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<fnref n="140" />, 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<fnref n="141" />. 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.

## 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="140">¹⁴⁰For 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="141">¹⁴¹Source: 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<fnref n="142" />. 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<fnref n="143" /> 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 107th 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<fnref n="144" /> (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="142">¹⁴²For instance, IPBES (2023, page 76) estimates that 37 000 species are established aliens, but only 5 250 are invasive alien species.</footnote>

<footnote n="143">¹⁴³The list is available at www.invasivespeciesinfo.gov/species-profiles-list.</footnote>

<footnote n="144">¹⁴⁴They 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<fnref n="145" />, 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<fnref n="146" />, four are on track to be achieved by 2025, and two will not be met<fnref n="147" />. New Zealand's situation is far from unique. In fact, many islands — especially those in the Pacific — face similar challenges (Simberloff, 2010).

<footnote n="145">¹⁴⁵Documents 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="146">¹⁴⁶This 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="147">¹⁴⁷This 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="148" /> (IPBES, 2023).

<figure><img src="image_224.png" /><figcaption>Figure 5.74: 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 5.74). 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="148">¹⁴⁸According to IPBES (2023, Figure SPM 3), 218 invasive alien species have caused 1215 local extinctions of native species.</footnote>
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.

**Types of biodiversity pollution** Because there is a wide range of contaminants<sup>149</sup>, pollution can also be divided into different categories. The eight major types of pollution are listed below:

<footnote n="149"><sup>149</sup>For 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="150" /> *or outdoor*<fnref n="151" /> *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 PM<sub>2.5</sub>, PM<sub>10</sub>, ultrafine particles, and dust), primary pollutants (those emitted directly into the atmosphere, such as carbon monoxide CO, nitrogen oxides NO<sub>x</sub>, and sulfur dioxide SO<sub>2</sub>), and secondary pollutants (those formed in the air through chemical reactions, such as acid rain, aerosols and ozone O<sub>3</sub>). 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="152" />. 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="150">¹⁵⁰Contamination 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="151">¹⁵¹Pollution in the open air, often from industrial or vehicular sources.</footnote>

<footnote n="152">¹⁵²Source: www.eea.europa.eu/en/topics/in-depth/chemicals.</footnote>
Box 5.17: Silent Spring by Rachel Carson (1962)

Silent Spring<sup>a</sup> 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_225.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 5.49). 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><sup>a</sup>The 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_226.png" /><figcaption>Table 5.49: 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="153" />: conventional pollutants, heavy metals, persistent organic pollutants, and emerging

<footnote n="153">¹⁵³In 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="154" /> 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<sup>155</sup>, 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<sup>156</sup>. Some well-known examples

<footnote n="154">¹⁵⁴Note 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="155">¹⁵⁵Longcore 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="156">¹⁵⁶See 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>

<footnote>"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>
Box 5.18: 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>
include disorientation of sea turtles, bird migration, insect disruption, human sleep disturbance, metabolic 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<sup>157</sup> 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 5.75 shows the evolution of global thermoplastic production<sup>158</sup> since 1950 and its projections to 2050. In 1950 the production

> 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="157"><sup>157</sup>Unwanted 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="158"><sup>158</sup>It 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</footnote>
<figure><img src="image_227.png" /><figcaption>Figure 5.75: 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.

was less 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="159" />. 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).

<footnote>remelted once formed.</footnote>

<footnote n="159">¹⁵⁹Vast gyres of marine debris created by ocean currents and the increasing influx of plastic pollution from human activities</footnote>
pines), Libmanan (Philippines), Ganges (India), Rio Grande de Mindanao (Philippines), and Agno (Philippines) (Meijer et al., 2021, Table S5). As a result<fnref n="160" />, 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="161" />, 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

<footnote n="160">¹⁶⁰The 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="161">¹⁶¹For 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>
the water (low levels indicate organic pollution or high nutrient loading, which leads to oxygen 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="162" />) as represented in Figure 5.76.

<figure><img src="image_228.png" /><figcaption>Figure 5.76: 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="162">¹⁶²The 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 5.19: 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.

**Dose-response relationship** The dose-response model<fnref n="163" /> 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_229.png" /><figcaption>Figure 5.77: Sigmoidal dose-response curve</figcaption></figure>

Figure 5.77 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="163">¹⁶³In 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="164" />:

$$y = f(x; \alpha, \beta, y_{\min}, y_{\max}) = y_{\min} + \frac{y_{\max} - y_{\min}}{1 + \exp(-\beta(\ln(x) - \ln(\alpha)))} = y_{\min} + \frac{y_{\max} - y_{\min}}{1 + \left(\frac{x}{\alpha}\right)^{-\beta}} \quad (5.29)$$

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="165" />. The second popular function is the log-normal model:

$$y = y_{\min} + (y_{\max} - y_{\min}) \Phi \left( \beta \ln \left( \frac{x}{\alpha} \right) \right) \quad (5.30)$$

Ritz (2010, Table 1, page 226) listed another class of dose-response model based on the Weibull distribution<fnref n="166" />:

$$y = y_{\min} + (y_{\max} - y_{\min}) \exp \left( - \left( \frac{x}{\alpha} \right)^{\beta} \right) \quad (5.32)$$

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:

$$y = y_{\min} + \frac{y_{\max} - y_{\min} + \gamma g(x)}{1 + \left(\frac{x}{\alpha}\right)^{-\beta}} \quad (5.33)$$

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 5.78 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).

$$y = y_{\min} + (y_{\max} - y_{\min}) \left(1 - \exp\left(-\left(\frac{x}{\alpha}\right)^{\beta}\right)\right) \quad (5.31)$$

<footnote n="164">¹⁶⁴The log-logistic probability distribution corresponds to $y_{\min} = 0$, $y_{\max} = 1$ and $\beta > 0$.</footnote>

<footnote n="165">¹⁶⁵The increasing dose-response curve in Figure 5.77 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="166">¹⁶⁶This 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_230.png" /><figcaption>Figure 5.78: 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="167" />:

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

<footnote n="167">¹⁶⁷Notice 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="168" /> (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_231.png" /><figcaption>Figure 5.79: 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="169" />. 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 in

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

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

<footnote n="168">¹⁶⁸We have:</footnote>

<footnote n="169">¹⁶⁹Tables 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>
Figure 5.79. 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 5.79 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 62** 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.

**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 5.50, 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="170" /> 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 populations, such as asthmatics, children, and the elderly) and

<footnote n="170">¹⁷⁰Particulate 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 5.50: Air quality standards (limit values for the protection of human health)</caption><thead><tr><th rowspan="2">Pollutant</th><th rowspan="2">Symbol</th><th rowspan="2">Unit</th><th rowspan="2">Period</th><th>WHO</th><th>EU</th><th>US</th><th>China</th><th>India</th><th>Brazil</th><th>Switzerland</th></tr><tr><th>2021</th><th>2008</th><th>2030</th><th>1990</th><th>2012</th><th>2009</th><th>1990</th><th>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>10</td></tr><tr><td rowspan="2">PM<sub>10</sub></td><td>24-hour</td><td>15</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>40/70</td><td>60</td><td></td><td>20</td><td></td></tr><tr><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>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>100</td><td>120</td><td>120</td><td>137</td><td>100/160</td><td>100</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>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></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></tr><tr><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 rowspan="3">Sulfur dioxide</td><td rowspan="3">SO<sub>2</sub></td><td rowspan="3">μg/m<sup>3</sup></td><td>Annual</td><td></td><td>20</td><td>26</td><td>20/60</td><td>20/50</td><td>40/80</td><td>30</td></tr><tr><td>24-hour</td><td>40</td><td>125</td><td>50</td><td>50/150</td><td>80</td><td>100/365</td><td>100</td></tr><tr><td>1 hour</td><td>350</td><td>350</td><td>196</td><td>150/500</td><td></td><td></td><td></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></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>8</td></tr><tr><td>8-hour</td><td>10</td><td>10</td><td>10</td><td>10</td><td></td><td>2</td><td>10</td></tr><tr><td>1-hour</td><td>35</td><td></td><td>40</td><td>10</td><td>4</td><td>40</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></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></td><td>0.5</td><td>0.5</td><td>0.5</td><td></td><td>0.5</td><td>0.5</td></tr><tr><td>3-month</td><td></td><td></td><td></td><td></td><td>0.15</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>100</td><td></td></tr><tr><td>Arsenic</td><td>As</td><td>μg/m<sup>3</sup></td><td>Annual</td><td>6.6</td><td>6</td><td>6</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>5</td><td></td></tr><tr><td>Benzo[a]pyrene</td><td>BaP</td><td>μg/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></td></tr><tr><td>Cadmium</td><td>Cd</td><td>μg/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></tr><tr><td>Nickel</td><td>Ni</td><td>μg/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></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>80/200</td><td></td><td>60/80</td><td></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.
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 63** 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="171" />.

**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:

$$I_j = I_{j,\text{low}} + \left( \frac{[C_j] - [C_j]_{\text{low}}}{[C_j]_{\text{high}} - [C_j]_{\text{low}}} \right) (I_{j,\text{high}} - I_{j,\text{low}}) \quad (5.34)$$

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="171">¹⁷¹In 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; Tissue Residue Quality Guidelines for the Protection of Wildlife Consumers of Aquatic Biota; Groundwater Quality Guidelines for the Protection of Environmental and Human Health.</footnote>
<table><caption>Table 5.51: 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 5.51). 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>172</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 (5.34) 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 5.80 shows the piecewise function (5.34) applied to particulate matter PM<sub>2.5</sub> and the corresponding AQI colors.

Figure 5.81 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="172"><sup>172</sup>Source: US EPA (2024, Table 6, page 14).</footnote>
<figure><img src="image_232.png" /><figcaption>Figure 5.80: 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_233.png" /><figcaption>Figure 5.81: 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.
**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>173</sup> represents around 1%, and light and biological pollution each account for less than 1%.

<table><caption>Table 5.52: 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 5.52 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="173"><sup>173</sup>The underrepresentation of chemical pollution stems from its overlap with air, soil, and water pollution.</footnote>
<table><caption>Table 5.53: 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 neurotoxics; 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>174</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>175</sup>. Fuller et al. (2022) found that the global

<footnote n="174"><sup>174</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 (WHO) in 1990, it is now managed by the Institute for Health Metrics and Evaluation (IHME) at the University of Washington. Data and results can be downloaded from https://vizhub.healthdata.org/gbd-results.</footnote>

<footnote n="175"><sup>175</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 5.53). 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 5.82 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_234.png" /><figcaption>Figure 5.82: 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="176" />. 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="176">¹⁷⁶Source: Our World in Data, https://ourworldindata.org/grapher/share-deaths-unsafe-water.</footnote>
Box 5.20: Non-monetary value of health impacts

The Global Burden of Disease (GBD) defines three non-monetary values of health effects:

*   **Years of life lost (YLL)**

    The YLL measures the burden of premature mortality. For an individual, it is calculated by comparing the age at which a person dies and the standard life expectancy. For example, if a person in a population dies at the age of 50 and the standard life expectancy is 75, the years of life lost are 25. For a homogeneous population we have:

$$YLL = \sum_{i=1}^{n} YLL_{i} = \sum_{i=1}^{n} (L_{i} - L^{*})$$

where $L_i$ is the age of the deceased, $L^*$ is the standard life expectancy of the population and $n$ is the number of deaths.

*   **Years lost/lived with disability (YLD)**

    The YLD measures the burden of living with a health condition that causes disability or reduced quality of life but does not result in death. For an individual, it is calculated as the product of the disability weight (DW) and the average duration of the condition. The disability weight is a value between 0 (for perfect health) and 1 (equivalent to death) that reflects the severity of the health condition. For a population and a given disease, the YLD is calculated as the sum of individual YLD values, which is the number of cases of the disease multiplied by the disability weight of the disease and the average duration of the disease.

*   **Disability-adjusted life years (DALY)**

    The DALY is the sum of YLL and YLD. It provides a single, comprehensive measure of health loss because it is a combined measure of both premature mortality and non-fatal health loss.

Another interesting study is the World Bank report, which uses data from the Global Burden of Disease<fnref n="177" /> 2019, but focuses only on particulate matter PM₂.₅, both outdoor (ambient air pollution) and indoor (household air pollution, i.e., the use of fuels for cooking and heating). Global pollution exposure to ambient PM₂.₅ was 43 µg/m³ in 2019 compared to the WHO recommended level of 5 µg/m³. World Bank (2022, page xiii) distinguishes two types of costs:

1.  Death and premature mortality;

2.  Morbidity due to illness and disability.

For premature deaths, World Bank (2022) reported that 6.45 million premature deaths in 2019 were attributed to exposure to PM₂.₅ pollution. PM₂.₅ was responsible for about 8.1% of global mortality. Globally, 64.2% of all PM₂.₅ deaths were due to ambient air pollution (outdoor pollution), while 35.8% were due to household air pollution from the use of solid fuels (indoor pollution). About 95% of these deaths occurred in low- and middle-income countries, with 27.7% in China, 24.6% in India, 3.6% in Pakistan, 3.1% in Nigeria, and 2.9% in Indonesia. In terms of morbidity, World Bank (2022) estimated that air pollution has caused 21 million years lived with disability (YLD) and 93 billion days lived with illness (DLI) in 2019. The YLD figures are calculated by the Global Burden

<footnote n="177">¹⁷⁷This is the same data used by Fuller et al. (2022) (see Footnote 174 on page 487).</footnote>
of Disease (GBD) using the methodology described in Box 5.20, while the DLI figures are estimated by the World Bank using this formula:

$$DLI = \frac{365 \times YLD}{DW}$$

where DW is the disability weight. The breakdown of the morbidity impact is shown in Table 5.54. Type 2 diabetes accounts for 33% of days lived with illness, COPD (chronic obstructive pulmonary disease) for 24%, stroke for 11%, cataracts for 12%, ischaemic heart disease (IHD) for 18%, and low respiratory infections (LRI) for 1%.

<table><caption>Table 5.54: Global burden of morbidity from PM<sub>2.5</sub> exposure in 2019</caption><thead><tr><th rowspan="2">Disease</th><th colspan="2">YLD</th><th colspan="2">DLI</th><th>DW</th></tr><tr><th>(in mn)</th><th>(in %)</th><th>(in bn)</th><th>(in %)</th><th>(in %)</th></tr></thead><tbody><tr><td>Type 2 diabetes</td><td>6.653</td><td>31.34</td><td>30.252</td><td>32.52</td><td>8.03</td></tr><tr><td>COPD</td><td>5.831</td><td>27.47</td><td>22.780</td><td>24.49</td><td>9.34</td></tr><tr><td>Stroke</td><td>5.028</td><td>23.68</td><td>10.497</td><td>11.29</td><td>17.48</td></tr><tr><td>Cataracts</td><td>2.143</td><td>10.10</td><td>11.370</td><td>12.22</td><td>6.88</td></tr><tr><td>IHD</td><td>1.248</td><td>5.88</td><td>16.654</td><td>17.90</td><td>2.74</td></tr><tr><td>LRI</td><td>0.198</td><td>0.93</td><td>1.214</td><td>1.31</td><td>5.95</td></tr><tr><td>Lung cancer</td><td>0.099</td><td>0.47</td><td>0.214</td><td>0.23</td><td>16.92</td></tr><tr><td>Neonatal disorders</td><td>0.019</td><td>0.09</td><td>0.035</td><td>0.04</td><td>20.32</td></tr><tr><td>Other</td><td>0.008</td><td>0.04</td><td>0.000</td><td>0.00</td><td></td></tr></tbody><tfoot><tr><td>Total</td><td>21.229</td><td>100.00</td><td>93.016</td><td>100.00</td><td>8.33</td></tr></tfoot></table>

Source: World Bank (2022, Table 3.6, page 22) & Author's calculations.

Understanding the health effects of pollution remains a complex and multifaceted challenge for researchers and policy makers. While significant progress has been made in certain areas, such as the study of the effects of particulate matter, many other forms of pollution remain poorly understood. PM<sub>2.5</sub> has been the subject of extensive scientific investigation due to its well-documented and profound effects on human health. A substantial body of literature, including the seminal work of Pope and Dockery (2006), has elucidated the biological mechanisms by which PM<sub>2.5</sub> contributes to a range of adverse health outcomes, such as cardiovascular and respiratory disease. Subsequent studies, such as those by Lelieveld et al (2015) and Thangavel et al. (2022), have expanded our understanding, highlighting the risk factors associated with long-term exposure to this pollutant and its contribution to global mortality. Despite this progress, our knowledge of the health effects of other forms of pollution is less comprehensive, leaving significant gaps in our understanding. Research conducted by the Lancet Commission has highlighted areas known as Zone 2 and Zone 3, which include emerging and less studied pollutants. These zones represent critical frontiers in pollution research that require further exploration and scientific investigation. For example, soil contamination by heavy metals such as lead and mercury has long been recognized as a public health concern, but its broader impacts on ecosystems and human health need to be better understood. Similarly, the effects of black carbon, a component of soot produced by incomplete combustion of fossil fuels and biomass, are increasingly understood to have both direct and indirect health effects. Another prominent example is glyphosate, a widely used herbicide that has generated considerable public and scientific debate. While some studies suggest potential health risks (Van Bruggen et al., 2018), such as links to cancer or endocrine disruption, others argue that these findings remain inconclusive due to methodological limitations and conflicting evidence. This controversy underscores the broader challenge of assessing the health effects of complex chemical exposures,
particularly in the absence of robust long-term studies. Moreover, the health effects of pollution are not limited to morbidity and mortality. Impacts on other dimensions of health must also be considered, such as cognitive and physical development, mental health, skin conditions, and more. Addressing these broader dimensions is critical to developing a comprehensive understanding of how pollution affects human well-being.

**Global economic costs** Estimating the economic costs of pollution poses significant challenges due to complex methodological issues and considerable data uncertainty. The time horizon is particularly important, as the inclusion of long-term costs yields very different results than the analysis of short-term impacts. Consequently, the following results should be interpreted with considerable caution. When examining such estimates, orders of magnitude and relative rankings tend to be more reliable indicators than absolute figures. This explains the considerable variation in results among the scientific research publications on this topic. In the following, we focus mainly on two reports: Quantifying the Economic Costs of Air Pollution from Fossil Fuels (Myllyvirta, 2020) and The Global Health Cost of PM<sub>2.5</sub> Air Pollution: A Case for Action Beyond 2021 (World Bank, 2022). But there are other reports that can be used. For example, the Lancet Commission estimated that welfare losses due to pollution are more than $4.6 trillion per year, or 6.2% of global economic output, and that 81.5% of these economic losses are due to ambient air pollution and household air pollution, with the remainder explained by lead exposure (9.8%) and water pollution (8.7%) (Landrigan et al., 2018, Table 5, page 487). These figures already give an idea of the global economic cost of pollution.

Myllyvirta (2020) proposes a simple method for estimating the economic cost of pollution. He divides the impacts of pollution into various health and economic outcomes. A common health outcome of air pollution is premature death, but pollution also causes other health issues such as childhood asthma, preterm births, illnesses, or disabilities, as well as economic outcomes like work absences or productivity losses. The total cost is calculated as the sum of the economic costs of these different health and economic outcomes:

$$C = \sum_{j=1}^{m} C_j = \sum_{j=1}^{m} n_j c_j$$

where *m* is the number of health or economic outcomes, *n*<sub>j</sub> is the number of cases of the *j*<sup>th</sup> outcome, and *c*<sub>j</sub> is the average unit cost of the *j*<sup>th</sup> outcome. Consider the example of a hypothetical country. If the average unit cost of a lost workday is $150 and pollution is responsible for 2.5 million lost workdays, the pollution-related cost of lost workdays is 2.5 × 10<sup>6</sup> × 150 = $375 mn. If the average unit cost of a preterm birth (including initial hospitalization and long-term health effects) is $30 000 and pollution is responsible for 2 000 preterm births, the pollution-related cost of preterm birth is 30 × 10<sup>3</sup> × 2 000 = $60 mn. The total cost of these two health and economic outcomes is then $435 million. Using published concentration-response functions (to estimate *n*<sub>j</sub>) and unit costs by country (to assess *n*<sub>j</sub>), and considering six health and economic outcomes, Myllyvirta (2020) estimated that air pollution from fossil fuels resulted in a global economic cost equivalent to 3.3% of GDP in 2018:

> "The economic costs of air pollution from fossil fuels are estimated at $2.9 trillion in 2018, or 3.3% of global GDP [...] An estimated 4.5 million people died in 2018 due to exposure to air pollution from fossil fuels. On average, each death was associated with a loss of 19 years of life. [...] Fossil fuel PM<sub>2.5</sub> pollution was responsible for 1.8 billion days of work absence, 4 million new cases of child asthma and 2 million preterm births, among other health impacts that affect healthcare costs, economic productivity and welfare." (Myllyvirta, 2020, page 2).
The distribution of this total cost is as follows: 84% is attributed to adult deaths, followed by disability due to chronic diseases (7%), sick leave (3.5%), preterm births (3.15%), child deaths (1.75%), and asthma (0.6%). The global figure of 3.3% masks disparities between countries, as shown in Table 5.55. China has the highest costs (6.6% of GDP), followed by Bulgaria and Hungary (6.0% of GDP). On the contrary, Brazil and Spain have low costs, less than 2% of their GDP. However, these figures do not reflect the full reality. In fact, by measuring costs by GDP, the analysis favors high-income countries because of their high GDP. Myllyvirta (2020) provided the economic cost of air pollution per capita. In this case, the country with the highest costs is Luxembourg ($2600 per capita), followed by the US ($1900 per capita), Switzerland ($1900 per capita), Austria ($1700 per capita) and Germany ($1700 per capita). Interestingly, the cost in France is $800 per capita.

<table><caption>Table 5.55: Economic costs of air pollution from fossil fuels (% of GDP, 2018)</caption><thead><tr><th>Country</th><th>Cost</th><th>Country</th><th>Cost</th></tr></thead><tbody><tr><td>China</td><td>6.6%</td><td>Bulgaria</td><td>6.0%</td></tr><tr><td>Hungary</td><td>6.0%</td><td>Ukraine</td><td>5.8%</td></tr><tr><td>Serbia</td><td>5.8%</td><td>Belarus</td><td>5.4%</td></tr><tr><td>India</td><td>5.4%</td><td>Romania</td><td>5.3%</td></tr><tr><td>Bangladesh</td><td>5.1%</td><td>Moldova</td><td>5.0%</td></tr><tr><td>Poland</td><td>4.9%</td><td>Russia</td><td>4.1%</td></tr><tr><td>Germany</td><td>3.5%</td><td>South Korea</td><td>3.4%</td></tr><tr><td>USA</td><td>3.0%</td><td>Japan</td><td>2.5%</td></tr><tr><td>UK</td><td>2.3%</td><td>France</td><td>2.0%</td></tr><tr><td>Spain</td><td>1.7%</td><td>Brazil</td><td>0.8%</td></tr></tbody></table>

Source: Myllyvirta (2020, page 6) & Centre for Research on Energy and Clean Air (CREA).

The report of the World Bank focuses only on the particulate matter PM<sub>2.5</sub>, and distinguishes two types of cost: (1) death and premature mortality and (2) morbidity due to illness and disability. The economic cost of premature deaths is estimated using the approach based on the value of statistical life (VSL), while the economic cost of morbidity is estimated by the years lost with disability (YLD) (see Box 5.21). The global economic cost of mortality and morbidity was estimated at $8.1 trillion, or 6.1% of global GDP in 2019, with the following breakdown: 85% from premature mortality and 15% from morbidity. Low- and middle-income countries bear a disproportionate share of these costs, accounting for more than 90% of the global health burden of PM<sub>2.5</sub> pollution. The most affected regions are South Asia, and East Asia and Pacific, with costs equivalent to 10.3% and 9.3% of GDP, respectively (Table 5.56). Table 5.57 lists the top three countries in each region ranked by percentage of GDP. For example, China ranks first in East Asia & Pacific (EAP) with an economic cost equivalent to 12.9% of GDP. In Europe, Serbia is the leading country with a cost of 18.9% of GDP. Table 5.58 provides the top 15 countries in terms of absolute cost in billions of dollars. For each country, we also indicate the breakdown between outdoor and indoor pollution, and the proportion attributed to mortality and morbidity. For instance, China has a total cost of $3029 billion, of which 79% arises from outdoor pollution, and 12% is attributed to morbidity.
<table><caption>Table 5.56: Annual cost of health damages from PM<sub>2.5</sub> by region (% of GDP, 2019)</caption><thead><tr><th>Region</th><th>Outdoor</th><th>Indoor</th><th>Mortality</th><th>Morbidity</th><th>Total</th></tr></thead><tbody><tr><td>East Asia and Pacific (EAP)</td><td>7.3%</td><td>2.0%</td><td>8.1%</td><td>1.2%</td><td>9.3%</td></tr><tr><td>Europe and Central Asia (ECA)</td><td>4.4%</td><td>0.2%</td><td>4.0%</td><td>0.6%</td><td>4.6%</td></tr><tr><td>Latin America and Caribbean (LAC)</td><td>2.7%</td><td>0.7%</td><td>2.9%</td><td>0.5%</td><td>3.4%</td></tr><tr><td>Middle East and North Africa (MNA)</td><td>5.5%</td><td>0.0%</td><td>4.7%</td><td>0.8%</td><td>5.5%</td></tr><tr><td>North America (NA)</td><td>1.7%</td><td>0.0%</td><td>1.3%</td><td>0.4%</td><td>1.7%</td></tr><tr><td>South Asia (SA)</td><td>5.9%</td><td>4.3%</td><td>8.3%</td><td>2.0%</td><td>10.3%</td></tr><tr><td>Sub-Saharan Africa (SSA)</td><td>3.6%</td><td>2.4%</td><td>5.2%</td><td>0.8%</td><td>6.0%</td></tr><tr><td>Low-income countries</td><td>1.3%</td><td>4.6%</td><td>5.0%</td><td>0.9%</td><td>5.9%</td></tr><tr><td>Lower-middle-income countries</td><td>5.4%</td><td>3.6%</td><td>7.5%</td><td>1.5%</td><td>9.0%</td></tr><tr><td>Upper-middle-income countries</td><td>7.1%</td><td>1.8%</td><td>7.8%</td><td>1.1%</td><td>8.9%</td></tr><tr><td>High-income non OECD countries</td><td>4.3%</td><td>0.2%</td><td>4.0%</td><td>0.5%</td><td>4.5%</td></tr><tr><td>High-income OECD</td><td>2.8%</td><td>0.0%</td><td>2.3%</td><td>0.5%</td><td>2.8%</td></tr></tbody></table>

Source: World Bank (2022, Figures 3.13 & 3.14, pages 20 & 21) & Author's calculations.

<table><caption>Table 5.57: Annual cost of health damages from PM<sub>2.5</sub> by country (% of GDP, 2019)</caption><thead><tr><th>Region</th><th>Top 1 country</th><th>Top 2 country</th><th>Top 3 country</th></tr></thead><tbody><tr><td>EAP</td><td>China</td><td>Papua New Guinea</td><td>Myanmar</td><td>11.4%</td></tr><tr><td>ECA</td><td>Serbia</td><td>Bulgaria</td><td>North Macedonia</td><td>15.9%</td></tr><tr><td>LAC</td><td>Barbados</td><td>Haiti</td><td>Trinidad/Tobago</td><td>7.8%</td></tr><tr><td>MNA</td><td>Egypt</td><td>Morocco</td><td>Tunisia</td><td>6.5%</td></tr><tr><td>NA</td><td>USA</td><td>Canada</td><td></td><td></td></tr><tr><td>SA</td><td>India</td><td>Nepal</td><td>Pakistan</td><td>8.9%</td></tr><tr><td>SSA</td><td>Burkina Faso</td><td>Mali</td><td>Central African Republic</td><td>8.7%</td></tr></tbody></table>

Source: World Bank (2022, Table 3.5, page 21).

<table><caption>Table 5.58: Annual cost of health damages from PM<sub>2.5</sub> by country in 2019 (Top 15)</caption><thead><tr><th>Country</th><th>Total (in $ bn)</th><th>Total (in % of GDP)</th><th>Outdoor (in %)</th><th>Indoor (in %)</th><th>Mortality (in %)</th><th>Morbidity (in %)</th></tr></thead><tbody><tr><td>China</td><td>3 029</td><td>12.9</td><td>79</td><td>21</td><td>88</td><td>12</td></tr><tr><td>India</td><td>1 022</td><td>10.6</td><td>60</td><td>40</td><td>81</td><td>19</td></tr><tr><td>United States</td><td>373</td><td>1.7</td><td>100</td><td>0</td><td>78</td><td>22</td></tr><tr><td>Russia</td><td>241</td><td>5.7</td><td>97</td><td>3</td><td>91</td><td>9</td></tr><tr><td>Indonesia</td><td>220</td><td>6.6</td><td>56</td><td>44</td><td>85</td><td>15</td></tr><tr><td>Japan</td><td>210</td><td>3.8</td><td>100</td><td>0</td><td>82</td><td>18</td></tr><tr><td>Germany</td><td>178</td><td>3.8</td><td>100</td><td>0</td><td>81</td><td>19</td></tr><tr><td>Turkey</td><td>134</td><td>5.8</td><td>99</td><td>1</td><td>85</td><td>15</td></tr><tr><td>Italy</td><td>132</td><td>5.0</td><td>99</td><td>1</td><td>83</td><td>17</td></tr><tr><td>Poland</td><td>127</td><td>9.8</td><td>91</td><td>9</td><td>86</td><td>14</td></tr><tr><td>South Korea</td><td>114</td><td>5.1</td><td>100</td><td>0</td><td>83</td><td>17</td></tr><tr><td>Egypt</td><td>105</td><td>8.6</td><td>100</td><td>0</td><td>87</td><td>13</td></tr><tr><td>Mexico</td><td>104</td><td>4.0</td><td>78</td><td>22</td><td>84</td><td>16</td></tr><tr><td>Saudi Arabia</td><td>96</td><td>5.7</td><td>100</td><td>0</td><td>89</td><td>11</td></tr><tr><td>Pakistan</td><td>94</td><td>8.9</td><td>48</td><td>52</td><td>82</td><td>18</td></tr></tbody></table>

Source: World Bank (2022, Table A.3, page 40) & Author's calculations.
Box 5.21: A basic economic model of pollution costs

Dechezleprêtre et al. (2019) consider a classical output function that uses capital and labor as factors of production, but also incorporates pollution as an additional variable: $Y = F(K, L, P)$, where $Y$ is economic output, $K$ is capital, $L$ is labor, and $P$ is pollution. The labor input $L$ can be expressed as $L = N \cdot A_L \cdot T_L$ where $N$ is the workforce size (or the population), $A_L$ is labor productivity, $T_L = \tau - \zeta$ is the time individuals spend working, which is the difference between the total endowment of labor time $\tau$ and sick time $\zeta$. It is assumed that all three variables ($N$, $A_L$, and $\zeta$) depend on the pollution $P$. Consequently, the output function can be rewritten as:

$$Y = F(K, N(P) A_L(P) (\tau - \zeta(P)), P)$$

From this, we deduce the derivative of the logarithm of output with respect to pollution:

$$\frac{d \ln Y}{dP} = \frac{\partial \ln Y}{\partial \ln L} \frac{\partial \ln L}{\partial P} + \frac{\partial \ln Y}{\partial P} = \epsilon_L \frac{\partial \ln L}{\partial P} + \frac{\partial \ln Y}{\partial P}$$

where $\epsilon_L \ge 0$ is the elasticity of output with respect to labor. Breaking this down further:

$$\frac{d \ln Y}{dP} = \epsilon_L \left( \frac{\partial \ln N}{\partial P} + \frac{\partial \ln A_L}{\partial P} + \frac{\partial \ln (\tau - \zeta(P))}{\partial P} \right) + \frac{\partial \ln Y}{\partial P}$$

Expanding the third term:

$$\frac{\partial \ln (\tau - \zeta(P))}{\partial P} = -\frac{1}{\tau - \zeta(P)} \frac{\partial \zeta(P)}{\partial P} = -\frac{\zeta(P)}{\tau - \zeta(P)} \frac{\partial \ln \zeta(P)}{\partial P}$$

Substituting this into the equation and introducing the notation $\theta = \frac{\zeta}{\tau - \zeta}$, which represents the ratio of sick time to effective labor time, we get:

$$\frac{d \ln Y}{dP} = \epsilon_L \underbrace{\left( \frac{\partial \ln N}{\partial P} + \frac{\partial \ln A_L}{\partial P} - \theta \frac{\partial \ln \zeta(P)}{\partial P} \right)}_{\text{Pollution-related labor impact}} + \frac{\partial \ln Y}{\partial P}$$

This equation can be expressed in the following compact form:

$$\beta_P = \epsilon_L \beta_{L,P} + \beta_{L,P}$$

Therefore, pollution has an indirect impact on output through the labor factor, which operates through three dimensions:

1. Pollution increases mortality, reducing the size of labor force: $\frac{\partial \ln N}{\partial P} < 0$.

2. Pollution increases morbidity, decreasing labor productivity: $\frac{\partial \ln A_L}{\partial P} < 0$.

3. Pollution increases morbidity, leading to more work absences: $\frac{\partial \ln \zeta(P)}{\partial P} > 0$.
Box 5.21: A basic economic model of pollution costs (Continued from previous page)

The labor-related impact of pollution also depends on the labor-output elasticity. A higher value of $\epsilon$ results in a higher cost of pollution, especially in labor-intensive industries (Graff Zivin and Neidell, 2013). Consequently, the labor-related impact of pollution is always negative: $\epsilon_L\beta_{L,P} \le 0$. In contrast, the direct impact of pollution on output can be either positive or negative: $\beta_{L,P} = \frac{\partial \ln Y}{\partial P} \le 0$. When pollution levels are low, increasing pollution can have a positive impact because GDP is boosted by an increase in energy supply. However, when pollution levels are very high, increasing pollution has a negative impact due to the negative externalities (e.g., infrastructure damage, reduced agricultural yields, water stress) that affect the production system. Therefore, the direct relationship follows a bell curve: $\beta_{L,P}$ is initially positive, but becomes negative as pollution increases. The aggregation of these two effects is not straightforward. While $\beta_P$ may be positive when pollution levels are low, it is certain to become negative when pollution levels are high.

**Economic costs in Europe** Studying the economic costs of air pollution in Europe is particularly valuable because of the availability of more reliable and comprehensive data. This allows researchers to consider additional pollutants beyond PM$_{2.5}$, such as heavy metals (e.g., arsenic) and organic pollutants (e.g., benzene). They can also examine trends in economic costs over time and assess the impact of policy regulations on air quality and associated costs. For instance, Dechezleprêtre et al. (2019) estimated that a 1 µg/m$^3$ increase in PM$_{2.5}$ concentration leads to a 0.8% reduction in real GDP within the same year. Notably, 95% of this impact is attributed to a decline in output per worker, which can result from higher absenteeism or reduced labor productivity. Since PM$_{2.5}$ pollution in Europe has decreased by 0.2µg/m$^3$ per year since 2000, reducing air pollution could increase real GDP by 1.6% per decade. Thus, this study shows that reducing air pollution generates economic growth through improved labor productivity.

More recently, Mejino-López and Oliu-Barton (2024) studied the allocation of EU funds among member states and the cost-effectiveness of European air pollution policies. Using the results of Dechezleprêtre et al. (2019), they estimated the costs of particulate matter PM$_{2.5}$ as follows$^{178}$:

$$C = \beta_P \cdot ([C] - AQG)^+ \cdot GDP = 0.8\% \cdot \max ([C]_{PM_{2.5}} - 5 \mu g/m^3, 0) \cdot GDP$$

On a global basis, they found that costs have declined since 2014, but remain at high levels:

> "Despite significant progress, air pollution still causes €600 billion in losses each year in the European Union — equal to 4% of its annual GDP. These costs stem from productivity losses such as increased absenteeism, the reduction of in-job productivity and harm to ecosystems. Air pollution costs are disproportionately high in eastern Europe and Italy, where losses are projected to remain above 6% of GDP until 2030. The EU's 10% most-polluted regions suffer 25% of the burden of mortality attributable to air pollution." (Mejino-López and Oliu-Barton, 2024, page 1).

The large differences between countries are shown in Figure 5.83. For each country, Mejino-López and Oliu-Barton (2024) calculated the cost of air pollution for three seven-year periods$^{179}$: 2014–2020,

<footnote>$^{178}$Since we have $\beta_P = \Delta \ln Y/\Delta P$, we deduce that $\Delta Y = \beta_P \cdot \Delta P \cdot Y$.</footnote>

<footnote>$^{179}$For the 2024–2030 period, they used World Bank projections of GDP and extrapolated PM$_{2.5}$ concentrations based on linear regressions.</footnote>
<figure><img src="image_235.png" /><figcaption>Figure 5.83: Estimated cost of air pollution by country (in % of GDP)</figcaption></figure>

Source: Mejimo-López and Oliu-Barton (2024, Figure 10, page 17).
2021–2027, and 2024–2030. Some countries, such as Bulgaria, Romania, Cyprus, Belgium, and the Netherlands have dramatically reduced air pollution when considering the gap 2014–2030. However, there are still some air pollution hotspots in Europe. Considering the 234 EU regions, Mejino-López and Oliu-Barton (2024) identified 16 hotspots: 5 in Bulgaria, 4 in Poland, 2 in Romania, and 1 each in Czechia, Croatia, and Hungary. These hotspots represent 7% of the EU population, but concentrate 14% of air pollution mortality.

EEA (2024a) uses a different methodology to estimate the economic costs of pollution. The analysis focuses on industrial facilities in Europe<fnref n="180" /> and considers the following groups of pollutants:

* Main air pollutants: particulate matter (PM<sub>2.5</sub>, PM<sub>10</sub>), sulfur dioxide (SO<sub>2</sub>), ammonia (NH<sub>3</sub>), nitrogen oxides (NO<sub>x</sub>), and non-methane volatile organic compounds (NM VOC);

* Greenhouse gases (GHG): carbon dioxide (CO<sub>2</sub>), methane (CH<sub>4</sub>) and nitrous oxide (N<sub>2</sub>O);

* Heavy metals: arsenic (As), cadmium (Cd), chromium VI (Cr), lead (Pb), mercury (Hg), and nickel (Ni);

* Organic pollutants: 1,3 butadiene, benzene, formaldehyde, polycyclic aromatic hydrocarbons, dioxins and furans.

The study examines only air pollution and estimates the external costs of these facilities, taking into account both health effects (mortality and morbidity) and non-health effects (damage to buildings, crops, and forests). Health effects for the main pollutants are quantified using concentration-response functions and unit costs based on the value of a statistical life (VSL) and the value of life year (VOLY). For greenhouse gases, negative externalities are assessed by calculating the marginal abatement cost of carbon emissions required to meet the Paris Agreement targets. The results, broken down by country, are presented in Table 5.59. EEA (2024a) estimates that the economic costs associated with the value of a statistical life and the value of a life year are 2.23% and 1.39% of GDP, respectively, for the EU-27. The most affected countries are Bulgaria, Poland, Greece, Romania and Estonia, while the top five Member States with facilities contributing the highest external costs are Germany, Poland, Italy, France and Spain. Table 5.60 shows the amount of negative externalities in millions of euro. In 2012, the costs for the EU-27 were 326.5 and 536.7 billion euros, depending on the approach (VOLY vs. VSL). In 2021, these figures become 219.4 and 352.7 billion euros, representing a decrease of 32.8% and 34.3% of total external costs, respectively. During the period 2012-2021, the cumulative externalities were 2.7 and 4.3 trillion euros, respectively.

We see that heavy metals and organic pollutants are responsible for less than 5% of the economic costs, and these costs are mainly concentrated on lead, followed by cadmium and mercury. For the group of major air pollutants, sulfur dioxide and nitrogen oxides are the main contributors. EEA (2024a) also finds that 129 facilities (out of about 9400 facilities) are responsible for about 50% of the total damage caused by air emissions:

> "It is worth noting that half (25) of the 50 most polluting facilities in 2021 were thermal power stations, with most of them located in Germany (nine) and Poland (six). Twenty-three of these 25 plants burn lignite or hard coal as their main fuel." (EEA, 2024a, page 10).

<footnote n="180">¹⁸⁰The study is based on the European Pollutant Release and Transfer Register (E-PRTR) dataset, a comprehensive database established under European Union Regulation 166/2006 to provide public access to environmental data from large industrial facilities across Europe. E-PRTR contains data reported annually by more than 30 000 industrial facilities in the EU, Iceland, Liechtenstein, Norway, Serbia, Switzerland and the United Kingdom from 65 economic activities and covers 91 pollutants, including emissions to air, water and land as well as waste transfers.</footnote>
<table><caption>Table 5.59: External costs of air pollution (2021)</caption><thead><tr><th rowspan="2">Country</th><th colspan="2">Relative cost</th><th colspan="2">Breakdown of external costs</th></tr><tr><th>VOLY/GDP</th><th>VSL/GDP</th><th>VOLY</th><th>VSL</th></tr></thead><tbody><tr><td>Austria</td><td>0.71%</td><td>1.07%</td><td>1.43%</td><td>1.34%</td></tr><tr><td>Belgium</td><td>1.59%</td><td>2.68%</td><td>3.96%</td><td>4.16%</td></tr><tr><td>Bulgaria</td><td>7.87%</td><td>16.11%</td><td>2.77%</td><td>3.53%</td></tr><tr><td>Croatia</td><td>1.72%</td><td>2.89%</td><td>0.50%</td><td>0.52%</td></tr><tr><td>Cyprus</td><td>2.89%</td><td>3.02%</td><td>0.34%</td><td>0.22%</td></tr><tr><td>Denmark</td><td>0.47%</td><td>0.64%</td><td>0.78%</td><td>0.66%</td></tr><tr><td>Estonia</td><td>3.35%</td><td>3.75%</td><td>0.52%</td><td>0.36%</td></tr><tr><td>Finland</td><td>2.12%</td><td>2.36%</td><td>2.63%</td><td>1.82%</td></tr><tr><td>France</td><td>0.68%</td><td>1.07%</td><td>8.39%</td><td>8.25%</td></tr><tr><td>Germany</td><td>1.54%</td><td>2.63%</td><td>27.41%</td><td>29.19%</td></tr><tr><td>Greece</td><td>2.93%</td><td>4.76%</td><td>2.63%</td><td>2.67%</td></tr><tr><td>Hungary</td><td>2.21%</td><td>4.27%</td><td>1.69%</td><td>2.03%</td></tr><tr><td>Ireland</td><td>0.50%</td><td>0.62%</td><td>1.06%</td><td>0.82%</td></tr><tr><td>Italy</td><td>1.06%</td><td>1.79%</td><td>9.35%</td><td>9.87%</td></tr><tr><td>Latvia</td><td>0.69%</td><td>1.05%</td><td>0.11%</td><td>0.11%</td></tr><tr><td>Luxembourg</td><td>0.35%</td><td>0.65%</td><td>0.13%</td><td>0.15%</td></tr><tr><td>Netherlands</td><td>1.37%</td><td>1.91%</td><td>5.81%</td><td>5.03%</td></tr><tr><td>Poland</td><td>5.63%</td><td>8.68%</td><td>16.06%</td><td>15.43%</td></tr><tr><td>Portugal</td><td>1.67%</td><td>2.18%</td><td>1.77%</td><td>1.45%</td></tr><tr><td>Romania</td><td>2.47%</td><td>4.55%</td><td>2.96%</td><td>3.38%</td></tr><tr><td>Slovenia</td><td>1.76%</td><td>2.99%</td><td>0.46%</td><td>0.48%</td></tr><tr><td>Spain</td><td>1.07%</td><td>1.77%</td><td>6.40%</td><td>6.58%</td></tr><tr><td>Sweden</td><td>1.07%</td><td>1.18%</td><td>2.86%</td><td>1.95%</td></tr><tr><td>EU-27</td><td>1.39%</td><td>2.23%</td><td></td><td></td></tr></tbody></table>

Source: EEA (2024b, Figure 4.2, Tables 4.2 & 4.3, pages 31–34), Author’s calculations & icons taken from

https://icons8.comicons.
<table><caption>Table 5.60: External costs of air pollution in € mn (2021)</caption><thead><tr><th>Pollutants</th><th>2012</th><th>2021</th><th>Cumulative</th><th>2021 Breakdown</th></tr></thead><tbody><tr><td>Main air (VOLY)</td><td>119 042</td><td>59 728</td><td>834 066</td><td>SO<sub>2</sub>: 45.3%, NO<sub>x</sub>: 41.1%, NH<sub>3</sub>: 7.5%, PM<sub>10</sub>: 5.0%, NM VOC: 1.2%</td></tr><tr><td>Main air (VSL)</td><td>329 152</td><td>193 056</td><td>2 426 585</td><td>SO<sub>2</sub>: 45.7%, NO<sub>x</sub>: 40.5%, NH<sub>3</sub>: 7.7%, PM<sub>10</sub>: 5.0%, NM VOC: 1.0%</td></tr><tr><td>GHG</td><td>193 641</td><td>150 657</td><td>1 728 224</td><td>CO<sub>2</sub>: 94.5%, CH<sub>4</sub>: 4.9%, N<sub>2</sub>O: 0.6%</td></tr><tr><td>Heavy metals</td><td>13 803</td><td>8 924</td><td>120 622</td><td>Pb: 79.6%, Cd: 15.9%, Hg: 3.2%, As: 1.3%, Cr(VI): 0.1%, Ni: 0.0%</td></tr><tr><td>Organic</td><td>66</td><td>69</td><td>1 071</td><td>Dioxins: 82.6%, B(a)P: 15.9%, Benzene: 1.4%</td></tr><tr><td>Total (VOLY)</td><td>326 553</td><td>219 378</td><td>2 683 984</td><td>GHG: 68.7%, Main air: 27.2%, Heavy metals: 4.1%, Organic: 0.0%</td></tr><tr><td>Total (VSL)</td><td>536 663</td><td>352 707</td><td>4 276 503</td><td>Main air: 54.7%, GHG: 42.7%, Heavy metals: 2.5%, Organic: 0.0%</td></tr></tbody></table>

Source: EEA (2024b, Table 4.1, Figures 4.4–4.7, pages 28 & 35–37) & Author’s calculations.

The technical report contains an interesting analysis of marginal damage costs (MDC) for different pollutants and countries. The MDC represents the monetary value of the damage caused by emitting one additional tonne of a specific pollutant into the environment. For the main air pollutants, the average marginal costs for 2019, expressed in 2021 thousand euros per kg of pollutant emitted into the air, are as follows<fnref n="181" />:

<table><thead><tr><th>Pollutant</th><th>NO<sub>x</sub></th><th>SO<sub>2</sub></th><th>PM<sub>10</sub></th><th>PM<sub>2.5</sub></th><th>NM VOC</th><th>NH<sub>3</sub></th></tr></thead><tbody><tr><td>MDC (VOLY)</td><td>15.4</td><td>16.2</td><td>51.5</td><td>86.5</td><td>1.8</td><td>19.0</td></tr><tr><td>MDC (VSL)</td><td>43.0</td><td>38.3</td><td>141.1</td><td>237.1</td><td>4.5</td><td>52.3</td></tr></tbody></table>

while for heavy metals and organic compounds they find these values:

<table><thead><tr><th>Pollutant</th><th>Arsenic</th><th>Cadmium</th><th>Chromium VI</th><th>Lead</th><th>Mercury</th></tr></thead><tbody><tr><td>MDC</td><td>10.3</td><td>253.1</td><td>0.7</td><td>45.2</td><td>16.8</td></tr><tr><td>Pollutant</td><td>Nickel</td><td>1,3 Butadiene</td><td>Benzene</td><td>B(a)P</td><td>Dioxins</td></tr><tr><td>MDC</td><td>0.02</td><td>0.00</td><td>0.00</td><td>1.4</td><td>132 600</td></tr></tbody></table>

We read these numbers as follows. One additional tonne of NO<sub>x</sub> emitted to the air induces an additional cost of 15 400 euros in the VOLY method, while one additional tonne of PM<sub>2.5</sub> emitted to the air induces an additional cost of 237 100 euros in the VSL method. The pollutant with the highest marginal damage cost is dioxins with an MDC of 132.6 million euro per kg.

**Remark 64** Although the EEA report is certainly one of the most comprehensive, well-documented and data-driven studies of the economic costs of air pollution, it also shows that this is a complex task and that there are many uncertainties about these costs. Key assumptions include the specification of concentration-response functions and the modelling of PM<sub>2.5</sub> impacts. In addition, this report is far from exhaustive as it does not include some important activities that do not correspond to industrial installations. For example, the industrial facilities reported in the E-PRTR database cover

<footnote n="181">¹⁸¹Source: EEA (2024a, Tables 3.1 & 3.4, pages 26 & 27).</footnote>
49% of SOx and 48% of mercury, but only 3% of PM10 and 10% of lead. Furthermore, the study only analyses outdoor pollution and does not consider indoor pollution, in particular the impact of emissions on workers inside the facilities.

Box 5.22: Monetary economic value of health impacts

In Box 5.21 on page 494, we have defined three non-monetary measures of health impact: years of life lost (YLL), years lived with disability (YLD) and disability-adjusted life years (DALY). To assess economic costs, we need to convert these physical measures into monetary ones. Some standard approaches are described below.

* The quality-adjusted life year (QALY) is a unit of measurement that combines both the quantity and quality of life lived into a single index. One QALY represents one year of perfect health, and zero QALYs represent one year of death. It can be used to evaluate the benefits of a policy<sup>a</sup>:

$$ \text{QALY} = \text{Years of Life Gained} \times \text{Average Quality of Life Weight} $$

This approach is called linear because it is equivalent to directly summing the annual quality of life weights:

$$ \text{QALY} = \sum_{u=t}^{T} Q(u) $$

where T is the maximum time horizon and $Q(t) \in [0, 1]$ is the quality life of weight at time t. According to Hammitt (2023, Equation 2.5), a non-linear approach is to calculate the quality-adjusted life expectancy (QALE)<sup>b</sup>:

$$ \text{QALE} = \frac{1}{S(t)} \int_{t}^{T} e^{-\varrho(u-t)} \mathbf{S}(u) \mathbb{E}[Q(u)] du $$

where $\mathbf{S}(t)$ is the survival function at time t, $\varrho$ is the discount rate and $\mathbb{E}[Q(t)]$ is the expected quality weight.

* The value of a statistical life (VSL) is the economic value placed on the benefit of avoiding a death. It is not the value of an individual's life per se, but rather a measure of society's collective willingness to pay for small reductions in mortality risk. As such, the VSL is closely related to the concept of willingness to pay. The VSL is based on the amount of money that individuals are willing to pay for a given reduction in the risk of premature death. Several approaches are used to estimate VSL, including revealed preferences (e.g., wage premiums for risky jobs) and stated preferences (e.g., surveys asking about risk reduction choices). Hammitt (2023) mathematically defines the VSL as follows:

$$ \text{VSL} = \frac{v}{\Delta L} $$

where v is the monetary value of the risk reduction and $\Delta L$ is the expected number

<footnote><sup>a</sup>When we want to evaluate the cost of a disease, we replace Years of Life Gained by Years of Life Lost.</footnote>

<footnote><sup>b</sup>T can be set to $\infty$, since $S(\infty) = 0$.</footnote>
Box 5.22: Monetary economic value of health impacts (Continued from previous page)

of lives saved. For example, if workers in an industry are paid an additional $1 000 per year to face a 1 in 10 000 increased risk of death, the VSL can be calculated as $VSL = \frac{1 000}{1/10 000} = \$10 mn$. In this example, the VSL is $10 million, reflecting the monetary value associated with risk reductions that collectively save one statistical life. In the case of the economic costs of air pollution, EEA (2024b, page 19) used a VSL of €4.2 million — for infant mortality, it is set to €6.5 million.

* The value per statistical life year (VSLY) — or the value of a life year (VOLY) — is equal to the value of a statistical life divided by the remaining expected life years Hammitt (2023, Equation 2.10):

$$VSLY = \frac{VSL}{\frac{1}{S(t)} \int_{t}^{T} e^{-\rho(u-t)} S(u) du}$$

It represents the economic value of extending the life of a population by one additional year. Using the previous example, if the average remaining expected life in the industry is 40 years, $VSLY = \frac{\$10 mn}{40} = \$250 000$. In the case of air pollution, EEA (2024b, page 19) used a VOLY of €111 470, which means that the remaining expected life years used for this study is 37.68 years.

* VSL, VSLY, and VOLY are not available for all countries, as their computation requires extensive data and statistical resources. These metrics are generally well documented for OECD countries, the United States, and Europe, where data availability and research capacity are higher. For other countries, country-specific figures can be estimated by adjusting a baseline statistic using a transfer function, as described by Hammitt and Robinson (2011) and Viscusi and Masterman (2017):

$$VSL_c = VSL_b \left( \frac{(Y/N)_c}{(Y/N)_b} \right)^{\epsilon}$$

where $VSL_c$ is the country-specific VSL, $VSL_b$ is the baseline VSL, $(Y/N)$ is the GDP per capita and $\epsilon$ is the income elasticity of VSL, which captures how VSL scales with income. For high-income countries, $\epsilon$ is typically less than 1, reflecting the diminishing marginal utility of income. For low-income countries, $\epsilon \ge 1$ because the value of risk reduction increase more sharply as income risesª.

Other approaches are available, but most are less popular than QALY and VSL, with the exception of willingness to payᵇ and cost of illness (COI). COI includes direct medical costs (medical care, hospitalization), direct non-medical costs (transportation to medical care, home modification), and indirect costs (loss of productivity and income).

<footnote>ªIn very poor countries, each additional dollar has extremely high utility for basic consumption. This makes people relatively less willing to trade income for risk reduction.</footnote>

<footnote>ᵇWillingness to pay is defined in Box 5.2 on page 314.</footnote>
Overexploitation and resource extraction

Overexploitation is the practice of harvesting renewable resources faster than they can be replenished. This unsustainable practice often leads to significant declines in species populations, ecosystem degradation, evolutionary consequences, and in some cases, extinction. It commonly occurs through activities such as overfishing, in which fish stocks are harvested at a rate that exceeds their ability to reproduce; deforestation, in which timber is harvested at a rate that exceeds forest regeneration; hunting and poaching, characterized by the excessive killing of animals for food, sport, or trade; and illegal wildlife trade, including the poaching of animals for their body parts or the pet trade, such as the ivory and rhino horn markets. The concept of overexploitation can also be applied to natural resources such as minerals (e.g., phosphorus and rare earth elements) and fossil fuels (e.g., oil and natural gas). Even if they are not expected to become extinct by 2100, many natural resources will face problems as high-grade deposits are rapidly depleted and easily accessible deposits become increasingly scarce. Cobalt and zinc are typical examples.

Overexploitation is neither a new nor a recent phenomenon. It has existed throughout history, with varying degrees of severity in different contexts:

"Although there is considerable variation in detail, there is remarkable consistency in the history of resource exploitation: resources are inevitably overexploited, often to the point of collapse or extinction." (Ludwig et al., 1993, page 17).

Peres (2010) highlights numerous examples of overexploitation that underscore the profound impact of human activities on wildlife. One notable pattern is the extinction of large-bodied vertebrates, which has been largely attributed to human overhunting and overkilling in the post-Pleistocene. Evidence suggests that humans historically shifted their hunting practices from larger to smaller animals after depleting populations of larger species. Large animals are particularly attractive targets because their size provides a greater yield of meat, hides, and bones, making them economically valuable. However, these species often have slower reproductive rates, characterized by longer gestation periods and fewer offspring per birth. This makes it difficult for their populations to recover from significant declines caused by hunting or habitat destruction. As large species declined or went extinct, humans increasingly relied on hunting smaller animals to meet their needs. This pattern — overhunting of large animals followed by a shift to smaller species — has been documented across regions and historical periods. Svenning et al. (2021, Figure 1, page 3) found that among terrestrial mammals, only 11 of 57 species of megaherbivores (mean adult body mass greater than 1000 kg) survived to 1000 AD:

<table><thead><tr><th>Status</th><th>Cetartiodactyla</th><th>Cingulata</th><th>Diprotodontia</th><th>Litopterna</th><th>Notoungulata</th><th>Rhinocerotidae</th><th>Pilosa</th><th>Elephantidae</th><th>Proboscidea</th><th>Total</th></tr></thead><tbody><tr><th>Survivor</th><td>4</td><td></td><td></td><td></td><td></td><td>4</td><td>3</td><td></td><td></td><td>11</td></tr><tr><th>Extinct</th><td>4</td><td>4</td><td>1</td><td>2</td><td>3</td><td>4</td><td>16</td><td>7</td><td>5</td><td>46</td></tr></tbody></table>

Survivors include three species of elephant, four species of rhinoceros, the common hippopotamus, the giraffe, and two species of cattle. The extinct species include seven species of elephant, four species of rhinoceros, one species of hippopotamus, the mastodon, etc. Ripple et al. (2019) studied the threats to megafauna, which are large vertebrate species. They considered all species weighing more than 100 kg for mammals, ray-finned fish, and cartilaginous fish, and all species weighing more than 40 kg for amphibians, birds, and reptiles. They found that the proportion of threatened
species was significantly higher among megafauna than among all vertebrates (58.6% vs. 21.3%). Furthermore, 70% of megafauna species have declining populations, with birds and amphibians being particularly affected (100% of species in these groups have declining populations), followed by cartilaginous fish (89.7%) and ray-finned fish (83.8%). Focusing on specific species, Ripple et al. (2019) identified various threats to megafauna. They concluded that harvesting of megafauna for human consumption<fnref n="182" /> is the single most important threat across all classes studied (Table 5.61), far outweighing other factors. Harvesting is a threat in more than 95% of cases, while invasive species and habitat development are threats in less than 40% of cases. Interestingly, climate change was found to be a threat in less than 20% of cases.

<table><caption>Table 5.61: Current threats to megafauna</caption><thead><tr><th></th><th>Megafauna</th><th>n</th><th>Animal husbandry</th><th>Climate</th><th>Cropping</th><th>Development</th><th>Harvesting</th><th>Invasives</th><th>Pollution</th><th>Transportation</th></tr></thead><tbody><tr><td></td><td>Cartilaginous fish</td><td>38</td><td>3%</td><td>11%</td><td></td><td>13%</td><td>100%</td><td></td><td>13%</td><td>8%</td></tr><tr><td></td><td>Mammals</td><td>73</td><td>53%</td><td></td><td>61%</td><td>56%</td><td>98%</td><td>54%</td><td></td><td>51%</td></tr><tr><td></td><td>Ray-finned fish</td><td>29</td><td></td><td></td><td></td><td>14%</td><td>100%</td><td>31%</td><td>40%</td><td>28%</td></tr><tr><td></td><td>Reptiles</td><td>20</td><td></td><td>40%</td><td>25%</td><td>40%</td><td>90%</td><td>65%</td><td></td><td>25%</td></tr></tbody></table>

Source: Ripple et al. (2019, Figure 2, page 5).

As explained by Peres (2010), overexploitation can lead to the rapid collapse of species. In some cases, just a few years or decades are sufficient, and it does not necessarily take centuries or millennia for a species to become nearly extinct. One of the best known examples is the North American buffalo (*Bison bison*), which experienced a dramatic collapse in less than 40 years:

> “Prior to European exploration and settlement of North America, the buffalo or American bison inhabited vast stretches of the continent. [...] At its greatest moment, the total numbers for the continent may have been as high as 25 to 30 million before white settlement. On the Great Plains, where the bison were most suited and most plentiful, its population is estimated to have been 20 million as late as 1800. Even by 1850, substantially more than 10 million bison roamed the plains. Yet, by 1890, these plains held just 1000 bison.” (Lueck, 2002, page 609).

After 1890, the story of the American bison took a more hopeful turn, thanks to conservation efforts. A few individuals established small herds on private ranches to preserve the species. The US government protected a small population of wild bison in Yellowstone, providing an important sanctuary. Laws were also passed prohibiting the hunting of bison. Over time, through the combined efforts of individuals, conservation groups, and the government, the bison population began to recover. Today, bison are no longer endangered. There are approximately 400 000 bison in North America, but most are managed as livestock on private ranches. In fact, only about 30 000 are wild bison<fnref n="183" />.

<footnote n="182">¹⁸²The unsustainable hunting of wild animals for food is called the bushmeat crisis.</footnote>

<footnote n="183">¹⁸³Source: https://bisoncentral.com/bison-by-the-numbers.</footnote>
Box 5.23: The Tragedy of the Commons

Published in Science in 1968, *The Tragedy of the Commons* by Garrett Hardin is a seminal essay that explores the conflict between individual interests and the common good in the context of shared resources. The article focuses on how individuals, acting in their own self-interest, can deplete or degrade shared resources (referred to as ‘*commons*’), even when it is not in the collective best interest to do so. Hardin (1968) illustrates this dilemma with a hypothetical example of a shared pasture (the commons) where each herder individually benefits by adding more cattle to the pasture. Each herder reasons that adding one more animal will bring him personal gain, while the negative consequences (overgrazing) are shared by all users of the commons. Therefore, from an individual perspective, it’s rational to add more animals. However, if every herder follows this logic, the collective overuse of the pasture leads to its destruction, as the resources become insufficient to sustain the community. This illustrates the dilemma of individual gain versus collective ruin.

The essay applies this principle to various domains, including national parks, pollution, and environmental issues. It had a profound and far-reaching impact across multiple fields, influencing academic thought, public policy, and environmental management. However, the article has also faced significant criticism. For instance, Nobel laureate Elinor Ostrom provided empirical evidence demonstrating that communities can often self-organize to manage commons effectively, challenging the assumption that the tragedy is inevitable. More recently, the concept of the tragedy of the commons has resonated with contemporary challenges such as climate change. It has been extensively revisited, notably inspiring the idea of the ‘*tragedy of the horizon*’ (Carney, 2015), which highlights the short-term focus of financial markets and policy-making in addressing long-term environmental risks.

Beyond species extinction, overexploitation occurs in other areas and can take different forms. One important form is the depletion and impoverishment of natural resources. We often think of excessive logging for timber, overgrazing by livestock, and unsustainable harvesting of medicinal plants, all of which involve the depletion of plants that reduce soil fertility and lead to erosion. However, natural resource depletion also includes other essential resources such as water, minerals, and energy resources. In this context, IPBES provides a highly critical assessment of resource extraction:

> "Extraction of living biomass and nonliving materials is increasing as both populations and per capita consumption increased sixfold from 1970 to 2010, while the demand for materials used in construction and industry quadrupled during that time. [...] Materials for construction and industry increased 4-fold, with the most dramatic increases for lower-middle (7-fold) and upper-middle income countries (11-fold) and the Asia and the Pacific region (10-fold for whole region) and, generally, the growing economies. The use of biomass, fossil fuels, metal ores and non-metallic minerals doubled from 2005 (26.3 billion tons) to 2015 (46.4 billion tons), growing an annual rate of 6.1%." (IPBES, 2019, page 121).

The root causes of overexploitation lie in the expanding size and growth of the human population, coupled with rising standards of living. These driving forces are described by various terms, such as ‘*the scale of the human enterprise*’ (Ehrlich, 1995; Gaston and Spicer, 2004), ‘*the great acceleration*’ (Steffen et al., 2015a), and others. Collectively, they underscore the profound impact of human activities on the planet’s natural systems.
**An example with freshwater** Overexploitation of water resources includes both the overdrawing of groundwater from aquifers for irrigation or consumption, and the unsustainable use of surface water, such as river diversions and lake exploitation. Figure 5.84 shows the annual freshwater withdrawals measured in trillion m³. We observe four main periods. From 1900 to 1950, the trend is relatively slow. Then there is a sharp acceleration in freshwater withdrawals until 1980, followed by a first slowdown from 1980 to 2010 and a second slowdown since 2010. This graph illustrates ‘*The Great Acceleration*’ described by Steffen et al. (2015a), which refers to the dramatic, rapid increase in human activity and its profound impact on Earth’s systems that began after World War II.

<figure><img src="image_236.png" /><figcaption>Figure 5.84: Global freshwater withdrawals (in trillion m³ per year)</figcaption></figure>

Source: Flörke et al. (2013), Steffen et al. (2015a), https://databank.worldbank.org/source/world-development-indicators & Author's calculations.

Freshwater resources and withdrawals are unevenly distributed. In Table 5.62, we report several statistics for different countries: (1) the total annual freshwater withdrawals in billion cubic meters in 2000, (2) the total annual freshwater withdrawals in billion cubic meters in 2021, (3, 4, 5) the distribution among agriculture, industry, and domestic use, (6) the renewable internal freshwater resources<fnref n="184" /> in billion cubic meters in 2021, (7) the renewable internal freshwater resources per capita, and (8) the water stress. The total volume of renewable freshwater resources worldwide is approximately 42.8 trillion cubic meters, with more than 50% concentrated in just seven countries: Brazil, Canada, China, India, Indonesia, Russia, and the United States. Some countries have very limited renewable freshwater resources. For instance, Egypt, Libya, and Saudi Arabia each have less than 2 billion cubic meters of freshwater resources, despite their large land areas. These disparities

<footnote n="184">¹⁸⁴Renewable internal freshwater resource flows measure the total volume of freshwater generated by natural processes within a country's borders. This includes water from precipitation (rain, snow) that contributes to rivers, lakes, and groundwater but excludes any water that flows in from other countries.</footnote>
<table><caption>Table 5.62: Freshwater withdrawals by country</caption><thead><tr><th rowspan="2">Country</th><th colspan="2">Total</th><th colspan="2">Agriculture</th><th colspan="2">Industry</th><th colspan="3">Domestic</th><th colspan="3">Renewable resources</th><th colspan="2">Renewable per capita</th><th colspan="2">Water stress</th></tr><tr><th>2000<br>(in bn m³)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th><th>2021<br>(in %)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th><th>2021<br>(in bn m³)</th><th>2021<br>(in %)</th></tr></thead><tbody><tr><td>Algeria</td><td>5.6</td><td>9.8</td><td>63.8</td><td>1.8</td><td>34.4</td><td></td><td></td><td>11</td><td></td><td>251</td><td></td><td>137.9</td><td></td><td></td><td></td><td></td></tr><tr><td>Argentina</td><td>30.4</td><td>37.7</td><td>73.9</td><td>10.6</td><td>15.5</td><td></td><td></td><td>292</td><td></td><td>6444</td><td></td><td>10.5</td><td></td><td></td><td></td><td></td></tr><tr><td>Australia</td><td>21.7</td><td>11.4</td><td>67.8</td><td>18.1</td><td>14.0</td><td></td><td></td><td>492</td><td></td><td>19155</td><td></td><td>4.6</td><td></td><td></td><td></td><td></td></tr><tr><td>Bangladesh</td><td></td><td>35.9</td><td>87.8</td><td>2.1</td><td>10.0</td><td></td><td></td><td>105</td><td></td><td>626</td><td></td><td>5.7</td><td></td><td></td><td></td><td></td></tr><tr><td>Brazil</td><td>56.1</td><td>67.3</td><td>61.3</td><td>14.5</td><td>24.2</td><td></td><td></td><td>5661</td><td></td><td>27015</td><td></td><td>1.5</td><td></td><td></td><td></td><td></td></tr><tr><td>Canada</td><td>41.9</td><td>36.3</td><td>11.4</td><td>74.2</td><td>14.4</td><td></td><td></td><td>2850</td><td></td><td>74530</td><td></td><td>3.7</td><td></td><td></td><td></td><td></td></tr><tr><td>China</td><td>550.9</td><td>568.5</td><td>62.1</td><td>17.7</td><td>20.1</td><td></td><td></td><td>2813</td><td></td><td>1992</td><td></td><td>41.5</td><td></td><td></td><td></td><td></td></tr><tr><td>Congo (DRC)</td><td>0.6</td><td>0.7</td><td>10.5</td><td>21.5</td><td>68.0</td><td></td><td></td><td>900</td><td></td><td>9077</td><td></td><td>0.2</td><td></td><td></td><td></td><td></td></tr><tr><td>Egypt</td><td>57.0</td><td>77.5</td><td>79.2</td><td>7.0</td><td>13.9</td><td></td><td></td><td>1</td><td></td><td>9</td><td></td><td>141.2</td><td></td><td></td><td></td><td></td></tr><tr><td>France</td><td>32.7</td><td>24.7</td><td>13.9</td><td>64.3</td><td>21.7</td><td></td><td></td><td>200</td><td></td><td>2948</td><td></td><td>21.6</td><td></td><td></td><td></td><td></td></tr><tr><td>Gabon</td><td>0.1</td><td>0.1</td><td>29.0</td><td>10.1</td><td>60.9</td><td></td><td></td><td>164</td><td></td><td>69003</td><td></td><td>0.5</td><td></td><td></td><td></td><td></td></tr><tr><td>Germany</td><td>44.9</td><td>25.8</td><td>4.2</td><td>54.3</td><td>41.5</td><td></td><td></td><td>107</td><td></td><td>1286</td><td></td><td>35.4</td><td></td><td></td><td></td><td></td></tr><tr><td>Iceland</td><td>0.2</td><td>0.3</td><td>0.1</td><td>71.1</td><td>28.7</td><td></td><td></td><td>170</td><td></td><td>456351</td><td></td><td>0.4</td><td></td><td></td><td></td><td></td></tr><tr><td>India</td><td>610.4</td><td>647.5</td><td>90.4</td><td>2.2</td><td>7.4</td><td></td><td></td><td>1446</td><td></td><td>1022</td><td></td><td>66.5</td><td></td><td></td><td></td><td></td></tr><tr><td>Indonesia</td><td>113.3</td><td>222.6</td><td>85.2</td><td>4.1</td><td>10.7</td><td></td><td></td><td>2019</td><td></td><td>7294</td><td></td><td>29.7</td><td></td><td></td><td></td><td></td></tr><tr><td>Iran</td><td>88.5</td><td>93.0</td><td>92.2</td><td>1.2</td><td>6.6</td><td></td><td></td><td>128</td><td></td><td>1453</td><td></td><td>81.3</td><td></td><td></td><td></td><td></td></tr><tr><td>Italy</td><td>45.1</td><td>33.6</td><td>50.2</td><td>22.7</td><td>27.1</td><td></td><td></td><td>182</td><td></td><td>3086</td><td></td><td>29.6</td><td></td><td></td><td></td><td></td></tr><tr><td>Kazakhstan</td><td>21.0</td><td>24.6</td><td>62.7</td><td>18.5</td><td>18.8</td><td></td><td></td><td>64</td><td></td><td>3259</td><td></td><td>34.1</td><td></td><td></td><td></td><td></td></tr><tr><td>Korea, Rep.</td><td>27.7</td><td>29.2</td><td>58.9</td><td>16.4</td><td>24.6</td><td></td><td></td><td>65</td><td></td><td>1253</td><td></td><td>85.2</td><td></td><td></td><td></td><td></td></tr><tr><td>Libya</td><td>4.3</td><td>5.7</td><td>83.2</td><td>4.8</td><td>12.0</td><td></td><td></td><td>1</td><td></td><td>98</td><td></td><td>817.1</td><td></td><td></td><td></td><td></td></tr><tr><td>Madagascar</td><td>13.4</td><td>13.5</td><td>95.9</td><td>1.2</td><td>2.9</td><td></td><td></td><td>337</td><td></td><td>11350</td><td></td><td>11.3</td><td></td><td></td><td></td><td></td></tr><tr><td>Malaysia</td><td>5.6</td><td>6.7</td><td>45.6</td><td>29.9</td><td>24.5</td><td></td><td></td><td>580</td><td></td><td>16918</td><td></td><td>3.4</td><td></td><td></td><td></td><td></td></tr><tr><td>Mexico</td><td>68.2</td><td>89.9</td><td>75.7</td><td>9.5</td><td>14.8</td><td></td><td></td><td>409</td><td></td><td>3204</td><td></td><td>45.0</td><td></td><td></td><td></td><td></td></tr><tr><td>Netherlands</td><td>8.4</td><td>7.9</td><td>1.0</td><td>73.5</td><td>25.5</td><td></td><td></td><td>11</td><td></td><td>627</td><td></td><td>16.1</td><td></td><td></td><td></td><td></td></tr><tr><td>Nigeria</td><td>10.3</td><td>12.5</td><td>44.2</td><td>15.8</td><td>40.1</td><td></td><td></td><td>221</td><td></td><td>1011</td><td></td><td>9.7</td><td></td><td></td><td></td><td></td></tr><tr><td>Pakistan</td><td>172.6</td><td>264.2</td><td>94.0</td><td>0.8</td><td>5.3</td><td></td><td></td><td>55</td><td></td><td>230</td><td></td><td>162.1</td><td></td><td></td><td></td><td></td></tr><tr><td>Philippines</td><td></td><td>89.0</td><td>76.2</td><td>13.4</td><td>10.3</td><td></td><td></td><td>479</td><td></td><td>4235</td><td></td><td>27.2</td><td></td><td></td><td></td><td></td></tr><tr><td>Qatar</td><td>0.2</td><td>0.2</td><td>33.3</td><td>4.3</td><td>62.4</td><td></td><td></td><td>0</td><td></td><td>22</td><td></td><td>431.0</td><td></td><td></td><td></td><td></td></tr><tr><td>Russia</td><td>75.9</td><td>64.8</td><td>28.8</td><td>44.8</td><td>26.5</td><td></td><td></td><td>4312</td><td></td><td>29790</td><td></td><td>4.1</td><td></td><td></td><td></td><td></td></tr><tr><td>Saudi Arabia</td><td>19.7</td><td>23.4</td><td>81.6</td><td>5.4</td><td>13.1</td><td></td><td></td><td>2</td><td></td><td>78</td><td></td><td>974.2</td><td></td><td></td><td></td><td></td></tr><tr><td>South Africa</td><td>12.7</td><td>20.9</td><td>61.3</td><td>21.2</td><td>17.4</td><td></td><td></td><td>45</td><td></td><td>728</td><td></td><td>66.9</td><td></td><td></td><td></td><td></td></tr><tr><td>Spain</td><td>36.1</td><td>29.0</td><td>65.3</td><td>19.0</td><td>15.7</td><td></td><td></td><td>111</td><td></td><td>2345</td><td></td><td>43.3</td><td></td><td></td><td></td><td></td></tr><tr><td>Sudan</td><td></td><td>26.9</td><td>96.2</td><td>0.3</td><td>3.5</td><td></td><td></td><td>4</td><td></td><td>83</td><td></td><td>118.7</td><td></td><td></td><td></td><td></td></tr><tr><td>Ukraine</td><td>18.3</td><td>9.5</td><td>31.0</td><td>40.9</td><td>28.1</td><td></td><td></td><td>55</td><td></td><td>1244</td><td></td><td>12.3</td><td></td><td></td><td></td><td></td></tr><tr><td>United Kingdom</td><td>12.5</td><td>8.4</td><td>14.0</td><td>12.0</td><td>74.0</td><td></td><td></td><td>145</td><td></td><td>2163</td><td></td><td>14.4</td><td></td><td></td><td></td><td></td></tr><tr><td>United States</td><td>473.5</td><td>444.4</td><td>39.7</td><td>47.2</td><td>13.1</td><td></td><td></td><td>2818</td><td></td><td>8487</td><td></td><td>28.2</td><td></td><td></td><td></td><td></td></tr><tr><td>Viet Nam</td><td>71.8</td><td>81.9</td><td>94.8</td><td>3.7</td><td>1.5</td><td></td><td></td><td>359</td><td></td><td>3633</td><td></td><td>18.1</td><td></td><td></td><td></td><td></td></tr><tr><td>World</td><td>3679.8</td><td>3948.7</td><td>71.6</td><td>15.1</td><td>13.1</td><td></td><td></td><td>42809</td><td></td><td>5429</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Source: https://databank.worldbank.org/source/world-development-indicators.
are even more pronounced when considering renewable internal freshwater resources per capita. For example, Canada has more than 70 000 m³ of freshwater per capita, while Egypt has less than 10 m³. In addition, a worrying downward trend in available freshwater resources has been observed (Figure 5.85). Over the past 60 years, the global volume of renewable internal freshwater resources has declined by about 60%. In India, this decline is even more severe, approaching 70%. This downward trend is primarily driven by high withdrawal rates. Globally, about 4 trillion cubic meters of freshwater are withdrawn each year. Agriculture is the largest contributor, accounting for 71% of total withdrawals, followed by industry at 15%. Domestic use accounts for 13% of total withdrawals worldwide. However, domestic water use has grown much faster than agricultural and industrial use, increasing sevenfold over the past 50 years. In some countries, domestic freshwater use accounts for more than 40% of total withdrawals, such as in many African countries, as well as in Germany and the United Kingdom. In Table 5.62, we also report the ratio of total freshwater withdrawals to total renewable freshwater resources, referring specifically to internal freshwater resources. This ratio is commonly known as water stress. Water stress is considered high when the ratio exceeds 75% and critical when it exceeds<fnref n="185" /> 100%. We observe that some countries are experiencing critical water stress, including Algeria, Egypt, Libya, Pakistan, Qatar, Saudi Arabia, and Sudan. In fact, as of 2021, there are 25 countries with water stress levels exceeding 75%.

<figure><img src="image_237.png" /><figcaption>Figure 5.85: Renewable internal freshwater resources per capita (base 100 in 1961)</figcaption></figure>

Source: https://databank.worldbank.org/source/world-development-indicators & Author's calculations.

<footnote n="185">¹⁸⁵A water stress level greater than 100% means that a country is withdrawing more freshwater annually than the total amount of renewable internal freshwater resources. This indicates overexploitation of additional water sources beyond what is naturally replenished within the country. For example, a country may rely on non-renewable groundwater, external freshwater resources that originate outside its borders and flow in through rivers and lakes (e.g., the Nile and the Danube), or desalination, which involves the conversion of seawater into freshwater (e.g., in Qatar and Saudi Arabia).</footnote>
**Mathematical models of population and resource ecology with harvesting** Historically, the Malthusian growth model is considered the first mathematical population model. In this case, the population growth rate is constant:

$$ \frac{dN(t)}{dt} = \delta N(t) $$

where $N(t)$ is the number of individuals, $N(t_0) = N_0$ is the initial population size and $\delta = \lambda - \mu$ is the difference between the birth rate and the death/mortality rate. Malthus (1798) believed that the population tends to grow exponentially$^{186}$, whereas he believed that food production and other resources increase at a linear rate due to the finite nature of land and labor. Therefore, Malthus predicted that the world would eventually face a crisis where resources would not be sufficient to support the growing population. However, his conclusions were later criticized by Verhulst (1838), who highlighted the role of the law of diminishing returns. Verhulst provided numerous examples demonstrating that population growth is inherently limited and cannot continue indefinitely. To model this, he proposed that population size follows the nonlinear differential equation:

$$ \frac{dN(t)}{dt} = \delta N(t) - \varphi(N(t)) $$

By considering the specific case where $\varphi(x) = \eta x^2$, Verhulst derived the well-known logistic population model:

$$ N(t) = \frac{\delta N_0 e^{\delta(t-t_0)}}{\delta + \eta N_0 (e^{\delta(t-t_0)} - 1)} $$

This model illustrates how population growth slows as it approaches a finite carrying capacity, offering a more realistic depiction of population dynamics compared to Malthus' original exponential growth predictions. In the 1920s, mathematician Vito Volterra introduced a class of population dynamics models describing multiple species competing for the same food or resources, or interacting as predators and prey (Volterra, 1928). During the same period, biophysicist Alfred Lotka independently developed similar equations to analyze predator-prey interactions (Lotka, 1925). These equations are now known as the Lotka-Volterra equations and form a pair of first-order nonlinear differential equations:

$$ \left\{ \begin{aligned} \frac{dx(t)}{dt} &= ax(t) - bx(t)y(t) \\ \frac{dy(t)}{dt} &= cx(t)y(t) - dy(t) \end{aligned} \right. \qquad (5.35) $$

where $x(t)$ is the prey population, $y(t)$ is the predator population, $a$ is the intrinsic growth rate of the prey (in the absence of predators), $b$ is the predation rate coefficient, $c$ is the reproduction rate of predators per prey consumed, and $d$ is the natural mortality rate of predators. These three models (Malthus, Verhulst, and Lotka-Volterra) form the basis for modeling population and resource dynamics with harvesting.

In the following, $x(t)$ represents the size of a population, the amount of a resource or the biomass stock of a species in a finite environment. When the stock $x(t)$ is small, the size of the environment has no impact, and $x(t)$ can grow at an exponential rate $\delta$, also known as the intrinsic growth rate. However, beyond a certain threshold, the density of the stock or population becomes too high to sustain the growth rate, and the regenerative rate of the stock decreases. This suggests the existence of a threshold $\kappa$ at which $x(t)$ remains constant. Therefore, we assume that the stock variation is determined by the product of three factors: the constant intrinsic growth rate $\delta$ (or

<footnote>$^{186}$The solution of the differential equation is an exponential curve: $N(t) = N_0 e^{\delta(t-t_0)}$.</footnote>
biotic potential), the regenerative rate<fnref n="187" /> $\xi(t) = \frac{\kappa - x(t)}{\kappa}$ (or biotic resistance), which depends on the distance between the current stock $x(t)$ and the threshold $\kappa$ which is called the carrying capacity, and the current stock $x(t)$. This results in the following differential equation:

$$ \frac{dx(t)}{dt} = \delta \left( \frac{\kappa - x(t)}{\kappa} \right) x(t) $$

This model corresponds to the logistic model formulated by Verhulst (1838), where $\eta = \delta/\kappa$. We deduce that the solution is:

$$ x(t) = \frac{\kappa N_0 e^{\delta(t-t_0)}}{\kappa + N_0 (e^{\delta(t-t_0)} - 1)} $$

We verify that $x(t)$ tends asymptotically to $\kappa$ as $t \to \infty$. This model can be easily modified by considering exploitation:

$$ \frac{dx(t)}{dt} = \delta x(t) \left(1 - \frac{x(t)}{\kappa}\right) - h(x(t)) $$

where $h(x(t))$ is the harvest, catch or removal rate. This model has been considered by Gordon (1954) and Schaefer (1954) in the case of fisheries management. The maximum sustainable yield (MSY) is the largest harvest rate of a renewable resource that can be sustained indefinitely without causing the population to decline. The sustainable harvest rate is given by:

$$ h(x(t)) = \delta x(t) \left(1 - \frac{x(t)}{\kappa}\right) $$

The maximum value of $h(x)$ is reached when $h'(x) = 0$ or $\delta \left(1 - \frac{x}{\kappa}\right) - \delta \frac{x}{\kappa} = 0$. We deduce that the maximum sustainable yield is achieved when the stock is at half the carrying capacity: $x(t) = \frac{\kappa}{2}$. We deduce that:

$$ \text{MSY} := \max h(x(t)) = h\left(\frac{\kappa}{2}\right) = \frac{\delta}{4\kappa} $$

Figure 5.86 shows the function $g(x) = \delta x \left(1 - \frac{x}{\kappa}\right) - h$ when $\delta = 30\%$, $\kappa = 200$ and $h = \epsilon \cdot \text{MSY}$. The stability analysis demonstrates that the number of stable equilibria depends on the harvest rate<fnref n="188" />. If $h = 0$, we have a stable equilibrium at $x^* = \kappa$ and an unstable equilibrium at $x^* = 0$. If $0 < h < \frac{\delta}{4\kappa}$, the two equilibria lie between 0 and $\kappa$. Among them, only the equilibrium $x^* = \frac{\delta\kappa + \sqrt{\delta\kappa(\delta\kappa - 4h)}}{2\delta}$ is stable. If $h = \text{MSY} = \frac{\delta}{4}\kappa$, the equilibrium at $x^* = \frac{\kappa}{2}$ is unstable. Indeed, if $x(t) > x^*$, $\frac{dx(t)}{dt} < 0$

$$ \frac{dx(t)}{dt} = g(x) = 0 \Leftrightarrow -\delta x^2 + \delta\kappa x - h\kappa = 0 $$

We have $\Delta = \delta\kappa(\delta\kappa - 4h)$. If $h > \text{MSY}$, then there is no root and $\frac{dx(t)}{dt} < 0$. It follows that $x(t)$ converges to the stable equilibrium $x_1^* = 0$. If $h = \text{MSY}$, there is a root: $x' = \kappa/2$. Therefore, we have two stable equilibria: $x_1^* = 0$ and $x_2^* = \kappa/2$. If $h < \text{MSY}$, we have $\sqrt{\Delta} < \delta\kappa$ and there are two roots: $x' = (\delta\kappa - \sqrt{\Delta}) / (2\delta)$ and $x'' = (\delta\kappa + \sqrt{\Delta}) / (2\delta)$. Therefore, we have two stable equilibria $x_1^* = 0$ and $x_3^* = (\delta\kappa + \sqrt{\Delta}) / (2\delta)$ and one unstable equilibrium $x_2^* = (\delta\kappa - \sqrt{\Delta}) / (2\delta)$.

<footnote n="187">¹⁸⁷The regenerative rate $\xi(t)$ is positive if $x(t) < \kappa$, zero at $x(t) = \kappa$, and negative if $x(t) < \kappa$. In the latter case, the stock is declining because the population density is too high to sustain it.</footnote>

<footnote n="188">¹⁸⁸We obtain a second order polynomial:</footnote>
<figure><img src="image_238.png" /><figcaption>Figure 5.86: Stability analysis of the logistic model with harvesting</figcaption></figure>

and $x(t)$ tends toward $x^*$, but if $x(t) < x^*$, $\frac{dx(t)}{dt} < 0$ and $x(t)$ tends to 0. Finally, if $h > \text{MSY}$, $x(t)$ tends asymptotically to 0. These results are summarized in Table 5.63. In Figure 5.87, we have simulated the model with three different starting values $x_0$ and four values of the parameter $\epsilon$. This shows the stability of each equilibrium. In particular, when $h = \text{MSY}$, we obtain an equilibrium at $x^* = \kappa/2$ only when the initial stock is already larger than the equilibrium.

<table><caption>Table 5.63: Sign table of $\frac{dx(t)}{dt}$</caption><thead><tr><th>x</th><th>0</th><th>δκ - √δκ(δκ - 4h) / 2δ</th><th>κ / 2</th><th>δκ - √δκ(δκ - 4h) / 2δ</th><th>κ</th><th>∞</th></tr></thead><tbody><tr><td>h = 0</td><td>0</td><td>+</td><td>+</td><td>+</td><td>+</td><td>0</td></tr><tr><td>0 < h < δ/4</td><td>—</td><td>—</td><td>0</td><td>+</td><td>+</td><td>—</td></tr><tr><td>h = δ/4</td><td>—</td><td>—</td><td>—</td><td>0</td><td>—</td><td>—</td></tr><tr><td>h > δ/4</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>
<figure><img src="image_239.png" /><figcaption>Figure 5.88: Equilibrium $x^*$ and harvest rate $h$</figcaption></figure>

<figure><img src="image_240.png" /></figure>
Figure 5.88 illustrates the equilibrium $x^*$ and the harvest rate $h$ as a function of the coefficient $\epsilon$. By construction, $x^*$ decreases with respect to $\epsilon$. When $\epsilon = 1$ or $h = \text{MSY}$, we verify that the equilibrium is unstable, indicating that $h = \text{MSY}$ is indeed a critical and undesirable harvest rate. To prevent overexploitation, it is essential that the absolute harvest rate remains below the maximum sustainable yield. Consequently, the relative harvest rate, defined as the ratio of the absolute harvest rate to the carrying capacity, must be less than one quarter of the intrinsic growth rate:

$$ \eta = \frac{h}{\kappa} < \eta^* = \frac{\delta}{4} $$

For example, if $\delta = 30\%$ per year, then $\eta^* = 7.5\%$, meaning that the relative harvest rate must be less than 7.5% per year. Conversely, if $\delta = 2\%$, the relative harvest rate must be much lower, less than 0.5% per year ($\eta^* = 0.5\%$). Here are some typical values of intrinsic growth rates:

* **Fish species**

In general, small and fast growing fish species such as sardines and anchovies can have rates of 100% or higher, while large and slow growing fish species such as sharks and tuna often have rates below 10%. Many commercial fish species, such as cod and haddock, have intrinsic growth rates between 10% and 50% per year.

* **Mammals**

Large mammals such as whales and elephants typically have low rates (5%–20% per year) because they reproduce slowly and have long gestation periods, while small mammals such as rodents and rabbits can have higher rates (50%–200% per year), reflecting their ability to reproduce rapidly.

* **Bacteria**

Bacteria can have very high intrinsic growth rates, sometimes doubling several times a day. For example, Escherichia coli (E. coli) can have rates of 20+ per day under optimal conditions.

Because large, slow-growing animals (such as many large fish species and mammals) have low intrinsic growth rates, they are highly vulnerable to overharvesting.

<table><caption>Table 5.64: Proportion in % of remaining buffalo under different harvest rate assumptions</caption><thead><tr><th>η (in %)</th><th>1.00</th><th>2.00</th><th>3.00</th><th>4.00</th><th>4.10</th><th>4.20</th><th>4.30</th><th>4.40</th></tr></thead><tbody><tr><td>10 years</td><td>93.55</td><td>86.81</td><td>79.77</td><td>72.40</td><td>71.65</td><td>70.89</td><td>70.12</td><td>69.36</td></tr><tr><td>20 years</td><td>90.88</td><td>80.64</td><td>68.95</td><td>55.35</td><td>53.85</td><td>52.34</td><td>50.79</td><td>49.22</td></tr><tr><td>30 years</td><td>89.71</td><td>77.32</td><td>61.63</td><td>40.10</td><td>37.45</td><td>34.68</td><td>31.78</td><td>28.74</td></tr><tr><td>40 years</td><td>89.18</td><td>75.41</td><td>55.85</td><td>21.32</td><td>16.04</td><td>10.18</td><td>3.62</td><td>0.00</td></tr></tbody></table>

Consider the dramatic collapse of the American buffalo. Suppose the intrinsic growth rate is 10% per year (Lueck, 2002; Jolles, 2007), and the initial buffalo population is at its carrying capacity ($x_0 = \kappa$). Table 5.64 shows the proportion of the remaining buffalo population under different relative harvest rate assumptions after 10, 20, 30, and 40 years.

* If the relative harvest rate $\eta$ is 1%, the remaining buffalo population after 10, 20, 30, and 40 years is 93.6%, 90.9%, 89.7%, and 89.2%, respectively.

* If the relative harvest rate is 4%, these figures decrease to 72.4%, 55.4%, 40.1%, and 21.3%.

* At a relative harvest rate of 4.4%, the buffalo population is completely wiped out (0% remaining) after 40 years.
The previous model can be extended in several directions (Quinn and Deriso, 1999). Gilpin et al. (1976) introduced a parameter $\theta \ge 0$ to control the asymmetry of the growth curve:

$$ \frac{dx(t)}{dt} = \delta x(t) \left( 1 - \left( \frac{x(t)}{\kappa} \right)^{\theta} \right) - h(x(t)) $$

In this formulation, $\theta$ allows the inflection point of the growth curve to vary between 0 and $\kappa$. When $\theta < 1$ (resp. $\theta > 1$), the maximum growth occurs for $x(t) < \kappa/2$ (resp. $x(t) < \kappa/2$). The case $\theta < 1$ is generally observed when resources are limited. Another extension is to consider different parameterizations of the harvest function. According to Begon and Townsend (2021), the three most popular functions $h(x)$ are:

1. Fixed quota (or constant catch) management

This specifies a predetermined, fixed number of animals that can be harvested. In this case, $h(x) = q$ is a constant, corresponding to the case we have already studied.

2. Fixed proportion harvesting

This specifies a proportion $e$ of animals that can be harvested, rather than a specific number:

$$ h(x) = ex $$

where $e$ is the exploitation rate expressed as a percentage.

3. Fixed escapement (or constant escapement rule)

This specifies not the number of animals to be harvested, but rather the number of animals to remain unharvested. In this approach, harvest occurs only when the population exceeds a threshold $x_{min}$, ensuring a minimum escapement:

$$ h(x) = e(x - x_{min})^{+} $$

Figure 5.89 shows the impact of the parameter $\theta$ and different harvesting management strategies on population size<fnref n="189" />. We note that the parameter $\theta$ has a significant impact when a fixed quota is used, whereas its effect is less pronounced under fixed proportion harvesting. In the latter case, the population dynamics follow the equation:

$$ \frac{dx(t)}{dt} = (\delta - e) x(t) - \delta \frac{x(t)^2}{\kappa} \left( \frac{x(t)}{\kappa} \right)^{\theta-1} $$

Here, the term $x(t)^2/\kappa$ has a greater magnitude than $(x(t)/\kappa)^{\theta-1}$, particularly when $\theta \ge 1$. We also observe that fixed escapement is the safest exploitation approach, as it ensures that $x^* > x_{min}$ — the limit case is obtained as $e \to \infty$.

Overexploitation can also be studied using a second class of multi-species models based on the Lotka-Volterra formulation. In the two-dimensional case, the system is given by:

$$ \left\{ \begin{aligned} \frac{dx(t)}{dt} &= ax(t) - bx(t)y(t) - h_x(x(t), y(t)) \\ \frac{dy(t)}{dt} &= cx(t)y(t) - dy(t) - h_y(x(t), y(t)) \end{aligned} \right. $$

<footnote n="189">¹⁸⁹The intrinsic growth rate $\delta$ is set to 30%, while $x_0$ and $\kappa$ are both equal to 100.</footnote>
<figure><img src="image_241.png" /><figcaption>Figure 5.89: Impact of the harvest function and the inflection point</figcaption></figure>

where $h_x(x, y)$ and $h_{x,y}(y)$ are the harvest functions of the prey and predator species, respectively. The classical Lotka-Volterra model is obtained by setting $h_x(x) = h_y(y) = 0$. This model has been extensively studied in both population dynamics modeling and the mathematical field of nonlinear systems, because it can be linked to the theory of deterministic chaos (characterized by sensitive dependence on initial conditions, strange attractors, and bifurcations). We can show that the classi-

cal Lotka-Volterra model has an unstable equilibrium at $(0,0)$ and a stable equilibrium at $(\frac{d}{c}, \frac{a}{b})$.

Let us assume that $a = 2$, $b = 3$, $c = 2$ and $d = 4$. Figure 5.90 shows the solutions $x(t)$ and $y(t)$ when the initial biomass values are $x_0 = 0.5$ and $y_0 = 1.5$ tonnes. Since there are initially too many predators and not enough prey, the predator population declines in the first phase. This allows the prey population to recover and reproduce, leading to an increase in prey biomass. In the second phase, as the prey population grows, the predators have more food available and begin to increase in number. Ultimately, this predator-prey system generates cyclical dynamics, as illustrated by the vector field analysis of the dynamical system (Figure 5.91). In this example, the cycle lasts 2.70 years. Figure 5.92 shows the phase portrait of the Lotka-Volterra model<fnref n="190" />, depicting the orbits or limit cycles generated by the system of differential equations.

$$ \frac{dy}{dx} = \frac{cxy - dy}{ax - bxy} $$

It follows that $(ax - bxy) dy = (cxy - dy) dx$. Dividing by $xy$, we get $c dx - d \frac{dx}{x} + b dy - a \frac{dy}{y} = 0$. We deduce that the solution is:

$$ cx - d \ln x + by - a \ln y = C \qquad (5.36) $$

where $C$ is a constant. The phase portrait is the set of solutions $(x, y)$ that satisfy Equation (5.36) for a given value of $C$.

<footnote n="190">¹⁹⁰We have:</footnote>
<figure><img src="image_242.png" /><figcaption>Figure 5.91: Vector field representation of the Lotka-Volterra model ($a = 2, b = 3, c = 2, d = 4$)</figcaption></figure>

<figure><img src="image_243.png" /></figure>
<figure><img src="image_244.png" /><figcaption>Figure 5.93: Simulation of the Lotka-Volterra model with harvesting ($a = 2, b = 3, c = 2, d = 4, e_y = 5, y_{min} = 1$)</figcaption></figure>

<figure><img src="image_245.png" /></figure>
Now let us consider exploitation. There are many ways to specify the harvest functions $h_x(x, y)$ and $h_y(x, y)$. If we aim to protect the prey species, we can set $h_x(x, y) = 0$ and $h_y(x, y) = e_y(y - y_{min})^+$, where $e_y$ is the exploitation rate of the predator species above the threshold $y_{min}$. This leads to a dynamic in which the biomass of both prey and predator species becomes more stable (Figure 5.93). Another approach is to protect the prey species when its population falls below a threshold $x_{min}$. In this case, for example, we can define the harvest function as $h_y(x, y) = e_y y (x_{min} - x)^+$.

**Remark 65** The Lotka-Volterra model can also be used to study the impact of invasive species, which can be considered as another form of overexploitation. In this context, $x$ represents the native species, while $y$ represents the invasive species (Roques et al., 2015).

After its publication, the Lotka-Volterra model was rapidly extended in many directions. In reviewing these developments, Solomon (1949) introduced the concepts of functional and numerical responses:

1. The ‘functional response’ describes how the predation rate (i.e., the number of prey consumed per predator) varies with prey density. It quantifies the efficiency of individual predators in capturing and consuming prey.

2. The ‘numerical response’ describes how predator population density changes in response to prey density. It reflects the total population-level effect of prey availability on predator numbers, including factors such as predator consumption, reproduction and migration, but excluding natural mortality.

From a mathematical point of view, we can write:

$$ \begin{cases} \frac{dx(t)}{dt} = \delta(t)x(t) - f(x(t), y(t))y(t) \\ \frac{dy(t)}{dt} = g(x(t), y(t))y(t) - \mu(t)y(t) \end{cases} $$

where $\delta(t)$ is the growth rate of the prey species, $f(x, y)$ is the functional response, $g(x, y)$ is the numerical response, and $\mu(t)$ is the mortality rate of the predator species. The classical Lotka-Volterra model is obtained by setting $\delta(t) = a$, $f(x, y) = bx$, $g(x, y) = cx$ and $\mu(t) = d$. In the late 1950s, Holling (1959a,b) conducted a comprehensive review of predation theory and proposed a classification of predation models based on the form of their functional responses. These types describe how predation rate varies with prey density:

* **Type I (linear)**
  Predation rate increases linearly with prey density until a maximum is reached. This simple, though somewhat unrealistic, model assumes that predators can process prey immediately upon encounter. It's often used in simplified models.

* **Type II (decelerating)**
  Predation rate still increases with prey density, but the rate of increase slows as prey becomes more abundant. This reflects factors such as predator handling time (the time it takes to consume each prey item) or satiation (when the predator becomes full).

* **Type III (sigmoidal)**
  Predation rate follows a sigmoidal curve, i.e., a slow initial increase at low prey densities, followed by an accelerated increase at moderate densities, and finally saturation at high densities.
This pattern often results from more complex predator behavior, such as learning, improved search efficiency, or the presence of prey refugia. It suggests that predators initially struggle to find or handle prey, but become more efficient over time.

Since Holling's publication, a fourth type has been added. Type IV responses are not monotonic. They increase to a maximum rate and decrease for higher values of x. The decrease can be explained by resource toxicity or predator confusion (Gentleman et al., 2003). These responses can be found for some bacterial processes. Below, we give some examples of functional responses:

<table><thead><tr><th>Type</th><th>I</th><th>II</th><th>III</th><th>IV</th></tr></thead><tbody><tr><td>f(x, y)</td><td>cx</td><td>αx / (β + x)</td><td>αx<sup>2</sup> / (β + x<sup>2</sup>)</td><td>αx / (β + x + γx<sup>2</sup>)</td></tr></tbody></table>

These responses are illustrated<fnref n="191" /> in Figure 5.94. Type II responses are the most well-known, as they are associated with the Michaelis-Menten-Monod equation.

<figure><img src="image_246.png" /><figcaption>Figure 5.94: Holling functional responses</figcaption></figure>

Tanner (1975) used the Holling Type II functional response and assumed that both prey and predator populations follow a logistic growth model. This leads to the Holling-Tanner predator-prey model:

$$ \begin{cases} \frac{dx(t)}{dt} = \delta x(t) \left(1 - \frac{x(t)}{\kappa}\right) - \frac{\alpha x(t)}{\beta + x(t)} y(t) \\ \frac{dy(t)}{dt} = \sigma y(t) \left(1 - \frac{y(t)}{\gamma x(t)}\right) \end{cases} $$

<footnote n="191">¹⁹¹We have used the following parameters: c = 0.2 (type I), α = β = 1 (types II and III), α = 4, β = 1 and γ = 2.5 (type IV).</footnote>
where $x(t)$ is the prey population and $y(t)$ is the predator population. Here, the carrying capacity of the predator population is related to the size of the prey population: $\kappa_y = \gamma x(t)$. The interpretation of the parameters is the following: $\delta$ is the intrinsic growth rate of the prey, $\kappa$ is the carrying capacity of the prey, $\alpha$ is the maximum predation rate, $\beta$ is the half-saturation constant that determines how prey abundance affects predation, $\sigma$ is the intrinsic growth rate of the predators, and $\gamma$ is the maximum predator-prey ratio. This model is more complex than the single logistic growth model because it can have four critical points<fnref n="192" />. Figure 5.95 shows the simulation<fnref n="193" /> of the Holling-Tanner predator-prey model when the initial values are $x_0 = 8$ and $y_0 = 5.5$, and the parameters are $\delta = 10\%$, $\kappa = 100$, $\alpha = 4$, $\beta = 20$, $\sigma = 20\%$, and $\gamma = 10\%$.

<figure><img src="image_247.png" /><figcaption>Figure 5.95: Simulation of the Holling-Tanner predator-prey model</figcaption></figure>

Previous functional responses depend only on the prey population. In a seminal paper, Arditi and Ginzburg (1989) challenge the traditional view of predator-prey interactions in which the predator's consumption rate depends solely on prey density. They propose an alternative approach in which

$$ \frac{dy(t)}{dt} = 0 \Leftrightarrow y(t) = 0 \land y(t) = \gamma x(t) $$

and:

$$ \frac{dx(t)}{dt} = 0 \Leftrightarrow \delta x(\kappa - x)(\beta + x) - \alpha \gamma \kappa x^2 = 0 $$

We can show that there can be four equilibria: $(0, 0)$, $(\kappa, 0)$, $(x_-, \gamma x_−)$ and $(x_+, \gamma x_+)$ where:

$$ x_{\pm} = \frac{(\delta\kappa - \delta\beta - \alpha\gamma\kappa) \pm \sqrt{(\delta\kappa - \delta\beta - \alpha\gamma\kappa)^2 + 4\beta\delta^2\kappa}}{2\delta} $$

<footnote n="192">¹⁹²The stability analysis implies that:</footnote>

<footnote n="193">¹⁹³It corresponds to the blue curve.</footnote>
the predator's consumption rate depends on the ratio of prey to predator densities, introducing the concept of ratio-dependent predation $r = x/y$:

$$f(x, y) = \frac{\alpha r}{\beta + r} = \frac{\alpha x}{\beta y + x}$$

In prey-dependent models (Holling type II), when prey is rare, predation is still significant. In ratio-dependent models, when prey is rare relative to predators, predation decreases dramatically, which is more realistic in nature. Figure 5.95 shows the effect of using a ratio-dependent model instead of a prey-dependent model<fnref n="194" />.

**Remark 66** The introduction of harvesting in the Holling-Tanner predator-prey model is the same as in the Lotka-Volterra model. We can then derive the equilibria (Diz-Pita and Otero-Espinar, 2021), analyze the effects of harvesting policy and define the maximum sustainable yield (Ghosh and Kar, 2013; Kar and Ghosh, 2013).

While predator-prey models describe interactions in which one species benefits at the expense of another, competition models describe interactions in which both species suffer from their coexistence due to competition for shared resources such as food, space, or other ecological resources (Polis et al., 1989). The most well-known competition model is the Lotka-Volterra multi-species competition model, which is mathematically similar to the predator-prey model but with negative interactions for both species (Case and Gilpin, 1974):

$$\frac{dx_i(t)}{dt} = \delta_i x_i(t) \left( 1 - \frac{\sum_{j=1}^{n} \omega_{i,j} x_j(t)}{\kappa_i} \right) \quad (5.37)$$

where $i = 1, \dots, n$ is the species index, $n$ is the number of species, $\delta_i$ and $\kappa_i$ are the intrinsic growth rate and the carrying capacity of species $i$, and $\omega_{i,j} \ge 0$ is the competition coefficient (how much species $j$ affects species $i$). Another interference competition model consists in considering that each species is a prey for the other species. In this case, we consider a multi-species logistic growth model and include Lotka-Volterra penalties:

$$\frac{dx_i(t)}{dt} = \delta_i x_i(t) \left( 1 - \frac{x_i(t)}{\kappa_i} \right) - \sum_{j \neq i} \alpha_{i,j} x_i(t) x_j(t) \quad (5.38)$$

where $\alpha_{i,j} \ge 0$ is the coefficient of interaction between species $i$ and $j$. More generally, interference competition models combine the logistic growth model and Holling functional responses:

$$\frac{dx_i(t)}{dt} = \delta_i x_i(t) \left( 1 - \frac{x_i(t)}{\kappa_i} \right) - \sum_{j \neq i} f_{i,j}(x_1(t), \dots, x_n(t)) x_j(t) \quad (5.39)$$

Model (5.38) is a special case of model (5.39) when we use a Holling type I linear response: $f_{i,j}(x_1, \dots, x_n) = \alpha_{i,j}x_i$. For Holling type II responses, we can write:

$$f_{i,j}(x_1, \dots, x_n) = \frac{\alpha_{i,j} x_i}{\beta_{i,j} + x_i}$$

These different models can exhibit chaotic behavior, even in low dimension. For instance,

<footnote n="194">¹⁹⁴We use exactly the same parameters and initial values as in the classical Holling-Tanner prey-dependent model. The blue curves correspond to the prey-dependent model, while the red curves correspond to the ratio-dependent model.</footnote>
Box 5.24: Symbiosis and interspecific interactions

The term symbiosis, derived from Greek roots meaning ‘together’ and ‘living’, describes a close and long-term biological interaction between two different organisms. An ecological community includes all the populations of different species that coexist in a given area. The interactions between these species are called interspecific interactions. They can be categorized as positive (+), negative (−), or neutral (0) based on their effects on the species involved (Polis et al., 1989). There are seven broad types of symbiosis:

1. Amensalism (−/0)

One species is harmed and the other is unaffected, often through the release of a chemical compound.

2. Commensalism (+/0)

One species benefits while the other remains unaffected. A classic example is bar-nacles that attach themselves to whales for transportation, gaining a mobile habitat while the whale remains indifferent.

3. Competition (−/−)

Both species are negatively affected by the limited availability of shared resources such as food, water, or nesting sites. For example, the swift fox (*Vulpes velox*) and coyotes (*Canis latrans*) competing for the same resources may both experience reduced reproductive success (Kitchen et al., 1999).

4. Mutualism (+/+)

Both species benefit from the interaction. A common example is the relationship between bees and flowers, where bees receive food (nectar) and flowers receive pol-lination assistance.

5. Neutralism (0/0)

Neither species is affected by the interaction. Although theoretically possible, true neutralism is difficult to prove definitively in complex ecosystems. For example, a butterfly and a snake living in the same habitat may appear neutral.

6. Parasitism (+/−)

One species (the parasite) benefits at the expense of the other (the host). Ticks that feed on the blood of a mammal are an example of this relationship, where the tick gains nourishment while the host experiences potential harm and irritation.

7. Predation (+/−)

One species (the predator) benefits by killing and consuming the other (the prey). A lion hunting a zebra is a clear example of predation.

Vano et al. (2006) studied model (5.37) with four species and the following parameters: $\delta = (1.00, 0.72, 1.53, 1.27)$, $\kappa = (10, 10, 10, 10)$ and:

$$ \Omega = (\omega_{i,j}) = \begin{pmatrix} 1 & 1.09 & 1.52 & 0 \\ 0 & 1 & 0.44 & 1.36 \\ 2.33 & 0 & 1 & 0.47 \\ 1.21 & 0.51 & 0.35 & 1 \end{pmatrix} $$
They showed that the chaotic attractor of this dynamical system corresponds to homoclinic orbits (Figure 5.96).

<figure><img src="image_248.png" /><figcaption>Figure 5.96: Phase portrait of the Lotka-Volterra four-species competition model</figcaption></figure>

Source: Vano et al. (2006, Figure 3, page 2386).

A second family of competition models explicitly introduces a set of resources. One of the first explicit resource competition models was proposed by MacArthur and Levins (1964). This model has been extensively used and extended by Robert MacArthur in several research papers and is now known as MacArthur consumer-resource model (Chesson, 1990). In MacArthur (1970), the model is formulated as follows:

$$ \left\{ \begin{aligned} \frac{dx_i(t)}{dt} &= \beta_i x_i(t) \left( \sum_{j=1}^{m} \alpha_{i,j} \omega_j y_j(t) \right) - \mu_i x_i(t) \\ \frac{dy_j(t)}{dt} &= \delta_j y_j(t) \left( 1 - \frac{y_j(t)}{\kappa_j} \right) - \sum_{i=1}^{n} \alpha_{i,j} x_i(t) \end{aligned} \right. $$

where $x_i(t)$ represents the population density of species i, $y_j(t)$ represents the population density of resource j (e.g., food resources), $\beta_i$ is a conversion factor that translates resource consumption into per capita growth rate, $\alpha_{i,j}$ is the rate at which species i captures resource j, $\omega_j$ is the value of a unit of resource j to the consumer (e.g., caloric energy), $\mu_i$ is the mortality rate of species i, and $\delta_j$ is the intrinsic growth rate of resource j. A variant of the MacArthur model assumes that resource availability depends on three factors: supply, depletion and consumption. In this case, we
Box 5.25: Robert H. MacArthur

Despite his tragically short life (1930–1972), Robert MacArthur was one of the most influential ecologists of the 20th century (Fretwell, 1975; Brown, 1999). He received his Ph.D. from Yale University in 1957 under the direction of G. E. Hutchinson and was a professor at the University of Pennsylvania and Princeton University. He is known for developing the theory of island biogeography, the study of limiting similarity (niche theory), consumer-resource theory, and his contributions to the complexity-stability debate. According to Brown (1999), “MacArthur’s influence stems not only from his substantial and frequently cited published works but also from his direct personal interactions and collaborations with contemporary scientists, especially young people”. He had a significant influence on his co-authors, all of whom went on to brilliant careers: Martin L. Cody, Joseph Hurd Connell, Jared Mason Diamond, Henry Stainken Horn, George Evelyn Hutchinson, James R. Karr, Peter Hubert Klopfer, Richard Levins, Robert McCredie May, Harry Frederick Recher, Eric Rodger Pianka, Michael L. Rosenzweig, and Edward Osborne Wilson.

<figure><img src="image_249.png" /></figure>

obtain the following Lotka-Volterra competition model with externally supplied resources (Cui et al., 2024):

$$ \left\{ \begin{aligned} \frac{dx_i(t)}{dt} &= \beta_i x_i(t) \left( \sum_{j=1}^{m} \alpha_{i,j} \omega_j y_j(t) \right) - \mu_i x_i(t) \\ \frac{dy_j(t)}{dt} &= \kappa_j - \varrho_j y_j(t) - \left( \sum_{i=1}^{n} \alpha_{i,j} x_i(t) \right) y_j(t) \end{aligned} \right. $$

where $\kappa_j$ is the supply of resource j, $\varrho_j$ is the natural depletion or decay rate of resource j, and $\alpha_{i,j}$ is the rate at which species i consumes resource j. Along with Robert MacArthur, David Tilman is another prolific researcher on competition models and their impact on community structure. In his book, Tilman (1982) used the following general formulation:

$$ \left\{ \begin{aligned} \frac{dx_i(t)}{dt} &= f_i(y_1(t), \dots, y_m(t)) x_i(t) - \mu_i(t) x_i(t) \\ \frac{dy_j(t)}{dt} &= g_j(y_j(t)) - \sum_{i=1}^{n} \alpha_{i,j} (y_1(t), \dots, y_m(t)) f_i(y_1(t), \dots, y_m(t)) x_i(t) \end{aligned} \right. $$

where $f_i(y_1, \dots, y_m)$ is the growth function of consumer i, $\mu_i(t)$ is the mortality rate function of consumer i, $g_j(y_j)$ is the growth function of resource j, and $\alpha_{i,j}(y_1, \dots, y_m)$ is the conversion factor function from resource j to consumer i. The MacArthur consumer-resource model and the Lotka-Volterra competition model with externally supplied resources are both special cases of Tilman’s general model<fnref n="195" />.

<footnote n="195">¹⁹⁵The MacArthur consumer-resource model is obtained by setting $f_i(y_1, \dots, y_m) = \beta_i \sum_{j=1}^{m} \alpha_{i,j} \omega_j y_j$, $\mu_i(t) = \mu_i$,</footnote>
The competitive exclusion principle (or Gause's law) states that two species competing for exactly the same resource cannot stably coexist indefinitely. One will outcompete the other. For coexistence to occur, the species must occupy slightly different niches or use resources differently (niche theory). This traditional interpretation of competitive exclusion and niche theory has been challenged by much research. In fact, although there are many examples where the traditional interpretation is valid<fnref n="196" />, there are also many examples where multiple competitive species can coexist<fnref n="197" />. Moreover, Armstrong and McGehee (1980) demonstrated that under certain conditions, multiple species can coexist with fewer resources in a Lotka-Volterra model of multi-species competition. In fact, the relationship between biodiversity and competition is more complex, as demonstrated by Chesson (1990), who examined the processes that allow multiple species to coexist within the same ecological community and addressed the apparent paradox of high biodiversity despite competitive interactions. He categorized mechanisms that promote species coexistence into two primary types: equalizing mechanisms (which reduce average fitness differences between species, minimizing competitive inequalities) and stabilizing mechanisms (which increase negative intraspecific interactions relative to interspecific interactions, promoting coexistence by ensuring that species limit their own population growth more than they limit that of others). He also emphasized that environmental variability, both spatial and temporal, can facilitate coexistence. It follows that competition and harvesting are not equivalent. It is not obvious that competition dramatically reduces biodiversity, which is not the case with harvesting. However, the effects of harvesting strategies in multi-species consumer-resource metapopulations are not well known. For example, Strevens and Bonsall (2011) found that certain harvesting strategies, particularly fixed proportion harvesting, resulted in larger regional population sizes, fewer local extinctions, and higher yields compared to unharvested metapopulations. This counterintuitive result suggests that increasing local mortality through specific harvesting methods can increase overall population sizes — a phenomenon referred to as the 'hydra effect'. However, as Abrams (2009) points out, there is little empirical evidence for hydra effects in nature. Thus, there is a gap between previous theoretical and empirical results.

**Overexploitation in aquatic systems** In the early 2000s, several important research papers alerted the scientific community to the threat of overfishing and the potential collapse of marine ecosystems. Jackson et al. (2001) examined how historical overfishing had led to the degradation and collapse of coastal ecosystems over time. Using a variety of historical data — including archaeological records, historical documents, and paleoecological studies — the authors described how the removal of top predators and key species (e.g., sharks, sea otters, cod, oysters) through overfishing could trigger cascading effects throughout the food web, leading to shifts in the abundance and distribution of other species. For example, the loss of large predators led to an increase in prey species, which in turn overgrazed habitats. In addition, the destruction of habitat-forming species (e.g., oyster

<footnote>$g_j(y_j) = \delta_j y_j (1 - \kappa_j^{-1} y_j)$, and $\alpha_{i,j} (y_1, \dots, y_m) = (\beta_i \sum_{j=1}^m \alpha_{i,j} \omega_j y_j)^{-1} \alpha_{i,j}$. For the Lotka-Volterra competition model with externally supplied resources, the generic functions for the resources are $g_j(y_j) = \kappa_j - \varrho_j y_j$, and $\alpha_{i,j} (y_1, \dots, y_m) = (\beta_i \sum_{j=1}^m \alpha_{i,j} \omega_j y_j)^{-1} \alpha_{i,j} y_j$.</footnote>

<footnote n="196">¹⁹⁶A famous example is the competition between the flour beetles *Tribolium castaneum* and *Tribolium confusum* (Park, 1962; Pointer et al., 2021).</footnote>

<footnote n="197">¹⁹⁷A well-known example that challenges the competitive exclusion principle is the plankton paradox, first described by Hutchinson (1961). In aquatic ecosystems, numerous species of phytoplankton coexist despite competing for a limited number of resources such as light, nitrogen, and phosphorus. According to the principle of competitive exclusion, only a few dominant species should survive because they would outcompete the others. In natural environments, however, dozens of phytoplankton species coexist in the same habitat. A second well-known example was described by MacArthur (1958), who studied five species of warblers (small songbirds) coexisting in the same forest areas and apparently feeding on the same insects. This apparent contradiction of competitive exclusion led to the development of the theory of niche differentiation.</footnote>
reefs, seagrass beds, corals) led to a decline in biodiversity and ecosystem functions. Pauly et al. (2002) introduced the concept of ‘fishing down marine food webs’, where fisheries increasingly target smaller, lower trophic level species as larger predatory fish become scarce. The authors emphasized that without significant intervention, global fisheries would continue to decline, putting marine biodiversity at risk. Pauly et al. (2005) built on these themes and expanded the discussion of the consequences of overfishing for marine ecosystems and global food security:

> "With the development of industrial fishing, and the resulting invasion of the refuges previously provided by distance and depth, our interactions with fisheries resources have come to resemble the wars of extermination that newly arrived hunters conducted 40 000–50 000 years ago in Australia, and 12 000–13 000 years ago against large terrestrial mammals in North America." (Pauly et al., 2005, page 5).

Another milestone was reached with the publication of empirical research by Myers and Worm (2003) and Worm et al. (2006) in *Nature* and *Science*. Myers and Worm (2003) defined the following biomass time-trend model:

$$N_i(t) = N_i(0) \left( (1 - \varphi_i) e^{-r_i(t-t_0)} + \varphi_i \right)$$

where $N_i(t)$ is the biomass at time $t$, $N_i(0)$ is the initial biomass before industrialized exploitation, $r_i$ is the rate of decline and $\varphi_i$ is the fraction of the community that remains at equilibrium as $t \to \infty$. Using large predator biomass data from nine oceanic ecosystems (tropical/subtropical/temperate × Atlantic/Indian/Pacific) and four shelf ecosystems (Gulf of Thailand, South Georgia, Southern Grand Banks, and Saint Pierre Banks), they estimated the coefficients $\hat{r}_i$ and $\hat{\varphi}_i$ by using the method of maximum likelihood, and the parameters of the nonlinear mixed-effects models assuming that $r_i \sim N(\mu_r, \sigma_r^2)$ and $\varphi_i \sim N(\mu_\varphi, \sigma_\varphi^2)$. Figure 5.97 shows the results for the global region and three specific regions<fnref n="198" />. The authors concluded that industrialized fisheries typically reduce community biomass by 80% within 15 years of exploitation, and that the biomass of large predatory fishes is now only about 10% of pre-industrial levels. Worm et al. (2006) “analyzed local experiments, long-term regional time series, and global fisheries data to test how biodiversity loss affects marine ecosystem services across temporal and spatial scales.” They found that “rates of resource collapse increased and recovery potential, stability, and water quality decreased exponentially with declining diversity.” They emphasized that their findings highlight the societal consequences of the ongoing erosion of biodiversity, which appears to be accelerating globally. Moreover, they expressed serious concern about this trend, as their regression model predicted the global collapse of all commercially

<table><thead><tr><th>Region</th><th>\hat{r}<sub>i</sub></th><th>\hat{\mu}<sub>r</sub></th><th>\hat{\varphi}<sub>i</sub></th><th>\hat{\mu}_{\varphi}</th></tr></thead><tbody><tr><td>Tropical Atlantic</td><td>16.6</td><td>16.7</td><td>12.1</td><td>11.9</td></tr><tr><td>Subtropical Atlantic</td><td>12.9</td><td>13.0</td><td>8.1</td><td>8.3</td></tr><tr><td>Temperate Atlantic</td><td>21.4</td><td>20.3</td><td>4.7</td><td>5.3</td></tr><tr><td>Tropical Indian</td><td>9.2</td><td>9.5</td><td>17.6</td><td>16.8</td></tr><tr><td>Subtropical Indian</td><td>6.5</td><td>6.8</td><td>8.2</td><td>9.2</td></tr><tr><td>Temperate Indian</td><td>30.7</td><td>27.7</td><td>5.5</td><td>6.3</td></tr><tr><td>Tropical Pacific</td><td>12.1</td><td>12.4</td><td>15.5</td><td>14.9</td></tr><tr><td>Subtropical Pacific</td><td>12.8</td><td>13.5</td><td>23.5</td><td>21.5</td></tr><tr><td>Temperate Pacific</td><td>20.8</td><td>20.4</td><td>8.2</td><td>8.5</td></tr><tr><td>Gulf of Thailand</td><td>25.6</td><td>22.2</td><td>9.3</td><td>9.8</td></tr><tr><td>South Georgia</td><td>166.6</td><td>30.8</td><td>20.9</td><td>16.0</td></tr><tr><td>Southern Grand Banks</td><td>4.0</td><td>5.7</td><td>0.0</td><td>10.0</td></tr><tr><td>Saint Pierre Banks</td><td>5.1</td><td>6.3</td><td>2.7</td><td>7.9</td></tr><tr><td>Global</td><td></td><td>16.0</td><td></td><td>10.3</td></tr></tbody></table>

<footnote n="198">¹⁹⁸Below, we report the estimated values found by Myers and Worm (2003, Table 1, page 281):</footnote>
fished taxa by the mid-21st century (specifically, by 2048). Some newspapers and journalists have focused on this figure, interpreting it as a prediction that “*the oceans will be empty by 2048*”. For example, this claim was mentioned in the controversial documentary *Seaspiracy*, which premiered on Netflix in 2021.

<figure><img src="image_250.png" /><figcaption>Figure 5.97: Time trends of community biomass in oceanic and shelf ecosystems</figcaption></figure>

Source: Myers and Worm (2003, Figure 1, page 280) & Author's calculations.

As Boris Worm later explained, this period marked the peak of pessimism. Indeed, Worm's study was not the only one with a gloomy outlook — many studies in the 2000s warned that the collapse of global fisheries could become a reality. Thurstan et al. (2010) analyzed annual demersal fish landings from bottom trawls in the United Kingdom from 1889 to 2007 (Figure 5.98). Their results showed a dramatic decline in the commercial productivity of fisheries, with landings per unit of fishing power falling by 94% over the past 118 years. Another well-known example is the collapse of the Atlantic cod fishery in eastern Canada (Myers et al., 1997). According to Schijns et al. (2021), “*the fishery for Northern Atlantic cod (Gadus morhua) off Newfoundland and Labrador, Eastern Canada, presents the most spectacular case of an exploited stock crashed in a few decades by an industrial bottom trawl fishery under a seemingly sophisticated management regime after half a millennium of sustainable fishing. The fishery, which had generated annual catches of 100 000 to 200 000 tonnes from the beginning of the 16th century to the 1950s, peaked in 1968 at 810 000 tonnes, followed by a devastating collapse and closure 24 years later.*” Figure 5.99 illustrates the evolution of cod harvests in eastern Canada. We observe a continuous increase throughout the 18th and 19th centuries, with a sharp acceleration in the 20th century, especially after 1960. Schijns et al. (2021) estimated the maximum sustainable yield at 380 000 tonnes, a level well below the harvest volumes recorded between 1960 and 1990. We have also reported the estimated stock levels in Figure 5.99, which
<figure><img src="image_251.png" /><figcaption>Figure 5.98: Fish catch in the United Kingdom</figcaption></figure>

Source: Thurstan et al. (2010, Figure 1a, page 2) & www.ourworldindata.org/fish-and-overfishing.

<figure><img src="image_252.png" /><figcaption>Figure 5.99: Northern cod catch in eastern Canada</figcaption></figure>

Source: Schijns et al. (2021, Figure 1, page 2679) & Author's calculations.