Individual differences, density dependence and offspring birth traits in a population of red deer

Stopher, Katie V.; Pemberton, Josephine M.; Clutton‐Brock, Tim; Coulson, Tim

doi:10.1098/rspb.2008.0502

Cited by 35 publications

(47 citation statements)

References 73 publications

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“…Plant biologists have long noted the persistent variation individuals in growth and reproductive output [29,61,62,72]. Studies of mammals have illustrated persistent individual differences in growth, maternal quality, and behaviour [8,66,67]. Similar observations have been made among fish [45,59].…”

Section: Introductionsupporting

confidence: 61%

Estimating von Bertalanffy parameters with individual and environmental variations in growth

Shelton

Mangel

2012

Journal of Biological Dynamics

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Variation among individuals is an ubiquitous feature of natural populations. However, the relative roles of intrinsic individual differences and stochastic processes in generating variation remain poorly understood. For somatic growth, identifying the contribution of individual and stochastic processes to observed variation in size has important implications both for basic and applied biology. Here we propose and develop methods for estimating individual variation in growth using size-at-age data. We modify the von Bertalanffy growth model to explicitly incorporate individual, environmental, and stochastic variation and provide analytic expressions for the mean and variance of length-at-age in populations. We use a Bayesian statistical model to estimate individual variation from length-at-age data and apply the model to simulated data to test its efficacy. Although a first step towards understanding individual variation, we demonstrate that estimating individual variation from observational samples is possible and provide a platform for future analytical and statistical developments.

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Section: Introductionsupporting

confidence: 61%

Estimating von Bertalanffy parameters with individual and environmental variations in growth

Shelton

Mangel

2012

Journal of Biological Dynamics

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“…Past success rate was more closely associated with breeding success and, in contrast to pair bond duration, was positive related. Pairs that have been successful together in the past are typically more likely to do so in the current breeding attempt, as has been shown in other studies (Newton 1985, 1989, Lewis et al 2006, van de Pol and Verhulst 2006, Stopher et al 2008. It may seem paradoxical that low quality pairs remain together despite having a very low productivity; presumably there is a greater cost than benefit of divorce, including the energetic cost of finding a mate, the possibility of securing a poorer quality individual, and the stress of being with a new mate (Angelier et al 2007).…”

Section: Discussionmentioning

confidence: 60%

“…Closely linked to these age-specific patterns are the effects of breeding experience and, among species with biparental care, duration of the pair bond, both of which have been generally shown to have a positive impact on breeding success, independent of age (Bradley et al 1990, Pärt 1995, Lewis et al 2006. Irrespective of age, individuals vary in quality (Newton 1985, Lewis et al 2006, van de Pol and Verhulst 2006, Stopher et al 2008. Numerous measures of quality have been put forward (reviewed by Moyes et al 2009), directly or indirectly linked to changing or persistent measures of fitness.…”

mentioning

confidence: 96%

“…Density dependence in age-specific reproduction (Wilson et al 2007) and survival (Coulson et al 2001) has also been demonstrated. Furthermore, a series of studies on red deer Cervus elaphus have identified interactions between certain individual quality measures and population density on birth date, calf mass and calf survival (Clutton-Brock et al 1987, Nussey et al 2005, Stopher et al 2008. Typically, individual differences are more marked as conditions deteriorate, with those age/experience/quality classes with poorer intrinsic abilities more strongly affected by an increase in competition or decrease in resources (Daunt et al 2007).…”

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confidence: 97%

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Effects of extrinsic and intrinsic factors on breeding success in a long lived seabird

Lewis¹,

Elston²,

Daunt³

et al. 2009

Oikos

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There is growing concern over the impacts of climate change on animal species. Many studies have demonstrated impacts of climate change at the population level, and density dependent effects of climate are frequently reported. However, there is an increasing recognition of the differential impact of such factors on individuals since there is marked variation in individual performance. We investigated the relationships between breeding success and environmental conditions (winter NAO and one year lagged winter NAO) and intrinsic effects (colony size, pair bond duration, past breeding success rate) in the northern fulmar Fulmarus glacialis, using data from a long-term study commenced in 1950. There was a negative trend in breeding success over time, and a negative relationship with winter NAO and lagged winter NAO, which themselves had shown positive increases over the study period. The effects of lagged winter NAO remained after accounting for the linear trend. There was no evidence of density dependence, with breeding success positively related to colony size. We found strong evidence that breeding success was negatively related to pair bond duration but positively related to past breeding success rate. There was also an interaction between these two intrinsic effects such that those pairs that had historically been successful maintained success with increasing pair bond duration, whereas less successful pairs showed a decline. The prediction that there would be a differential impact of extrinsic factors among pairs was supported by an interaction between past breeding success rate and winter NAO, such that pairs with low past success rate exhibited a sharp decline in breeding success with increasing winter NAO, whereas more successful pairs did not. It is critically important to understand interactions between extrinsic factors and individual heterogeneity since a differential impact on individuals will affect population structure, and hence population dynamics.

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“…Indeed there are a large number of deterministic (and numerically approximable) systems that evolve without the assistance of a PDE. We will study a mathematical framework which exposes the consequences of persistent differences between individuals in the population dynamics (see [28] for a study of such a phenomenon in the context of red deer populations).…”

Section: Introductionmentioning

confidence: 99%

Evolving communities with individual preferences

Cass¹,

Lyons

2014

Proceedings of the London Mathematical Society

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The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space (Ω, F, ν) where ν determines the abundance of individual preferences. The preferences of an individual ω ∈ Ω are described by a measurable choice X(ω) of a rough path.We aim to identify, for each individual, a choice for the forward evolution Y t(ω) for an individual in the community. These choices Y t(ω) must be consistent so that Yt(ω) correctly accounts for the individual's preference and correctly models their interaction with the aggregate behaviour of the community.In general, solutions are continuum of interacting threads analogous to the huge number of individual atomic trajectories that together make up the motion of a fluid. The evolution of the population need not be governed by any over-arching partial differential equation (PDE). Although one can match the standard non-linear parabolic PDEs of McKean-Vlasov type with specific examples of communities in this case. The bulk behaviour of the evolving population provides a solution to the PDE.We focus on the case of weakly interacting systems, where we are able to exhibit the existence and uniqueness of consistent solutions.An important technical result is continuity of the behaviour of the system with respect to changes in the measure ν assigning weight to individuals. Replacing the deterministic ν with the empirical distribution of an independent and identically distributed sample from ν leads to many standard models, and applying the continuity result allows easy proofs for propagation of chaos.The rigorous underpinning presented here leads to uncomplicated models which have wide applicability in both the physical and social sciences. We make no presumption that the macroscopic dynamics are modelled by a PDE.This work builds on the fine probability literature considering the limit behaviour for systems where a large number of particles are interacting with independent preferences; there is also work on continuum models with preferences described by a semi-martingale measure. We mention some of the key papers.

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Individual differences, density dependence and offspring birth traits in a population of red deer

Cited by 35 publications

References 73 publications

Estimating von Bertalanffy parameters with individual and environmental variations in growth

Estimating von Bertalanffy parameters with individual and environmental variations in growth

Effects of extrinsic and intrinsic factors on breeding success in a long lived seabird

Evolving communities with individual preferences

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