (GFW) is an online platform, available at www.globalforestwatch.org and developed by the World Resources Institute (WRI), that provides near real-time

<footnote n="80">⁸⁰Forest expansion refers to the growth of forest on land previously used for other purposes, involving a change of land use from non-forest to forest. It includes both afforestation (planting of trees on land that was not previously forested) and natural expansion of forests. Deforestation is the conversion of forested land to other land uses, whether this change is caused by human activities or by natural processes. Reforestation is the reestablishment of forest on land that is still classified as forest, typically through planting or deliberate seeding. Unlike forest expansion, it does not involve a change in land use.</footnote>
<table><caption>Table 28: Forest characteristics, ownership and annual change (top 20 countries and six world regions)</caption><thead><tr><th>Country/region</th><th>Forest area (10<sup>6</sup> ha)</th><th>Protected (%)</th><th>Regenerative (%)</th><th>Planted (%)</th><th>Private ownership (%)</th><th>Public ownership (%)</th><th>Expansion (10<sup>3</sup> ha/year)</th><th>Deforestation (10<sup>3</sup> ha/year)</th><th>Reforestation (10<sup>3</sup> ha/year)</th><th>Coverage (%)</th><th>Net change (10<sup>3</sup> ha/year)</th></tr></thead><tbody><tr><td>Russia</td><td>815</td><td>2.3</td><td>97.7</td><td>2.3</td><td>0.0</td><td>100.0</td><td>76</td><td>0</td><td>945</td><td>100.0</td><td>76</td></tr><tr><td>Brazil</td><td>497</td><td>30.1</td><td>97.7</td><td>2.3</td><td>44.2</td><td>55.8</td><td>243</td><td>1 696</td><td>257</td><td>100.0</td><td>-1 453</td></tr><tr><td>Canada</td><td>347</td><td>8.5</td><td>94.8</td><td>5.2</td><td>8.2</td><td>91.4</td><td>0</td><td>38</td><td>427</td><td>100.0</td><td>-38</td></tr><tr><td>United States of America</td><td>310</td><td>10.2</td><td>91.1</td><td>8.9</td><td>58.1</td><td>41.9</td><td></td><td></td><td>691</td><td>0.0</td><td>-60</td></tr><tr><td>China</td><td>220</td><td>13.8</td><td>61.5</td><td>38.5</td><td>41.3</td><td>58.7</td><td>2 070</td><td>133</td><td>273</td><td>100.0</td><td>1 937</td></tr><tr><td>Australia</td><td>134</td><td>18.0</td><td>98.2</td><td>1.8</td><td>32.3</td><td>67.0</td><td></td><td></td><td></td><td>0.0</td><td>182</td></tr><tr><td>Congo (DRC)</td><td>126</td><td>19.3</td><td>100.0</td><td>0.0</td><td>0.0</td><td>100.0</td><td></td><td></td><td></td><td>0.0</td><td>-1 101</td></tr><tr><td>Indonesia</td><td>92</td><td>56.2</td><td>95.1</td><td>4.9</td><td>1.1</td><td>91.2</td><td>71</td><td>650</td><td>7</td><td>100.0</td><td>-579</td></tr><tr><td>Peru</td><td>72</td><td>31.6</td><td>98.5</td><td>1.5</td><td>16.0</td><td>84.0</td><td>6</td><td>179</td><td></td><td>100.0</td><td>-173</td></tr><tr><td>India</td><td>72</td><td>19.4</td><td>81.6</td><td>18.4</td><td>18.5</td><td>81.5</td><td>935</td><td>668</td><td></td><td>100.0</td><td>266</td></tr><tr><td>Angola</td><td>67</td><td>2.8</td><td>98.8</td><td>1.2</td><td>0.0</td><td>100.0</td><td></td><td></td><td>0</td><td>0.0</td><td>-555</td></tr><tr><td>Mexico</td><td>66</td><td></td><td>99.8</td><td>0.2</td><td>79.3</td><td>3.6</td><td>38</td><td>166</td><td>159</td><td>100.0</td><td>-128</td></tr><tr><td>Colombia</td><td>59</td><td>21.0</td><td>99.3</td><td>0.7</td><td>30.4</td><td>66.0</td><td>1</td><td>199</td><td>497</td><td>100.0</td><td>-199</td></tr><tr><td>Bolivia</td><td>51</td><td>24.5</td><td>99.9</td><td>0.1</td><td>0.1</td><td>99.9</td><td>4</td><td>243</td><td>3</td><td>100.0</td><td>-239</td></tr><tr><td>Venezuela</td><td>46</td><td>98.6</td><td>97.1</td><td>2.9</td><td>2.3</td><td>97.7</td><td>18</td><td>108</td><td>4</td><td>100.0</td><td>-90</td></tr><tr><td>Tanzania</td><td>46</td><td>62.3</td><td>98.8</td><td>1.2</td><td>7.3</td><td>4.1</td><td>5</td><td>474</td><td>27</td><td>100.0</td><td>-469</td></tr><tr><td>Zambia</td><td>45</td><td>71.0</td><td>99.9</td><td>0.1</td><td>6.4</td><td>26.2</td><td>2</td><td>190</td><td>4</td><td>100.0</td><td>-188</td></tr><tr><td>Mozambique</td><td>37</td><td>41.4</td><td>99.8</td><td>0.2</td><td>0.2</td><td>99.8</td><td>28</td><td>267</td><td>2</td><td>100.0</td><td>-239</td></tr><tr><td>Papua New Guinea</td><td>36</td><td>3.8</td><td>99.8</td><td>0.2</td><td>99.9</td><td>0.1</td><td>0</td><td>34</td><td>0</td><td>99.4</td><td>-34</td></tr><tr><td>Argentina</td><td>29</td><td>6.7</td><td>95.0</td><td>5.0</td><td>4.4</td><td>0.0</td><td>30</td><td>135</td><td>17</td><td>100.0</td><td>-105</td></tr><tr><td>Africa</td><td>637</td><td>24.8</td><td>98.2</td><td>1.8</td><td>5.5</td><td>71.4</td><td>404</td><td>2 149</td><td>353</td><td>44.0</td><td>-3 969</td></tr><tr><td>Asia</td><td>623</td><td>21.9</td><td>78.2</td><td>21.7</td><td>21.6</td><td>76.8</td><td>3 477</td><td>1 922</td><td>1 221</td><td>118.2</td><td>1 316</td></tr><tr><td>Europe</td><td>1 017</td><td>4.9</td><td>91.3</td><td>7.4</td><td>9.1</td><td>88.2</td><td>255</td><td>69</td><td>1 593</td><td>56.0</td><td>331</td></tr><tr><td>North and Central America</td><td>753</td><td>9.5</td><td>93.7</td><td>6.2</td><td>35.2</td><td>60.5</td><td>79</td><td>372</td><td>1 322</td><td>84.2</td><td>-348</td></tr><tr><td>Oceania</td><td>185</td><td>15.7</td><td>97.1</td><td>2.6</td><td>47.2</td><td>52.2</td><td>16</td><td>40</td><td>56</td><td>-15.0</td><td>163</td></tr><tr><td>South America</td><td>844</td><td>30.5</td><td>97.6</td><td>2.4</td><td>31.9</td><td>61.6</td><td>460</td><td>2 962</td><td>947</td><td>100.9</td><td>-2 481</td></tr><tr><td>World</td><td>4 059</td><td>17.3</td><td>92.4</td><td>7.2</td><td>21.7</td><td>71.5</td><td>4 691</td><td>7 514</td><td>5 492</td><td>56.6</td><td>-4 987</td></tr></tbody></table>

Source: FAO (2020), https://fra-data.fao.org/assessments/fra/2020, & Author's calculations.
<table><caption>Table 29: Distribution of habitable land on Earth (excluding glaciers and deserts)</caption><thead><tr><th>Time</th><th>Forests</th><th>Cropland</th><th>Grazing land</th><th>Wild grassland and shrubs</th><th>Urban and built-up land</th></tr></thead><tbody><tr><td>10 000 years ago</td><td>57%</td><td></td><td></td><td>42%</td><td></td></tr><tr><td>5 000 years ago</td><td>55%</td><td></td><td>1%</td><td>44%</td><td></td></tr><tr><td>1700</td><td>52%</td><td>3%</td><td>6%</td><td>38%</td><td></td></tr><tr><td>1900</td><td>48%</td><td>8%</td><td>16%</td><td>27%</td><td></td></tr><tr><td>1950</td><td>44%</td><td>12%</td><td>31%</td><td>12%</td><td>1%</td></tr><tr><td>2020</td><td>37%</td><td>16%</td><td>31%</td><td>14%</td><td>2%</td></tr></tbody></table>

Source: Our World in Data, https://ourworldindata.org/forest-area & Author's calculations

monitoring of global forest change. It uses advanced satellite technology, big data, and open access to empower users to monitor forests and take action against deforestation.

* Academic studies are extensively documented on specific regions and provide high-level analysis of data provided by GFA, GFR, GFW and other datasets. They may include a new way of observing forests, for example using satellite imagery<sup>81</sup>, an in-depth analysis of forms of forest degradation<sup>82</sup>, etc.

According to the Global Forest Review, the top 10 countries with the highest global tree cover loss between 2001 and 2023 are Russia (83.7 Million hectares or Mha), Brazil (68.9 Mha), Canada (57.5 Mha), the United States (47.9 Mha), Indonesia (30.8 Mha), the Democratic Republic of Congo (19.7 Mha), China (12.1 Mha), Malaysia (9.2 Mha), Australia (9 Mha), and Bolivia (8 Mha). However, tree cover loss does not always equate to deforestation. In some cases, such as commercial forestry, tree cover loss is temporary because forests are allowed to regrow after harvesting. This is particularly true in countries such as Russia and Canada, which have a permanent tree cover loss rate of 0%. Similarly, the United States, China and Australia have permanent loss rates of less than 5%. In contrast, countries such as Indonesia, Malaysia and Bolivia have permanent tree cover loss rates of more than 80%, indicating significant deforestation. Brazil and the Democratic Republic of the Congo fall between these two extremes, with permanent forest loss rates of 71% and 35%, respectively. Together, these 10 countries are responsible for 71% of the global tree cover loss of 488 Mha between 2001 and 2023. Curtis et al. (2018) propose a classification of forest loss into five main drivers (Box 11). Forestry accounts for 32% of global forest loss between 2001 and 2023, followed by shifting agriculture and wildfires, each contributing 23%. Commodity-driven deforestation accounts for 21%, while urbanization is responsible for less than 1%. According to the Global Forest Review, the drivers of forest loss vary significantly from one region to another (Figure 44). While commodity-driven deforestation is the leading cause of forest loss in Latin America and Southeast Asia, its impact is minimal in other regions, which are dominated by wildfires and forestry, with the exception of Africa, where 95% of forest loss is attributed to shifting agriculture.

The Global Forest Review also provides many interesting figures for understanding deforestation. For example, we learn that seven commodities account for 57% of all agricultural-related tree cover

<footnote n="81"><sup>81</sup>Three notable examples are the studies by Hansen et al. (2013b) and Potapov et al. (2022), which use a dataset of land cover at a 30-meter spatial resolution derived from NASA's Landsat program, and the study by Lesiv et al. (2022), which is based on a dataset of forest management practices at a 100-meter resolution for the year 2015, derived from the European Space Agency's PROBA-V satellite imagery program.</footnote>

<footnote n="82"><sup>82</sup>See for example Lapola et al. (2023), who studied four primary disturbances contributing to Amazon forest degradation: timber extraction, fire (sometimes used for land clearing, which can escape control and damage surrounding forests), edge effects (resulting from deforestation and habitat fragmentation), and extreme drought.</footnote>
Box 11: Drivers of forest loss

* Forestry

Large-scale forestry operations in managed forests or tree plantations where future regrowth is likely. Regrowth may occur through natural regeneration or tree planting.

* Commodity-driven deforestation

Long-term permanent conversion of forest and shrubland to non-forest land for commodity production, including agriculture, mining, or oil and gas production.

* Wildfire

Burning of vegetation without visible human conversion or agricultural activity afterward. Some of these fires occur naturally, but others are set by humans. In humid tropical forests, fires are not natural to the ecosystem and are almost always set by humans, usually to clear land for agriculture.

* Shifting agriculture

Agricultural practices in which forests are cleared, used for agricultural production for a few years, and then temporarily abandoned to allow trees to regrow. Shifting agriculture involves many different types of smallholder farming practices.

* Urbanization

Permanent conversion of forests to human settlements for the expansion and intensification of existing urban centers.

Source: Curtis et al. (2018, pages 1108-1109).

Figure 44: Drivers of tree cover loss by region (2001–2023)

<figure><img src="image_77.png" /></figure>

Source: https://research.wri.org/gfr/global-forest-review.
loss between 2001 and 2015, with cattle (pasture use) alone accounting for 36%, followed by oil palm (8%), soy (6.5%) and cocoa (2%). As mentioned earlier, forest loss and deforestation are major drivers of biodiversity loss<sup>83</sup>, but forest degradation also plays a significant role in this process. In particular, the detrimental consequences of forest degradation have been highlighted by Barlow et al. (2016) and Watson et al. (2018), who showed that the impact of degradation can equal that of deforestation in some regions. However, the concept of forest degradation is not easy to define and requires a multi-dimensional analysis:

> "Forest degradation is broadly defined as a reduction in the capacity of a forest to produce ecosystem services such as carbon storage and wood products as a result of anthropogenic and environmental changes. [...] There is, however, no generally recognized way to identify a degraded forest because perceptions of forest degradation vary depending on the cause, the particular goods or services of interest, and the temporal and spatial scales considered. [...] the types of degradation can be represented using five criteria that relate to the drivers of degradation, loss of ecosystem services and sustainable management, including: productivity, biodiversity, unusual disturbances, protective functions, and carbon storage." (Thompson et al., 2013, page 1).

Among the 11 indicators proposed by Thompson et al. (2013, Table 1, page 3), the Global Forest Review has selected three approaches to measure forest degradation and forest disturbance:

1. Forest area experiencing a partial (more than 20% and less than 90%) loss of tree canopy cover;

2. Tree cover extent experiencing tree cover loss due to fire;

3. Intact forest landscapes that can no longer be considered intact due to evidence of human disturbance.

Their results are as follows<sup>84</sup>. Between 2001 and 2012, 185 Mha of forest experienced a partial reduction in tree canopy cover, representing 5% of the global forest area, with 85% of this occurring in tropical forests. Additionally, 113 Mha of tree cover loss was associated with fire between 2001 and 2023, accounting for 2.8% of the global forest area. Lastly, 155 Mha of forest area classified as intact in 2000 could no longer be considered intact by 2020, representing 4% of the global forest area.

## 3.2 Invasive species

An invasive species is a non-native (or alien) species (plants, animals, or microorganisms) that is intentionally or accidentally introduced into a new environment and poses a threat to native species and biodiversity. The main characteristics of invasive species are:

*   **Non-native**

Invasive species are plants and animals that live in areas where they do not naturally exist. However, not all non-native species are invasive. For instance, corn is not native to Europe but is not considered an invasive species.

<footnote n="83"><sup>83</sup>For example, Betts et al. (2017) examined how deforestation affects biodiversity in different landscapes. They found that deforestation significantly increased the likelihood of species being listed as threatened, upgraded to higher threat categories, or experiencing population declines. Crucially, "*these risks were disproportionately high in relatively intact landscapes; even minimal deforestation had severe consequences for vertebrate biodiversity loss.*" In contrast, in already fragmented landscapes, the effects of forest loss were less pronounced.</footnote>

<footnote n="84"><sup>84</sup>Source: https://research.wri.org/gfr/forest-condition-indicators/forest-degradation.</footnote>
* Rapid spread
  Invasive species tend to reproduce and grow very quickly because they lack natural predators in the new environment.

* Harmful effects
  Invasive species often outcompete native species for resources, take over habitats, and disrupt native ecosystems.

These three characteristics are typically assessed to determine whether a species is invasive<sup>85</sup>. In addition, invasive species are usually introduced with (intentional or accidental) human assistance (Simberloff et al., 2013). One of the greatest challenges is managing alien invasions because eradication of established invaders is rare and post-invasion control is difficult (Mack et al., 2000).

Many countries have developed their own taxonomy of invasive alien species (IAS). For example, the National Invasive Species Information Center (NISIC), established in 2005 under the US Department of Agriculture (USDA), manages the website www.invasivespeciesinfo.gov, which lists invasive species in the United States. As of December 2024, 194 species are reported to be invasive in the United States. In alphabetical order, the first invasive species listed<sup>86</sup> is the African clawed frog (*Xenopus laevis*), which is native to Africa. It was introduced to California in 1968 and imported for laboratory research and the pet trade. This species negatively impacts native amphibian and fish populations. The 107<sup>m</sup>athrmth invasive species on the list is kudzu (*Pueraria montana*), which is native to Asia. It was introduced to the USA in the late 1800s as an ornamental plant and for erosion control. Kudzu vine outcompetes native species and disrupts ecosystems. In the European Union, invasive alien species are controlled by EU Regulation 1143/2014, which contains a set of measures to be taken throughout the EU in relation to invasive alien species. In addition, the European Union has established a list of 88 regulated invasive alien species<sup>87</sup> (47 animal species and 41 plant species). Here are some examples of invasive species: Egyptian goose (*Alopochen aegyptiaca*), western mosquitofish (*Gambusia affinis*), fox squirrel (*Sciurus niger*), tropical fire ant (*Solenopsis geminata*), African clawed frog (*Xenopus laevis*), Senegal tea plant (*Gymnocoronis spi-lanthoides*), floating pennywort (*Hydrocotyle ranunculoides*), water primrose (*Ludwigia grandiflora*), kudzu vine (*Pueraria montana*). At the global level, the Global Invasive Species Database (GISD) is a free, online, searchable source of information on alien and invasive species that negatively impact biodiversity. However, this database was developed in 2000 and is no longer maintained in the 2020s.

The previous examples focus on invasive animal and plant species. However, invasive species can also include infectious diseases and microorganisms. For example, Berger et al. (1998) studied the devastating effects of the amphibian chytrid fungus (*Batrachochytrium dendrobatidis*) and its impact on amphibian mortality and population decline. While these authors suggested that environmental factors such as climate change and habitat modification were responsible for the spread of the fungus, Weldon et al. (2004) found that “Africa was the origin of amphibian chytrid and that the international trade in *Xenopus laevis* frogs, which began in the mid-1930s, was the means of dissemination.” Although the chytrid fungus is not a traditional invasive species in the sense of an animal or plant, it is an example of an invasive pathogen that has had a devastating impact on native amphibian populations. Another example is the *Pseudogymnoascus destructans* fungus that causes white-nose syndrome, a fatal disease that has killed millions of bats in North America (Blehert et al., 2009). This fungus is thought to have originated in Europe, where local bats evolved resistance. It

<footnote n="85"><sup>85</sup>For instance, IPBES (2023, page 76) estimates that 37 000 species are established aliens, but only 5 250 are invasive alien species.</footnote>

<footnote n="86"><sup>86</sup>The list is available at www.invasivespeciesinfo.gov/species-profiles-list.</footnote>

<footnote n="87"><sup>87</sup>They are listed in the 187-page report *An Introduction to the Invasive Alien Species of Union Concern*, published by the European Commission in 2022.</footnote>
was introduced to North America by humans and has since become an invasive pathogen for native
bats in North America.

Primack (2014, pages 226-237) and Simberloff (2010, pages 131-142) report numerous striking
cases of invasive species. For example, the introduction of predatory snakes has led to a decline in
bird populations on several small islands. Simberloff (2010, page 136) notes that predators have
often been intentionally introduced as biological control agents for specific target species, but in
some cases these predators have also attacked non-target species and driven them to extinction:

“One of the worst such disasters was the introduction of the rosy wolf snail (Euglandina rosea), native to Central America and Florida, to many Pacific islands to control the previously introduced giant African snail (Achatina fulica). The predator not only failed to control the targeted prey (which grows to be too large for the rosy wolf snail to attack it) but caused the extinction of over 50 species of native land snails [...] The small Indian mongoose, implicated as the sole cause or a contributing cause in the extinction of several island species of birds, mammals, and frogs, was deliberately introduced to all these islands as a biological control agent for introduced rats [...] The mosquitofish (Gambusia affinis) from Mexico and Central America has been introduced to Europe, Asia, Africa, Australia, and many islands for mosquito control. Its record on this score is mixed [...] However, it preys on native invertebrates and small fishes and in Australia is implicated in extinction of several fish species.” (Simberloff, 2010, page 137).

Biological control is one of the reasons for the introduction of alien species, the other three being
European colonization (birds, mammals, and fish for food), agriculture (including horticulture and
aquaculture), and accidental transport (especially rats, snakes, and insects) (Primack, 2014, page
226). Among the regions most affected by invasive species, New Zealand is a special case. Non-
native predators kill over 25 million native birds annually, and many native land species have already
been lost, including sixty bird species, three frog species, seven vascular plants, and numerous
invertebrates. Currently, more than 3000 native land species are either threatened or endangered.
In July 2016, the New Zealand government launched the *Predator Free 2050* initiative<sup>88</sup>, which aims
to completely eradicate certain introduced predators by the year 2050. The goals of Predator Free
2050 are ambitious, seeking to restore New Zealand's ecosystems to a state where native species
can thrive without the constant threat of introduced predators. The initiative targets three primary
groups of invasive species:

1. Mustelids: stoats (*Mustela erminea*), ferrets (*Mustela furo*), and weasels (*Mustela nivalis*).

2. Rats: ship rats (*Rattus rattus*), Norway rats (*Rattus norvegicus*), and kiore (*Rattus exulans*).

3. Possums: brushtail possums (*Trichosurus vulpecula*).

In 2024, New Zealand's Department of Conservation published the biennial progress report (2021-
2023) to evaluate progress toward the seven interim targets. One target was achieved<sup>89</sup>, four are on
track to be achieved by 2025, and two will not be met<sup>90</sup>. New Zealand's situation is far from unique.
In fact, many islands — especially those in the Pacific — face similar challenges (Simberloff, 2010).

<footnote n="88"><sup>88</sup>Documents on the strategy, implementation plan, and progress report are available at www.doc.govt.nz/nature/pests-and-threats/predator-free-2050.</footnote>

<footnote n="89"><sup>89</sup>This relates to Goal 1 (“By 2025, we will increase by 1 million hectares (compared with 2016) the area of New Zealand mainland where predators are suppressed, through Predator Free 2050 project”).</footnote>

<footnote n="90"><sup>90</sup>This relates to Goal 3 (“By 2025, we will have eradicated all mammalian predators from New Zealand’s uninhabited offshore islands”) and Goal 4 (“By 2025, we will have developed a breakthrough science solution that would be capable of eradicating at least one small mammal predator from the New Zealand mainland”).</footnote>
The isolation of island habitats favors the evolution of endemic species, but this same isolation also makes these species exceptionally vulnerable to the threats posed by invasive species:

> "Because they evolved in the absence of selective pressures from mammalian grazers and predators, many endemic island plants and animals have evolutionarily lost or never developed defenses against these enemies and often lack a fear of them. Many island plants do not produce the bad-tasting, tough vegetative tissue that discourages herbivores, nor do they have the ability to resprout rapidly following damage. Some birds have lost the power of flight and simply build their nests on the ground." (Primack, 2014, pages 228-229).

This vulnerability of endemic species helps explain why invasive alien species have contributed to 60% of recent species extinctions, of which 90% occurred on islands<fnref n="91" /> (IPBES, 2023).

<figure><img src="image_78.png" /><figcaption>Figure 45: Average annual cost of invasive species (in 2017 $ mn)</figcaption></figure>

Source: IPBES (2023, figure 4.25, page 455).

Using the methodology and database developed by Diagne et al. (2021), IPBES (2023) estimated that the global annual economic cost of biological invasions amounted to $423 billion in 2019. Of these costs, 92% are due to the negative impacts of invasive alien species on nature's contribution to people or quality of life, while only 8% are related to the management of biological invasions. A significant proportion of these costs are attributed to reductions in food supply (66%), followed by impacts on human health, livelihoods, and water security. Notably, these costs have been observed to quadruple every decade (Figure 45). Over the past 50 years (1970–2019), the cumulative economic costs of biological invasions amount to $1.738 trillion when considering only the most reliable data (observed and high reliability). When potential and low-reliability costs are included, the total rises to $11.633 trillion (IPBES, 2023, Box 4.13, page 456).

<footnote n="91">⁹¹According to IPBES (2023, Figure SPM 3), 218 invasive alien species have caused 1215 local extinctions of native species.</footnote>
## 3.3 Pollution

According to the IPBES glossary, “pollution is the introduction of contaminants into the natural environment that cause adverse change”. This is a general definition that can lead to different interpretations. If we refer to the UN Data glossary, pollution is the “presence of substances and heat in environmental media (air, water, land) whose nature, location, or quantity produces undesirable environmental effects” and is the “activity that generates pollutants”. A pollutant or contaminant is a substance present in concentrations that can harm organisms (humans, plants, and animals) or exceed an environmental quality standard. In this context, concentration is a critical factor, as pollution is typically associated with quantities that excess thresholds, leading to a reduction in quality of life. We generally distinguish between point source and non-point source pollution:

* Point source pollution comes from a single, identifiable source, such as a pipe, drain, or specific location. It is easier to monitor and control because the source is clearly identified.

* Non-point source pollution comes from multiple diffuse sources rather than a single point of origin. It is often carried into water bodies by rainfall, snowmelt, or runoff.

It's impossible to give an exact number of pollutants in the world because many pollutants can undergo chemical reactions to form different compounds in the environment, creating secondary pollutants, and new chemical compounds are constantly being created by industrial processes. Nevertheless, we can categorize pollutants in three main ways:

* By source:

- Natural pollutants occur without human intervention, such as volcanic eruptions, forest fires, and natural decomposition processes;

- Anthropogenic pollutants result from human activities, including industrial emissions, vehicle exhaust, and agricultural practices;

* By chemical composition:

- Organic pollutants contain carbon-based compounds, such as pesticides, petroleum products, and plastic waste;

- Inorganic pollutants lack carbon in their structure, including heavy metals (such as mercury and lead), mineral acids, and inorganic salts;

* Through environmental persistence:

- Persistent pollutants remain in the environment for long periods of time without breaking down, such as certain pesticides, heavy metals, and some industrial chemicals;

- Non-persistent pollutants break down relatively quickly through natural processes, such as many biological wastes and some air pollutants.

### 3.3.1 Types of biodiversity pollution

Because there is a wide range of contaminants<fnref n="92" />, pollution can also be divided into different categories. The eight major types of pollution are listed below:

<footnote n="92">⁹²For example, the European Chemicals Agency has registered 26 865 unique chemical substances that can be placed on the European Economic Area market by companies with a valid registration as of November 2024 (https://echa.europa.eu/information-on-chemicals). In the United States, the non-confidential portion of EPA's Toxic Substances Control Act (TSCA) Inventory contains 86 770 chemicals, of which 42 377 are active as of May 2024 (www.epa.gov/tsca-inventory).</footnote>
1. Air pollution

According to the WHO glossary, “*air pollution is contamination of the indoor*<fnref n="93" /> or *outdoor*<fnref n="94" /> *environment by any chemical, physical or biological agent that modifies the natural characteristics of the atmosphere*”. It can harm living organisms, damage the natural environment, or degrade air quality. Pollutants can be in the form of solid particles, liquid droplets, or gases, and can be either natural (such as volcanic ash) or man-made (such as industrial emissions). Air pollutants can be classified as particulate matter (such as PM₂.₅, PM₁₀, ultrafine particles, and dust), primary pollutants (those emitted directly into the atmosphere, such as carbon monoxide CO, nitrogen oxides NOₓ, and sulfur dioxide SO₂), and secondary pollutants (those formed in the air through chemical reactions, such as acid rain, aerosols and ozone O₃). Air pollution measurement is the assessment of air quality, or the concentration of pollutants in the air. This is done using ground-based stations or satellite-based monitoring (remote sensing). Measurements are typically expressed in terms of concentration (e.g., milligrams per cubic meter) or parts per million/billion by volume (ppmv/ppbv).

2. Biological pollution

Biological pollution refers to the introduction of harmful or invasive living organisms into an ecosystem where they do not occur naturally. It includes invasive species, the spread of pathogens, and biologically active agents (such as some genetically modified organisms (GMOs) or antibiotic-resistant microbes). Biological pollution often intersects with air, chemical, and water pollution. For example, nutrient runoff from fertilizers (chemical pollution) creates conditions for harmful algal blooms (biological pollution). Similarly, cholera is an example of biological pollution, because it involves the contamination of water with a pathogenic microorganism, the bacterium *Vibrio cholerae*.

3. Chemical pollution

Chemical pollution refers to the release of harmful chemical substances into the environment — air, water, soil, or living organisms — causing adverse effects on ecosystems. Consequently, chemical pollution is often a component of other pollution categories: air pollution, plastic pollution, soil pollution, and water pollution. Given its significant impact and the serious challenges it poses to humanity, governments and the UN Environment Assembly (UNEA) are planning to establish a global intergovernmental science-policy panel on chemicals, waste, and pollution prevention. The number of chemical pollutants is unknown because there is no comprehensive inventory of chemical substances. However, Wang et al. (2020) estimated that more than 350 000 chemicals and chemical mixtures have been produced and synthesized by humans. Moreover, the global use of chemicals is expected to increase by 70% between 2020 and 2030 (Naidu et al., 2021, page 2), with the largest growth anticipated in China, which is projected to account for nearly 50% of the global chemical market by 2030. Of course, not all chemicals are harmful and dangerous, but a large proportion are. For example, the European Environment Agency (EEA) estimates that about 60% of the total volume consumed in Europe is hazardous to health, and that 8% of deaths can be attributed to hazardous chemicals<fnref n="95" />. It is not easy to find a universally accepted classification of hazardous chemicals in the context of biodiversity. However, in the context of industrial activities, the Globally Harmonized System

<footnote n="93">⁹³Contamination of the air inside a home or building, often caused by cooking, smoking, or poor ventilation. According to González-Martín et al. (2021), more than 5 million people die each year from diseases caused by indoor air pollution. The problem of exposure to indoor air pollution is growing as people spend more time indoors. In Europe, for example, people spend 90% of their time indoors.</footnote>

<footnote n="94">⁹⁴Pollution in the open air, often from industrial or vehicular sources.</footnote>

<footnote n="95">⁹⁵Source: www.eea.europa.eu/en/topics/in-depth/chemicals.</footnote>
Box 12: Silent Spring by Rachel Carson (1962)

Silent Springª is a landmark environmental book published in 1962 by Rachel Carson. It's considered one of the most influential environmental books ever written and is widely credited with launching the modern environmental movement. The book documents the harmful effects of pesticides on the environment and wildlife. Carson focused particularly on DDT, which was widely used after World War II. She showed how these chemicals not only harmed pests, but also accumulated in ecosystems, harming wildlife and humans. The book faced fierce opposition from the chemical industry, but captured widespread public attention and sparked debates about environmental health and the unregulated use of chemicals. It led to the eventual ban of DDT in the United States in 1972 and inspired stricter pesticide regulations worldwide.

<figure><img src="image_79.png" /></figure>

of Classification and Labelling of Chemicals (GHS) is an internationally recognized system for classifying and communicating the hazards of chemical substances and mixtures. The GHS defines a set of nine hazard classes, such as flammables, oxidizers, corrosives, and acute toxins, and divides each class into categories based on the severity of the hazard (Table 30). Another approach to classifying hazardous chemicals is by the source of contamination. This classification helps to understand the origin of these chemicals and their potential impact on the environment:

* Industrial emissions

These are chemicals released into the environment during industrial processes such as manufacturing, chemical production, and power generation. Common pollutants from industrial emissions include volatile organic compounds (VOCs), heavy metals (mercury, lead), persistent organic pollutants (POPs), and solvents, which can contaminate air, water, and soil.

* Agricultural runoff

Agricultural activities contribute significantly to chemical pollution, especially through runoff of pesticides, herbicides, fertilizers (containing nitrates and phosphates), and animal waste. These chemicals are often washed into rivers and lakes when it rains, contaminating the water and harming aquatic life.

<footnote>ªThe title refers specifically to the absence of birdsong in spring, traditionally a time when birds sing and nature comes back to life after winter.</footnote>
<figure><img src="image_80.png" /><figcaption>Table 30: Globally harmonized system of classification and labelling of chemicals (GHS) pictogram for hazardous substances</figcaption></figure>

Source: https://unece.org/transport/dangerous-goods/ghs-pictograms.

* Household and municipal waste

Household products, including cleaning products (containing solvents and disinfectants), pharmaceuticals, personal care products, paints, batteries, and plastics, contribute to pollution when disposed of improperly. Wastewater from homes and businesses can carry contaminants such as detergents, synthetic chemicals, and pharmaceuticals into sewage systems, which are not always fully treated before being released into the environment.

* Petroleum products

Oil spills and runoff from petroleum-related activities are also sources of chemical pollutants. Petroleum products such as gasoline, diesel, and oils, can have a devastating effect on aquatic ecosystems, because they are toxic to marine life and persist in the environment for long periods of time.

* Transportation emissions

Road vehicles, aircraft, and ships, especially those powered by fossil fuels, emit harmful pollutants such as nitrogen oxides (NOx), sulfur dioxide (SO2), carbon monoxide (CO), and particulate matter (PM) into the air. These pollutants contribute to air quality problems, acid rain, and human respiratory illnesses. Additionally, the particulate matter can affect soil and water quality.

An alternative to the previous classification is to divide hazardous chemicals into four categories<fnref n="96" />: conventional pollutants, heavy metals, persistent organic pollutants, and emerging

<footnote n="96">⁹⁶In both classifications, a chemical may belong to more than one category.</footnote>
contaminants. Conventional pollutants typically refer to pollutants that have been recog-
nized and regulated for many years (e.g., CO, NOₓ, SO₂, PM). Heavy metals are a group
of metallic elements that have a relatively high density and are toxic to humans and wildlife
even at low concentrations. In biodiversity, a density greater than 5 g/cm³ is used to define
them. Examples of heavy metals hazardous to human health<fnref n="97" /> include arsenic (As), cadmium
(Cd), chromium (Cr), lead (Pb), and mercury (Hg). According to the Stockholm Convention
on Persistent Organic Pollutants, POPs "are organic chemical substances, that is, they are
carbon-based. They possess a particular combination of physical and chemical properties such
that, once released into the environment, they remain intact for exceptionally long periods of
time (many years); they become widely distributed throughout the environment as a result of
natural processes involving soil, water and, most notably, air; they accumulate in the living or-
ganisms including humans, and are found at higher concentrations at higher levels in the food
chain; and they are toxic to both humans and wildlife." When this international environmental
treaty was signed in 2001, 12 POPs were recognized and classified into 3 categories: pesti-
cides (aldrin, chlordane, DDT, dieldrin, endrin, heptachlor, hexachlorobenzene HCB, mirex,
toxaphene), industrial chemicals (hexachlorobenzene HCB, polychlorinated biphenyls PCB),
and by-products (hexachlorobenzene HCB, polychlorinated dibenzo-p-dioxins PCDD and poly-
chlorinated dibenzofurans PCDF, polychlorinated biphenyls PCB). The Stockholm Convention
has been revised several times. As of December 2024, there are 32 POPs. The last category con-
cerns emerging contaminants, which are chemical substances that are not commonly monitored
or regulated, pose potential risks, and may be persistent. Examples of emerging contaminants
include pharmaceuticals and personal care products (PPCP), endocrine-disrupting chemicals
(EDC), micro and nanoplastics, antibiotic-resistant genes (ARG), among others (Wang et al.,
2024, Table 1, page 4). The challenge with emerging contaminants is tracking these substances
and assessing the potential risks posed by novel chemical mixtures. For example, Escher et
al. (2020) reported that "the number of new chemicals is rising, with the Chemical Abstract
Service Registry growing from 20 million to 156 million chemicals between 2002 and 2019",
which equates to approximately 20 000 new chemical products being synthesized every day.

4. Light pollution

Light pollution is the presence of unwanted, excessive, misdirected, or obtrusive artificial light that interferes with the natural environment. It occurs when artificial lighting disrupts the natural darkness of the night<fnref n="98" />, affecting processes such as wildlife migration, reproduction, and feeding. It is often the result of poor lighting design, over-illumination, or the scattering of light in the atmosphere. Only recently has light pollution been widely recognized as a significant threat to biodiversity and a growing environmental concern (Hölker et al., 2010). Although the full effects of light pollution are not yet known, we now have a better understanding of how it affects ecosystems, species, and human health<fnref n="99" />. Some well-known examples include disorientation of sea turtles, bird migration, insect disruption, human sleep disturbance, metabolic

> "For most of history, the only lights made by humans were naked flames. Daily life was governed by the times of sunrise and sunset, outdoor nighttime activities depended on the phase of the Moon, and viewing the stars was a common and culturally important activity. Today, the widespread deployment of outdoor

<footnote n="97">⁹⁷Note that some metals are essential to human health in trace amounts, meaning that they are necessary for proper biological functions and play critical roles in enzymes, metabolism, immune functions, protein synthesis, etc. Typical examples include calcium (Ca), copper (Cu), iron (Fe), potassium (K), magnesium (Mg), and zinc (Zn). However, even essential metals can be toxic in excess.</footnote>

<footnote n="98">⁹⁸Longcore and Rich (2004) distinguished between ‘astronomical light pollution’, which obscures the view of the night sky, and ‘ecological light pollution’, which alters the natural light regime in terrestrial and aquatic ecosystems.</footnote>

<footnote n="99">⁹⁹See the special issue *Light Pollution* (Volume 380, Issue 6650) published by *Science* on June 16, 2023. Below is the introduction to this special issue:</footnote>
Box 13: Persistent organic pollutants

According to the Stockholm Convention on Persistent Organic Pollutants (Annex D, pages 74-75, 2023 version), the assessment of POPs focuses on four key properties<sup>a</sup>:

* **Persistence**

The chemical must resist degradation by environmental processes and persist in the environment for long periods of time. In particular, its half-life must be greater than 2 months (60 days) in water or 6 months (180 days) in soil/sediment.

* **Bioaccumulation**

The chemical must accumulate in the tissues of living organisms, and increases in concentration as it moves up the food chain (biomagnification). In particular, its bio-concentration factor (BCF) is greater than 5 000 or its log $K_{ow}$ (n-octanol-water partition coefficient) is greater than 5.

* **Potential for long-range environmental transportation**

The chemical can travel long distances through air and water, affecting ecosystems far from its original source. In particular, its half-life in air must be greater than 2 days, which is equivalent to a distance of 690 km, assuming an average wind speed of 4 m/s (Scheringer et al., 2012, page 384).

* **Adverse effects**

The chemical has a significant level of toxicity or ecotoxicity.

Below we report figures of different chemicals, which has been collected by Scheringer et al. (2012, Supporting material):

<table><thead><tr><td>CAS</td><td>Chemical</td><td>Half-life</td><td>log K<sub>ow</sub></td><td>Transportation</td><td>Toxicity</td></tr></thead><tbody><tr><td>50-29-3</td><td>DDT</td><td>289</td><td>6.85</td><td>3.11</td><td>Yes</td></tr><tr><td>53-19-0</td><td>Mitotane</td><td>130</td><td>5.87</td><td>2.46</td><td>Yes</td></tr><tr><td>57-74-9</td><td>Chlordane</td><td>1 440</td><td>6.24</td><td>2.12</td><td>Yes</td></tr><tr><td>95-94-3</td><td>Tetrachlorobenzene</td><td>86</td><td>4.61</td><td>130</td><td>Yes</td></tr><tr><td>118-74-1</td><td>Hexachlorobenzene</td><td>229</td><td>5.79</td><td>158</td><td>Yes</td></tr><tr><td>307-43-7</td><td>Perflubrodec</td><td>5 670</td><td>7.91</td><td>10<sup>6</sup></td><td>Yes</td></tr><tr><td>307-45-9</td><td>Perfluorodecane</td><td>7 960</td><td>7.51</td><td>10<sup>6</sup></td><td>No</td></tr><tr><td>2172-49-8</td><td>Propionyl chloride</td><td>192</td><td>6.45</td><td>2.13</td><td>Yes</td></tr><tr><td>3182-02-3</td><td>Dichlorophenyl</td><td>344</td><td>6.08</td><td>2.35</td><td>Yes</td></tr><tr><td>13947-96-1</td><td>Trichloromethyl</td><td>213</td><td>4.86</td><td>198</td><td>Yes</td></tr><tr><td>25267-15-6</td><td>Polychloropinene</td><td>4 410</td><td>8.09</td><td>10.80</td><td>No</td></tr><tr><td>27753-52-2</td><td>Nonabrom biphenyl</td><td>2 060</td><td>11.77</td><td>439</td><td>Yes</td></tr></tbody></table>

By applying the screening criteria of persistence, bioaccumulation, long-range transport potential and toxicity to a set of 93 144 organic chemicals, they identified 510 chemicals that exceed all four criteria and can be considered potential POPs. They also estimated that the number of potential POPs ranges from 190 (lower bound) to 1 200 (upper bound) chemicals.

<footnote><sup>a</sup>Source: www.pops.int.</footnote>
disorders, and increased risk of some cancers (Walker et al., 2020). Recently, Anderson et al. (2024) estimated that the annual loss of ecosystem service value due to light pollution is $3.4 trillion, which is about 3% of the total global value of ecosystem services and 3% of global GDP.

## 5. Noise pollution

Noise pollution refers to unwanted, disturbing, or excessive<fnref n="100" /> sounds that negatively affect the health and well-being of humans, animals, and the environment. It typically results from human activities and disrupts natural auditory environments. The emergence of noise pollution as a biodiversity threat precedes that of light pollution, with research studies dating back to the 1990s. However, as with light pollution, much remains to be learned about its full extent and long-term consequences. To date, the impacts of noise pollution are evident in both human health — such as hearing loss, sleep disturbance, mental health issues, and cognitive impairments — and wildlife — where it disrupts communication, leads to habitat abandonment, and interferes with pollination processes. Among these effects, marine noise pollution is a well-documented issue (Di Franco et al., 2020; Solé et al., 2023) because fish rely on sound for essential activities such as mating calls, territorial defense, predator alerts, and navigation during migration. Underwater communication is vital to their survival, but can be severely disrupted by shipping traffic, sonar noise and other anthropogenic sounds.

## 6. Plastic pollution

Plastic pollution is the accumulation of plastic materials and particles in the environment. Plastics are a wide range of synthetic or semi-synthetic materials made from polymers derived from fossil fuels such as natural gas or petroleum. In general, plastic pollutants are categorized by size as nano-, micro-, or macro-debris. Plastics pose a critical environmental threat to wildlife through multiple mechanisms: direct physical harm through suffocation and entanglement, and chemical toxicity through leaching. A particularly insidious threat comes from micro-plastics — fragments smaller than 5 mm — which are readily ingested by both marine and terrestrial organisms. These particles not only accumulate throughout the food chain, but also act as vectors for concentrated toxins and pollutants. When ingested, they can trigger cascading health effects, compromising animals' immune systems, disrupting endocrine function and impairing reproductive capabilities, ultimately threatening species survival rates. Plastic pollution is pervasive and highly persistent in the environment due to slow natural degradation processes. This explains its widespread presence in diverse ecosystems around the world, including deserts, farms, mountaintops, oceans, and even Arctic snow (MacLeod et al., 2021). Furthermore, plastic emissions are increasing and are projected to continue rising, even under optimistic waste reduction scenarios. Figure 46 shows the evolution of global thermoplastic production<fnref n="101" /> since 1950 and its projections to 2050. In 1950 the production was less

> electric lighting means that the night is no longer dark for most people — few can see the Milky Way from their homes. Outdoor lighting has many legitimate uses that have benefited society. However, it often leads to illumination at times and locations that are unnecessary, excessive, intrusive, or harmful: light pollution.” (Smith et al., 2023).

<footnote n="100">¹⁰⁰Unwanted sound refers to any unpleasant or disruptive noise. Disturbing sounds interfere with daily activities like sleeping, working, or communicating. Excessive sounds are those that are too loud or too frequent.</footnote>

<footnote n="101">¹⁰¹It is difficult to obtain reliable figures on global plastics production because the definition of plastics is not standardized and because of double counting in production statistics. Thermoplastics are a type of plastic that becomes soft and malleable when heated and hardens when cooled. They account for about 85% of all plastics produced worldwide. The other major category of plastics is thermosets, which, unlike thermoplastics, cannot be remelted once formed.</footnote>
<figure><img src="image_81.png" /><figcaption>Figure 46: Global production of thermoplastics with projections, 1950–2050 (in Mt)</figcaption></figure>

Source: www.iea.org/data-and-statistics/charts/production-of-key-thermoplastics-1980-2050.

than 2 million tonnes, in 2023 it was 414 million tonnes, and we expect a production of 590 million tonnes in 2050. The expected annual growth rate over the next 30 years is 1.3% — lower than the 4.6% annual growth observed over the past three decades, but still significant. This indicates that plastics production will continue to grow, making the search for solutions to establish a circular economy an ongoing and critical discussion. According to OECD (2022), approximately 25% of plastic waste is mismanaged, with a small fraction (less than 1%) eventually being transported into the oceans. This has led to the formation of garbage patches<fnref n="102" />. One of the best-known plastic accumulation zones is the Great Pacific Garbage Patch (GPGP), located in the subtropical waters between California and Hawaii. This patch covers an area of approximately 1.6 million square kilometers — comparable to the size of Mongolia or Iran. A study by Lebreton et al. (2018) estimated that at least 79 000 tonnes (ranging between 45 000 and 129 000 tonnes) of marine plastics are currently floating within the GPGP. Notably, over 75% of the mass of the GPGP consists of debris larger than 5 centimeters, with discarded fishing nets accounting for at least 46% of the total. While microplastics make up only 8% of the total mass, they account for a staggering 94% of the estimated 1.8 trillion (ranging from 1.1 to 3.6 trillion) pieces of plastic floating in the region. About 1 600 rivers are responsible for 80% of marine plastic pollution, which is estimated to be between 0.8 and 2.7 million tonnes of plastic waste discharged into the oceans annually (Meijer et al., 2021). The top 10 plastic-emitting rivers are Pasig (Philippines), Tullahan (Philippines), Ulhas (India), Klang (Malaysia), Meycauayan (Philippines), Pampanga (Philippines), Libmanan (Philippines), Ganges (India), Rio

<footnote n="102">¹⁰²Vast gyres of marine debris created by ocean currents and the increasing influx of plastic pollution from human activities</footnote>
Grande de Mindanao (Philippines), and Agno (Philippines) (Meijer et al., 2021, Table S5). As a result<fnref n="103" />, Asia accounts for 81% of marine plastic pollution, followed by Africa (8%), South America (5.5%) and North America (4.5%).

## 7. Soil pollution

Soil pollution (or soil contamination) is the presence or accumulation of toxic substances, harmful chemicals, salts, pathogens, or other contaminants in soil that adversely affect soil quality, reduce soil fertility, and pose risks to human health and ecosystems. The most common sources of soil pollution are industrial activities (e.g., chemical pollutants, heavy metals, radioactive contaminants), agricultural practices (e.g., soil degradation and the use of fertilizers, pesticides and herbicides), waste disposal and mining (e.g., petroleum hydrocarbons, solvents). The impacts of soil pollution are many, but the most important are health risks, food security<fnref n="104" />, ecosystem degradation and habitat loss. A typical example of soil pollution is the use of nitrogen-based products (e.g., ammonium nitrate, ammonium sulfate) commonly found in fertilizers and pesticides. Stevens et al. (2004) and Clark and Tilman (2008) conducted extensive studies on the long-term effects of chronic, low-level nitrogen deposition in prairie grasslands. Their research showed that even modest nitrogen inputs significantly reduced plant species diversity over time by favoring nitrogen-tolerant species, ultimately disrupting ecological balance. These findings were further supported by Bobbink et al. (2010), whose comprehensive synthesis of the effects of nitrogen deposition on terrestrial plant diversity showed that excessive nitrogen inputs fundamentally alter soil chemistry. Their work showed that this change creates conditions that favor fast-growing species while reducing overall biodiversity in different ecosystems.

## 8. Water pollution

Water pollution is the contamination of water bodies (e.g., rivers, lakes, oceans, groundwater, and streams) by harmful substances that degrade water quality and make water unsafe for drinking, swimming, agriculture, and other uses. It occurs when pollutants such as chemicals, waste, or microorganisms are discharged into water systems without adequate treatment to remove harmful compounds. Water pollution also includes thermal (or heat) pollution, which occurs when hot water is discharged from industrial processes, raising water temperatures. This increase in temperature depletes oxygen levels and disrupts species adapted to cooler environments. This example shows that water pollution is not a single phenomenon, but comes in many forms. The same is true for other types of pollution. This diversity presents a challenge in accurately measuring pollution. For water pollution in particular, there are several ways to measure it. The five most common are: (1) pH level, which measures the acidity or alkalinity of water (normal readings range from 6.5 to 8.5); (2) biological oxygen demand (BOD), which measures the amount of oxygen required by microorganisms to break down organic matter (high BOD indicates high levels of organic pollution because microorganisms require more oxygen); (3) turbidity, which measures the presence of suspended solids such as silt, clay, or organic matter (high turbidity can harm aquatic organisms and block sunlight needed for photosynthesis); (4) dissolved oxygen (DO), which measures the amount of dissolved oxygen in the water (low levels indicate organic pollution or high nutrient loading, which leads to oxygen

<footnote n="103">¹⁰³The top 15 countries contributing to marine plastic pollution are the Philippines, India, Malaysia, China, Indonesia, Brazil, Vietnam, Bangladesh, Thailand, Nigeria, Turkey, Cameroon, Sri Lanka and Guatemala.</footnote>

<footnote n="104">¹⁰⁴For example, Zhang et al. (2015) emphasized that soil contamination by heavy metals is a major concern in China, posing a significant risk to food safety and public health. They found that 10.18% of farmland soils in China are polluted with heavy metals, primarily cadmium (Cd), mercury (Hg), copper (Cu), and Nickel (Ni). Furthermore, approximately 13.86% of grain production in China is potentially contaminated with heavy metals.</footnote>
depletion); and (5) nitrate and phosphate levels (excessive nutrients lead to eutrophication, which causes algal blooms and oxygen depletion). However, this list is far from exhaustive. For example, Syeed et al. (2023) list a total of 69 water quality parameters (6 biological indicators, 10 physical indicators, and 53 chemical indicators<fnref n="105" />) as represented in Figure 47.

<figure><img src="image_82.png" /><figcaption>Figure 47: Taxonomy of the 69 water quality parameters along their natural factors (biological, physical, chemical)</figcaption></figure>

Source: Syeed et al. (2023, Figure 5, page 7).

<footnote n="105">¹⁰⁵The 53 chemical measures are pH, total dissolved solid (TDS), oxidation-reduction potential (ORP), dissolved oxygen (DO), ammonia (NH₃), colored dissolved organic matter, Sulphide (S²⁻), chemical oxygen demand (COD), biochemical oxygen demand (BOD), chloride (Cl⁻), nitrate (NO₃⁻), salinity, tryptophan (C₁₁H₁₂N₂O₂), bicarbonate (NaHCO₃), alkalinity (HCO₃⁻), total hardness as CaCO₃, arsenic (As), zinc (Zn), phosphate (PO₄³⁻), chlorine (Cl), fluoride (F⁻), aluminum (Al), chromium (Cr), copper (Cu), iron (Fe), nitrogen (N) total, potassium (K), organic matter by KMnO₄, barium (Ba), carbonate (HCO₃⁻), chromium hexavalent (Cr(VI)), hydrocarbons (CₙH₂n+₂), sulfate (SO₄²⁻), hydrogen sulphide as H₂S, beryllium (Be), dissolved organic carbon (DOC), silver (Ag), phosphorus (P), carbon tetrachloride (CCl₄), iodine (I), tin (Sn), Boron (B), manganese (Mn), mercury (Hg), nickel (Ni), selenium (Se), lead (Pb), cyanide (CN⁻), pesticides, nitrogen (N), cadmium (Cd), calcium (Ca) and sodium (Na).</footnote>
Box 14: Environmental toxicology and ecotoxicology

The study and assessment of pollution impacts fall under the disciplines of environmental toxicology and ecotoxicology. Environmental toxicology primarily focuses on how toxic substances — such as pollutants, chemicals, heavy metals, and pesticides — affect humans, animals, plants, and other living organisms. It also investigates the mechanisms by which these contaminants enter the environment, their distribution, and how they are metabolized or eliminated by organisms. Ecotoxicology, while closely related, is more concerned with studying pollution at the ecosystem level rather than focusing on individual organisms. It examines how contaminants affect populations, communities, and ecological processes. Despite this distinction, there is considerable overlap between the two fields. For instance, two foundational textbooks *Environmental Toxicology* (Wright and Welbourn, 2002) and *Fundamentals of Ecotoxicology* (Newman, 2019) cover substantially similar content and concepts.

### 3.3.2 Dose-response relationship

The dose-response model<fnref n="106" /> describes how the amount of a contaminant (dose) affects health or environmental outcomes (response). Toxicologists use this model to understand how different doses of pollutants cause different levels of harm.

<figure><img src="image_83.png" /><figcaption>Figure 48: Sigmoidal dose-response curve</figcaption></figure>

Figure 48 shows a typical dose-response curve, with the applied dose plotted on the x-axis and the observed response plotted on the y-axis. The curve is generally sigmoidal in shape and can be classified into two distinct forms depending on the nature of the response:

* Increasing response

In this form, the response increases with the concentration of the substance. For example, mortality rates may increase with increasing levels of air, soil, or water pollution.

<footnote n="106">¹⁰⁶In the scientific literature, this relationship is also known as the concentration-response relationship or exposure-response relationship. The World Health Organization (WHO) and the European Environment Agency (EEA) use the term concentration-response function (CRF).</footnote>
• Decreasing response

In this form, the response decreases with increasing concentration. For example, physical char- acteristics such as production levels, weight, or height may decrease in response to increasing levels of air, soil, or water pollution.

According to Ritz et al. (2015), the (generalized) log-logistic function is the most commonly dose-response model<fnref n="107" />:

$$y = f(x; \alpha, \beta, y_{\min}, y_{\max}) = y_{\min} + \frac{y_{\max} - y_{\min}}{1 + \exp(-\beta(\ln(x) - \ln(\alpha)))} = y_{\min} + \frac{y_{\max} - y_{\min}}{1 + \left(\frac{x}{\alpha}\right)^{-\beta}} \quad (26)$$

where $x \ge 0$ is the concentration rate of the dose, $y \in (y_{\min}, y_{\max})$ is the response, $\alpha > 0$ is the scale parameter, and $\beta \in \mathbb{R}$ is the shape parameter. If $\beta > 0$, the dose-response curve is increasing, otherwise it is decreasing<fnref n="108" />. The second popular function is the log-normal model:

$$y = y_{\min} + (y_{\max} - y_{\min}) \Phi \left( \beta \ln \left( \frac{x}{\alpha} \right) \right) \quad (27)$$

Ritz (2010, Table 1, page 226) listed another class of dose-response model based on the Weibull distribution<fnref n="109" />:

$$y = y_{\min} + (y_{\max} - y_{\min}) \exp \left( - \left( \frac{x}{\alpha} \right)^{\beta} \right) \quad (29)$$

The three previous classes of models ignore the hormesis phenomenon, where a substance or environmental factor produces opposite effects at low and high doses. Specifically, the substance may have a stimulatory effect at low doses, while the same substance becomes toxic at high doses. To account for hormesis, a popular approach is to include a bump term in the log-logistic model:

$$y = y_{\min} + \frac{y_{\max} - y_{\min} + \gamma g(x)}{1 + \left(\frac{x}{\alpha}\right)^{-\beta}} \quad (30)$$

where $\gamma \ge 0$ and $g(x)$ is the bump function. In the Brain-Cousens model, $g(x) = x$, whereas in the Cedergreen-Ritz-Streibig model, $g(x) = \exp(-x^{-\eta})$ (Cedergreen et al., 2005). Figure 49 shows the different dose-response models and the biological phenomenon of hormesis. The parameters are $\alpha = 20$, $\beta = -3.5$, $y_{\min} = 0$, $y_{\max} = 5$. The Brain-Cousens model uses $\gamma = 0.2$, while the parameters of the Cedergreen-Ritz-Streibig model are $\gamma = 3$ and $\eta = 0.4$. An example of hormesis in biodiversity toxicology is provided by Eze et al. (2021), who analyzed 15 plant species to assess their tolerance to diesel fuel toxicity. The dose-response analysis showed that increasing diesel fuel concentrations in soil generally resulted in a consistent decrease in biomass for 13 species. However, the study found that hydrocarbons had a statistically significant hormetic effect on alfalfa (Medicago sativa), where low concentrations of diesel fuel stimulated growth, but higher concentrations resulted in a decrease in biomass. Carbon monoxide and oxygen are other examples of hormesis. Similarly, radiation hormesis refers to the hypothesis that low doses of ionizing radiation may induce beneficial biological effects, such as enhanced DNA repair mechanisms or improved immune system function. However, while the concept of radiation hormesis is intriguing and has supporting data, it remains controversial, particularly in public health and regulatory contexts (Calabrese and Mattson, 2017).

$$y = y_{\min} + (y_{\max} - y_{\min}) \left( 1 - \exp \left( - \left( \frac{x}{\alpha} \right)^{\beta} \right) \right) \quad (28)$$

<footnote n="107">¹⁰⁷The log-logistic probability distribution corresponds to $y_{\min} = 0$, $y_{\max} = 1$ and $\beta > 0$.</footnote>

<footnote n="108">¹⁰⁸The increasing dose-response curve in Figure 48 was generated using the following set of parameters: $\alpha = 20$, $\beta = 3.5$, $y_{\min} = 0$ and $y_{\max} = 100$. The decreasing dose-response curve uses $\alpha = 15$, $\beta = -3.5$, $y_{\min} = 0$ and $y_{\max} = 5$.</footnote>

<footnote n="109">¹⁰⁹This model is called Weibull-1 and generates an increasing response. To model a decreasing response, we consider the Weibull-2 function:</footnote>
<figure><img src="image_84.png" /><figcaption>Figure 49: Hormesis biological phenomenon</figcaption></figure>

It is clear that a dose-response model can be thought of as a nonlinear regression model, where the dependent variable *y* represents the response or effect, and the independent variable *x* is the dose or concentration. In general, different types of response are distinguished: (1) continuous response (measures a continuous variable, such as biomass); (2) binary response (measures the presence or absence of a specific event, such as dead/alive); (3) time-to-response (measures the time it takes for a response to occur after exposure to a dose, such as the time to onset of toxicity after exposure to a chemical); (4) discrete or categorical response (the response falls into one of several ordered categories, such as none, mild, moderate, or severe effects). From a dose-response model where the response is the percentage of individuals who respond to a given dose of a drug, we can calculate the statistic EDₚ, which is the dose required to achieve the desired therapeutic effect in *p*% of the population. When *p* = 50%, we obtain the median effective dose, ED₅₀, which is the dose of the drug that produces the therapeutic response in 50% of the population. ED₅₀ is a standard statistic in pharmacology. By analogy, we can define the median toxic dose TD₅₀ and the median lethal dose LD₅₀, which represent the dose at which 50% of the population will experience a specific toxic effect or die, respectively. When the dose refers to the concentration of a pollutant or chemical, we use the terms half-maximal effective concentration EC₅₀ or half-lethal concentration LC₅₀ instead. In the log-logistic and log-normal models, the median effective concentration corresponds to the parameter *α* of the function<fnref n="110" />:

$$y = \frac{y_{\max} + y_{\min}}{2} \Leftrightarrow x = EC_{50} = \alpha$$

<footnote n="110">¹¹⁰Notice that $\frac{y_{\max} + y_{\min}}{2} = y_{\min} + \frac{y_{\max} - y_{\min}}{2}$. This implies that $(\frac{x}{\alpha})^{-\beta} = 1$ in the case of the log-logistic model and $\Phi(\beta \ln(\frac{x}{\alpha})) = \frac{1}{2}$ in the case of the log-normal model.</footnote>
This result is not surprising because dose-response curves are related to the famous Hill equation<fnref n="111" /> (Goutelle et al., 2008):

$$E = E_0 + (E_{\max} - E_0) \frac{[C]^n}{EC_{50}^n + [C]^n}$$

where E is the effect produced by the drug/agonist at concentration [C], E₀ is the baseline response, Emax is the maximum effect, EC₅₀ is the concentration that produces half the maximum effect, and n is the Hill coefficient (or the slope of the curve).

<figure><img src="image_85.png" /><figcaption>Figure 50: Threshold concentration</figcaption></figure>

Because dose-response curves help identify relationships between exposure levels and effects, they are widely used to set safe exposure limits (threshold concentrations) to prevent adverse health outcomes in humans and adverse effects on the environment. For instance, the World Health Organization has developed a dose-response framework to measure the risk of chemicals on health (World Health Organization, 2009). Similarly, in 2021, the US Environmental Protection Agency (EPA) published tabulated dose-response assessments for both chronic and acute exposures to air pollutants<fnref n="112" />. The European Union has long used dose-response curves linking traffic noise to annoyance and sleep disturbance to inform and shape public policy on noise pollution mitigation. To understand how thresholds and safe exposure limits are set, let's examine the dose-response curves

$$\frac{E - E_0}{E_{\max} - E_0} = \frac{1}{1 + \left( \frac{[C]}{EC_{50}} \right)^{-n}}$$

and we identify the parameters of the log-logistic dose-response model: α = EC₅₀, β = n, ymin = E₀, and ymax = Emax.

<footnote n="111">¹¹¹We have:</footnote>

<footnote n="112">¹¹²Tables with values for long-term (chronic) inhalation and oral exposure and values for short-term (acute) inhalation exposure are available at www.epa.gov/fera/dose-response-assessment-assessing-health-risks-associated-exposure-hazardous-air-pollutants.</footnote>
in Figure 50. The figure shows two functions: one that measures toxicity and another that measures mortality. From these curves, we can determine critical values including TC₅₀ and LC₅₀, as well as two key regulatory statistics:

* NOAEL (no observed adverse effect level) represents the highest dose or concentration at which no adverse effects are observed. This metric is fundamental to establishing maximum safe exposure levels for humans and ecosystems, as it indicates the threshold below which a substance demonstrates no harmful effects.

* LOAEL (lowest observed adverse effect level) is the lowest dose or concentration at which adverse effects are first observed. This measure helps policymakers identify the point at which a substance begins to pose a risk.

Figure 50 illustrates NOAEL and LOAEL values for both toxic and lethal effects. For toxicity, the data shows a NOAEL of 10 µg/m³ and a LOAEL of 20 µg/m³, suggesting a potential threshold concentration of 10 µg/m³. In contrast, if mortality alone is considered, the threshold concentration could be set as high as 40 µg/m³. In practice, the setting of threshold concentrations involves several considerations. While theoretical best practice suggests using the NOAEL as the threshold, regulatory agencies often default to the LOAEL. To ensure adequate protection for vulnerable populations — including children, elderly individuals, and those with pre-existing health conditions — authorities often apply safety factors to these baseline values. The final threshold concentration is then calculated by dividing either the NOAEL or LOAEL by the appropriate safety factor.

**Remark 10** In the case of pollution, safe exposure limits are set primarily in terms of toxic effects. In the case of medicine and pharmacology, agencies use both therapeutic effects, toxic effects, and lethal effects, i.e., there is a trade-off between benefits and risks.

### 3.3.3 Application to air quality standards

The previous framework has been extensively used to set air quality standards. In 2000, the World Health Organization published a report entitled "Guidelines for Air Quality". This report has been updated twice, in 2006 and 2021 (World Health Organization, 2006, 2021). The purpose of these reports is to provide recommended limits for key air pollutants to protect public health. The methodology is based on the concentration-response function (CRF), which is another term for the dose-response relationship. In Table 31, we present the WHO air quality guidelines (AQG), which represent the concentration levels of pollutants below which adverse health effects are expected to be minimal (World Health Organization, 2021). For example, the AQG level for particulate matter<fnref n="113" /> PM₂.₅ is 5 µg/m³ on an annual basis. We have also included air quality standards for several regions and countries (Brazil, China, EU, India, US, and Switzerland), which generally correspond to the limit values established to protect human health. For a long time, air quality standards in Europe were governed by Directive 2008/50/EC. Since October 2024, the EU has introduced a new directive (2024/2881) that sets limit values for the year 2030. It is important to note that the limit values depend on the time period, but they can also vary depending on the objective. For example, there are different limits for the protection of human health, vegetation, and ecosystems. In the United States, limits are set under the Clean Air Act, which was last amended in 1990. For some pollutants, two separate standards are set: primary standards (which focus on protecting the health of sensitive

<footnote n="113">¹¹³Particulate matter consists of microscopic particles of solid or liquid substances suspended in the air. They are generally divided into three categories. Inhalable coarse particles, designated PM₁₀, are particles with a diameter of 10 µm or less. Fine particles, designated PM₂.₅, are particles with a diameter of 2.5 µm or less. Finally, ultrafine particles (UFP) are particles with a diameter of 100 nm or less.</footnote>
<table><caption>Table 31: Air quality standards (limit values for the protection of human health)</caption><thead><tr><th>Pollutant</th><th>Symbol</th><th>Unit</th><th>Period</th><th>WHO 2021</th><th>EU 2008</th><th>2030</th><th>US 1990</th><th>China 2012</th><th>India 2009</th><th>Brazil 1990</th><th>Switzerland 2024</th></tr></thead><tbody><tr><td rowspan="3">Particulate matter</td><td>PM<sub>2.5</sub></td><td>µg/m<sup>3</sup></td><td>Annual</td><td>5</td><td>25</td><td>10</td><td>9/15</td><td>15/35</td><td>40</td><td></td><td>10</td></tr><tr><td rowspan="2">PM<sub>10</sub></td><td rowspan="2"></td><td>24-hour</td><td>15</td><td></td><td>25</td><td>35</td><td>35/75</td><td>60</td><td></td><td></td><td></td></tr><tr><td>Annual</td><td>15</td><td>40</td><td>20</td><td></td><td>40/70</td><td>60</td><td></td><td>20</td><td></td></tr><tr><td></td><td></td><td></td><td>24-hour</td><td>45</td><td>50</td><td>45</td><td>150</td><td>50/150</td><td>100</td><td></td><td>50</td></tr><tr><td>Ozone</td><td>O<sub>3</sub></td><td>µg/m<sup>3</sup></td><td>Peak-season</td><td>60</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Nitrogen dioxide</td><td rowspan="3">NO<sub>2</sub></td><td rowspan="3">µg/m<sup>3</sup></td><td>8-hour</td><td>100</td><td>120</td><td>120</td><td>137</td><td>100/160</td><td>100</td><td></td><td></td></tr><tr><td>Annual</td><td>10</td><td>40</td><td>20</td><td>100</td><td>40</td><td>30/40</td><td>100</td><td>30</td><td></td></tr><tr><td>24-hour</td><td>25</td><td></td><td>50</td><td></td><td>80</td><td>80</td><td></td><td>80</td><td></td></tr><tr><td rowspan="3">Sulfur dioxide</td><td rowspan="3">SO<sub>2</sub></td><td rowspan="3">µg/m<sup>3</sup></td><td>1-hour</td><td>200</td><td>200</td><td>200</td><td>188</td><td>200</td><td></td><td>190/320</td><td></td></tr><tr><td>Annual</td><td>40</td><td>125</td><td>50</td><td>26</td><td>20/60</td><td>20/50</td><td>40/80</td><td>30</td><td></td></tr><tr><td>24-hour</td><td>1 hour</td><td>350</td><td>350</td><td>196</td><td>150/500</td><td></td><td>80</td><td>100/365</td><td>100</td></tr><tr><td></td><td></td><td></td><td>10-minute</td><td>500</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="3">Carbon monoxide</td><td rowspan="3">CO</td><td rowspan="3">mg/m<sup>3</sup></td><td>24-hour</td><td>4</td><td></td><td>4</td><td></td><td>4</td><td></td><td>2</td><td>10</td><td></td></tr><tr><td>8-hour</td><td>10</td><td>10</td><td>10</td><td>10</td><td></td><td></td><td>4</td><td>40</td><td></td></tr><tr><td>1-hour</td><td>35</td><td></td><td>40</td><td></td><td>10</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td>15-minute</td><td>100</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Lead</td><td rowspan="2">Pb</td><td rowspan="2">µg/m<sup>3</sup></td><td>Annual</td><td>0.5</td><td>0.5</td><td>0.5</td><td>0.5</td><td>0.5</td><td>0.5</td><td></td><td></td></tr><tr><td>3-month</td><td></td><td></td><td></td><td>0.15</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Amonia</td><td>NH<sub>3</sub></td><td>µg/m<sup>3</sup></td><td>Annual</td><td></td><td></td><td></td><td></td><td></td><td></td><td>100</td><td></td></tr><tr><td>Arsenic</td><td>As</td><td>ng/m<sup>3</sup></td><td>Annual</td><td>6.6</td><td>6</td><td>6</td><td></td><td></td><td></td><td>6</td><td></td></tr><tr><td>Benzene</td><td>C<sub>6</sub>H<sub>6</sub></td><td>µg/m<sup>3</sup></td><td>Annual</td><td>1.7</td><td>5</td><td>3.4</td><td></td><td></td><td></td><td>5</td><td></td></tr><tr><td>Benzo[a]pyrene</td><td>BaP</td><td>ng/m<sup>3</sup></td><td>Annual</td><td>0.12</td><td></td><td>1</td><td></td><td></td><td>1</td><td>1</td><td></td></tr><tr><td>Cadmium</td><td>Cd</td><td>ng/m<sup>3</sup></td><td>Annual</td><td>5</td><td>5</td><td>5</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Nickel</td><td>Ni</td><td>ng/m<sup>3</sup></td><td>Annual</td><td>25</td><td>20</td><td>20</td><td></td><td></td><td>20</td><td></td><td></td></tr><tr><td>Total suspended particles</td><td>TSP</td><td>µg/m<sup>3</sup></td><td>Annual</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>60/80</td></tr></tbody></table>

Source: World Health Organization (2021, Tables 0.1 & 0.2, pages xvii-xviii), Directive 2008/50/EC (https://eur-lex.europa.eu/eli/dir/2008/50/oj), EU Directive 2024/2881 (https://eur-lex.europa.eu/eli/dir/2024/2881/oj), NAAQS Table (www.epa.gov/criteria-air-pollutants/naaqs-table), www.transportpolicy.net/topic/air-quality-standards (Brazil, China and India), Switzerland OAPC (www.fedlex.admin.ch/eli/cc/1986/208_208_208) & Au-thor's calculations.
populations, such as asthmatics, children, and the elderly) and secondary standards (which focus on protecting the welfare of the public, including animals, crops, vegetation, and buildings). In China, India, and Brazil, air quality standards may also include two separate limits. The first generally applies to special regions, such as national parks and protected areas, while the second applies to all other areas.

**Remark 11** Similar figures are established for other quality standards (e.g., noise pollution, soil pollution, water pollution), but they are less comprehensive than those for air quality<fnref n="114" />.

### 3.3.4 Air quality index

An air quality index (AQI) is a standardized system used to communicate air quality to the public in an understandable way. It provides a single number that indicates the level of air pollution and its potential impact on health. The concept of air quality indices was first developed by academics in the 1950s and later adopted by environmental agencies, typically at the federal, provincial, or municipal level, in the 1960s and 1970s (Ott and Thorn, 1976; Ott, 1978). The first country-wide AQI systems were introduced in Canada (1970) and the United States (1976), followed by several European countries in the 1980s. Today, most countries have established their own air quality index systems. While these systems share some common features and have become more consistent over time, they are still not uniform. They often differ in the pollutants measured, the critical thresholds used, and, most importantly, the scales on which their indices are reported, making cross-country comparisons difficult. For example, Canada's AQI scale ranges from 1 to 10+, while China's ranges from 0 to 500. In Europe, the index typically ranges from 0 to 100+, and in Australia from 0 to 200+. These variations highlight the difficulties of harmonizing AQI systems across regions, despite their common goal of informing and protecting public health. The World Health Organization has published numerous guidelines to harmonize standards and reduce disparities between countries. However, we are still far from a single global AQI system. Nevertheless, several initiatives are helping to compare air quality indices across countries. One of the most prominent is the World Air Quality Index project (aqicn.org and waqi.info), which collects data from government monitoring stations in over 100 countries.

Although there is no globally harmonized AQI system, the one developed by the US EPA is undoubtedly one of the most widely used and has served as a model for many other countries' AQI frameworks. For example, the US AQI system is also used by the World Air Quality Index project. The US AQI is calculated based on five key pollutants: carbon monoxide (CO), nitrogen dioxide (NO₂), ground-level ozone (O₃), particulate matter (PM₁₀ and PM₂.₅), and sulfur dioxide (SO₂). For each pollutant, a sub-index is calculated based on its concentration:

$$I_j = I_{j,\text{low}} + \left( \frac{[C_j] - [C_j]_{\text{low}}}{[C_j]_{\text{high}} - [C_j]_{\text{low}}} \right) (I_{j,\text{high}} - I_{j,\text{low}}) \quad (31)$$

where j represents the pollutant, [Cj] is the concentration of the pollutant in the air, [Cj]low and [Cj]high are the breakpoints for the concentration range, and Ij,low and Ij,high are the sub-index values corresponding to the low and high breakpoints, respectively. The overall Air Quality Index (AQI) is then calculated as the maximum of the sub-indices for all pollutants:

$$\text{AQI} = \max_j I_j$$

<footnote n="114">¹¹⁴In Canada, these figures are available on the CCME website (https://ccme.ca/en/summary-table), where users can select a chemical and obtain the following limits: Water Quality Guidelines for the Protection of Agriculture; Sediment Quality Guidelines for the Protection of Aquatic Life; Soil Quality Guidelines for the Protection of Environmental and Human Health; etc.</footnote>
<table><caption>Table 32: US AQI categories</caption><thead><tr><th>Category</th><th>AQI band</th><th>Levels of concern</th><th>Daily AQI color</th></tr></thead><tbody><tr><td>1</td><td>0 to 50</td><td>Good</td><td>Green</td></tr><tr><td>2</td><td>51 to 100</td><td>Moderate</td><td>Yellow</td></tr><tr><td>3</td><td>101 to 150</td><td>Unhealthy for sensitive groups</td><td>Orange</td></tr><tr><td>4</td><td>151 to 200</td><td>Unhealthy</td><td>Red</td></tr><tr><td>5</td><td>201 to 300</td><td>Very unhealthy</td><td>Purple</td></tr><tr><td>6</td><td>301 and higher</td><td>Hazardous</td><td>Maroon</td></tr></tbody></table>

Source: US EPA (2024, Tables 1 and 5, paged 3–12).

Since the highest breakpoint is typically 500, each sub-index is mapped to a score between 0 and 500. Once calculated, the sub-index is assigned to one of six categories, each represented by a specific color that indicates the health risk posed by the level of air pollution (Table 32). For instance, if the sub-index is less than 50, the category is good and the color is green, meaning that air quality is satisfactory, air pollution poses little or no risk, and it's great to be active outside. If the sub-index is between 101 and 150, members of sensitive groups may experience health effects and need to limit outdoor activity, while the general public is less likely to be affected.

To understand how the air quality index is calculated, we consider an example with particulate matter PM<sub>2.5</sub>. Below we report the breakpoints [C<sub>j</sub>]<sub>low</sub> and [C<sub>j</sub>]<sub>high</sub> for the concentration range, and the values I<sub>j,low</sub> and I<sub>j,high</sub> of the corresponding AQI band<sup>115</sup>:

<table><thead><tr><th>AQI category</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>[C<sub>j</sub>]<sub>low</sub> (in µg/m<sup>3</sup>)</td><td>0.0</td><td>9.1</td><td>35.5</td><td>55.5</td><td>125.5</td><td>225.5</td></tr><tr><td>[C<sub>j</sub>]<sub>high</sub> (in µg/m<sup>3</sup>)</td><td>9.0</td><td>35.4</td><td>55.4</td><td>125.4</td><td>225.4</td><td>500.4</td></tr><tr><td>I<sub>j,low</sub></td><td>0</td><td>51</td><td>101</td><td>151</td><td>201</td><td>301</td></tr><tr><td>I<sub>j,high</sub></td><td>50</td><td>100</td><td>150</td><td>200</td><td>300</td><td>500</td></tr></tbody></table>

Suppose we have a 24-hour PM<sub>2.5</sub> value of 27.4 µg/m<sup>3</sup>. This value falls into the second AQI category, those concentration values that are above 9.1 and below 35.4. Applying Equation (31) gives:

$$I_{\text{PM}_{2.5}} = 51 + \left( \frac{27.4 - 9.1}{35.4 - 9.1} \right) (100 - 51) = 85.0951$$

A 24-hour PM<sub>2.5</sub> value of 27.4 µg/m<sup>3</sup> then corresponds to an air quality index of 85. Figure 51 shows the piecewise function (31) applied to particulate matter PM<sub>2.5</sub> and the corresponding AQI colors.

Figure 52 illustrates the AQI levels for particulate matter PM<sub>2.5</sub> in 2024 across four cities: New Delhi, Beijing, Paris, and Montreal. The data show significant disparities in air quality between these cities. In particular, New Delhi experienced 175 days with an AQI above 150, compared to 41 days in Beijing. In contrast, the maximum AQI value observed in Paris and Montreal was 113 and 104, respectively. In 2024, the average AQI values for these cities were 164 (New Delhi), 91 (Beijing), 49 (Paris), and 31 (Montreal). This indicates that Paris was more polluted than Montreal, as Paris had 136 days with an AQI above 50, while Montreal reported only 44 such days.

<footnote n="115">¹¹⁵Source: US EPA (2024, Table 6, page 14).</footnote>
<figure><img src="image_86.png" /><figcaption>Figure 51: US air quality index for particulate matter PM<sub>2.5</sub></figcaption></figure>

Source: US EPA (2024) & Author's calculations.

<figure><img src="image_87.png" /><figcaption>Figure 52: 2024 AQI PM<sub>2.5</sub> values in New Delhi, Beijing, Paris, and Montreal</figcaption></figure>

Source: World Air Quality Index (WAQI), https://aqicn.org/data-platform & Author's calculations.
### 3.3.5 The cost of pollution

Measuring the costs of pollution is a complex challenge for several reasons. The first difficulty lies in defining what is meant by the term 'cost'. Pollution does not result in a single type of cost, but rather a wide range of impacts, including health-related costs, lost productivity, damage to infrastructure and property, ecosystem degradation, reduced crop yields, resource depletion, and cleanup efforts. Identifying and categorizing these diverse costs is a fundamental step that adds to the complexity of the task. The second challenge is how to estimate these costs. Measuring the economic impact of pollution requires making assumptions and building statistical models. Results can vary widely depending on the methods and assumptions used, underscoring the importance of careful model selection in producing reliable estimates. A third major obstacle is the availability and relevance of data. Pollution measurements are often incomplete or inconsistent across countries because some countries lack the infrastructure to monitor certain pollutants. In addition, global coverage of pollutants is far from comprehensive. For example, particulate matter PM<sub>2.5</sub> is the most widely measured pollutant in the world, but reliable data on other types of pollution, such as soil, water, noise, and light pollution, remain scarce. This lack of comprehensive data makes it particularly difficult to assess the global impacts of these less-studied forms of pollution. Given these complexities, our discussion will focus primarily on two key issues: the health impacts and the economic costs associated with air pollution.

**Health impacts** The health effects of pollution are well documented in the scientific literature. However, air pollution is the most extensively studied topic, followed by water and plastic pollution. We estimate that 70% to 85% of health impact studies focus on air pollution. Research on water and plastic pollution each accounts for approximately 7% to 13%, while studies on soil and noise pollution make up about 2% to 4% each. Chemical pollution<sup>116</sup> represents around 1%, and light and biological pollution each account for less than 1%.

<table><caption>Table 33: Human health effects of pollution</caption><thead><tr><th>Health impact</th><th>Air</th><th>Biological</th><th>Chemical</th><th>Light</th><th>Noise</th><th>Plastic</th><th>Soil</th><th>Water</th></tr></thead><tbody><tr><td>Cancer</td><td>✓</td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Cardiovascular problems</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td></tr><tr><td>Cognitive development</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Endocrine disruption</td><td></td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Food contamination</td><td></td><td>✓</td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Hearing loss</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td></td><td></td></tr><tr><td>Infectious diseases</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td></tr><tr><td>Mental health</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td></tr><tr><td>Neurological effects</td><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Physical development</td><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>✓</td></tr><tr><td>Poisoning</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>Respiratory problems</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td></tr><tr><td>Skin problems</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>✓</td></tr><tr><td>Sleep disruption</td><td>✓</td><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td></tr></tbody></table>

Source: Author's research.

In Table 33 we summarize the different effects of the eight pollution categories on human health. Most scientific studies typically look at only a subset of pollution types and health categories. For example, consider the famous study by the Lancet Commission on Pollution and Health (Landrigan

<footnote n="116">¹¹⁶The underrepresentation of chemical pollution stems from its overlap with air, soil, and water pollution.</footnote>
<table><caption>Table 34: Global estimated pollution-attributable deaths (in millions) in 2019</caption><thead><tr><th>Pollution type</th><th>Female</th><th>Male</th><th>Total</th><th>in %</th></tr></thead><tbody><tr><td>Total air pollution</td><td>2.92</td><td>3.75</td><td>6.67</td><td>74.0</td></tr><tr><td>Household air</td><td>1.13</td><td>1.18</td><td>2.31</td><td>25.6</td></tr><tr><td>Ambient particulate</td><td>1.70</td><td>2.44</td><td>4.14</td><td>45.9</td></tr><tr><td>Ambient ozone</td><td>0.16</td><td>0.21</td><td>0.37</td><td>4.1</td></tr><tr><td>Total water pollution</td><td>0.73</td><td>0.63</td><td>1.36</td><td>15.1</td></tr><tr><td>Unsafe sanitation</td><td>0.40</td><td>0.36</td><td>0.76</td><td>8.4</td></tr><tr><td>Unsafe source</td><td>0.66</td><td>0.57</td><td>1.23</td><td>13.7</td></tr><tr><td>Total occupational pollution</td><td>0.22</td><td>0.65</td><td>0.87</td><td>9.7</td></tr><tr><td>Carcinogens</td><td>0.07</td><td>0.28</td><td>0.35</td><td>3.9</td></tr><tr><td>Particulates</td><td>0.15</td><td>0.37</td><td>0.52</td><td>5.8</td></tr><tr><td>Lead pollution</td><td>0.35</td><td>0.56</td><td>0.90</td><td>10.0</td></tr><tr><td>Total pollution</td><td>3.92</td><td>5.09</td><td>9.01</td><td>100.0</td></tr></tbody></table>

Source: Fuller et al. (2022).

et al., 2018). The Lancet Commission has divided the pollutome (i.e., the totality of all forms of pollution that have the potential to harm human health) into three zones:

* “Zone 1 includes well established pollution-disease pairs, for which there are robust estimates of their contributions to the global burden of disease. The associations between ambient air pollution and noncommunicable disease are the prime example.”

* Zone 2 includes the emerging effects of known pollutants, where evidence of causation is building, but associations between exposures and disease are not yet fully characterised and the burden of disease has not yet been quantified. Examples include associations between PM<sub>2.5</sub> air pollution and diabetes, pre-term birth, and diseases of the central nervous system, including autism in children, and dementia in the elderly. [...]

* Zone 3 includes new and emerging pollutants, most of them chemical pollutants whose effects on human health are only beginning to be recognised and are not yet quantified. [...] This zone includes developmental neurotoxicants; endocrine disruptors; new classes of pesticides such as the neonicotinoids; chemical herbicides such as glyphosate and nano-particles; and pharmaceutical wastes.” (Landrigan et al., 2018, page 11).

Focusing on Zone 1, the Lancet Commission estimated<sup>117</sup> that pollution is the leading environmental cause of disease and premature death, responsible for 9 million deaths in 2015 — 15.6% of the global 54.75 million deaths — disproportionately affecting the poor, vulnerable, and children in low- and middle-income countries (more than 90% of pollution-related deaths). These figures have been updated for 2019 using the same set of pollution types<sup>118</sup>. Fuller et al. (2022) found that the global

<footnote n="117"><sup>117</sup>The data used by the Lancet Commission (and many other international bodies studying pollution) come from the Global Burden of Disease (GBD) study, which is both a comprehensive research program and a database designed to quantify the impact of diseases, injuries, and risk factors on the health of populations worldwide. Initiated by the World Health Organization in 1990, it is now managed by the Institute for Health Metrics and Evaluation at the University of Washington. Data and results can be downloaded from https://vizhub.healthdata.org/gbd-results.</footnote>

<footnote n="118"><sup>118</sup>The study covers the pollution related to the contamination of air by fine particulate matter (PM<sub>2.5</sub>); ozone; sulfur and nitrogen oxides; freshwater pollution; contamination of the ocean by mercury, nitrogen, phosphorus, plastic, and petroleum waste; and poisoning of the land by lead, mercury, pesticides, industrial chemicals, electronic waste, and radioactive waste.</footnote>
figure of 9 million deaths remains unchanged, accounting for one in six global deaths (Table 34). While deaths from poverty-related pollution (household air and water) have decreased, deaths from modern pollution sources (ambient air and chemicals such as lead) have increased by 7% since 2015 and 66% since 2000. Pollution — especially air pollution, which accounts for about 75% of pollution-related deaths each year — is now the leading risk factor for morbidity and mortality. It is on a par with smoking and far ahead of malnutrition, drug and alcohol use, HIV, and road traffic injuries (Fuller et al., 2022, Figure 1, page 536).

The differences in air pollution-related deaths between regions and countries are significant. Figure 53 shows the proportion of deaths attributable to air pollution in 2021. The top five countries are North Korea (30.7%), Solomon Islands (27.3%), Vanuatu (23.4%), Bangladesh (22.2%), and Myanmar (21.2%), while the bottom five countries are Finland (0.8%), Sweden and Iceland (1%), and Canada, Estonia, and Norway (1.2%). The figures for China and India are 20.1% and 18.5% respectively. In South Asia, more than 18% of deaths are due to air pollution, compared with less than 2% in North America. There is also a significant difference between low-income countries (13.6%) and high-income countries (3.3%).

<figure><img src="image_88.png" /><figcaption>Figure 53: Share of deaths attributed to air pollution (2021)</figcaption></figure>

Source: Our World in Data, https://ourworldindata.org/air-pollution.

A significant number of deaths attributed to pollution from unsafe water sources are concentrated in Africa, India, and Southeast Asia<fnref n="119" />. The top five countries with the highest proportion of such deaths are Chad (7.0%), South Sudan (6.6%), Niger (5.3%), Somalia (4.1%), and Kiribati (4.0%). In sub-Saharan Africa, 2.5% of deaths are related to unsafe water sources, compared with 0% in North America and Europe. Again, the difference between low-income countries (2.3%) and high-income countries (0%) is large.

<footnote n="119">¹¹⁹Source: Our World in Data, https://ourworldindata.org/grapher/share-deaths-unsafe-water.</footnote>