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Unifying Ecological and EvolutionaryDynamics Through ExperimentalStochastic DemographyIsabel M. Smallegange a & Tim Coulson aa Division of Biology, Imperial College London, Silwood Park,Ascot, SL5 7PY, UKPublished online: 14 Mar 2013.

To cite this article: Isabel M. Smallegange & Tim Coulson (2009) Unifying Ecological andEvolutionary Dynamics Through Experimental Stochastic Demography, Israel Journal of Ecology& Evolution, 55:3, 199-205, DOI: 10.1560/IJEE.55.3.199

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ISRAEL JOURNAL OF ECOLOGY & EVOLUTION, Vol. 55, 2009, pp. 199–205DOI: 10.1560/IJEE.55.3.199

*Author to whom correspondence should be addressed. E-mail: i.smallegange@imperial.ac.ukReceived 8 July 2009, accepted 30 August 2009.

Unifying ecological and evolUtionary dynamics throUgh experimental stochastic demography

Isabel M. sMallegange* and TIM Coulson

Imperial College London, Division of Biology, Silwood Park, Ascot, SL5 7PY, UK

AbSTRACT

Ecological and evolutionary dynamics depend upon variation in birth and death rates. Consequently characterizing birth and death rates, and identify-ing factors that explain variation in these rates, should be the foundation of population and evolutionary ecology. Given the central role of birth and death, it is perhaps surprising that relatively few population biologists apply the most recent demographic approaches to their research. This may be be-cause demography is seen as little more than accounting, and therefore dull, or because stochastic demography is seen as mathematically challenging. It is our belief that ecologists and evolutionary biologists have much to gain through increased mastery of stochastic demography. Its applications could push forward our understanding of eco-evolutionary dynamics in stochastic environments, and the outcome could further the unification of ecology and evolution. In this essay we briefly explain why mastering demographic ap-proaches should be a desirable objective for any evolutionary ecologist. We start by describing some aspects and insights gained through application of demographic methods, before suggesting an area where we believe applica-tion could prove insightful.

Keywords: environmental change, experiment, life-history, long-run stochastic growth rate, perturbation analysis, population dynamics, prospective analysis

A bRIEF PRIMER

Although the derivations underpinning many of the fundamental equations in demography, and especially stochastic demography, are somewhat fearsome, the biological logic of de-mography, and application of the equations, is straightforward. First, a quantity is identified that summarizes the population dynamics. For density-independent stochastic environments this quantity is the long-run stochastic growth rate (Tuljapurkar, 1990). Next, one assesses the consequences of changing a demographic rate associated with the quantity. In stochastic demography one might investigate the consequences of altering the temporal distribution of adult survival on the long-run stochastic growth rate. If demographic rates depend on phe-notypic traits that may have a genetic component, then analyses of the long-run stochastic growth rate can inform us about both ecological and evolutionary dynamics.

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Central to the application of demography is perturbation analysis, including, in stochastic demography, sensitivity, and elasticity (proportional sensitivity) (Caswell, 2001) of the long-run stochastic growth rate to changes in survival, growth, and re-production at different life stages (Tuljapurkar et al., 2003). Whereas sensitivity is the rate of change in a quantity describing population growth in response to changes in a particular demographic rate, elasticity is the relative contribution of different life stages (Caswell, 2001). Such perturbation analyses of demographic models for systems living in stochastic environments have been applied to field data to compare the sensitivity of different animal and plant species to changes in life-history traits due to climate vari-ability (Morris et al., 2008), and to investigate whether the contribution of vital rates to the stochastic population growth rate differs between spatially separated populations (Morris and doak, 2005).

Applications of perturbation analyses are far-reaching: they can be combined with other tools, including adaptive dynamics (Geritz et al., 1998), or quantities, such as selection gradients, to provide evolutionary insight. We give three examples. First, Met-calf et al. (2008) combined adaptive dynamics with stochastic demographic models to accurately predict flowering decisions in a stochastic, density-dependent environment. The predicted values of flowering strategies were evolutionarily stable. Metcalf et al. (2008) were also able to reveal that certain sets of flowering strategies formed protected genetic polymorphisms maintained by negative frequency-dependent selection. This is an important insight, as the existence of protected polymorphisms provides a mecha-nism to maintain genetic diversity—a key topic of investigation in population biology. Our second example comes from work trying to identify mechanisms behind one of many recently reported case studies on rapidly changing heritable phenotypic traits in the face of environmental change (Coltman et al., 2003; Hsieh et al., 2006; Carroll et al., 2007). Coulson et al. (2003) coupled selection gradients with elasticities of popula-tion growth to demographic rates to show that the demographic rate via which selection on birth mass and birth date in red deer operated most strongly, varied with time as a function of environmental variation. Their detailed examination of observed change provides one of very few examples where the observed and predicted response to selec-tion were reconciled. Selection will also leave a signature in ecological dynamics, and our third example of the potential utility of demographic approaches to link ecology and evolution comes from numerous studies characterizing the ecological signatures associated with changes in the distribution of phenotypic traits (Hairston et al., 2005; Coulson et al., 2006; Hesse et al., 2008). Hairston et al. (2005) decomposed population dynamics in a population of Darwin’s finch and reported that a greater proportion of dynamical change was caused by evolutionary processes operating on beak morphology than by ecological processes. These examples demonstrate that recent developments in deriving stochastic elasticities have substantially increased the number of questions that ecologists and evolutionary biologists can now address. Unfortunately, the technical nature of some of the literature on stochastic elasticities can be daunting to those without a mathematical background.

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VOL. 55, 2009 ExPERIMENTAL STOCHASTIC dEMOGRAPHY 201

HOW CAN I USE STOCHASTIC dEMOGRAPHIC APPROACHES?

The methods to calculate stochastic elasticities rely upon constructing life tables and population projection matrices of the species of interest for the different environments it experiences. Defining discrete environments and associated life tables might seem difficult or impossible when natural populations living in continuous environments are concerned, but this need not be the case. Ezard et al. (2008) used tree regression (Ven-ables and Ripley, 1999) to generate discrete environmental classes from the (continuous) environmental variables influencing population growth in their study population. Each unique combination of the different environmental classes is then a unique, discrete environment, and it is possible to assign each year of the study period to one of these unique environments (Tuljapurkar et al., 2003). Life tables associated with each envi-ronment can then be constructed using observations on the demography of the study population of the time period characterized by each of the different environments. This procedure is now routinely done for a large number of plant, invertebrate, and vertebrate species in the lab and field, and in both terrestrial and aquatic environments. It is also possible to calculate transition probabilities from one environment to the other and sum-marize them in a Markov chain. This Markov chain is then used to simulate a sequence of different environments over which the long-run stochastic growth rate is calculated and perturbation analysis applied (Tuljapurkar et al., 2003). It is then easy to define Markov chains to generate any desired frequency of environments, and to examine how altering the frequency influences model predictions.

FROM THE FIELd TO THE LAb

detailed understanding of ecological systems arises from being able to explain past ob-served patterns (retrospective analyses) and from making testable predictions when the sto-chastic environment changes (prospective models). Insights from our three examples arise from retrospective analyses of past dynamics (Fig. 1). Although these insights are exciting,

Fig. 1. The empirical cycle. Retrospective analysis arises from past dynamics. In prospective analysis (denoted by dark-gray arrows) hypotheses are derived from empirical observations and from the results of retrospective analysis. The hypotheses are tested in experiments and if neces-sary, new experiments are designed for further hypothesis testing (light-gray arrow).

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the potential of stochastic demography as a set of powerful tools to investigate ecological and evolutionary dynamics would benefit from the testing of prospective models (Fig. 1). For example, there is great interest in the impact of harvesting on population growth and on the adaptive responses of phenotypes to harvesting, such as reduced age at first repro-duction in exploited fish populations (Conover and Munch, 2002; Walsh et al., 2006). Predicting the impact of selective harvesting on population growth is generally achieved by perturbation analysis of demographic models, yet few studies have tested their predictions because of the logistical challenges of implementing an experimental test in the field.

Laboratory systems are ideally suited for conducting experiments on replicated popu-lations to test predictions from perturbation analyses (Huffaker et al., 1963; Costantino et al., 1995; Mueller and Joshi, 2000; Ellner et al., 2001; benton et al., 2004; Sabelis et al., 2005). However, there has been no published research using these powerful sto-chastic demographic methods on laboratory models to explore stochastic demography. One of the reasons for this may be that parameterization of the demographic models has traditionally relied upon data collected from marked individuals. In many labora-tory populations, including, for example, acarid mites (Rhizoglyphus spp, Sancassania spp.) and Drosophila, it is unfeasible to mark and follow individuals throughout their lives. However, parameterization of demographic models does not necessarily require data from recognizable individuals. Survival components can be estimated from cohort studies, and recruitment through counting eggs. It is even possible to individually sepa-rate individuals and to monitor their performance over their lifetime (e.g., Gerson et al., 1983). Once life tables have been constructed for different environments, the methods can be applied and the long-run stochastic growth rate and its elasticities calculated. Hypotheses based on the consequences of altering the temporal distribution of demo-graphic rates on the long-run stochastic growth rate can then be experimentally tested, for example by imposing mortality regimes to assess effects of selective harvesting (Conover et al., 2009). Alternatively, one could alter the temporal distribution of demo-graphic rates by altering the frequency with which the population is exposed to different environments. Specifically, one could compare the dynamics of populations in systems characterized by red noise (low-frequency oscillations in which the environment rarely changes) or blue noise (high-frequency oscillations where the system jumps between environments more frequently than expected by chance). Such studies are important to assess effects of environmental stochasticity on the dynamics of populations, as the type of environmental noise may alter the frequency of population fluctuations (Reuman et al., 2006), or affect the relative importance of, and variation in, demographic rates. Most importantly, however, laboratory species generally have short generation times, so that the environmental regime imposed by the experimenter, or feedback between individu-als and environmental conditions, may lead to selection for novel traits (Sabelis et al., 2005). Evolution of novel traits not only highlights the importance of assessing whether models of stochastic demography are evolutionarily robust, but also underscores the importance of evolutionary analysis in stochastic demography. Laboratory populations are ideal model systems to explore and test both issues and to assess the importance and impact of rapid evolutionary change on population growth and demographic structure.

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FUTURE FINdINGS?

So what insights would the application of recently developed stochastic demographic methods to laboratory systems provide? We believe it has the potential to generate many novel insights that can further the unification of ecology and evolutionary biology. We outline four of these below:

(1) Most organisms that have been subjected to stochastic demographic methods are relatively similar in their life histories. Predictions from species with much more variable dynamics, more plastic life histories, and much faster generation times could potentially lead to generalizations that are currently not possible. For exam-ple, does the contribution of environmental variation to ecological and evolutionary dynamics vary systematically with life history?

(2) The high reactivity of laboratory organisms to environmental change due to their short generation times makes them ideal candidates to increase insight into the interplay between selection of traits and demographic structure of populations in varying environments. Such experiments and analyses could allow predictions of how species with short generations may be affected by environmental change.

(3) Although the stochastic demographic methods offer huge potential to increase our understanding of ecological and evolutionary processes, they are based on assump-tions, such as no density-dependence, that are likely violated in field populations. Arguments have been made (e.g., Caswell, 2001; Roff, 2008) that the methods should provide adequate approximations when these assumptions are relaxed, as it has yet to be empirically shown that the theoretical conditions under which the as-sumptions fail are biologically realistic (Roff, 2008). Laboratory experiments could provide more insight as to whether stochastic demographic models can be applied in environments that assume density- or frequency-dependence. These insights would help guide the development of new theory describing ecological and evolutionary dynamics in density- and frequency-dependent stochastic environments.

(4) A key notion in stochastic demography is that the long-run stochastic growth rate measures the fitness of individuals in varying environments (Metz et al., 1992) and selection must therefore act through it. Fitness is assumed to be optimized at the level of a subpopulation of individuals that share a certain phenotype or genotype, or at the level of a whole population. However, the appropriate definition of fitness depends on the model assumptions on density-dependence, frequency dependence, finite or infinite population size, etc. (Roff, 2008), but it remains yet to be shown empirically what currency is maximized under which environmental conditions. Laboratory experiments using model systems should increase our understanding of what is fitness, and if that indeed is the currency being optimized by evolution. One way to do this would be through experimental manipulation of different fitness currencies (e.g., clutch size) of individuals with known life-history traits, followed by monitoring offspring survival in different environments.

All too often we hear calls for interdisciplinary research, with fields like conserva-

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tion genomics, community epigenetics, and eco-informatics springing into existence at a frightening rate. Understanding patterns of birth and death is central to all these fields because all ecological and evolutionary dynamics depend upon understanding variation in birth and death rates. demography is consequently key to nearly every question of interest to population biologists, and this explains the exponential rise in papers using demographic methods. However, despite the explosion of interest in demography, and especially stochastic demography, there are still many areas where its application could prove fruitful. We have focused on just one—bringing demographic methods into the lab. We believe that the application of stochastic demography to experimental model systems has enormous potential to provide detailed understanding of links between genes, phenotype, demography, and dynamics in stochastic environments. It would be a shame if the next generation of population biologists were turned off stochastic demog-raphy because they fear its mathematics, have a misguided perception that the field is dreary, or a belief that evolutionary biology and ecology have been formally unified.

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