Integral projections models, their construction and use in posing hypotheses in ecology

Replicated experiments at the level of the population are often not feasible for field systems. Despite this, population-level observational studies play a critical role in biology. For example, they have revealed how environmental change generates ecological and evolutionary change in free-living populations. When replicated experiments are impossible, constructing models and using these to conduct in silico experiments is the next best thing. Recent advances in the construction and analysis of integral projection models (IPMs) mean they offer a remarkably powerful tool to study ecological and evolutionary dynamics. IPMs can be parameterised using data frequently collected by ecologists, but the ease with which they can be constructed and analysed is perhaps not as widely appreciated as it could be. In this paper, which is loosely related to the talk I gave when receiving the Per Brinck Oikos Award in 2012, I show how easily IPMs can be constructed and analysed, and I argue they play an important role in posing and testing hypotheses in population biology.

[1]  L. Lefkovitch.  The study of population growth in organisms grouped by stages , 1965 .

[2]  L. Kruuk,et al.  Estimating the functional form for the density dependence from life history data. , 2008, Ecology.

[3]  T. Clutton‐Brock,et al.  Individuals and populations: the role of long-term, individual-based studies of animals in ecology and evolutionary biology. , 2010, Trends in ecology & evolution.

[4]  B T Grenfell,et al.  Age, sex, density, winter weather, and population crashes in Soay sheep. , 2001, Science.

[5]  T. Clutton‐Brock,et al.  Soay sheep: dynamics and selection in an island population. , 2003 .

[6]  E. A. Catchpole,et al.  Conditional methodology for individual case history data , 2004 .

[7]  T. Coulson,et al.  The stochastic demography of two coexisting male morphs. , 2011, Ecology.

[8]  Douglas W. Smith,et al.  Yellowstone after Wolves , 2003 .

[9]  Arpat Ozgul,et al.  Coupled dynamics of body mass and population growth in response to environmental change , 2010, Nature.

[10]  Tim Coulson,et al.  Modeling Effects of Environmental Change on Wolf Population Dynamics, Trait Evolution, and Life History , 2011, Science.

[11]  S. Hubbell,et al.  Mortality Rates of 205 Neotropical Tree and Shrub Species and the Impact of a Severe Drought , 1995 .

[12]  Shripad Tuljapurkar,et al.  Using evolutionary demography to link life history theory, quantitative genetics and population ecology , 2010, The Journal of animal ecology.

[13]  M. Rees,et al.  Evolution of flowering decisions in a stochastic, density-dependent environment , 2008, Proceedings of the National Academy of Sciences.

[14]  D. Marshall,et al.  Temperature-induced maternal effects and environmental predictability , 2011, Journal of Experimental Biology.

[15]  Stephen P. Ellner,et al.  Integral projection models for populations in temporally varying environments , 2009 .

[16]  T. Clutton‐Brock,et al.  Predicting trait values and measuring selection in complex life histories: reproductive allocation decisions in Soay sheep. , 2011, Ecology letters.

[17]  S. Ellner,et al.  SIZE‐SPECIFIC SENSITIVITY: APPLYING A NEW STRUCTURED POPULATION MODEL , 2000 .

[18]  S. Ellner,et al.  Integral Projection Models for Species with Complex Demography , 2006, The American Naturalist.

[19]  Shripad Tuljapurkar,et al.  The Many Growth Rates and Elasticities of Populations in Random Environments , 2003, The American Naturalist.

[20]  David R. Anderson,et al.  Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach with Case Studies , 1992 .

[21]  Stephen P. Ellner,et al.  Stochastic stable population growth in integral projection models: theory and application , 2007, Journal of mathematical biology.

[22]  P. H. Leslie.  On the use of matrices in certain population mathematics. , 1945, Biometrika.

[23]  J. Hadfield,et al.  Testing the phenotypic gambit: phenotypic, genetic and environmental correlations of colour , 2007, Journal of evolutionary biology.

[24]  T. Clutton‐Brock.  Reproductive success : studies of individual variation in contrasting breeding systems , 1989 .

[25]  J. Pemberton,et al.  Wild pedigrees: the way forward , 2008, Proceedings of the Royal Society B: Biological Sciences.

[26]  Byron J. T. Morgan,et al.  Factors influencing Soay sheep survival , 2000 .

[27]  Tim Coulson,et al.  Small‐scale spatial dynamics in a fluctuating ungulate population , 1999 .

[28]  Arpat Ozgul,et al.  The Dynamics of Phenotypic Change and the Shrinking Sheep of St. Kilda , 2009, Science.