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Future Directions and Advanced Topics

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Data-driven Modelling of Structured Populations

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Abstract

This chapter is a collection of some advanced and cutting-edge topics that we think are important directions for future research on IPMs. (1) Fitting more flexible IPM kernels using nonlinear and/or nonparametric regression. (2) Putting demographic stochasticity into IPMs. (3) IPMs where some of the individual state variables have deterministic dynamics or are subject to deterministic constraints. Theory and numerical methods are totally undeveloped for these models. (4) More kinds of data. We revisit our assumption that the modeler has accurate observations on state and fate for marked individuals who can be re-found at each census. Better methods for fitting IPMs using mark-recapture data where recapture is not certain, or data on unmarked individuals, will greatly expand the scope for IPM applications, especially applications to animal populations.

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Notes

  1. 1.

    We recommend the sections on Monte Carlo integration in the Numerical Recipes for your programming language of choice.

  2. 2.

    This material is new, and untested apart from what we do here, so by the time you read this it may be superseded or discredited.

  3. 3.

    www.phidot.org/software/mark.

  4. 4.

    www.cefe.cnrs.fr/en/biostatistics-and-biology-of-populations/software.

  5. 5.

    www.phidot.org/software/mark/docs/book/.

  6. 6.

    In some studies, such as the Soays, individuals may be seen and known to be alive, but not recaptured and remeasured.

References

  • Allen EJ, Allen LJS, Arciniega A, Greenwood PE (2008) Construction of equivalent stochastic differential equation models. Stoch Anal Appl 26:274–297

    Article  MathSciNet  MATH  Google Scholar 

  • Banks HT, Botsford LW, Kappel F, Wang C (1991) Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis). J Math Biol 30:125–150

    Article  MATH  Google Scholar 

  • Banks HT, Sutton KL, Thompson WC, Bocharov G, Doumic M, Schenkel T, Argilaguet J, Giest S, Peligero C, Meyerhans A (2011) A new model for the estimation of cell proliferation dynamics using CFSE data. J Immunol Methods 373(1–2):143–160

    Article  Google Scholar 

  • Bonner SJ, Morgan BJT, King R (2010) Continuous covariates in mark-recapture-recovery analysis: a comparison of methods. Biometrics 66:1256–1265

    Article  MathSciNet  MATH  Google Scholar 

  • Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc Ser B Methodol 26(2):211–252

    MathSciNet  MATH  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 

  • Choquet R, Reboulet A-M, Pradel R, Gimenez O, Lebreton J-D (2004) M-SURGE: new software specifically designed for multistate capture-recapture models. Anim Biodivers Conserv 27:207–215

    Google Scholar 

  • de Roos AM, Persson L (2013) Population and community ecology of ontogenetic development. Monographs in population biology, vol. 51. Princeton University Press, Princeton

    Google Scholar 

  • de Valpine P (2009) Stochastic development in biologically structured population models. Ecology 90(10):2889–2901

    Article  Google Scholar 

  • Dennis B, Desharnais R, Cushing J, Costantino R (1995) Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments. Ecol Monogr 65(3):261–281

    Article  Google Scholar 

  • Dennis B, Desharnais R, Cushing J, Henson S, Costantino R (2001) Estimating chaos and complex dynamics in an insect population. Ecol Monogr 71(2):277–303

    Article  MathSciNet  Google Scholar 

  • Engen S, Lande R, Sæther B-E, Festa-Bianchet M (2007) Using reproductive value to estimate key parameters in density-independent age-structured populations. J Theor Biol 244:308–317

    Article  MathSciNet  Google Scholar 

  • Erhardt V (2009) corcounts: generate correlated count random variables. R package version 1.4.

    Google Scholar 

  • Ewens WJ (1979) Mathematical population genetics. Biomathematics, vol. 9. Springer, New York

    Google Scholar 

  • Ewens WJ (2004) Mathematical population genetics 1: Theoretical introduction. Biomathematics, vol. 9. Springer, New York

    Google Scholar 

  • Ghosh S, Gelfand AE, Clark JS (2012) Inference for size demography from point pattern data using integral projection models. J Agric Biol Environ Stat 17(4):641–677

    Article  MathSciNet  MATH  Google Scholar 

  • Harris TE (1963) The theory of branching processes. Die Grundlehren der Mathematischen Wissenschaften, vol. 119. Springer, Berlin

    Google Scholar 

  • Heiss F, Winschel V (2008) Likelihood approximation by numerical integration on sparse grids. J Econ 144(1):62–80

    Article  MathSciNet  Google Scholar 

  • Hodges JL, Le Cam L (1960) The poisson approximation to the poisson binomial distribution. Ann Math Stat 31(3):737–740

    Article  MathSciNet  MATH  Google Scholar 

  • Karlin S, Taylor HM (1981) A second course in stochastic processes. Academic, San Diego

    MATH  Google Scholar 

  • Kooijman S (2010) Dynamic energy budget theory for metabolic organisation, 3rd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Lande R, Engen S, Sæther B-E (2003) Stochastic population dynamics in ecology and conservation. Oxford series in ecology and evolution. Oxford University Press, Oxford

    Book  MATH  Google Scholar 

  • Langrock R, King R (2013) Maximum likelihood analysis of mark-recapture-recovery models in the presence of continuous covariates. Ann Appl Stat 7:1709–1732

    Article  MathSciNet  MATH  Google Scholar 

  • McCauley E, Nisbet RM, de Roos AM, Murdoch WW, Gurney WSC (1996) Structured population models of herbivorous zooplankton. Ecol Monogr 66(4):479–501

    Article  Google Scholar 

  • Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations. Springer, Berlin/New York

    Book  MATH  Google Scholar 

  • Nichols J, Sauer J, Pollock KH, Hestbeck JB (1992) Estimating transition probabilities for stage-based population projection matrices using capture-recapture data. Ecology 73:306–312

    Article  Google Scholar 

  • Nisbet RM, Gurney WSC, Murdoch WW, McCauley E (1989) Structured population models - a tool for linking effects at individual and population level. Biol J Linn Soc 37(1–2):79–99

    Article  Google Scholar 

  • Nisbet RM, Muller EB, Lika K, Kooijman SALM (2000) From molecules to ecosystems through dynamic energy budget models. J Anim Ecol 69:913–926

    Article  Google Scholar 

  • Ovaskainen O, Meerson B (2010) Stochastic models of population extinction. Trends Ecol Evol 25(11):643–652

    Article  Google Scholar 

  • Schreiber SJ, Ross N (2016) Individual-based integral projection models: the role of size-structure on extinction risk and establishment success. Methods in Ecology and Evolution (in press)

    Google Scholar 

  • Turchin P, Wood SN, Ellner SP, Kendall BE, Murdoch WW, Fischlin A, Casas J, McCauley E, Briggs CJ (2003) Dynamical effects of plant quality and parasitism on population cycles of larch budmoth. Ecology 84(5):1207–1214

    Article  Google Scholar 

  • Vindenes Y, Engen S, Sæther B-E (2011) Integral projection models for finite populations in a stochastic environment. Ecology 92(5):1146–1156

    Article  Google Scholar 

  • Vindenes Y, Sæther B-E, Engen S (2012) Effects of demographic structure on key properties of stochastic density-independent population dynamics. Theor Popul Biol 82(4):253–263

    Article  MATH  Google Scholar 

  • Williams B, Nichols JD, Conroy MJ (2002) Analysis and management of animal populations. Academic, San Diego

    Google Scholar 

  • Worthington H, King R, Buckland ST (2014) Analysing mark-recapture-recovery data in the presence of missing covariate data via multiple imputation. J Agric Biol Environ Stat 20(1):28–46

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Ecology and Evolutionary Biology, Cornell University, Corson Hall, Ithaca, NY, USA

    Stephen P. Ellner

  2. Animal and Plant Sciences, University of Sheffield, Yorkshire, UK

    Dylan Z. Childs & Mark Rees

Authors
  1. Stephen P. Ellner
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  2. Dylan Z. Childs
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  3. Mark Rees
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Ellner, S.P., Childs, D.Z., Rees, M. (2016). Future Directions and Advanced Topics. 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_10

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