Section: Evolutionary Biology
Topic: Evolution, Population biology, Ecology

Density dependent environments can select for extremes of body size

Coulson, Tim1  ; Felmy, Anja2 ; Potter, Tomos3 ; Passoni, Gioele1 ; Montgomery, Robert A1; Gaillard, Jean-Michel4 ; Hudson, Peter J5 ; Travis, Joseph3 ; Bassar, Ronald D6 ; Tuljapurkar, Shripad D7 ; Marshall, Dustin8 ; Clegg, Sonya M1 
1 Department of Biology, University of Oxford, Oxford, OX1 3SZ, UK
2 Department of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland
3 Department of Biological Science, Florida State University, Tallahassee FL 32306, USA
4 Laboratoire de Biométrie et Biologie Evolutive, University of Lyon 1, Lyon, France
5 The Huck Institutes, Penn State University, State College, PA 16802, USA
6 Department of Biological Sciences, 120 W Samford Avenue, Auburn University, Auburn, AL 36849, USA
7 Department of Biology, Stanford University, Palo Alto, CA 94305, USA
8 School of Biological Sciences, Monash University, Melbourne, Victoria, Australia 3800

Corresponding author(s): Coulson, Tim (tim.coulson@biology.ox.ac.uk)

10.24072/pcjournal.162 - Peer Community Journal, Volume 2 (2022), article no. e49.

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Body size variation is an enigma. We do not understand why species achieve the sizes they do, and this means we also do not understand the circumstances under which gigantism or dwarfism is selected. We develop size-structured integral projection models to explore evolution of body size and life history speed. We make few assumptions and keep models simple: all functions remain constant across models except for the one that describes development of body size with age. We set sexual maturity to occur when size attains 80% of the asymptotic size, which is typical of a large mammal, and allow negative density dependence to only affect either reproduction or juvenile survival. Fitness -- the quantity that is maximized by adaptive evolution -- is carrying capacity in our models, and we are consequently interested in how it changes with size at sexual maturity, and how this association varies with development rate. The simple models generate complex dynamics while providing insight into the circumstances when extremes of body size evolve. The direction of selection leading to either gigantism or dwarfism crucially depends on the proportion of the population that is sexually mature, which in turn depends on how the development function determines the survivorship schedule. The developmental trajectories consequently interact with size-specific survival or reproductive rates to determine the best life history and the optimal body size emerges from that interaction. These dynamics result in trade-offs between different components of the life history, with the form of the trade-off that emerges depending upon where in the life history density dependence operates most strongly. Empirical application of the approach we develop has potential to help explain the enigma of body size variation across the tree of life.

Published online:
DOI: 10.24072/pcjournal.162
Type: Research article

Coulson, Tim 1; Felmy, Anja 2; Potter, Tomos 3; Passoni, Gioele 1; Montgomery, Robert A 1; Gaillard, Jean-Michel 4; Hudson, Peter J 5; Travis, Joseph 3; Bassar, Ronald D 6; Tuljapurkar, Shripad D 7; Marshall, Dustin 8; Clegg, Sonya M 1

1 Department of Biology, University of Oxford, Oxford, OX1 3SZ, UK
2 Department of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland
3 Department of Biological Science, Florida State University, Tallahassee FL 32306, USA
4 Laboratoire de Biométrie et Biologie Evolutive, University of Lyon 1, Lyon, France
5 The Huck Institutes, Penn State University, State College, PA 16802, USA
6 Department of Biological Sciences, 120 W Samford Avenue, Auburn University, Auburn, AL 36849, USA
7 Department of Biology, Stanford University, Palo Alto, CA 94305, USA
8 School of Biological Sciences, Monash University, Melbourne, Victoria, Australia 3800
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Density dependent environments can select for extremes of body size},
     journal = {Peer Community Journal},
     eid = {e49},
     publisher = {Peer Community In},
     volume = {2},
     year = {2022},
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     url = {https://peercommunityjournal.org/articles/10.24072/pcjournal.162/}
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Coulson, Tim; Felmy, Anja; Potter, Tomos; Passoni, Gioele; Montgomery, Robert A; Gaillard, Jean-Michel; Hudson, Peter J; Travis, Joseph; Bassar, Ronald D; Tuljapurkar, Shripad D; Marshall, Dustin; Clegg, Sonya M. Density dependent environments can select for extremes of body size. Peer Community Journal, Volume 2 (2022), article  no. e49. doi : 10.24072/pcjournal.162. https://peercommunityjournal.org/articles/10.24072/pcjournal.162/

PCI peer reviews and recommendation, and links to data, scripts, code and supplementary information: 10.24072/pci.evolbiol.100146

Conflict of interest of the recommender and peer reviewers:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.

[1] Audzijonyte, A.; Richards, S. A.; Stuart-Smith, R. D.; Pecl, G.; Edgar, G. J.; Barrett, N. S.; Payne, N.; Blanchard, J. L. Fish body sizes change with temperature but not all species shrink with warming, Nature Ecology & Evolution, Volume 4 (2020) no. 6, pp. 809-814 | DOI

[2] Burke, D. M.; Nol, E. Landscape and fragment size effects on reproductive success of forest-breeding birds in ontario, Ecological Applications, Volume 10 (2000) no. 6, pp. 1749-1761 | DOI

[3] Caswell, H. Matrix population models: Construction, analysis, and interpretation, Sinauer Associates, 2001

[4] Charlesworth, B. Selection in Populations with Overlapping Generations. V. Natural Selection and Life Histories, The American Naturalist, Volume 107 (1973) no. 954, pp. 303-311 | DOI

[5] Charlesworth, B. Evolution in Age-Structured Populations, Cambridge University Press, 1994 | DOI

[6] Charnov, E. L.; Downhower, J. F. A trade-off-invariant life-history rule for optimal offspring size, Nature, Volume 376 (1995) no. 6539, pp. 418-419 | DOI

[7] Childs, D. Z.; Rees, M.; Rose, K. E.; Grubb, P. J.; Ellner, S. P. Evolution of size–dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model, Proceedings of the Royal Society of London. Series B: Biological Sciences, Volume 271 (2004) no. 1537, pp. 425-434 | DOI

[8] Clegg, S. M.; Owens, P. F. The ‘island rule’ in birds: medium body size and its ecological explanation, Proceedings of the Royal Society of London. Series B: Biological Sciences, Volume 269 (2002) no. 1498, pp. 1359-1365 | DOI

[9] Coulson, T.; Benton, T.; Lundberg, P.; Dall, S.; Kendall, B.; Gaillard, J.-M. Estimating individual contributions to population growth: evolutionary fitness in ecological time, Proceedings of the Royal Society B: Biological Sciences, Volume 273 (2005) no. 1586, pp. 547-555 | DOI

[10] Coulson, T. Integral projections models, their construction and use in posing hypotheses in ecology, Oikos, Volume 121 (2012) no. 9, pp. 1337-1350 | DOI

[11] Coulson, T. Environmental perturbations and transitions between ecological and evolutionary equilibria: an eco-evolutionary feedback framework, Peer Community Journal, Volume 1 (2021) | DOI

[12] Coulson, T.; Kendall, B. E.; Barthold, J.; Plard, F.; Schindler, S.; Ozgul, A.; Gaillard, J.-M. Modeling Adaptive and Nonadaptive Responses of Populations to Environmental Change, The American Naturalist, Volume 190 (2017) no. 3, pp. 313-336 | DOI

[13] Coulson, T.; MacNulty, D. R.; Stahler, D. R.; vonHoldt, B.; Wayne, R. K.; Smith, D. W. Modeling Effects of Environmental Change on Wolf Population Dynamics, Trait Evolution, and Life History, Science, Volume 334 (2011) no. 6060, pp. 1275-1278 | DOI

[14] Coulson, T.; Tuljapurkar, S.; Childs, D. Z. Using evolutionary demography to link life history theory, quantitative genetics and population ecology, Journal of Animal Ecology, Volume 79 (2010) no. 6, pp. 1226-1240 | DOI

[15] Covas, R. Evolution of reproductive life histories in island birds worldwide, Proceedings of the Royal Society B: Biological Sciences, Volume 279 (2012) no. 1733, pp. 1531-1537 | DOI

[16] Day, T.; Taylor, P. D. Von Bertalanffy's Growth Equation Should Not Be Used to Model Age and Size at Maturity, The American Naturalist, Volume 149 (1997) no. 2, pp. 381-393 | DOI

[17] Depczynski, M.; Bellwood, D. R. Shortest recorded vertebrate lifespan found in a coral reef fish, Current Biology, Volume 15 (2005) no. 8 | DOI

[18] Dieckmann, U.; Heino, M.; Parvinen, K. The adaptive dynamics of function-valued traits, Journal of Theoretical Biology, Volume 241 (2006) no. 2, pp. 370-389 | DOI

[19] Ellner, S. P.; Childs, D. Z.; Rees, M. Data-driven Modelling of Structured Populations, Lecture Notes on Mathematical Modelling in the Life Sciences, Springer International Publishing, Cham, 2016 | DOI

[20] English, S.; Bateman, A. W.; Clutton-Brock, T. H. Lifetime growth in wild meerkats: incorporating life history and environmental factors into a standard growth model, Oecologia, Volume 169 (2012) no. 1, pp. 143-153 | DOI

[21] Fisher, R. A. The genetical theory of natural selection, Clarendon Press, Oxford, 1930 | DOI

[22] Gaillard, J.-M.; Pontier, D.; Allaine, D.; Loison, A.; Herve, J.-C.; Heizman, A. Variation in growth form and precocity at birth in eutherian mammals, Proceedings of the Royal Society of London. Series B: Biological Sciences, Volume 264 (1997) no. 1383, pp. 859-868 | DOI

[23] Gimenez, O.; Anker-Nilssen, T.; Grosbois, V. Exploring causal pathways in demographic parameter variation: path analysis of mark-recapture data, Methods in Ecology and Evolution, Volume 3 (2012) no. 2, pp. 427-432 | DOI

[24] Goldbogen, J. A. Physiological constraints on marine mammal body size, Proceedings of the National Academy of Sciences, Volume 115 (2018) no. 16, pp. 3995-3997 | DOI

[25] Grafen, A. Formal Darwinism, the individual–as–maximizing–agent analogy and bet–hedging, Proceedings of the Royal Society of London. Series B: Biological Sciences, Volume 266 (1999) no. 1421, pp. 799-803 | DOI

[26] Grant, A. Selection pressures on vital rates in density–dependent populations, Proceedings of the Royal Society of London. Series B: Biological Sciences, Volume 264 (1997) no. 1380, pp. 303-306 | DOI

[27] Gulland, F. Impact of Infectious Diseases on Wild Animal Populations: a Review, Ecology of Infectious Diseases in Natural Populations, Cambridge University Press, 1995, pp. 20-51 | DOI

[28] Hone, D.; Benton, M. The evolution of large size: how does Cope's Rule work?, Trends in Ecology & Evolution, Volume 20 (2005) no. 1, pp. 4-6 | DOI

[29] Jones, J. H.; Tuljapurkar, S. Measuring selective constraint on fertility in human life histories, Proceedings of the National Academy of Sciences, Volume 112 (2015) no. 29, pp. 8982-8986 | DOI

[30] Jones, J. H.; Tuljapurkar, S. Measuring selective constraint on fertility in human life histories, Proceedings of the National Academy of Sciences, Volume 112 (2015) no. 29, pp. 8982-8986 | DOI

[31] Jones, O. R.; Gaillard, J.-M.; Tuljapurkar, S.; Alho, J. S.; Armitage, K. B.; Becker, P. H.; Bize, P.; Brommer, J.; Charmantier, A.; Charpentier, M.; Clutton-Brock, T.; Dobson, F. S.; Festa-Bianchet, M.; Gustafsson, L.; Jensen, H.; Jones, C. G.; Lillandt, B.-G.; McCleery, R.; Merilä, J.; Neuhaus, P.; Nicoll, M. A. C.; Norris, K.; Oli, M. K.; Pemberton, J.; Pietiäinen, H.; Ringsby, T. H.; Roulin, A.; Saether, B.-E.; Setchell, J. M.; Sheldon, B. C.; Thompson, P. M.; Weimerskirch, H.; Jean Wickings, E.; Coulson, T. Senescence rates are determined by ranking on the fast-slow life-history continuum, Ecology Letters, Volume 11 (2008) no. 7, pp. 664-673 | DOI

[32] Kentie, R.; Clegg, S. M.; Tuljapurkar, S.; Gaillard, J.; Coulson, T. Life‐history strategy varies with the strength of competition in a food‐limited ungulate population, Ecology Letters, Volume 23 (2020) no. 5, pp. 811-820 | DOI

[33] Kingsolver, J. G.; Hoekstra, H. E.; Hoekstra, J. M.; Berrigan, D.; Vignieri, S. N.; Hill, C. E.; Hoang, A.; Gibert, P.; Beerli, P. The Strength of Phenotypic Selection in Natural Populations, The American Naturalist, Volume 157 (2001) no. 3, pp. 245-261 | DOI

[34] Kooijman, B. Dynamic Energy Budget Theory for Metabolic Organisation, Cambridge University Press, 2009 | DOI

[35] Koziowski, J.; Weiner, J. Interspecific Allometries Are by-Products of Body Size Optimization, The American Naturalist, Volume 149 (1997) no. 2, pp. 352-380 | DOI

[36] Kozłowski, J. Optimal allocation of resources to growth and reproduction: Implications for age and size at maturity, Trends in Ecology & Evolution, Volume 7 (1992) no. 1, pp. 15-19 | DOI

[37] Kozłowski, J.; Konarzewski, M.; Czarnoleski, M. Coevolution of body size and metabolic rate in vertebrates: a life‐history perspective, Biological Reviews, Volume 95 (2020) no. 5, pp. 1393-1417 | DOI

[38] Lachish, S.; Brandell, E. E.; Craft, M. E.; Dobson, A. P.; Hudson, P. J.; MacNulty, D. R.; Coulson, T. Investigating the Dynamics of Elk Population Size and Body Mass in a Seasonal Environment Using a Mechanistic Integral Projection Model, The American Naturalist, Volume 196 (2020) no. 2 | DOI

[39] Lande, R.; Engen, S.; Sæther, B.-E. An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment, Philosophical Transactions of the Royal Society B: Biological Sciences, Volume 364 (2009) no. 1523, pp. 1511-1518 | DOI

[40] Lande, R.; Engen, S.; Sæther, B.-E. Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations, Proceedings of the National Academy of Sciences, Volume 114 (2017) no. 44, pp. 11582-11590 | DOI

[41] Law, R. Optimal Life Histories Under Age-Specific Predation, The American Naturalist, Volume 114 (1979) no. 3, pp. 399-417 | DOI

[42] Lomolino, M. V. Body size evolution in insular vertebrates: generality of the island rule, Journal of Biogeography, Volume 32 (2005) no. 10, pp. 1683-1699 | DOI

[43] MacArthur, R. H. Some generalized theorems of natural selection, Proceedings of the National Academy of Sciences, Volume 48 (1962) no. 11, pp. 1893-1897 | DOI

[44] Major, R. E.; Kendal, C. E. The contribution of artificial nest experiments to understanding avian reproductive success: a review of methods and conclusions, Ibis, Volume 138 (1996) no. 2, pp. 298-307 | DOI

[45] McGraw, J. B.; Caswell, H. Estimation of Individual Fitness from Life-History Data, The American Naturalist, Volume 147 (1996) no. 1, pp. 47-64 | DOI

[46] McNab, B. K. On the Ecological Significance of Bergmann's Rule, Ecology, Volume 52 (1971) no. 5, pp. 845-854 | DOI

[47] Merilä, J.; Sheldon, B.; Kruuk, L. Explaining stasis: microevolutionary studies in natural populations, Genetica, Volume 112/113 (2001), pp. 199-222 | DOI

[48] Meszéna, G.; Kisdi, É.; Dieckmann, U.; Geritz, S. A. H.; Metz, J. A. J. Evolutionary Optimisation Models and Matrix Games in the Unified Perspective of Adaptive Dynamics, Selection, Volume 2 (2002) no. 1-2, pp. 193-220 | DOI

[49] Metcalf, C. J. E.; Rose, K. E.; Childs, D. Z.; Sheppard, A. W.; Grubb, P. J.; Rees, M. Evolution of flowering decisions in a stochastic, density-dependent environment, Proceedings of the National Academy of Sciences, Volume 105 (2008) no. 30, pp. 10466-10470 | DOI

[50] Mylius, S. D.; Diekmann, O. On Evolutionarily Stable Life Histories, Optimization and the Need to Be Specific about Density Dependence, Oikos, Volume 74 (1995) no. 2 | DOI

[51] Nielsen, J.; Hedeholm, R. B.; Heinemeier, J.; Bushnell, P. G.; Christiansen, J. S.; Olsen, J.; Ramsey, C. B.; Brill, R. W.; Simon, M.; Steffensen, K. F.; Steffensen, J. F. Eye lens radiocarbon reveals centuries of longevity in the Greenland shark (Somniosus microcephalus), Science, Volume 353 (2016) no. 6300, pp. 702-704 | DOI

[52] Nussey, D. H.; Froy, H.; Lemaitre, J.-F.; Gaillard, J.-M.; Austad, S. N. Senescence in natural populations of animals: Widespread evidence and its implications for bio-gerontology, Ageing Research Reviews, Volume 12 (2013) no. 1, pp. 214-225 | DOI

[53] Ozgul, A.; Tuljapurkar, S.; Benton, T. G.; Pemberton, J. M.; Clutton-Brock, T. H.; Coulson, T. The Dynamics of Phenotypic Change and the Shrinking Sheep of St. Kilda, Science, Volume 325 (2009) no. 5939, pp. 464-467 | DOI

[54] Parker, G. A.; Begon, M. Optimal Egg Size and Clutch Size: Effects of Environment and Maternal Phenotype, The American Naturalist, Volume 128 (1986) no. 4, pp. 573-592 | DOI

[55] Plard, F.; Barthold Jones, J. A.; Gaillard, J.; Coulson, T.; Tuljapurkar, S. Demographic determinants of the phenotypic mother–offspring correlation, Ecological Monographs, Volume 91 (2021) no. 4 | DOI

[56] Raia, P.; Meiri, S. The island rule in large mammals: paleontology meets ecology, Evolution, Volume 60 (2006) no. 8, pp. 1731-1742 | DOI

[57] Reznick, D. A.; Bryga, H.; Endler, J. A. Experimentally induced life-history evolution in a natural population, Nature, Volume 346 (1990) no. 6282, pp. 357-359 | DOI

[58] Reznick, D.; Endler, J. A. The impact of predation on life history evolution in trinidadian guppies (Poecilia reticulata), Evolution, Volume 36 (1982) no. 1, pp. 160-177 | DOI

[59] Roff, D. Evolution of life histories: Theory and analysis, Springer Science & Business Media, 1993

[60] Sander, P. M.; Christian, A.; Clauss, M.; Fechner, R.; Gee, C. T.; Griebeler, E.-M.; Gunga, H.-C.; Hummel, J.; Mallison, H.; Perry, S. F.; Preuschoft, H.; Rauhut, O. W. M.; Remes, K.; Tütken, T.; Wings, O.; Witzel, U. Biology of the sauropod dinosaurs: the evolution of gigantism, Biological Reviews, Volume 86 (2011) no. 1, pp. 117-155 | DOI

[61] Sandvig, E. M.; Coulson, T.; Clegg, S. M. The effect of insularity on avian growth rates and implications for insular body size evolution, Proceedings of the Royal Society B: Biological Sciences, Volume 286 (2019) no. 1894 | DOI

[62] Savage, V. M.; Gillooly, J. F.; Woodruff, W. H.; West, G. B.; Allen, A. P.; Enquist, B. J.; Brown, J. H. The predominance of quarter-power scaling in biology, Functional Ecology, Volume 18 (2004) no. 2, pp. 257-282 | DOI

[63] Seip, D. R. Factors limiting woodland caribou populations and their interrelationships with wolves and moose in southeastern British Columbia, Canadian Journal of Zoology, Volume 70 (1992) no. 8, pp. 1494-1503 | DOI

[64] Smallegange, I. M.; Caswell, H.; Toorians, M. E. M.; Roos, A. M. Mechanistic description of population dynamics using dynamic energy budget theory incorporated into integral projection models, Methods in Ecology and Evolution, Volume 8 (2017) no. 2, pp. 146-154 | DOI

[65] Smith, C. C.; Fretwell, S. D. The Optimal Balance between Size and Number of Offspring, The American Naturalist, Volume 108 (1974) no. 962, pp. 499-506 | DOI

[66] Stearns, S. C. The Evolution of Life History Traits: A Critique of the Theory and a Review of the Data, Annual Review of Ecology and Systematics, Volume 8 (1977) no. 1, pp. 145-171 | DOI

[67] Stearns, S. The evolution of life histories, Oxford University Press, Oxford, 1992

[68] Steiner, U. K.; Tuljapurkar, S.; Coulson, T.; Horvitz, C. Trading stages: Life expectancies in structured populations, Experimental Gerontology, Volume 47 (2012) no. 10, pp. 773-781 | DOI

[69] Takada, T.; Nakajima, H. An analysis of life history evolution in terms of the density-dependent Lefkovitch matrix model, Mathematical Biosciences, Volume 112 (1992) no. 1, pp. 155-176 | DOI

[70] Takada, T.; Nakajima, H. Theorems on the invasion process in stage-structured populations with density-dependent dynamics, Journal of Mathematical Biology, Volume 36 (1998) no. 5, pp. 497-514 | DOI

[71] Toïgo, C.; Gaillard, J.-M. Causes of sex-biased adult survival in ungulates: sexual size dimorphism, mating tactic or environment harshness?, Oikos, Volume 101 (2003) no. 2, pp. 376-384 | DOI

[72] Travis, J.; Reznick, D.; Bassar, R. D.; López-Sepulcre, A.; Ferriere, R.; Coulson, T. Do Eco-Evo Feedbacks Help Us Understand Nature? Answers From Studies of the Trinidadian Guppy, Eco-Evolutionary Dynamics, Elsevier, 2014, pp. 1-40 | DOI

[73] Tuljapurkar, S.; Gaillard, J.-M.; Coulson, T. From stochastic environments to life histories and back, Philosophical Transactions of the Royal Society B: Biological Sciences, Volume 364 (2009) no. 1523, pp. 1499-1509 | DOI

[74] Tuljapurkar, S. Population Dynamics in Variable Environments, Lecture Notes in Biomathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 1990 | DOI

[75] Turchin, P. Population Regulation: A Synthetic View, Oikos, Volume 84 (1999) no. 1 | DOI

[76] Watson, W.; Walker, H. J. The world’s smallest vertebrate, Schindleria brevipinguis, a new paedomorphic species in the family Schindleriidae (Perciformes: Gobioidei), Records of the Australian Museum, Volume 56 (2004) no. 2, pp. 139-142 | DOI

[77] West, G. B.; Brown, J. H.; Enquist, B. J. A General Model for the Origin of Allometric Scaling Laws in Biology, Science, Volume 276 (1997) no. 5309, pp. 122-126 | DOI

[78] White, T. C. R. The role of food, weather and climate in limiting the abundance of animals, Biological Reviews, Volume 83 (2008) no. 3, pp. 227-248 | DOI

[79] Winkler, D. W.; Wallin, K. Offspring Size and Number: A Life History Model Linking Effort Per Offspring and Total Effort, The American Naturalist, Volume 129 (1987) no. 5, pp. 708-720 | DOI

[80] Yoshida, T.; Jones, L. E.; Ellner, S. P.; Fussmann, G. F.; Hairston, N. G. Rapid evolution drives ecological dynamics in a predator–prey system, Nature, Volume 424 (2003) no. 6946, pp. 303-306 | DOI

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