Wolf in sheep's clothing: Model misspecification undermines tests of the neutral theory for life histories

Abstract

Understanding the processes behind change in reproductive state along life-history trajectories is a salient research program in evolutionary ecology. Two processes, state dependence and heterogeneity, can drive the dynamics of change among states. Both processes can operate simultaneously, begging the difficult question of how to tease them apart in practice. The Neutral Theory for Life Histories (NTLH) holds that the bulk of variations in life-history trajectories is due to state dependence and is hence neutral: Once previous (breeding) state is taken into account, variations are mostly random. Lifetime reproductive success (LRS), the number of descendants produced over an individual's reproductive life span, has been used to infer support for NTLH in natura. Support stemmed from accurate prediction of the population-level distribution of LRS with parameters estimated from a state dependence model. We show with Monte Carlo simulations that the current reliance of NTLH on LRS prediction in a null hypothesis framework easily leads to selecting a misspecified model, biased estimates and flawed inferences. Support for the NTLH can be spurious because of a systematic positive bias in estimated state dependence when heterogeneity is present in the data but ignored in the analysis. This bias can lead to spurious positive covariance between fitness components when there is in fact an underlying trade-off. Furthermore, neutrality implied by NTLH needs a clarification because of a probable disjunction between its common understanding by evolutionary ecologists and its translation into statistical models of life-history trajectories. Irrespective of what neutrality entails, testing hypotheses about the dynamics of change among states in life histories requires a multimodel framework because state dependence and heterogeneity can easily be mistaken for each other.

References Adami, C. (2016). What is information? Technical report, Michigan State University. Retrieved from http://arxiv.org/abs/1601.06176. Arulampalam, W., Booth, A., & Taylor, M. (2000). Unemployment persistence. Oxford Economic Papers, 52, 24–50. Authier, M., Cam, E., & Guinet, C. (2011). Selection for increased body length in subantarctic fur seals on Amsterdam Island. Journal of Evolutionary Biology, 24, 607–616. Bartels, B., Box-Steffensmeier, J., Smidt, C., & Smith, R. (2011). The dynamic properties of individual-level party identification in the United States. Electoral Studies, 30, 210–222. Bates, D.Maechler, M., Bolker, B., & Walker, S. (2013). lme4: Linear mixed-effects models using Eigen and S4. Retrieved from http://CRAN.R-project.org/package=lme4. Bergeron, P., Baeta, R., Pelletier, F., Réale, D., & Garant, D. (2011). Individual quality: Tautology or biological reality? Journal of Animal Ecology, 80, 361–364. Bolker, B., Brooks, M., Clark, C., Geange, S., Poulsen, J., Stevens, M., & White, J.-S. (2009). Generalized linear mixed models: A practical guide for ecology and evolution. Trends in Ecology and Evolution, 24, 127–135. Bonnet, T., & Postma, E. (2016). Successful by chance? The power of mixed models and neutral simulations for the detection of individual fixed heterogeneity in fitness components. American Naturalist, 187, 60–74. Browne, W., McCleery, R., Sheldon, B., & Pettifor, R. (2007). Using cross-classified multivariate mixed response models with application to life-history traits in great tits (Parus major). Statistical Modelling, 7, 217–238. Burnham, K., & Anderson, D. (2002). Model selection and multimodel inference. A practical information-theoretic approach (pp. 488). 2nd ed. New York, USA: Springer. Burnham, K., & Anderson, D. (2004). Understanding AIC and BIC in model selection. Sociological Methods and Research, 33, 261–304. Burnham, K. P., & White, G. C. (2002). Evaluation of some random effects methodology applicable to bird ringing data. Journal of applied statistics, 29, 245–264. Cam, E., Aubry, L., & Authier, M. (2016). The conundrum of heterogeneity in life history studies. Trends in Ecology & Evolution, 31, 872–886. Cam, E., Gimenez, O., Alpizar-Jara, R., Aubry, L., Authier, M., Cooch, E., … Pradel, R. (2013). Looking for a needle in a haystack: Inferences about individual fitness components in a heterogeneous population. Oikos, 122, 739–753. Cam, E., Link, W., Cooch, E., Monnat, J.-Y., & Danchin, E. (2002). Individual covariation in life-history traits: Seeing the trees despite the forests. American Naturalist, 159, 96–105. Caswell, H. 2001. Matrix population models (pp. 722). 2nd ed. Sunderland, Massachusetts, USA: Sinauer Associates. Caswell, H. (2009). Stage, age and individual stochasticity in demography. Oikos, 118, 1763–1782. Chamberlin, T. (1965). The method of multiple working hypotheses. Science, 148, 754–756. Chambert, T., Rotella, J., & Garrott, R. (2014). An evolutionary perspective on reproductive individual heterogeneity in a marine vertebrate. Journal of Animal Ecology, 83, 1158–1168. Chambert, T., Rotella, J., & Higgs, J. (2014). Use of posterior predictive checks as an inferential tool for investigating individual heterogeneity in animal population vital rates. Ecology and Evolution, 4, 1389–1397. Chambert, T., Rotella, J., Higgs, J., & Garrott, R. (2013). Individual heterogeneity in reproductive rates and cost of reproduction in a long-lived vertebrate. Ecology and Evolution, 3, 2047–2060. Chave, J. (2008). Chapter 7 – Neutral theory and community ecology, pages 165–190. In Fernando Valladares, Antonio Camacho, Arturo Elosegi, Carlos Gracia, Marta Estrada, Joan Carles Senar & Josep-María Gili (Eds.), Unity in diversity – Reflections on ecology after the legacy of Ramon Margalef (pp. 504). 1st ed. Bilbao, Spain: Fundación BBVA. Chave, J., Muller-Landau, H., & Levin, S. (2002). Comparing classical community models: Theoretical consequences for patterns of diversity. The American Naturalist, 159, 1–23. Fay, R., Barbraud, C., Delord, K., & Weimerskirch, H. (2016). Variation in the age of first reproduction: Different strategies or individual quality? Ecology, 97, 1842–1851. Flatt, T., & Heyland, A. (2011). Mechanisms of life history evolution: The genetics and physiology of life History traits and trade-offs (pp. 506). 1st ed. New York, USA: Oxford University Press. Fox, C., Roff, C., &Fairbairn, D., (Eds). 2001. Evolutionary ecology. Concepts and case studies (pp. 448). 1st ed. New York, USA: Oxford University Press. Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24, 997–1016. Gelman, A., & Tuerlinckx, F. (2000). Type-S error rates for classical and Bayesian single and multiple comparison procedures. Computational Statistics, 15, 373–390. Gottschlich, C., & Schuhmacher, D. (2014). The shortlist method for fast computation of the earth mover's distance and finding optimal solutions to transportation problems. PLoS One, 9, e110214. Gould, S., & Lewontin, R. (1979). The spandrels of San Marco and the Panglossian paradigm: A critique of the adaptationist programme. Proceedings of the Royal Society of London series B, 205, 581–598. Halliday, T. (2008). Heterogeneity, state dependence and health. Econometrics Journal, 11, 499–516. Heckman, J. (1981). Chapter 3 - Heterogeneity and State Dependence, pages 91–139. In Sherwin, Rosen (Ed.), Studies in labour markets (pp. 406). 1st ed. Cambridge, Massachusetts: The University of Chicago Press. Hsiao, C. (2014). Analysis of panel data (pp.562). 3rd ed. New York, USA: Cambridge University Press. Jenouvrier, S., Péron, C., & Weimerskirch, H. (2015). Extreme climate events and individual heterogeneity shape life-history traits and population dynamics. Ecological Monographs, 85, 605–624. Lefkovitch, L. P. (1965). The study of population growth in organisms grouped by stages. Biometrika, 35, 183–212. Leigh, E. G. (2007). Neutral theory: A historical perspective. Journal of Evolutionary Biology, 20, 2075–2091. Lesaffre, E., & Spiessens, B. (2001). On the effect of the number of quadrature point in a logistic random-effects model: An example. Journal of the Royal Statistical Society Series C, 50, 325–335. Link, W., Barker, R (2009). Bayesian Inference with Ecological Applications (pp. 354).1st edition. London, UK: Associated Press. Metcalf, C. J. E. (2016). Invisible trade-offs: Van Noordwijk and de Jong and life-history evolution. The American Naturalist, 187, iii–v. Metcalf, C. J. E., & Parvard, S. (2007). Why evolutionary biologists should be demographers. Trends in Ecology and Evolution, 22, 205–212. Mood, C. (2010). Logistic regression: Why we cannot do what we think we can do, and what we can do about it. European Sociological Review, 26, 67–82. Morano, S., Stewart, K. M., Sedinger, J. S., Nicolai, C. A., & Vavra, M. (2013). Life-history strategies of North American elk: Trade-offs associated with reproduction and survival. Journal of Mammalogy, 94, 162–172. Mourocq, E., Bize, P., Bouwhuis, S., Bardley, R., Charmantier, A., de la Cruz, C., … Griesser, M. (2016). Life span and reproductive cost explain interspecific variation in the optimal onset of reproduction. Evolution, 70, 296–313. Munoz, F., & Huneman, P. (2016). From the neutral theory to a comprehensive and multiscale theory of ecological equivalence. The Quarterly Review of Biology, 91, 321–342. Naves, L., Monnat, J.-Y., & Cam, E. (2006). Breeding performance, mate fidelity, and nest site fidelity in a long-lived seabird: Behaving against the current? Oikos, 115, 263–276. Nichols, J., Hines, J., Pollock, K., Hinz, R., & Link, W. (1994). Estimating breeding proportions and testing hypotheses about costs of reproduction with capture-recapture data. Ecology, 75, 2052–2065. van Noordwijk, A., & de Jong, G. (1986). Acquisition and allocation of resources: Their Influence on variation in life history tactics. American Naturalist, 128, 137–142. Orzack, S. H., Steiner, U. K., Tuljapurkar, S., & Thompson, P. (2011). Static and dynamic expression of life history traits in the northern fulmar Fulmarus glacialis. Oikos, 120, 369–380. Pigliucci, M., & Kaplan, J. (2000). The fall and rise of Dr Pangloss: Adaptationism and the Spandrels paper 20 years later. Trends in Ecology and Evolution, 15, 66–70. Pigliucci, M., Kaplan, J. (2006). Making sense of evolution. The conceptual foundations of evolutionary biology. (pp. 236). 1st ed. Chicago, USA: The University of Chicago Press. Plard, F., Bonenfant, C., Delorme, D., & Gaillard, J. (2012). Modeling reproductive trajectories of Roe Deer females: Fixed or dynamic heterogeneity? Theoretical Population Biology, 82, 317–328. R Development Core Team, 2015. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing, r version 3.2.3 (2015-12-10) – “wooden christmas-tree” edition. Retrieved from URL http://www.R-project.org/. Reznick, D., Nunney, L., & Tessier, A. (2000). Big houses, big cars, superfleas and the costs of reproduction. Trends in Ecology & Evolution, 15, 421–425. Roff, D. A., Mostowy, S., & Fairbairn, D. J. (2002). The evolution of trade-offs: Testing predictions on response to selection and environmental variation. Evolution, 56, 84–95. Steiner, U., & Tuljapurkar, S. (2012). Neutral theory for life histories and individual variability in fitness components. Proceedings of the National Academy of Sciences of the USA, 109, 4684–4689. Steiner, U., Tuljapurkar, S., & Orzack, S. (2010). Dynamic heterogeneity and life history variability in the kittiwake. Journal of Animal Ecology, 79, 436–444. Tuljapurkar, S., Steiner, U., & Orzack, S. (2009). Dynamic heterogeneity in life histories. Ecology Letters, 12, 93–106. Van de Pol, M., & Wright, J. (2009). A simple method for distinguishing within-versus between-subject effects using mixed models. Animal Behaviour, 77, 753–758. Warren, R. II, Skelly, D., Schmitz, O., & Bradford, M. (2011). Universal ecological patterns in college basketball communities. PLoS ONE, 6, e17342. Wienke, A. (2010). Frailty models in survival analysis(pp. 324). 1st ed. Boca Raton, Florida, USA: Chapman & Hall/CRC. Wilson, A., & Nussey, D. (2010). What is individual quality? An evolutionary perspective. Trends in Ecology and Evolution, 25, 207–2014. Wintrebert, C., Zwinderman, A., Cam, E., Pradel, R., & van Houwelingen, J. (2005). Joint modelling of breeding and survival in the kittiwake using frailty models. Ecological Modelling, 181, 203–213.