Theoretical Population Biology 82 (2012) 317–328 Contents lists available at SciVerse ScienceDirect Theoretical Population Biology journal homepage: www.elsevier.com/locate/tpb Modeling reproductive trajectories of roe deer females: Fixed or dynamic heterogeneity? F. Plard a , C. Bonenfant a , D. Delorme b , J.M. Gaillard a,∗ a Université de Lyon, F-69000, Lyon; Université Lyon 1; CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, F-69622, Villeurbanne, France b Centre National d’Etudes et de Recherches Appliquées Cervidés-Sangliers, Office National de la Chasse et de la Faune Sauvage, 87 avenue de Wagram, 75008 Paris, France article info Article history: Available online 9 April 2012 Keywords: Individual quality Life history Reproductive status Reproductive success Fecundity abstract The relative role of dynamic and fixed heterogeneity in shaping the individual heterogeneity observed in most life-history traits remains difficult to quantify. In a recent work, Tuljapurkar et al. (2009) suggested modeling individual heterogeneity in lifetime reproductive success by a null model building reproductive trajectories from a first-order Markov chain. According to this model, among-individual differences in reproductive trajectories would be generated by the stochastic transitions among reproductive states (such as breeder and non-breeder) due to dynamic heterogeneity. In this work, we analyze the individual variation in three reproductive metrics (reproductive status, fecundity, and reproductive success) in two populations of roe deer intensively monitored using Tuljapurkar et al. (2009)’s dynamic model. Moreover, we challenge the Tuljapurkar model previously used as a biological null model to test whether the observed distribution of reproductive success over the lifetime was generated by a stochastic process by modifying two steps of the previous model to build a full stochastic model. We show that a distribution generated by the full dynamic model proposed by Tuljapurkar et al. (2009) can be consistently interpreted as only generated from a stochastic biological process provided that the probabilities of transition among reproductive states used are independent of the current reproductive state and that the positive co- variation that usually occurs between survival and reproduction among individuals is removed. Only the reproductive status of roe deer females could be restricted to a stochastic process described by the full stochastic model, probably because most females (>90%) were breeders in a given year. The fecundity of roe deer females could not be adequately described by the full dynamic and full stochastic model, and the observed distribution of female reproductive success differed from the one generated by a full dynamic model in which each individual reproductive trajectory was independent of the individual lifespan (second step of the full dynamic model changed). While there was clear evidence that dynamic heterogeneity occurred and accounted for a large part of the observed among-individual variation in reproductive trajectories of roe deer females, a stochastic process did not provide a suitable model for all reproductive metrics. Consequently, models including additional fixed and dynamic traits need to be built in order to separate the relative role of fixed and dynamic heterogeneities in generating reproductive trajectories. © 2012 Elsevier Inc. All rights reserved. 1. Introduction Individual heterogeneity is pervasive in most organisms, and it corresponds to the variation observed in a trait among individ- uals within a given population. These differences need to be ac- counted for to assess within-individual changes in age-dependent life-history traits reliably (Vaupel and Yashin, 1985). Diversity in maternal and environmental factors generates differences in in- dividual reproductive abilities (Cam and Monnat, 2000; Beauplet ∗ Corresponding author. E-mail address: Jean-Michel.Gaillard@univ-lyon1.fr (J.M. Gaillard). et al., 2006; Knape et al., 2011) and modifies the shape of age de- pendence in survival. The positive co-variation between survival and reproduction induced by phenotypic and environmental vari- ations can often mask actuarial senescence (Service, 2000; Nussey et al., 2008). Individual heterogeneity, thus, plays a main role in shaping population dynamics (Bjørnstad and Hansen, 1994; Cam et al., 2002; Vindenes et al., 2008; Kendall et al., 2011). The different sources of heterogeneity are often poorly investigated, and their relative roles in structuring the observed variation in life-history traits remain unknown. A recent study by Tuljapurkar et al. (2009) provided a way to disentangle the dynamic and fixed heterogeneity. Dynamic heterogeneity involves within-individual differences in life-history traits that are generated by a random process that produces transitions between 0040-5809/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.tpb.2012.03.006