Ecology of a Changed World 2022 PDF

Ecology of a Changed World Front cover: Between 1970 and 2021, the number of people in the world doubled to nearly 8 billion and the number of chickens increased fivefold to 26 billion. The number of wild birds in North America declined by 30% (the illustration runs to 2017, when bird abundances w...

Ecology of a Changed World Front cover: Between 1970 and 2021, the number of people in the world doubled to nearly 8 billion and the number of chickens increased fivefold to 26 billion. The number of wild birds in North America declined by 30% (the illustration runs to 2017, when bird abundances were estimated). There may now be fewer birds in North America than people in the world. See Figures 11.2, 12.3, and 24.5. Illustration by Allison Johnson.  Ecology of a Changed World T R EVO R P R IC E University of Chicago, Chicago Illustrated by AVA R A I N E 1  3 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2022 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-​in-​Publication Data Names: Price, Trevor, 1953– author. Title: Ecology of a changed world / Trevor Price ; illustrated by Ava Raine. Description: New York : Oxford University Press, | Includes bibliographical references and index. Identifiers: LCCN 2021029388 (print) | LCCN 2021029389 (ebook) | ISBN 9780197564172 (hardback) | ISBN 9780197564196 (epub) Subjects: LCSH: Ecology. | Global environmental change. | Biodiversity—Environmental aspects. Classification: LCC QH541. P735 2021 (print) | LCC QH541 (ebook) | DDC 577—dc23 LC record available at https://lccn.loc.gov/2021029388 LC ebook record available at https://lccn.loc.gov/2021029389 DOI: 10.1093/​oso/​9780197564172.001.0001 1 3 5 7 9 8 6 4 2 Printed by Integrated Books International, United States of America Royalties for this book will be donated to savingnature.org  Contents Preface  vii Acknowledgments  ix About the Companion Website xi 1. The Changed World  1 PA RT 1. T H E R I SE A N D FA L L O F P O P U L AT IO N S 2. Population Growth  9 3. Population Regulation  21 4. Interactions between Species: Mutualisms and Competition  31 5. Predation and Food Webs  43 6. Parasites and Pathogens  52 7. Evolution and Disease  64 8. The Human Food Supply: Competition, Predation, and Parasitism  75 9. Food Security  83 PA RT 2. T H E T H R E AT S T O B IO D I V E R SI T Y 10. Prediction  97 11. Human Population Growth  110 12. Growth of Wealth and Urbanization  121 13. Habitat Conversion  132 14. Economics of Habitat Conversion  143 15. Climate Crisis: History  155 16. Predictions of Future Climate and its Effects  166 17. Pollution  176 18. Invasive Species  184 vi Contents 19. Introduced Disease  194 20. Harvesting on Land  205 21. Harvesting in the Ocean  215 22. Harvesting: Prospects  226 PA RT 3. AV E RT I N G E X T I N C T IO N S 23. Species  239 24. Population Declines  248 25. Extinction  261 26. Species across Space  273 27. Island Biogeography and Reserve Design  283 28. The Value of Species  294 Notes and References  303 Subject Index  331 Species Index 337  Preface This book has been updated over 15 years in order to keep up with the rapid changes of the twenty-​first century, and it will continue to be updated through an associated website, which also contains appendices to chapters, and worked examples. The coronavirus pandemic, the Black Lives Matter movement, excep- tional fires and heatwaves exmplify the changes and the challenges of our times. A book on the science behind the biodiversity crisis has much to say about the pandemic and climate change. The SARS CoV-​2 virus crossed into humans most likely from the hunting of bats for food. So, we might ask, what would happen if there were no bats in the world? The science is clear. Every time a species is lost, others become more common, making new disease transmission and virulence even more likely. We can see this in the rapid spread of coronavirus through the dense human population. We can also observe more directly effects of bat loss in North America, where white nose disease inadvertently introduced from Europe in 2006 has killed millions of bats, which in turn has been linked to increased insecticide use by farmers attempting to combat the insect pests the bats would otherwise have eaten. This book moves beyond specific examples and beyond disease. We want to quantify biodiversity loss and the consequences for human well-​being as we go forward. What about Black Lives Matter? As sports writer Barney Ronay put it: “so much unhappiness is created, so much talent is lost, so many people who should be doing things and have opportunities to do those things, don’t receive those opportunities.” (Complete citations are in the references section at the end of the book.) What can we say about connections between these injustices and con- servation? Asymmetries and inequalities lie beyond race. They include gender, sexual orientation, disability, caste, religion, nationality, and wealth. Such inequalities are not only morally indefensible, but contribute to the crisis of na- ture. As a middle-​class white male, my concern with the natural world comes from privilege and past experience. Others have not had this same fortune, and one feels that nothing but good could come out of more such opportunity. In this book I focus on one important inequality: that of wealth. Aside from the other benefits of having money, many are not able to buy enough food, de- spite there being more than enough food now produced to feed everyone. Like other forms of inequality, poverty is not something I have personally had to deal with, but it is something I have witnessed firsthand, working in India. Wealth disparities impact conservation greatly, from the direct effects of being poor viii Preface (e.g., it leads people to hunt bats) to the more general lack of opportunity that is associated with all types of discrimination. Within countries, wealth inequality continues to increase, but the economic growth of Asian and South American countries has meant that across the world inequality has been decreasing, at least until the recent economic downturn. On average, people have been becoming richer and healthier, and we hope this trend will pick up again soon. Such wel- come changes have huge implications for the conservation of biodiversity. These changes are covered in the book, and many of the consequences surely apply more generally to the mitigation of all social injustices.  Acknowledgments Chris Andrews, Bettina Harr, Julia Weiss, and several anonymous reviewers read the whole book. Various pieces have been read by Erin Adams, Sarah Cobey, Ben Freeman, Peter Grant, Sean Gross (who made the compelling suggestion to delete a chapter), Rebia Khan, Kevin Lafferty, Karen Marchetti, Robert Martin, Natalia Piland, Yuvraj Pathak, Uma Ramakrishnan, Mark Ravinet, Matthew Schumm, David Wheatcroft, and anonymous reviewers. Many people have responded to requests for information, including David Archer, Sherri Dressel, Clinton Jenkins, David Gaveau, Kyle Hebert, David McGee, Loren McClenachan, Nate Mueller, Natalia Ocampo-​Peñuela and Stuart Sandin. The copy editor, Betty Pesagno, made an excellent and thorough review. Kaustuv Roy has always been supportive and a great friend. I appreciated the R programming environment (citations are in the Notes and References section at the end of the book). I par- ticularly wish to thank Angela Marroquin and Bettina Harr for much help with the figures and Ava Raine for her outstanding drawings. The book is dedicated to local activists, who are at the frontline of conserving the planet’s biodiversity, sometimes at considerable risk to themselves. They in- clude Homero Gómez González and Raúl Hernández Romero, who were mur- dered in 2020, apparently by illegal loggers. Their work involved conserving the winter habitat of the emblematic monarch butterfly which migrates from the eastern United States to a few mountain tops in central Mexico. Not so long ago the monarch population numbered in the many hundreds of millions, but in the last 10 years, never more than 100 million (Chapter 24).  About the Companion Website http://global.oup.com/us/companion.websites/9780197564172/ins_res/l0k-res/. Oxford has created a website to accompany Ecology of a Changed World. As the world continues to change, the site will be used to post regular updates to various chapters and figures. In addition, the website carries study questions and their solutions, plus an appendix that covers the measurement of uncertainty and some mathematical derivations. The reader is encouraged to consult this resource as a complement to the book. Color plate 1 (Figure 4.1) Left: Mutualism: Bees and flowers form a mutualism, whereby an increase in the population size of one causes an increase of the other, and a decrease in one causes a decrease of the other. Right: Competition: Roots of ground ivy (stained green) and wild strawberry (stained blue) compete for nutrients and water. An increase in one species causes a decrease in the other, and a decrease in one species leads to an increase in the other. For furter details see the text figure. Color plate 2 (Figure 6.4) Food web from Carpinteria Bay. Each circle is a species in the web, with plants along the base, predators in blue and parasites in red (circle size relates to abundance; J. P. McLaughlin and K. D. Lafferty). Left: the cercaria larva of a flatworm, one of the flatworm’s secondary hosts, the California killifish, and one of its primary hosts, the great blue heron, in which the adult worm infests the liver. Right: Pickleweed, American coot and striped shore crab at their corresponding positions in the web. For further details see the text figure. Color plate 3 (Figure 8.2) Vetch has evolved a mimic seed, resembling lentil seeds. For further details see the text figure. Color plate 4 (Figure 9.3) The extent to which crop yields of the three major grains (wheat, corn, rice) were below the maximum possible in the year 2000, given technology and fertilizer available at that time. For further details see the text figure. Color plate 5 (Figure 10.2) Left: Annual deviations from the average of 1880–​1919 for global mean surface temperature up to 2005 (in places one sees more than one line because three different assessments have been made). Thin lines represent the average of different models of temperature change, accounting for both human and natural causes, with the shading around them different run of the models. The blue lines represent a more recent set of models than the orange lines and reproduce the past more faithfully. Right: Global temperature 1990–​2020. For further details see the text figure. Color plate 6 (Figure 13.1) Above: Estimated net primary productivity (NPPpristine) as it would be in the absence of humans. The units are grams carbon/​ m2/​ year. Below Human Appropriated Net Primary Productivity (HANPP) as a percentage of NPPpristine for the year 2000. Blue areas are places where human effects have been to increase NPP. For further details see the text figure. Color plate 7 (Figures 13.2 and 13.3) Above: Exploitation of the planet by humans, after weighting land by its calorific value (Table 13.1), estimated for the year 2011. Below: Requirements from the planet if everyone in the world had per capita consumption patterns of the five countries listed, based on 2010 data. The left bar is identical to the upper figure. From the Global Footprint Network: see figure legends for further details. Qatar now somewhat exceeds China. It is a desert country whose excessive use of energy results in a low land use footprint. Color plate 8 (Figure 13.4) Above left: Forest inferred for c. 8,000 years before present and in 1990. Above right: Average cover in 3km*3km grid squares estimated by remote sensing across the world in the year 2001. Below: Red dots indicate 3km*3km grid squares that have experienced at least some forest loss between 2001 and 2019, superimposed on the above right figure. For further details see the text figure. Color plate 9 (Figure 13.7) Borneo land use in 1973 and 2018. The lower graphs show an expanded version of the white rectangle, which covers Gunung Palang National Park and its surroundings. (Compiled by the Center for International Forestry Research; nusantara-​atlas.org). Color plate 10 (Figure 14.3) Benefits and costs of conservation across the upper watershed of the Jejuí River in eastern Paraguay. The opportunity cost of conservation is estimated from the cost of purchasing land, which depends on soil quality, topography, and who owns it. Left: The benefit of retaining forest from harvesting and aesthetic value alone. Right: Harvesting, aesthetic value, and carbon storage. Black: benefits of conservation outweigh costs. Gray: costs of conservation outweigh benefits. White: not forested nor considered. A park (red outline) and indigenous areas (green outline) are already protected, and hence the cost of purchasing the land for conservation is absent or low. For further details see the text figure. Color plate 11 Temperature anomalies across Australia from 1910 to 2019, with respect to the 1961–​1990 average. Temperatures vary from –​3°C to +3°C. (Australian Bureau of Meteorology, www.bom.gov.au/​climate). Attribution 3.0 Australia (CC BY 3.0 AU) Color plate 12 (Figure 16.3) Predicted changes in precipitation averaged over the years 2041–​2060, with respect to the average in the period 1986–​2005. Changes are modeled on the scenario leading to 2.5°C, with probability 0.5 by the year 2100 (Figure 16.1). In this case, wet, wetter, and very much wetter are annual increases of 40 cm a year, respectively. For further details see the text figure. Color plate 13 (Figure 19.2) Dates of first occurrence of confirmed or suspected white-​nose disease, or else, in 15% of the cases, the detected presence of the fungus, in counties of the US and administrative districts of Canada. (North American Bat Monitoring Program). Color plate 14 (Figure 21.4) Photographs of the state of the reef from the Line Islands, central Pacific, on a gradient from heavily fished (G, H, bottom) to protected (A, B, top). Note the number of sharks in protected areas. Figure provided by Stuart Sandin. Color plate 15 (Figure 23.2) Monarch flycatchers’ distributions and relationships. The right panel shows relationships between 10 individual birds based on differences in DNA sequence: individuals separated by shorter branches are more similar in sequence than those that are separated by longer branches. Picture drawn by Emiko Paul. For further details see the text figure. Color plate 16 (Figure 23.5) Cryptic species. Left Four species of skipper butterfly, each represented by the male, female, and caterpillar, not known to be different species until DNA sequencing. Right Two species of flycatcher warbler classified as the same species until 1999. Song and DNA sequence data, plus their presence in the same place with no evidence of interbreeding, unequivocally shows that they are different biological species. Painting of the birds by Ian Lewington. For further details see the text figure. Color plate 17 (Figure 24.4) Counts of horned larks along 108 Breeding Bird Survey routes in Colorado (yellow outline). The black line is the average. The grey shading provide a 95% confidence limit for numbers across the state as a whole (i.e., in 95% of the time when we conduct such censuses, the constructed confidence limit should contain the true value). The horned lark shows one of the largest declines of all species, by an estimated 66%, equivalent to 180 million fewer birds now breeding when compared to 1970. Shades on the map indicate locations showing an annual increase or decrease. (Photo by Brad Imhoff). For further details see the text figure. Color plate 18 (Figure 24.7) Fraction of all species in different IUCN categories for the three best known groups, as of September 2020. The total number of species is given at the base. “Extinct” is all species that have gone extinct in the past 500 years but includes two mammal, two amphibian, and five bird species that are extinct in the wild but held in captivity. Data deficient means the species have yet to be assessed. (IUCN Red List of Threatened Species) Color plate 19 (Figure 26.2) Top and middle Numbers of species across the globe for four groups. Below Distributions of bird and mammal species in the IUCN threatened category. The plant map is a result of interpolating between the relatively few sites on the globe where diversity has been measured and is less certain than the others; dark green is the top 1% of all grid cells. For further details and citations see the text figure. Color plate 20 (Figure 26.7) Conservation International’s biodiversity hotspots. Hotspots cover 16% of the land surface area and contain more than 60% of the world’s species but have lost around 85% of their habitat. (Accessed through Global Forest Watch www.global​fore​stwa​tch.org). The original paper identified 25 hotspots and others were subsequently added (N. Myers, R. A. Mittermeier, C. G. Mittermeier, et al. 2000. Biodiversity hotspots for conservation priorities Nature 403: 853–​858).  1 The Changed World About 66 million years ago, an asteroid hit what is now the Yucatan region of Mexico, setting off a major extinction of species on Earth. Remarkably, over the present century, the environment will change more rapidly than it has over any corresponding timespan since that devastating impact. Sixty-​six million years is a long time, and the magnitude of the changes we will face in the near future is especially remarkable because these changes have been brought about entirely by humans. Some changes are for the better, at least for humanity: more people than ever are living longer, healthier lives, and standards of living in Asia and Latin America are improving at an impressive rate. Yet, the negative impacts of popu- lation growth and consumption on the environment are huge and may catch up with us sooner rather than later, making it crucial that we appreciate the basics of ecology in the context of what is happening. That is the purpose of this volume. Mass extinctions in the past have been defined as periods of exceptionally high species loss (as indicated by the fossil record of mollusks on the continental shelf, which is more complete than that on land.) Scientists have traditionally recog- nized five such events as having happened in the past 600 million years, each characterized by the loss of at least 75% of all species. A mass extinction com- parable to those of the big five could happen as soon as the next 100 years (see Chapter 25). Indeed, many important species have already been lost. The geolog- ical record indicates that recovery and diversification of species to pre–​mass ex- tinction levels can take as long as 5–​10 million years. Further, the loss of a species means loss of its scientific, cultural, aesthetic, recreational, health, and economic value. But it is also likely to have far-​reaching consequences for other species, which are connected to one another through various paths, including predation, parasitism, mutualism, and competition. Consequently, when a few species are lost, many others may follow or become dramatically reduced in numbers, and some may become common pests. Any mass extinction will undoubtedly have negative consequences for human quality of life and even life itself. We remain highly dependent on nature and its resources. In a world out of balance, it is impossible to predict with much certainty what will happen. Scenarios range from small impacts that deprive people from visiting wild places, with associated economic impacts for tour operators, up to the spread of dev- astating diseases that eliminate us and/​or our food. The recent arrival of the coro- navirus in our midst is one case in point. It is unfortunate that so much work and Ecology of a Changed World. Trevor Price, Oxford University Press. © Oxford University Press 2022. DOI: 10.1093/oso/9780197564172.003.0001 2 Ecology of a Changed World research are reactionary, staving off pandemics and other crises as they appear rather than proactively focusing on preventing the imbalances that cause such problems. The last mass extinction marked the beginning of the Cenozoic era. The Cenozoic era is divided into seven different epochs, each characterized by distinct kinds of animals and plants, as preserved in the fossil record. Transitions between epochs are driven by climate change and extinctions. The Pleistocene epoch, which began about 2.5 million years ago, saw the initiation of periods of cooling and glaci- ation interrupted by interglacial periods that experienced temperatures occasion- ally up to about 1oC higher than today (2oC higher than 100 years ago). The end of the last glacial period about 12,000 years ago was followed by the rise of agriculture and consequent increased human population density. This transformative change in earth’s ecology initiated the seventh epoch of the Cenozoic, the Holocene. The consensus is that we are entering an eighth epoch, again marked by rapid and large-​scale environmental changes, termed the Anthropocene. People de- bate when we should date the start of this epoch. In keeping with the way past epochs are defined, the main criterion is that a characteristic feature in the fossil record should be widespread across the world, so hypothetical future intelligent life could map its beginning. One research group has placed the date precisely at 1610, which is associated with a rapid cooling of the earth, as recorded by oxygen isotopes (Chapter 15). This group somewhat controversially attributes that cooling to the death of 50 million humans in the Americas due to disease, followed by subsequent growth of forests, thereby removing the greenhouse gas CO2 from of the atmosphere. Whether that is a plausible scenario is consid- ered several times in this book. Others prefer 1950 as the date, which marked the start of what has become known as the “Great Acceleration” in development. For example, we manufacture more than 350 million tonnes (see Table 1.1 for conversion of units) of plastic and 4 billion tonnes of concrete a year, and these products were just becoming available in 1950. Because epochs are defined by a feature preserved in the rocks, the signature development defining the start of the Anthropocene in this case is the nuclear fallout associated with the atom bomb, its testing, and, in two cases, its detonation in population centers. Today’s loss of species differs from previous extinctions in at least four key ways. First, humans both intentionally and unintentionally transport organisms all over the world, mixing up communities and affecting the way species interact with each other (Europeans imported diseases that killed an estimated 50 mil- lion North and South Americans in the 1500s; see Chapter 19). Second, we have removed large animals, often predators, which has ramifying effects on other species. Third, changes are happening very quickly, and the threats are multiple, compounding each other. Fourth, humans usurp a large fraction of the earth’s resources (see Fig. 1.1); left unchecked, few resources will be left for other species for the indefinite future. These topics will be revisited in detail in this book. Table 1.1. Weights and Measures* Metric Equivalents Weights Kilogram (kg) 2.2 pounds Tonne =​1000 kg 1.1 US tons (0.98 UK tonnes) Distances Kilometer (km) 0.62 miles (approximately 5/​8 mile) Area Hectare (ha) =​10,000 m2 2.2 acres Volumes Liter 2.11 US pints (1.76 UK pints) Greenhouse gas Carbon (tonnes) Carbon dioxide/​3.667 (tonnes) *Metric is used throughout this text. Carbon emissions are sometimes reported in terms of CO2 and sometimes in terms of carbon. Carbon is used in this book. Figure 1.1 Left: An estimate of the proportion of the world's annual historical plant growth that is on land now used by humans (either to grow crops, graze domestic animals, or be used for cities and towns) and what the proportion would be if everyone had the same consumption pattern as the United States does at present, with no change in agricultural practices (see Chapter 13). Right: Estimated biomass of the world’s mammals 100,000 years ago and at the present day. (Y. Bar-​On, R. Phillips, and R. Milo.. The biomass distribution on earth. Proceedings of the National Academy of Sciences 115: 6506–​6511). Images are those of the largest Australian mammal, Diprotodon octatum, which went extinct 44,000 years ago, and the African elephant. 4 Ecology of a Changed World In 2002, the naturalist E. O. Wilson published an important book, The Future of Life, in which he summarized the major threats to nature using the acronym HIPPO: Habitat loss, Invasive species, Pollution, Population sizes of humans af- fecting everything else, and Overharvesting. Presently, habitat loss is still thought to be the largest contributor to the endangerment of species, and it is clear that many species introduced from one place in the world to another have caused considerable harm in their new location. Harvesting has led to dramatic species declines and continues to do so, most notably in fisheries, but rather surpris- ingly in many tropical forests as well. As noted above and repeatedly emphasized throughout this book, the decline of species that humans hunt affects population sizes of many other species too. Wilson briefly discussed but did not elaborate on three other ingredients that contribute to threats to nature. First, the problem is not just too many people. The human population is presently increasing at the rate of about 200,000 people per day and population size is the ultimate stressor, but rapid increases in consumption are at least as great a threat to the environment. Real income per person has increased by 50% since the year 2000, to an av- erage of almost $11,000 per year in 2020 (this is an average, of course, and is skewed somewhat by the steep increases in income of the very wealthiest; see Chapter 12). Second, climate change has developed over the past 15 years into a full-​blown emergency, aptly named the Climate Crisis. With a 1oC global rise over the past 100 years, heatwaves, droughts, floods, and unusual storms are already affecting humans directly, as well as indirectly through impacts on other species. Given that carbon emissions continue to grow, albeit with a slight downturn during the pandemic, and the amount of CO2 in the at- mosphere is higher than it has been for at least 2.5 million years and perhaps much longer, it is unclear how and if we can mitigate these effects. Third, di- sease outbreaks are having devastating impacts on many species, including our own. While many of these outbreaks are a result of transport of, for ex- ample, a virus, from one location where its effects are mild to one where they are debilitating (hence part of the general problem of invasive species), they also involve jumps between species. To fully summarize the most pressing threats to our planet, we update Wilson’s HIPPO acronym by adding a C for climate change and a D for di- sease: COPHID. COPHID is the organizing framework for this book, further modifying the earlier acronym by removing the P for population. This is done to emphasize that population and wealth are not the direct causes of environ- mental deterioration, but have instead created those direct threats. The orga- nizing framework used here was originally introduced in a paper published in 2003, which asked why amphibians (frogs, toads, salamanders) had been declining steeply at least since the early 1980s.  The Changed World 5 Figure 1.2 Paths of influence from human populations to the natural world. The six threats in the center correspond to Climate Change, Overharvesting, Pollution, Habitat loss, Invasive species, and Disease (COPHID). A positive sign (+​) indicates that an increase in the factor at the base of the arrow causes an increase in the factor that the arrow points to (and also that a decrease causes a decrease). A minus sign means that an increase causes a decrease and a decrease causes an increase. To get the overall effect of human influences on natural resources through, for example, harvesting, one multiplies the values along the connecting paths, which in all cases is one “+​” and one “–​” so the product is negative (population increase causes harvesting to go up, which causes natural resources to go down). To calculate the total effect of human population size on species, one would then sum across all six connecting paths ([human → pollution → nature] +​[human → habitat → nature], etc.). All paths are negative, so the sum must be negative. One can extend this figure by considering how each factor affects humans. The path from natural resources to humans is clearly positive. The summed path from humans to pollution (+​) to nature (–​) to and back to humans (+​) is the product of +​, –​, +​, which is negative. Such a negative feedback loop may be one ultimate control on human population size. In principle, one can place values on the arrows (e.g., a value of 0.1 on the arrow leading to harvesting would imply that a tenfold increase in human influence would cause harvesting to increase by a factor of one), but these values are typically uncertain and not constant. Figure 1.2 depicts these various factors and their impacts as a path diagram in which the factors are connected by arrows. The sign of each arrow indicates how the factor at the arrowhead would change given a change in the magnitude of the factor at the base. A plus sign means the factor at the arrowhead changes in the same way as the one at the base (i.e., if the base factor increases, so does the head factor, and if the base factor decreases, so does the head factor). A minus sign means the factor at the arrowhead changes in the opposite direction (i.e., if the base increases, the head declines, and if the base decreases, the tip increases). Such diagrams are a useful way to model the world and are considered further in Chapter 4. Rapid changes in a complex world make it very difficult to predict what will happen in the future. One possible and favorable outcome is that as standards 6 Ecology of a Changed World of living and educational opportunities improve, the trend for people to have smaller families will continue. The human population may then stop growing as early as midcentury and start to decline. It is also plausible that as standards of living rise and natural areas become scarcer, nature itself will become more highly valued, with a greater clamor for, and investment in, its preservation. In this view, the time we are living through now is a bottleneck for life. This rea- soning led Wilson to declare in the Future of Life (p.189): “The central problem of the new century, I have argued, is how to raise the poor to a decent standard of living worldwide while preserving as much of the rest of life as possible.” This statement summarizes the organization of the book. The first section (­Chapters 2–​9) considers ecological and evolutionary principles underlying the factors that cause populations to increase or decrease, whether they be humans or other species; the second section (­Chapters 10–​22) describes COPHID in more detail; and the third section (­Chapters 23–​28) explores the history of extinctions, and underlying principles of conservation biology that inform the goal of reducing future extinctions.  PART 1 T HE R ISE A N D FA LL OF POP U L AT IONS  2 Population Growth A population is a collection of individuals belonging to one species, present in a specified geographical area. Sometimes the population refers to the whole spe- cies and sometimes to a subset. Population size is the number of individuals in the population. As of October 2021, the human population size was approaching 7.9 billion, and the population size of London, for example, was more than 9.3 million. Predicting how the numbers of both humans and other species will change in the future is essential to understanding environmental impacts. This chapter: (1) Investigates simple models of population growth, which inevitably lead to either impossibly large population sizes or extinction. The word “model” is used to mean a mathematical description of an ecological process. (2) Considers the value of a model in understanding the past and predicting the future. 2.1 Models of Population Growth Fruit flies are used widely in labs across the world because they reproduce quickly, so it is possible to investigate genetic and evolutionary change in a few months or years. They are also useful for ethical reasons because no one is con- cerned about the scientist’s daily slaughter of flies. A female fruit fly in a test tube with plenty of food lays about 100 eggs, which within 20 days themselves be- come 100 reproducing fruit flies. The 50 or so females among those 100 flies are themselves able to lay 100 eggs, if each is placed in its own test tube. I estimated that about 250 billion flies are needed to tightly pack into the buildings of a typ- ical university (based on the volume of buildings and the number that can fit into a test tube). To cover the earth (land and sea) a mile (1.6 km) deep in flies requires perhaps 7,500,000,000,000,000,000,000,000 (7.5 × 1024) flies, which is more than 1,000 times the number of stars in the universe. How long would it take our reproducing fruit flies to achieve these population sizes? The answer is that it would take about 4 months to fill the university and another 6 months to fill the world. A shortage of food means we have no need to shut down the fruit Ecology of a Changed World. Trevor Price, Oxford University Press. © Oxford University Press 2022. DOI: 10.1093/​oso/​9780197564172.003.0002 10 Ecology of a Changed World Table 2.1. Symbols Used. N Size of a population (number of individuals). t Time, often in years. N0 The initial size of a population, at time t =​0. Nt The size of a population t units later. b Birth rate, babies/​individual/​time interval. d Death rate, deaths/​individual/​time interval. r =​ b–​d, per capita growth rate, for geometric or exponential growth. More generally, the intrinsic rate of increase (Chapter 3). K The number of individuals at carrying capacity (Chapter 3) fly labs. Environmental resources, such as food and habitat, limit the growth of populations. One might think that it would take much, much, longer to fill the world with fruit flies if food is unlimited. But consider the math. After one genera- tion (20 days), 50 females are breeding. After two generations (40 days), 50 × 50 females are breeding. After three generations (60 days), 503 females are breeding. And after t generations 50t females are breeding. Ten months is 15 generations. Enter 5015 into a spreadsheet and multiple by two to account for males, and you will get close to the result for filling the world. We have built a model that describes the growth of the fly population: N t = N 0 × 50t Nt is the population size (number of females) at time t in generations after the present day (t =​0) (see Table 2.1). N0 is the number of females present at day 0, which in the above example was 1. It is immediately obvious that a model is often needed because in the fruit fly example, intuition can be misleading. A model is useful for at least two other important reasons: (1) A model clearly states the assumptions. In the case of the flies, the assumptions were that a female consistently gives rise to 50 daughters and then dies, and that all these daughters survive to reproduce. (2) If past changes do not match predictions, a model can be used to identify how the assumptions are violated. For example, the fact that fruit flies are not taking over the world must be either because females produce fewer  Population Growth 11 daughters or because fewer daughters survive. In the case of the fruit flies, it is because few daughters survive. To predict the number of females we would observe at some time in the future, given the present number, we only need know the number of daughters a female has. The number of surviving daughters is known as a parameter of the model, and we will give it the symbol B. Thus, we could write the equation above more generally: N t = N 0 × Bt This equation describes geometric growth. In the fruit fly example, the param- eter, B =​50 females, but the equation would be true for all values of B. (No, the starting number of females, is also a parameter, but it is more often called the initial condition.) To make predictions, we need values for all parameters in the model. For example, if each female had B =​6 surviving daughters and we started with N0 =​2 females, then after t =​3 generations, N3 =​2 × 63 =​432 females would be present, which again seems quite a large number for such innocuous production. Birth and Death Rates The fruit fly example illustrates the usefulness of a simple mathematical model. To make the model generally applicable, we separate change in the numbers of individuals over a certain time interval into those added (births) and those subtracted (deaths). The decomposition into change in the numbers of births and deaths enables us to evaluate much more easily why populations are increasing or decreasing. One parameter, the birth rate, b, is the average number of surviving babies produced by all individuals over a given time interval. (Table 2.1 lists all the symbols.) The birth rate for humans from July 1, 1992 to June 30, 1993 was b =​0.0245 persons/​person/​year (Table 2.2) and is often written as a percentage (i.e., 2.45%). While twins and early mortality affect the actual number of people who gave birth, it appears that about one in forty of all people had a baby in that year. This is surprising, given that about half of all people are male and many females were too young or too old to reproduce. The second parameter, the death rate, d, is the number of individuals dying per individual present at the beginning of the time interval (equivalently, the proportion of all individuals that died over the time interval, or the probability of an individual dying). Over that same 1992–​1993 interval, the death rate was d =​0.009 persons/​person/​year. That is, just under 1% of all people alive at the beginning of the year died (Table 2.2). 12 Ecology of a Changed World Table 2.2. World Human Population, 1992–​1993.* Population size 5.5 billion Births 135 million Birth rate, b 0.0245 babies/​person/​year Deaths 50 million Death rate, d 0.009 people/​person/​year *Data are from July 1 to June 30 (United Nations, https://​pop​ulat​ion.un.org/​ wpp). Note that these are estimates, and other databases differ slightly. The number of babies present at the end of the year is b × N, where N is the number of people present at the beginning. From mid-​1992 to mid-​1993, the number of babies born was 0.0245 x 5.5 billion =​~135 million. Over this same period, the number of individuals dying, d × N, was ~50 million. The change in population size (ΔN) per time interval (ΔT) is then: ∆N = bN − dN = (b − d ) × N ∆T ∆N Between mid-​1992 and mid-​1993, the world added =​individuals, more than twice the current population size of California. ∆T For many applications, birth and death rates are commonly collapsed into a single parameter, r =​b –​d. Here, we define r as the per capita growth rate—​the number of individuals added over the time interval as a fraction of the number present at the beginning. If r > 0, the birth rate exceeds the death rate, and the population increases. If r < 0, the death rate exceeds the birth rate, and the pop- ulation decreases. The per capita growth rate is an important quantity, crop- ping up in statistical reports all the time, not only for population increases, but also for such things as increases in prices over years, growth in productivity, and declines in populations. In humans from 1992 to 1993, r is estimated as b –​ d =​0.0245 –0.009 =​0.0155 individuals/​individual/​per year. As in the case of birth and death rates, in most reports, one sees r written as a percentage (i.e., the human population increased between 1992 and 1993 by r =​1.55%). The critical assumption of the model we now develop is that the birth and death rates do not change over time. If these rates do not change, we can project future human population size, just as we did in the fruit fly example, by multi- plying the population size measured on July 1 each year by 1.55% (Fig. 2.1). As in that example, the plot shows geometric increase. The number of people added to  Population Growth 13 Figure 2.1 In the middle of 1992, the human population was estimated to be 5.5 billion, and it grew by 1.55% that year (Table 2.2). If the growth rate were to stay constant, future population sizes can be predicted by iteratively multiplying the population size by 1.55% (illustrated by the points), demonstrating a geometric increase. The smooth gray curve drawn through the points follows the exponential equation, Nt =​ Noert (Appendix). No and Nt are two population sizes, separated by t years, and r is the per capita growth rate (individuals added/​individual/​year; see Figure 2.2). the population is higher every year than it was in the preceding year. This is be- cause at the beginning of every year there are more people reproducing than in the previous one. Given that the increase from 1992 to 1993 was 85 million, 5.585 billion people were present at the end of the year. To predict the increase over the next year, we assume that birth and death rates do not change and we multiply this number by 1.55%, giving a total of 86.6 million people added the following year. That process can be repeated iteratively to give projected population size through time, as in Figure 2.1. Model of Exponential Growth The census intervals in Figure 2.1 were taken every year on July 1, but of course many populations, including that of humans, change continuously. We can rep- resent such continuous growth as a smooth curve drawn through the points (Fig. 2.1), which is then termed the exponential curve. The two types of curves describe exactly the same relationship, but whereas geometric growth meas- ures population at equally spaced time intervals, exponential growth records 14 Ecology of a Changed World change continuously. To derive a formula for the exponential curve, bring the time points close together by writing: ∆N = rN ∆T as dN = rN dT The only difference is that the time interval is small. The formula for the expo- nential is then developed through integration (see the online Appendices for this chapter). It is as follows: N t = N o e rt This formula is exceptionally useful because it can be used to predict popula- tion size at any time into the future. Here, ert means the number e (the irrational number 2.71828...) raised to the power rt (the e part is what gives the curve the name “exponential”). If we have values for the present population size No and the per capita growth rate, r, we can plug these into the equation to predict population sizes in the future. For example, if the human population continued to grow at the 1992 rate of 1.55% per year, we would predict that population on July 1, 2020 would be 5.5 × e0.0155*28 =​8.49 billion, but we could also predict the population size on any other day. In this book, we will frequently refer to and employ the exponential curve. It is one of only two equations we consider (the other one, the logistic one, appears in Chapter 3). Neither equation is particu- larly intuitive, and both are worth spending some time thinking about (see the online questions). The use of the exponential equation requires that we know the value of r. We could obtain r by measuring the population at two time points (e.g., the begin- ning and end of the year). Then we could rearrange the equation Nt =​ No ert, as follows: N  r = ln  t  / t  N0  where ln symbolizes natural logarithm. Assuming that the population is truly growing exponentially (i.e., that birth and death rates do not change), all we would have to do is measure the population size at two points, take the log of  Population Growth 15 ∆N dN Figure 2.2 To model continuous growth, replace =​ rN in the text with =​ dN ∆ T dT rN. Here, is the slope of the tangent to the curve at a given population size (N) dT and is termed the instantaneous rate of population increase. It is the increase we would see if the rate at that particular point was fixed, which will underestimate the true increase because at every time step, more individuals are reproducing. We may approximate the tangent by measuring the difference in population sizes across a ∆N ∆N certain time interval. The shorter the timescale over which we measure , ∆T ∆T the more similar the slope is to the tangent. Provided r is measured over a timescale ∆N that the increase is less than 10%, the use of is a good approximation, but ∆T beyond that one should use the exact formula for r. their ratio, and divide by the time separating the two points. This is what the United Nations does in its reports, despite presenting the data as if it had been calculated as the proportionate increase over a year, which is the difference be- tween the population sizes divided by the starting population: N N  r ≅  t − 0  /​t  N0  where the ≅ symbol means that the two sides are approximately equal. The right side of the equation is how we presented r in the section on geometric growth above, but the geometric growth estimate of r and the exponential growth esti- mate only hold true when the estimate is made over a short period of time. It is for this reason that when geometric growth is modeled one often sees the birth rate, death rate, and growth rate written, respectively, with the capital letters B, D, and R. 16 Ecology of a Changed World Figure 2.2 illustrates the difference between the two methods: the first for- mula is based on the tangent to the curve of population growth (that is the in- stantaneous rate of change), whereas the second is derived from the difference between two points on the curve. In practice, provided that the change is meas- ured over a short enough time interval that the population increase is less than ∆N about 10%, the two methods yield very similar figures. In other words, is a dN ∆T good estimate of when measured over a sufficiently short time. In our earlier dT discussion of geometric growth in humans, we equated the percentage increase across a year with r, which was acceptable because that increase was small (1.545%). The exact method gives a correct value of 1.533%, which is scarcely different (see the Appendices). However, later in this chapter we consider the spread of a disease, where the percentage increase was measured over a year as 170%. In this case, r must be estimated using the exact method, r =​ln(Nt /​No)/​t. Once we have an accurate estimate of r, we can easily predict population size at any time point, so the remainder of the book only uses the continuous (exponen- tial), rather than the discrete (geometric) model. Doubling Times An important feature of geometric and exponential growth is that the doubling time—​the time it takes for a population to double in size—​is constant. Thus, a population grows from ten to twenty in the same time as it grows from one mil- lion to two million. The doubling time can be derived from the equation, Nt =​ Noert, by setting Nt =​2No. Rearranging, we get t double = ln (2) / r Here ln(2) is the natural logarithm of 2, or approximately 0.7. Thus, if r =​0.01 individuals/​individual/​year, the doubling time would be about 70 years. We can also turn this around and estimate r from the time it takes a population to double in size. 2.2 The Value of a Model Predicting the future is fraught with difficulties (Chapter 10), but with a model in hand, we can state with confidence what would happen if the assumptions of the model were to be met. To reiterate, the value of the model is not only that intui- tion often fails us but that the assumptions that underlie predictions are explicit.  Population Growth 17 This brings us to the second use of a model, which is to help understand what happened in the past. What are the most important factors we need to invoke to explain a particular change? Human population size has not increased as fast as expected from our 1992 projection, which predicted a population size in 2016 of about 1 billion more people than there actually were. The assumption of constant birth and death rates must be violated, and in this case birth rates have been de- clining (Chapter 11). The most useful models are those that can sufficiently account for trends in the data but make as few assumptions as possible. As we add more assumptions to a model, we introduce more parameters to explain the data. This will al- ways help improve the fit of the model to observed patterns but also increase the number of plausible explanations, making them difficult to separate. For example, in the growth model for fruit fly populations, we assumed females al- ways lay 50 eggs and then die after reproducing. If we find fewer flies than the model predicted and are prepared to assume that females continue to lay 50 eggs, then the only possible explanation is that more young are dying. Alternatively, if we include in the model both the possibility that some young do not survive or that fewer eggs are laid, then myriad possible combinations of number of eggs, hatching eggs, and survivors can explain the same pattern. Trying to work out how each contributes becomes increasingly difficult. It is not helpful to add more parameters if one factor explains most of the observations anyway, because we can use that parameter to well predict the future. Use of a Model: Early Spread of HIV in the United States An excellent example of the value of a model comes from an application of ex- ponential growth to predict the transmission of the human immunodeficiency virus (HIV) in the United States. HIV is the cause of AIDS, which attacks the cells involved in the immune response, making people especially vulnerable to other diseases, such as tuberculosis. HIV is thought to have initially arrived in the United States in the late 1960s, probably from Haiti, to which it had been brought from West Africa, where it had been contracted from a chimpanzee. The virus was first identified in 1981. Worldwide, about 37 million people may be currently infected, of which perhaps two-​thirds are in Africa and 1 million in the United States. Cases of AIDS reported in the United States increased approximately ex- ponentially over the first few years that records were kept (Fig. 2.3, left side). This created a great deal of worry because the steep trajectory shown in Figure 2.3 suggested that HIV might rapidly infect a large fraction of the popula- tion. At the time, few studies had been done, and little was known about how 18 Ecology of a Changed World Figure 2.3 Left: Increase in the number of AIDS cases reported in the United States during the early years of infection. Right: Increase in HIV presence in blood samples from the San Francisco homosexual community. Lines are fit by eye and appear approximately exponential. On the right graph, the curve fit indicates a rise from 3.5 to 27% over the first two years. Using the formula r =​ln(Nt /​No )/​t, this gives a growth rate of r =​1 new seropositive sample/​seropositive sample/​year. (The U.S. Center for Disease Control; R. M Anderson and R. M. May.. Transmission dynamics of HIV infection. Nature 326: 137–​141) easily it was transmitted. Models of population growth were used to estimate transmission rates. One analysis addressed the early spread of the virus in San Francisco. As part of a study on the presence of hepatitis B in the gay community in San Francisco, blood samples from 785 individuals were stored from 1978 onward. Fortunately, the samples were preserved in such a way that they could subse- quently be screened for HIV and used to estimate the rate of infection. The frac- tion of seropositive samples (Fig. 2.3, right) shows the rapid rise in infections. This and other studies suggest a doubling time of 8–​10 months during the early stages of infection (i.e., tdouble is approximately 0.7 years). As we showed above, the per capita rate of increase, r, can be determined from the doubling time: r = ln (2) / t double From this we get r =​1 infection per infected person per year. The death rate over the first few years of infection was negligible (d =​0), so r is equivalent to the birth rate, b. In other words, one infected individual was estimated to, on average, in- fect one more individual each year during these early stages. Additional data indicated that gay and bisexual men in this population aver- aged about twenty sexual partners per year. Given the estimate of 1 i​nfection/​ infected person/​year, this value implied a transmission rate of about 0.05 per  Population Growth 19 partner, which seemed low to investigators at the time. However, despite the rel- atively small sample size and simplifying assumptions of the model, this early estimate of the transmission rate is in accord with the present-​day understanding that HIV is not easy to contract. We have an excellent illustration of how models can be used to inform. First, one could use the model to ask if HIV is likely to be sustainable. That is, what factors are required for r =​ b –​ d to become negative? The model was made more complex by including additional parameters. Assuming that the most sexually active individuals become infected quickly, adding an extra term to the model to account for this leads to lower estimated transmission rates among the re- maining population. The revised model thus predicts that individuals with few partners per year may be quite unlikely to transmit the virus. This in itself may be sufficient for the virus to become extinct. Similarly, the spread of coronavirus in 2020 initially followed an exponential curve but soon increased more slowly, as chances of transmission were reduced by social distancing and quarantine (Chapter 19). Indeed, the model can be used to ask how changing habits might affect the chances of transmission and persistence of AIDS. In San Francisco, the average number of partners per month declined twofold from 1982 to 1984, and the use of condoms rapidly increased. If we assume that infected individuals who practice safe sex or develop AIDS are no longer sources of new infections, ac- cording to the models the level of infection may decline, perhaps below sustain- able limits. In the case of AIDS in the United States at least, these practices led to a decline in new infections up to about 2012. The number has since leveled off at about 39,000 per year, apparently because some sections of the population do not practice safe sex and have limited access to health care. 2.3 Conclusions The simplest model of population growth leads, often quite rapidly, to impossibly large population sizes. In 1798, Malthus, aware of the power of geometric growth, recognized that something must act to keep growing populations in check. In his book, he argued that food was the final limit on human population growth, but the desperate conditions so produced will lead to other factors that raise the death rate. First, he observed, war might help slow population growth. But if that fails, pestilence will “sweep off their thousands and tens of thousands.” However, if “success” is incomplete, “gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world.” The growth rate of any population must on average be close to zero. But the growth rate of a population can be slowed not only by increasing mortality (d going up) but by a 20 Ecology of a Changed World decreasing birth rate (b going down). Malthus was correct when he noted that populations must reach a limit, but it turns out he was wrong that this inevitably leads to war, disease, and famine. For humans, population growth is slowing, but remarkably that seems to be happening through the more benign process of a declining birth rate rather than an increasing death rate. We explore these demo- graphic shifts in Chapter 11.  3 Population Regulation In Chapter 2 we introduced a simple model of population growth that assumed unchanging birth and death rates over time. If that assumption is met and the birth rate exceeds the death rate, a population increases in size forever. On the other hand, if the death rate exceeds the birth rate, the population decreases con- tinuously and eventually becomes extinct. In nature, all populations vary in size over time, but they generally fluctuate within certain bounds and neither get very small nor grow excessively large. In this chapter, we investigate limitations on a species population size. The chapter covers: (1) An introduction to competition for resources as one means of regulating population size. (2) Derivation of a simple model of competition by adding an additional pa- rameter to the model of exponential growth. This model predicts a stable long-​term population size and thus, in principle could apply in nature. (3) Consideration of real examples of population fluctuations to ask what causes deviations from the predictions of this model. (4) Application of the model to the problem of sustainable fisheries. 3.1 Competition for Resources The gray heron is a large bird that eats fish, frogs and other animals, and typi- cally breeds in small colonies. Bird watchers in the United Kingdom have sur- veyed gray heron populations over the past 80 years (Fig. 3.1). A particularly harsh winter in 1963 caused a major drop in their numbers. Prior to that year, populations seemed to fluctuate around an average of about 7,000 pairs, and af- terward around an average of about 8,000 pairs, as suggested by the horizontal lines shown in Figure 3.1. These numbers might approximate the carrying ca- pacity (K) of the environment, which is the number of individuals the environ- ment can support as a result of available resources. Apparently, the carrying capacity increased after 1963 (i.e., K =​about 7,000 pairs in the early years, and K =​about 8,000 pairs in the later years). The higher value in later years reflects improvements in water quality—​the provision of new habitat as artificial ponds created through gravel extraction filled with water—​and increased feeding Ecology of a Changed World. Trevor Price, Oxford University Press. © Oxford University Press 2022. DOI: 10.1093/oso/9780197564172.003.0003 22 Ecology of a Changed World Figure 3.1 Estimated number of herons breeding in England and Wales combined. The gray horizontal lines are drawn by eye and are considered here to approximate carrying capacity during earlier and later years. (D. Massimino, I. D. Woodward, M. J. Hammond, et al. BirdTrends 2019: trends in numbers, breeding success and survival for UK breeding birds. BTO Research Report 722. BTO, Thetford. www.bto.org/​birdtrends) opportunities at freshwater fisheries. The number of individuals present may also be affected by predation, notably by humans, but the carrying capacity con- cept assumes that food and other resources, such as nest sites, are the main limit. Fluctuations around the carrying capacity baseline occur for many reasons that affect birth and death rates. For example, major drops in population size associ- ated with cold weather probably act largely through reduced food supply (e.g., ponds freeze over). Density Dependence and Density Independence It should be apparent from Figure 3.1 that something keeps heron populations within certain bounds: they neither grow to be very large nor decline to be very small. Consider the possibility that the same amount of food is available every year to a population. When the population size is low, each female garners a large share, and she raises many offspring (birth rates increase). When populations are large, however, each female has less food and she raises fewer offspring (birth rates decrease). In this case, food supply is a density-​dependent factor, ultimately responsible for keeping the population size regulated between certain limits. The test for density dependence is to plot birth rates or death rates against population  Population Regulation 23 Figure 3.2 Seed counts on a grass (the dune fescue, Vulpia fasciculata) from Wales, UK, after an experiment in which plants were grown at different densities. A decline in birth rate with increasing density implies density dependence. (A. R. Watkinson and A. J. Davy.. Population biology of salt-​marsh and sand dune annuals. Vegetatio 62: 487–​497) size. Figure 3.2 shows the number of seeds per grass following an experiment where grasses were planted on sand dunes at different densities. At higher densi- ties, each plant produced fewer seeds. Competition for food, water, and other resources such as nest sites is a major cause of density-​dependent population regulation. As the population increases, more individuals compete for the same quantity of a resource. Competition may take two forms: interference and exploitative. In interference competition, indi- viduals fight with each other to gain access to resources. In exploitative com- petition, individuals use up available resources—​that is, they compete without directly interacting with one another. Interference and exploitative competition are often both present in the same system. For example, grasses grown at high densities on sand dunes have low seed set, which is mostly attributed to com- petition for water (exploitative competition). However, they may also exhibit aggression in the form of chemicals sent out by one plant that inhibit the root growth of others. In another example, foxes fight with each other to maintain territories (interference) but will often sneak into a neighbor’s territory for food (exploitation). Various density-​ independent factors are superimposed on density-​ de- pendent factors. Density independence implies that the birth rates or death rates are unaffected by the number of individuals present. If the government issues hunting permits based on population size so that roughly the same proportion 24 Ecology of a Changed World of animals is killed each year, this would be a density-​independent factor (death rate, d, =​constant). Density-​independent factors cannot in themselves regulate populations. If only density independence operates, the population will even- tually grow to a very large size or become extinct. While we focus on density-​ dependent factors for this reason, most episodes of mortality and reproduction involve both density dependence and density independence. Herons may die because of extreme cold even if they are at very low densities (density indepen- dence), but the mortality rate would certainly be higher if the population was large, leading herons to compete for open water sites in which to fish (density dependence). 3.2 Model of Logistic Growth In the exponential model we considered in Chapter 2, the change in population size was given by the equation: dN = rN , dT where N is the population size at the beginning of the time interval and r is equal to the per capita growth rate (individuals added/​individual/​unit time). Exponential growth may be approximated in nature over short intervals, but it cannot lead to a stable population. The simplest model that does lead to a stable population is the logistic growth curve, which introduces an extra parameter, K, to the exponential model. To obtain the logistic growth equation, we multiply the N exponential equation by 1 − : K dN  N = rN  1 −  dT  K The left side of the equation is the change in population size over a certain time N interval. From the right side, one can see that when N is very small, that is, is K close to 0, the population growth rate is close to rN (i.e., exponential). We might expect this to be so because competition is low. That explains why we need to de- fine r as the intrinsic rate of increase and not the per capita growth rate as it was presented in Chapter 1; it is the per capita growth rate expected when no density-​ dependent factors are operating, and the population is growing exponentially.  Population Regulation 25 Figure 3.3 The logistic growth curve. The smooth curve plots the logistic equation, dN K −N = rN . Population size grows from a small number to K, the carrying dT  K  capacity (10,000 individuals); r, the intrinsic growth rate, is 0.064 individuals/​ individual/​year. Tangents to the curve at three population sizes (1,000, 5,000, 9,000) give the number of individuals added over a year. Note that population growth is highest at intermediate densities. One heuristic way to see why is to consider that at low population sizes, one individual might produce three offspring (three total); at intermediate population sizes, two might produce two (four in total); and at high population sizes three individuals produce one each (again three in total). N In the logistic equation, when N =​ K, 1–​ = 0 so the population growth K rate is zero, it is neither increasing nor decreasing. A plot of logistic population growth starting from a small number, with K =​10,000 individuals and r =​0.064 individuals/​individual/​year is shown in Figure 3.3. This is the second (and last) mathematical model in the book, and we will use it in several chapters as the sim- plest model of population growth with density-​dependent regulation. 3.3 Fluctuations of Population Size in Nature The logistic curve is a simple model for evaluating predictions of density de- pendence. Some population increases seem to fit the model quite well. For ex- ample, the wildebeest population in the African Serengeti declined to low levels in the early 1960s due to rinderpest, a viral disease related to measles that spilled over from domestic cattle (the word “rinderpest” comes from the German meaning “cattle plague”). Once a vaccine was developed for cattle, rinderpest was no longer a threat to the wildebeest population. The population initially increased and then leveled off in a way that roughly matches logistic growth 26 Ecology of a Changed World Figure 3.4 Left; Population size of wildebeest in the Serengeti, Tanzania, between 1960 and 1980, based on aerial censuses. Right: Death rate of wildebeest in the dry season plotted against density with respect to measured food resources. (A. R. E. Sinclair.. The eruption of the ruminants. In: A. Sinclair and M. Norton-​ Griffiths, M. [eds.] Serengeti: dynamics of an ecosystem. Chicago: University of Chicago Press; A. R. E. Sinclair and M. Norton-​Griffiths. (1982). Does competition or facilitation regulate migrant ungulate populations in the Serengeti? A test of hypotheses. Oecologia 53: 364–​369) (Fig. 3.4). Figure 3.4 shows how food availability correlates with number of individuals surviving and implies density-​dependent growth. The death rate, d, was four times higher in 1968 than in 1970, associated with just one-​tenth the amount of food available to an individual. Most populations do not follow such a simple pattern. Instead, fluctuations in population size are common, attributed to the many factors that affect death and reproduction (e.g., Fig. 3.1). The population sizes of some species vary enormously from one year to the next. In November 2004, a birdwatcher on a 230 ​km drive in Morocco estimated that he passed 69 billion desert locusts on the ground and “the air was full of them.” In other years, locusts are scarcely seen. Large fluctuations in locust population size in China have been moni- tored over a 2,000-​year period. Locust outbreaks most commonly occurred in cool and dry periods, likely because such periods were associated with both floods and droughts, which generate receding waters, leaving wet soil favor- able for locust development. Between 2019 and 2020, east Africa suffered from a devastating locust outbreak, the worst, in fact, for more than 25 years. This event was linked to the increasing frequency of tropical storms, generated by a warming ocean, which created lakes in the deserts of Saudi Arabia and receding waters. That event was followed by another storm that prolonged the wet conditions and hence food, and yet another one whose winds helped the locusts spread south.  Population Regulation 27 Besides climate, populations of locusts fluctuate dramatically because adults produce offspring in such large numbers that they overshoot the carrying ca- pacity of the environment. Under these conditions, the large number of individ- uals present eat all the food, causing the population to collapse to small numbers. This phenomenon is called delayed-​density dependence because the effects on reproduction or survival do not operate instantly, as they do in the logistic growth model. We can observe effects of delayed-​density dependence on both predators and prey. When predators become scarce, the prey can recover and grow to a large population size, which in turn increases the predator’s food avail- ability. Such predator–​prey interactions may lead populations of predators and prey to cycle over time. 3.4 Maximum Sustainable Yields In the logistic model, when populations are at low density individuals have access to plentiful resources. Therefore, each individual has a high chance of survival and produces many offspring—​the per capita growth rate is high. Consequently, the population starts to grow, competition for resources increases, and the per capita growth rate steadily declines, until, at carrying capacity, it is equal to zero. At this point, each individual exactly replaces herself: one mother has one sur- viving daughter. Unlike the per capita growth rate, which steadily declines as populations grow, dN the number of individuals added to the population per unit time, , is highest dT at intermediate population sizes (Fig. 3.3). When populations are small, few reproducing individuals are present in the population, even if they are producing many offspring. With a moderate number of reproducing individuals popula- tion growth is higher even though each of these individuals has fewer surviving offspring than an individual would in a very small population. When there are many individuals in the population, they have few surviving offspring, and pop- ulation growth rate is again low. In the logistic model, the point of maximum population growth is reached when N =​ K/​2 (see the discussion in the Appendices for this chapter, in the sec- tion “Maximum Sustainable Yield in the Logistic Equation”)—​that is, when the population size is at half the carrying capacity. This is known as the point of maximum sustainable yield because it is the population size at which one can sustainably remove the most individuals. For the parameters in Figure 3.3, one could continue to remove 160 individuals if the population was maintained at half the carrying capacity, but one would need to remove fewer individuals to maintain populations at either higher or lower levels. On the other hand, if one 28 Ecology of a Changed World always removed more than 160, the population would decline to zero. In the rest of this chapter, we develop the principle of maximum sustainable yields further, drawing on fisheries. Some early attempts to manage fisheries simply used the model of logistic growth to guide the harvest. The pre-​fishing population size was assumed to be the carrying capacity. The intrinsic rate of increase is estimated (e.g., from growth rates in a depleted population) and the quota accordingly set. Chapter 20 describes this approach for estimating sustainable yields from hunting of ante- lope in West Africa. However, the logistic equation is a simple model of den- sity dependence, and all populations deviate to some extent, as illustrated by the examples of herons (Fig. 3.1), locusts, and wildebeest (Fig. 3.4). Many com- plexities, both of the density-​dependent and density-​independent type, come into play. More sophisticated models of population growth have tried to take some of these complexities into account. One prominent goal is to estimate the maximum economic yield, which depends not only on the number of fish but also on their size, as well as the number of boats required to catch the fish. We consider a model developed for George’s Bank, an area larger than the state of Massachusetts and of relatively shallow water (several to tens of meters) off the northeast coast of the United States. George’s Bank used to be home to millions of cod. Yields declined throughout the twentieth century because of harvesting beyond the maximum sustainable yield. Presently, total fish biomass is less than 10% of estimated historical levels (see Chapter 21). In 1993, Canada declared a moratorium on the fishing of cod in the northern part of George’s Bank, which it controls, and placed limits on the catch of other species. Between 1990 and 1994, cod on the southern part, which the United States controls, declined by 40%. The United States also closed some areas but allowed limited fishing in others. The model evaluates the effect of fishing on total fish biomass summed across all twenty-​one commercial fish species, including cod, by adding more parameters to the simple logistic growth equation (which as we have seen has two parameters, r and K, plus the initial condition, N0). Among these parameters are those for how quickly an individual grows in the presence of competitors (fish grow more quickly to a large size when they have abundant food) and the effects of predation (e.g., cod eat herring). Values for these parameters were esti- mated from field studies. The exploitation rate is defined as the proportion of the mass of all fish that is removed each year. A 50% exploitation rate implies that when fish are rare, few fish are caught, but when they are abundant, many are caught. The modelers found that the maximum sustainable biomass that can be harvested, termed the multispecies maximum sustainable yield, is achieved with about a 50%  Population Regulation 29 Figure 3.5 A model for fisheries exploitation on George’s bank off Massachusetts. Mass is the total weight of fish in the sea, as a proportion of what it would be without any harvesting, considered to be the carrying capacity. Exploitation, on the X axis, is the proportion of the mass available that is removed in a year. The arrow indicates the point of maximum sustainable yield, where the exploitation rate =​0.48. Note that this is a model and that no data are plotted. However, data are used to estimate the various parameters, such as r, K, and individual growth. (B. Wörm, R. Hilborn, J. K. Baum, et al.. Rebuilding global fisheries. Science 325: 578–​585) exploitation rate (Fig. 3.5). Unlike the simple logistic growth model, however, this occurs when the total biomass is at about 35% of the maximum possible, partly because low densities increase not only per capita growth rates (as in the logistic model), but also the rate at which individuals grow. According to the model, the mass of fish caught would be about the same with a harvesting rate of 20% or 80% of the standing biomass (Fig. 3.5). In the case of a 20% harvest, many fish remain, only a few fishermen are needed to haul in the fish, and the environment is much closer to its natural state. In the case of 80% only a few fish are present, and many species would be considered collapsed, defined as a population 99% kill rate, but over years the rate has declined, and more rabbits now survive an outbreak. One reason for the fewer deaths is that the rabbits have evolved to be more resistant. To show this resistance, after a series of epidemics at one Figure 7.2 Left: Australian rabbit populations that have experienced multiple epidemics are more resistant to myxomatosis virus (rabbits were tested with the original virus that had been maintained in the lab). For this study, rabbits were taken from the wild and challenged with a virus that typically caused 70%–​90% mortality. Right: Virulence in three countries in the 1960s. The virus had been introduced 10–​15 years earlier, when it had a kill rate of close to 100% in all three locations. In the report, virulence was divided into five classes (90% in 10 years >70% in 10 years >50% in 10 years population size Small geographic