Being able to simultaneously investigate the dynamics of populations, phenotypic characters, estimates of their additive genetic variances, and life history parameters, would provide a useful step in identifying linkages between population ecology, evolutionary biology and life history theory. Such a framework could also be used to gain insight into the dynamics of life history variables ( Caswell 2001). If the entire character distribution could be tracked the dynamics of the character and the dynamics of population size could be jointly investigated within a single model ( Easterling, Ellner & Dixon 2000). For individual characters, like body mass, the total size (or weight) of the character distribution constructed from a population at a point in time is the population size at that time. In contrast, population ecologists have traditionally been uninterested in the means and variances of these distributions but instead focus on how population size fluctuates. Evolutionary questions are usually couched in terms of understanding distributions of quantitative characters and why means and variances of these distributions change with time. The fields of population ecology and evolutionary biology often appear poorly integrated although both study different aspects of the same distribution. Using data from a population of Soay sheep Ovis aries we demonstrate the ease in which such a model can be constructed, parameterized and analysed. Once such a model is constructed associations between these fundamental quantities can be examined through analysis of the model. In this paper we show how a demographic model can be derived and parameterized in a way that allows many fundamental quantities in population ecology, evolutionary biology and life history theory to be calculated. Such understanding could also help explain patterns in the data biologists have collected on within and between species patterns in fitness-related phenotypic characters and population dynamics. This begs the question, how are these quantities related, and should we expect them to change simultaneously when populations are perturbed? Theoretical and empirical understanding of relationships between fundamental quantities underpinning population biology would greatly extend our understanding of the dynamics of populations, life histories and quantitative characters. A growing number of studies report joint change in various pairs of these quantities when populations experience environmental change ( Hairston et al. Life history descriptors such as generation time and mean lifetime reproductive success, ecological variables including population growth rate and structure, and evolutionary quantities like heritability, selection differentials and phenotypic and genetic variances provide the foundations on which population biology is built. The approach we describe has the potential to explain within and between species patterns in quantitative characters, life history and population dynamics. A wide range of joint dynamics of life history, quantitative characters and population growth can be generated in response to changes in different character-demography associations we argue this explains the diversity of observations on the consequences of environmental change from studies of free-living populations.ħ. Perturbation analysis is used to investigate how the quantities listed in summary point 4 change as each parameter in each character-demography function is altered.Ħ. We showcase the method through parameterization of a model using data from a well-studied population of Soay sheep Ovis aries.ĥ. These models can be used to calculate a wide range of useful biological quantities including population growth and structure terms in the Price equation including selection differentials estimates of biometric heritabilities and life history descriptors including generation time. Age-stage-structured models can be constructed from character-demography associations that describe age-specific relationships between the character and: (i) survival (ii) fertility (iii) ontogenetic development of the character among survivors and (iv) the distribution of reproductive allocation.Ĥ. The parameterization and analysis of such a model for a specific system can be used to predict how a population will respond to environmental change.ģ. Insight into the joint dynamics of populations, quantitative characters and life history can be gained by deriving a model that allows the calculation of fundamental quantities that underpin population ecology, evolutionary biology and life history. We do not have a well-developed understanding of links between the dynamics of these quantities.Ģ. There is a growing number of empirical reports of environmental change simultaneously influencing population dynamics, life history and quantitative characters.
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