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Evolutionary Demography

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Data-driven Modelling of Structured Populations

Abstract

Patterns of survival and reproduction determine fitness and so it should come as no surprise that there is a rich body of theory linking demography with evolution. Here we provide an overview of these methods showing how evolutionary dynamics and selection can be understood using IPMs. We show how selection can be approximated using sensitivities and how this leads to an approximation for trait dynamics. The endpoints of evolution – what we expect to see in nature – are explored using ideas from Adaptive Dynamics, the key methods based on Evolutionarily Stable Strategies and Convergence Stability. Efficient methods for finding ESS are presented. We then extend these ideas to cover stochastic environments and function-valued traits. For function-valued traits we model the entire function rather than the underlying parameters, and so we are not tied to a specific fitted function.

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Notes

  1. 1.

    One last time: or any other continuously varying trait or traits.

  2. 2.

    The corresponding function for Windows is parLapply in the parallel package, which works a bit differently.

References

  • Abrams P, Matsuda H, Harada Y (1993) Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol Ecol 7(5):465–487

    Article  Google Scholar 

  • Barfield M, Holt RD, Gomulkiewicz R (2011) Evolution in stage-structured populations. Am Nat 177(4):397–409

    Article  Google Scholar 

  • Beder JH, Gomulkiewicz R (1998) Computing the selection gradient and evolutionary response of an infinite-dimensional trait. J Math Biol 36:299–319

    Article  MathSciNet  MATH  Google Scholar 

  • Bell G, Collins S (2008) Adaptation, extinction and global change. Evol Appl 1(1):3–16

    Article  Google Scholar 

  • Benton TG, Solan M, Travis JMJ, Sait SM (2007) Microcosm experiments can inform global ecological problems. Trends Ecol Evol 22(10):516–521

    Article  Google Scholar 

  • Bruno JF, Ellner SP, Vu I, Kim K, Harvell CD (2011) Impacts of aspergillosis on sea fan coral demography: modeling a moving target. Ecol Monogr 81(1):123–139

    Article  Google Scholar 

  • Charlesworth B (1994) Evolution in age-structured populations. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Chesson P (1982) The stabilizing effect of a random environment. J Math Biol 15:1–36

    Article  MathSciNet  MATH  Google Scholar 

  • Chesson P (2000) Mechanisms of maintenance of species diversity. Annu Rev Ecol Syst 31:343–366

    Article  Google Scholar 

  • Chevin L-M (2015) Evolution of adult size depends on genetic variance in growth trajectories: a comment on analyses of evolutionary dynamics using integral projection models. Meth Ecol Evol 6(9):981–986

    Article  Google Scholar 

  • Childs DZ, Coulson TN, Pemberton JM, Clutton-Brock TH, Rees M (2011) Predicting trait values and measuring selection in complex life histories: reproductive allocation decisions in Soay sheep. Ecol Lett 14(10):985–992

    Article  Google Scholar 

  • Childs DZ, Rees M, Rose KE, Grubb PJ, Ellner SP (2003) Evolution of complex flowering strategies: an age- and size-structured integral projection model. Proc R Soc Lond Ser B Biol Sci 270(1526):1829–1838

    Article  Google Scholar 

  • Childs DZ, Rees M, Rose KE, Grubb PJ, Ellner SP (2004) Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model. Proc R Soc Lond Ser B Biol Sci 271(1537):425–434

    Article  Google Scholar 

  • Christiansen F (1991) On conditions for evolutionary stability for a continuous character. Am Nat 138(1):37–50

    Article  Google Scholar 

  • Collins S (2013) New model systems for experimental evolution. Evolution 67:1847–1848

    Article  Google Scholar 

  • Coulson T, Catchpole EA, Albon SD, Morgan BJT, Pemberton JM, Clutton-Brock TH, Crawley MJ, Grenfell BT (2001) Age, sex, density, winter weather, and population crashes in Soay sheep. Science 292(5521):1528–1531

    Article  Google Scholar 

  • Coulson T, MacNulty D, Stahler D, vonHoldt B, Wayne R, Smith D (2011) Modeling effects of environmental change on wolf population dynamics, trait evolution, and life history. Science 334:1275–1278

    Article  Google Scholar 

  • Coulson T, Tuljapurkar S, Childs DZ (2010) Using evolutionary demography to link life history theory, quantitative genetics and population ecology. J Anim Ecol 79(6):1226–1240

    Article  Google Scholar 

  • Datta MS, Korolev KS, Cvijovic I, Dudley C, Gore J (2013) Range expansion promotes cooperation in an experimental microbial metapopulation. Proc Natl Acad Sci USA 110:7354–7359

    Article  Google Scholar 

  • Dercole F, Rinaldi S (2008) Analysis of evolutionary processes: the adaptive dynamics approach and its applications. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Dieckmann U, Heino M, Parvinen K (2006) The adaptive dynamics of function-valued traits. J Theor Biol 241:370–389

    Article  MathSciNet  MATH  Google Scholar 

  • Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34(5–6):579–612

    Article  MathSciNet  MATH  Google Scholar 

  • Ellner S, Hairston NG Jr, (1994) Role of overlapping generations in maintaining genetic variation in a fluctuating environment. Am Nat 143(3):403–417

    Article  Google Scholar 

  • Ellner SP (2013) Rapid evolution: from genes to communities, and back again? Funct Ecol 27:1087–1099

    Article  Google Scholar 

  • Engen S, Lande R, Sæther B-E (2013) A quantitative genetic model of r- and K-selection in a fluctuating population. Am Nat 181(6):725–736

    Article  Google Scholar 

  • Eshel I (1983) Evolutionary and continuous stability. J Theor Biol 103(1):99–111

    Article  MathSciNet  Google Scholar 

  • Eshel I, Motro U (1981) Kin selection and strong evolutionary stability of mutual help. Theor Popul Biol 19(3):420–433

    Article  MathSciNet  MATH  Google Scholar 

  • Falconer DS, Mackay TF (1996) Introduction to quantitative genetics, 4th edn. Pearson Education Limited, Harlow

    Google Scholar 

  • Geritz SAH, Kisdi E, Meszena G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12(1):35–57

    Article  Google Scholar 

  • Geritz SAH, Metz JAJ, Kisdi E, Meszena G (1997) Dynamics of adaptation and evolutionary branching. Phys Rev Lett 78(10):2024–2027

    Article  Google Scholar 

  • Geritz SAH, van der Meijden E, Metz JAJ (1999) Evolutionary dynamics of seed size and seedling competitive ability. Theor Popul Biol 55(3):324–343

    Article  MATH  Google Scholar 

  • Gratten J, Pilkington JG, Brown EA, Clutton-Brock TH, Pemberton JM, Slate J (2012) Selection and microevolution of coat pattern are cryptic in a wild population of sheep. Mol Ecol 21(12):2977–2990

    Article  Google Scholar 

  • Gremer JR, Venable DL (2014) Bet hedging in desert winter annual plants: optimal germination strategies in a variable environment. Ecol Lett 17(3):380–387

    Article  Google Scholar 

  • Hanski I, Saccheri I (2006) Molecular-level variation affects population growth in a butterfly metapopulation. PLoS Biol 4(5):719–726

    Article  Google Scholar 

  • Hesse E, Rees M, Müeller-Schäerer H (2008) Life-history variation in contrasting habitats: flowering decisions in a clonal perennial herb (Veratrum album). Am Nat 172(5):E196–E213

    Article  Google Scholar 

  • Iwasa Y, Pomiankowski A, Nee S (1991) The evolution of costly mate preferences. II. The “handicap” principle. Evolution 45(6):1431–1442

    Article  Google Scholar 

  • Johnston SE, Gratten J, Berenos C, Pilkington JG, Clutton-Brock TH, Pemberton JM, Slate J (2013) Life history trade-offs at a single locus maintain sexually selected genetic variation. Nature 502(7469):93–95

    Article  Google Scholar 

  • Kingsolver JG, Gomulkiewicz R, Carter PA (2001) Variation, selection and evolution of function-valued traits. Genetica 112:87–104

    Article  Google Scholar 

  • Kirkpatrick M, Heckman N (1989) A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters. J Math Biol 27(4):429–450

    Article  MathSciNet  MATH  Google Scholar 

  • Kuss P, Rees M, Ægisdóttir HH, Ellner SP, Stöcklin J (2008) Evolutionary demography of long-lived monocarpic perennials: a time-lagged integral projection model. J Ecol 96(4):821–832

    Article  Google Scholar 

  • Lande R (1982) A quantitative genetic theory of life history evolution. Ecology 63(3):607–615

    Article  Google Scholar 

  • Lande R (2007) Expected relative fitness and the adaptive topography of fluctuating selection. Evolution 61(8):1835–1846

    Article  Google Scholar 

  • Lande R, Engen S, Sæther B-E (2009) An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment. Philos Trans R Soc B Biol Sci 364(1523):1511–1518

    Article  Google Scholar 

  • Levin S, Muller-Landau H (2000) The evolution of dispersal and seed size in plant communities. Evol Ecol Res 2:409–435

    Google Scholar 

  • Lynch M, Walsh B (1998) Genetics and analysis of quantitative traits. Sinauer Associates, Sunderland

    Google Scholar 

  • Metcalf CJE, Rose KE, Childs DZ, Sheppard AW, Grubb PJ, Rees M (2008) Evolution of flowering decisions in a stochastic, density-dependent environment. Proc Natl Acad Sci USA 105(30):10466–10470

    Article  Google Scholar 

  • Metz JAJ, Mylius SD, Diekmann O (2008) When does evolution optimize? Evol Ecol Res10(5):629–654

    Google Scholar 

  • Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define “fitness” for general ecological scenarios? Trends Ecol Evol 7(6):198–202

    Article  Google Scholar 

  • Miller TEX, Williams JL, Jongejans E, Brys R, Jacquemyn H (2012) Evolutionary demography of iteroparous plants: incorporating non-lethal costs of reproduction into integral projection models. Proc R Soc Lond Ser B Biol Sci 279(1739):2831–2840

    Article  Google Scholar 

  • Mylius SD, Diekmann O (1995) On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74(2):218–224

    Article  Google Scholar 

  • Parvinen K, Dieckmann U, Heino M (2006) Function-valued adaptive dynamics and the calculus of variations. J Math Biol 52(1):1–26

    Article  MathSciNet  MATH  Google Scholar 

  • Parvinen K, Heino M, Dieckmann U (2013) Function-valued adaptive dynamics and optimal control theory. J Math Biol 67(3):509–533

    Article  MathSciNet  MATH  Google Scholar 

  • Price G (1970) Selection and covariance. Nature 227:520–521

    Article  Google Scholar 

  • Ramsay J, Hooker G, Graves S (2009) Functional data analysis with R and Matlab. Springer, New York

    Book  MATH  Google Scholar 

  • Ramsay JO, Silverman BW (2005) Functional data analysis. Springer series in statistics, 2nd edn. Springer, New York

    Google Scholar 

  • Rees M, Childs DZ, Metcalf CJE, Rose KE, Sheppard AW, Grubb PJ (2006) Seed dormancy and delayed flowering in monocarpic plants: selective interactions in a stochastic environments. Am Nat 168(2):E53–E71

    Article  Google Scholar 

  • Rees M, Childs DZ, Rose KE, Grubb PJ (2004) Evolution of size-dependent flowering in a variable environment: partitioning the effects of fluctuating selection. Proc R Soc Ser B Biol Sci 271(1538):471–475

    Article  Google Scholar 

  • Rees M, Ellner SP (2009) Integral projection models for populations in temporally varying environments. Ecol Monogr 79:575–594

    Article  Google Scholar 

  • Rees M, Ellner SP (2016) Evolving integral projection models: evolutionary demography meets eco-evolutionary dynamics. Methods in Ecology and Evolution 7:157–170

    Article  Google Scholar 

  • Rees M, Rose KE (2002) Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach. Proc R Soc Ser B Biol Sci 269(1499):1509–1515

    Article  Google Scholar 

  • Rees M, Sheppard AW, Briese D, Mangel M (1999) Evolution of size-dependent flowering in Onopordum illyricum: a quantitative assessment of the role of stochastic selection pressures. Am Nat 154(6):628–651

    Article  Google Scholar 

  • Robertson A (1966) A mathematical model of the culling process in dairy cattle. Anim Prod 8:95–108

    Article  Google Scholar 

  • Roff DA (2002) Life history evolution. Sinauer Associates, Sunderland

    Google Scholar 

  • Rose KE, Rees M, Grubb PJ (2002) Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris. Evolution 56(7):1416–1430

    Article  Google Scholar 

  • Santure AW, de Cauwer I, Robinson MR, Poissant J, Sheldon BC, Slate J (2013) Genomic dissection of variation in clutch size and egg mass in a wild great tit (Parus major) population. Mol Ecol 22(15):3949–3962

    Article  Google Scholar 

  • Stearns SC (1992) The evolution of life histories. Oxford University Press, London

    Google Scholar 

  • Stinchcombe JR, Function-valued Traits Working Group, and Kirkpatrick, M. (2012). Genetics and evolution of function-valued traits: understanding environmentally responsive phenotypes. Trends Ecol Evol 27:637–647

    Article  Google Scholar 

  • van Noordwijk A, de Jong G (1986) Acquisition and allocation of resources: their influence on variation in life-history tactics. Am Nat 128(1):137–142

    Article  Google Scholar 

  • Vindenes Y, Langangen Ø (2015) Individual heterogeneity in life histories and eco-evolutionary dynamics. Ecol Lett 18(5):417–432

    Article  Google Scholar 

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Ellner, S.P., Childs, D.Z., Rees, M. (2016). Evolutionary Demography. In: Data-driven Modelling of Structured Populations. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-28893-2_9

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