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Disentangling evolutionary , plastic and demographic processes underlying trait dynamics : A review of four frameworks

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Abstract

1.Biologists are increasingly interested in decomposing trait dynamics into underlying processes, such as evolution, plasticity and demography. Four important frameworks that allow for such a decomposition are the quantitative genetic animal model (AM), the ‘Geber’ method (GM), the age-structured Price equation (APE), and the integral projection model (IPM). However, as these frameworks have largely been developed independently, they differ in the assumptions they make, the data they require, as well as their outcomes and interpretation.

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... Surprisingly, however, little is still known about the relative contributions of mechanisms underlying these shifts [5]. Within a population, phenotypic distributions may change due to a change in population structure (e.g., age structure or sex ratio), due to phenotypic plasticity (within or between individuals), and due to genetic change [6][7][8]. The exact mixture of mechanisms driving phenotypic change will determine the future of a population facing a prolonged change in environmental conditions [9], for several reasons. ...
... The exact mixture of mechanisms driving phenotypic change will determine the future of a population facing a prolonged change in environmental conditions [9], for several reasons. First, the consequences of changing population structure are variable and may be idiosyncratic (e.g., [8,10]). Second, phenotypic plasticity can provide an efficient way to cope with a changing environment, but its effect may be short-lived and even maladaptive [11][12][13]. ...
... The mismatch is not surprising given that several mechanisms of phenotypic change, with a genetic basis or not, have been identified on the Rum red deer population (in our analyses presented here as well as in [41,42]). More generally, our results illustrate how phenotypic change can be simultaneously due to both plastic and genetic changes [6,8,47]. Plastic changes in response to climate change appear common in natural populations, but that does not preclude concurrent evolutionary change in response to climate change [14]. ...
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Changing environmental conditions cause changes in the distributions of phenotypic traits in natural populations. However, determining the mechanisms responsible for these changes—and, in particular, the relative contributions of phenotypic plasticity versus evolutionary responses—is difficult. To our knowledge, no study has yet reported evidence that evolutionary change underlies the most widely reported phenotypic response to climate change: the advancement of breeding times. In a wild population of red deer, average parturition date has advanced by nearly 2 weeks in 4 decades. Here, we quantify the contribution of plastic, demographic, and genetic components to this change. In particular, we quantify the role of direct phenotypic plasticity in response to increasing temperatures and the role of changes in the population structure. Importantly, we show that adaptive evolution likely played a role in the shift towards earlier parturition dates. The observed rate of evolution was consistent with a response to selection and was less likely to be due to genetic drift. Our study provides a rare example of observed rates of genetic change being consistent with theoretical predictions, although the consistency would not have been detected with a solely phenotypic analysis. It also provides, to our knowledge, the first evidence of both evolution and phenotypic plasticity contributing to advances in phenology in a changing climate.
... However, the ecological contribution to the total change calculated by the Eco-Evo assay was up to 35% higher than estimated by the established metrics. Diverging eco-evolutionary partitioning results by different metrics using the same data are not unusual (van Benthem et al., 2016;Govaert et al., 2016) and can partly result of distinct underlying definitions of the included components (van Benthem et al., 2016). One example is that the Geber method does in contrast to other approaches not account for the directionality of changes from an ancestral to an affected community, but instead defines and calculates relative ecological and evolutionary contributions to a mean change using both ambient and novel as ancestral environment. ...
... However, the ecological contribution to the total change calculated by the Eco-Evo assay was up to 35% higher than estimated by the established metrics. Diverging eco-evolutionary partitioning results by different metrics using the same data are not unusual (van Benthem et al., 2016;Govaert et al., 2016) and can partly result of distinct underlying definitions of the included components (van Benthem et al., 2016). One example is that the Geber method does in contrast to other approaches not account for the directionality of changes from an ancestral to an affected community, but instead defines and calculates relative ecological and evolutionary contributions to a mean change using both ambient and novel as ancestral environment. ...
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Shifts in microbial communities and their functioning in response to environmental change result from contemporary inter‐ and intraspecific diversity changes. Interspecific changes are driven by ecological shifts in species composition, while intraspecific changes are here assumed to be dominated by evolutionary shifts in genotype frequency. Quantifying the relative contributions of inter‐ and intraspecific diversity shifts to community change thus addresses the essential, yet understudied question as to how important ecological and evolutionary contributions are to total community changes. This debate is to date practically constrained by (i) a lack of studies integrating across organizational levels, (ii) a mismatch between data requirements of existing partitioning metrics and the feasibility to collect such data, especially in microscopic organisms like phytoplankton. We experimentally assessed the relative ecological and evolutionary contributions to total phytoplankton community changes using a new design and validated its functionality by comparisons to established partitioning metrics. We used a community of coexisting Emiliania huxleyi and Chaetoceros affinis with initially nine genotypes each. First, we exposed the community to elevated CO2 concentration for 80 days (~50 generations) to induce inter‐ and intraspecific diversity changes and a total abundance change. Second, we independently manipulated the induced inter‐ and intraspecific diversity changes in an assay to quantify the corresponding ecological and evolutionary contributions to the total change. Third, we applied existing partitioning metrics to our experimental data and compared the outcomes. Total phytoplankton abundance declined to one fifth in the high CO2 exposed community compared to ambient conditions. Consistently across all applied partitioning metrics, the abundance decline could predominantly be explained by ecological shifts and to a low extent by evolutionary changes. We discuss potential consequences of the observed community changes on ecosystem functioning. Further, we explain that the low evolutionary contributions likely resulted of intraspecific diversity changes that occurred irrespectively of CO2. We discuss how the assay could be upscaled to more realistic settings, including more species and drivers. Overall, the presented calculations of eco‐evolutionary contributions to phytoplankton community changes constitute another important step towards understanding future phytoplankton shifts, and eco‐evolutionary dynamics in general.
... However, in reality, this will rarely be the case. Different research questions require different statistical frameworks (model structures) and a thorough understanding of the definitions and components of the frameworks as well as of the study system is crucial for making biologically meaningful inferences (Benthem et al., 2017). Therefore, identifying a proper model structure (that fits the data well) and that addresses a biological question properly is by no means trivial and probably one of the largest challenges in the art of modelling. ...
... Quantitative genetics resolves this apparent impasse by providing an analytical framework that treats the summed contribution of all loci as the unit of interest, an approach that has proven highly successful in predicting the responses of domestic populations to artificial selection 8 . In particular, the 'individual animal model' 9 estimates the genetic value of each individual in the sample population, providing a robust methodology for quantifying evolutionary change in the wild 1, 10,11 . However, published demonstrations of adaptive evolution of quantitative traits in response to climate change have been conspicuously absent since the realization that earlier applications are strongly anticonservative 10,12 . ...
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Secondary sexual traits have high heritabilities and are exposed to strong, environmentally sensitive selection, and so are expected to evolve rapidly in response to sustained environmental change. We examine the eco-evolutionary dynamics of ornament expression in a long-term study population of collared flycatchers, Ficedula albicollis, in which forehead patch size, which positively influences male reproductive success, declined markedly over 34 years. Annual fitness selection on forehead patch size switched from positive to negative during the study, a reversal that is accounted for by rising spring temperatures at the breeding site: highly ornamented males were selectively favoured following cold breeding seasons but selected against following warm breeding seasons. An ‘individual animal model’ describes a decline in the genetic values of breeding males during the study, which simulations showed was unlikely to result from drift alone. These results are thus consistent with adaptive evolution of a sexually selected trait in response to climate change.
... Several methods have been developed to decompose trait changes into their ecological and evolutionary components (overview in van Benthem et al. 2017). When sufficient data are available, the best approach is to use a pedigree-based quantitative genetics model (e.g., the animal model; Kruuk 2004) to evaluate the genetic basis of a trait, which can then be combined with the Geber approach developed by Ellner et al. (2011) to partition the effects of plastic and evolutionary trait change on population growth. ...
Article
Recent studies suggest that evolutionary changes can occur on a contemporary time scale. Hence, evolution can influence ecology and vice-versa. To understand the importance of eco-evolutionary dynamics in population dynamics, we must quantify the relative contribution of ecological and evolutionary changes to population growth and other ecological processes. To date, however, most eco-evolutionary dynamics studies have not partitioned the relative contribution of plastic and evolutionary changes in traits on population, community and ecosystem processes. Here, we quantify the effects of heritable and non-heritable changes in body mass distribution on survival, recruitment and population growth in wild bighorn sheep (Ovis canadensis) and compare their importance to the effects of changes in age structure, population density and weather. We applied a combination of a pedigree-based quantitative genetics model, statistical analyses on demography and a new statistical decomposition technique, the Geber method, to a long-term dataset of bighorn sheep on Ram Mountain (Canada), monitored individually from 1975 to 2012. We show three main results: (1) The relative importance of heritable change in mass, non-heritable change in mass, age structure, density and climate on population growth rate changed substantially over time. (2) An increase in body mass was accompanied by an increase in population growth through higher survival and recruitment rate. (3) Over the entire study period, changes in the body mass distribution of ewes, mostly through non-heritable changes, affected population growth to a similar extent as changes in age structure or in density. The importance of evolutionary changes was small compared to that of other drivers of changes in population growth but increased with time as evolutionary changes accumulated. Evolutionary changes became increasingly important for population growth as the length of the study period considered increased. Our results highlight the complex ways in which ecological and evolutionary changes can affect population dynamics and illustrate the large potential effect of trait changes on population processes. This article is protected by copyright. All rights reserved.
... Ecological models incorporating nongenetical models of inheritance (particularly integral projection models, or IPMs; Coulson, Tuljiapurkar, and Childs (2010)) have recently been used to make very strong claims about the scope for rapid contemporary evolution of quantitative traits. However, comprehensive descriptions based on principles by which genetic variation relates to the evolutionary process have shown why purely phenotypic models cannot, in general, recover phenotypic covariances between kin that are critical for modelling evolution (Chevin, 2015;Hedrick, Coltman, Festa-Bianchet, & Pelletier, 2014;Janeiro, Festa-Bianchet, Pelletier, Coltman, & Morrissey, 2016;van Bentham et al., 2017). Therefore, claims about (non)evolution based on these models are misleading (Coulson, Schindler, Traill, & Kendall, 2017 Key examples and papers associated with their first appearances at previous WAMBAMs include the following: multimatrix inference (Stopher et al., 2012), the use of Bayesian mixed models (especially using MCMCglmm, Hadfield, 2010), and improvements in how predicted breeding values (estimates of the additive genetic component of individual phenotypes) are used in evolutionary inferences (see Postma, 2006;Hadfield, Wilson, Garant, Sheldon, and Kruuk (2010)). ...
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The sixth Wild Animal Models Bi-Annual Meeting was held in July 2017 in Québec, with 42 participants. This report documents the evolution of questions asked and approaches used in evolutionary quantitative genetic studies of wild populations in recent decades, and how these questions and approaches were represented at the recent meeting. We explore how ideas from previous meetings in this series have developed to their present states, and consider how the format of the meetings may be particularly useful at fostering the rapid development and proliferation of ideas and approaches.
... Boyce and Krausman (2018) question the magnitude of evolutionary change caused by trophy hunting and our ability to detect it. They cite van Benthem et al. (2016) to claim that "the animal model from quantitative genetics estimates evolution with a negative bias." Van Benthem et al. (2016) report a negative bias only when simulated maternal effects decrease but are not correctly modeled. ...
... In addition, the rapidity of human-induced changes may exceed the rate of evolution. The scarcity of evidence for evolutionary responses to human-induced environmental changes can also be due to the difficulty of separating plastic and genetic responses in the wild (Merila & Hendry, 2014;Prokuda & Roff, 2014;van Benthem et al., 2017). One potential example of an evolutionary response is the sexually selected forehead patch of the collared flycatcher (Ficedula albicollis), which has become smaller during a 34-year period of climate change, apparently because of a trade-off with survival (Evans & Gustafsson, 2017). ...
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Human activities by altering environmental conditions are influencing the mate choice of animals. This is by impacts on: (i) the production and expression of traits evaluated by mate choosers; (ii) the transmission of information about potential mates to choosers; (iii) the reception and processing of the information by choosers; and (iv) the final mate choice. Here, I first discuss how these four stages of the mate‐choice process can be altered by environmental change, and how these alterations, in turn, can influence individuals, populations, and communities. Much evidence exists for human‐induced environmental changes influencing mate choice, but the consequences for the fitness of courters and choosers are less well known, and even less is known about the impact on population dynamics, species interactions and community composition. More evidence exists for altered mate‐choice systems influencing interspecific matings and thereby community composition and biodiversity. I then consider whether plastic adjustments and evolutionary changes can rescue adaptive mate‐choice systems, and reflect on the possibility of non‐adaptive mate‐choice systems becoming less maladaptive under environmental change. Much evidence exists for plastic adjustments of mate‐choice systems, but whether these are adaptive is seldom known, as is the contribution of genetic changes. Finally, I contemplate the possibility of mate‐choice systems rescuing populations from decline in changing environments. I explain how this is context dependent with both positive and negative outcomes possible. In summary, while much evidence exists for human‐induced environmental changes influencing mate‐choice systems, less is known about the consequences for ecological and evolutionary processes. Considering the importance that mate choice plays in determining individual fitness and population viability, the effects of environmental change on mate‐choice systems should be considered in studies on the ecological and evolutionary consequences of human disturbances to habitats.
... These eco-evolutionary dynamics potentially play an important role in shaping populations, communities and ecosystems (Bassar, Marshall, et al., 2010;Fussmann, Loreau, & Abrams, 2007;Matthews, Aebischer, Sullam, Lundsgaard-Hansen, & Seehausen, 2016;Strauss, 2014). Discriminating between ecological and evolutionary processes and quantifying their relative importance are challenging, especially in natural populations, but different frameworks exist that aim to disentangle different processes (Coulson & Tuljapurkar, 2008;Ellner, Geber, & Hairston, 2011;Hairston et al., 2005;van Benthem et al., 2017). Experiments on eco-evolutionary dynamics can be very useful in addition to longterm field observations, as experiments allow for manipulating and tracking ecological and evolutionary processes (Becks, Ellner, Jones, & Hairston, 2012;Turcotte, Reznick, & Daniel Hare, 2013;Yoshida, Jones, Ellner, Fussmann, & Hairston, 2003). ...
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1Changes in population dynamics due to interacting evolutionary and ecological processes are the direct result of responses in vital rates, i.e. stage‐specific growth, survival and fecundity. Quantifying through which vital rates population fitness is affected, instead of focusing on population trends only, can give a more mechanistic understanding of eco‐evolutionary dynamics. 2The aim of this study was to estimate the underlying demographic rates of aphid (Myzus persicae) populations. We analysed unpublished stage‐structure population dynamics data of a field experiment with caged and uncaged populations in which rapid evolutionary dynamics were observed, as well as unpublished results from an individual life table experiment performed in a greenhouse. 3Using data on changes in population abundance and stage distributions over time, we estimated ransition matrices with inverse modelling techniques, in a Bayesian framework. The model used to fit across all experimental treatments included density as well as clone‐specific caging effects. We additionally used individual life table data to inform the model on survival, growth and reproduction. 4Results suggest that clones varied considerably in vital rates, and imply trade‐offs between reproduction and survival. Responses to densities also varied between clones. Negative density‐dependence was found in growth and reproduction, and the presence of predators and competitors further decreased these two vital rates, while survival estimates increased. Under uncaged conditions, population growth rates of the evolving populations were increased compared to the expectation based on the pure clones. 5Our inverse modelling approach revealed how much vital rates contributed to the eco‐evolutionary dynamics. The decomposition analysis showed that variation in population growth rates in the evolving populations were to a large extent shaped by plant size. Yet, it also revealed an impact of evolutionary changes in clonal composition. Finally, we discuss that inverse modelling is a complex problem, as multiple combinations of individual rates can result in the same dynamics. We discuss assumptions and limitations, as well as opportunities, of this approach. This article is protected by copyright. All rights reserved.
... Community rescue may be brought about by physiological and developmental processes ( plasticity), evolutionary processes (adaptation of species through natural selection) and ecological processes (changes in composition caused by species sorting). A complete accounting of plastic, evolutionary and ecological processes and their interactions (for example, species may differ in the plasticity they express or evolve) cannot be provided by an observational survey and instead requires a reciprocal transplant experiment or a detailed population pedigree [5,6] (M.D. Jewell & G.B. 2018, unpublished data). Moreover, the term 'rescue', as we have defined it, implies that some general criterion (such as productivity or trophic structure) must be specified in advance; it may be only partially satisfied, and, whether fully or partially satisfied, does not imply that any other criterion would lead to the same conclusion. ...
Article
Community rescue occurs when a community that experiences lethal stress persists only through the spread of rare types, either genotypes or species, resistant to the stress. Rescue interacts with trophic structure because physical stress experienced by a focal assemblage within the community may also be experienced by its predators and prey. In general, trophic structure will facilitate rescue only when a stress has a less severe effect on a focal assemblage than on its predators. In other circumstances, when stress affects prey or has only a weak effect on predators, trophic structure is likely to hamper rescue. We exposed a community of phytoplankton and zooplankton derived from a natural lake to acidification in outdoor mesocosms large enough to support trophically complex communities. Rescue of the phytoplankton from severe acidification was facilitated by prior exposure to sublethal stress, confirming previous results from microcosm experiments. Even communities that have previously been less highly stressed were eventually rescued, however, because their zooplankton predators were more sensitive to acidification and became extinct. Our experiment shows how community rescue following severe stress is modulated by the differential effect of the stress relative to trophic level.
... Phenotypes, rather than genotypes, are fundamental to understanding the interface between ecology and evolution (Hendry 2016;Hendry and Green 2018). Yet, because phenotypes are influenced by both genetic and plastic effects, an essential question of evolutionary biology is to tease out plastic and genetic contributions to trait differences (Cote et al. 2012;Van Benthem et al. 2017). In this study, a similar proportion of different forms of keratinized beaks was observed between different age groups in the same population. ...
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Megalobrama pellegrini, a cyprinid endemic to the upper Yangtze River China, has thick keratinized beaks on the jaws and feeds on algae and molluscs. The size of keratinized beaks varies among different individuals. In the present study, two populations, from Longxihe (LXH) and Chishui (CSH) Rivers, were examined in order to explore the morphological variation of keratinized beaks, together with an analysis of intestine length and of stable isotopes. The results showed that the ratio of upper to lower keratinized beaks varied from 0.84 to 2.06. We defined the ratio < 1.25 as equal beak (EB) form, while >1.26 as thicker upper beak (TUB) form. In the LXH population, there were more TUB forms, while EB forms dominated in CSH population. Intestine length showed a negative relationship with the upper to lower beak ratio (Pearson correlation coefficient = −0.697, P < 0.01) indicating the possible adaptation of beak size to food type. In addition, analysis of stable isotope showed that these two populations differed in their food, and there was a positive relationship between trophic niche and size of beaks (R = 0.5530 and 0.4927, respectively). This further supported the suggestion that the beak size was possibly adapted to food type, with the TUB form to a higher trophic niche and the EB form to a lower trophic niche.
... However, in reality, this will rarely be the case. Different research questions require different statistical frameworks (model structures) and a thorough understanding of the definitions and components of the frameworks as well as of the study system is crucial for making biologically meaningful inferences (Benthem et al., 2017). Therefore, identifying a proper model structure (that fits the data well) and that addresses a biological question properly is by no means trivial and probably one of the largest challenges in the art of modelling. ...
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1. Body condition is an important concept in behaviour, evolution and conservation, commonly used as a proxy of an individual’s performance, for example in the assessment of environmental impacts. Although body condition potentially encompasses a wide range of health state dimensions (nutritional, immune or hormonal status), in practice most studies operationalize body condition using a single (univariate) measure, such as fat storage. One reason for excluding additional axes of variation may be that multivariate descriptors of body condition impose statistical and analytical challenges. 2. Structural equation modelling (SEM) is used in many fields to study questions relating multidimensional concepts, and we here explain how SEM is a useful analytical tool to describe the multivariate nature of body condition. In this “How To” paper, we show how SEM can be used to resolve different challenges in analysing the multivariate nature of body condition, such as (i) variable reduction and conceptualization, (ii) specifying the relationship of condition to performance metrics, (iii) comparing competing causal hypothesis, and (iv) including many pathways in a single model to avoid stepwise modelling approaches. We illustrated the use of SEM on a real‐world case study, and provide R‐code of worked examples as a learning tool. 3. We compared the predictive power of SEM with conventional statistical approaches that integrate multiple variables into one condition variable: multiple regression and principal component analysis. We show that model performance on our dataset is higher when using SEM, and led to more accurate and precise estimates compared to conventional approaches. 4. We encourage researchers to consider SEM as a flexible framework to describe the multivariate nature of body condition and thus understand how it affects biological processes, thereby improving the value of body condition proxies for predicting organismal performance. Finally, we highlight that it can be useful for other multidimensional ecological concepts as well, such as immunocompetence, oxidative stress and environmental conditions.
... All rights reserved. & Langangen, 2015;van Benthem et al., 2016). Particularly, Chevin (2015) identified some issues addressed in this paper, presenting insightful numerical examples that illuminate the main concern with the cross-age structure of the inheritance function. ...
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Integral projection models (IPMs) are extremely flexible tools for ecological and evolutionary inference. IPMs track the distribution of phenotype in populations through time, using functions describing phenotype-dependent development, inheritance, survival and fecundity. For evolutionary inference, two important features of any model are the ability to (i) characterize relationships among traits (including values of the same traits across ages) within individuals, and (ii) characterize similarity between individuals and their descendants. In IPM analyses, the former depends on regressions of observed trait values at each age on values at the previous age (development functions), and the latter on regressions of offspring values at birth on parent values as adults (inheritance functions). We show analytically that development functions, characterized this way, will typically underestimate covariances of trait values across ages, due to compounding of regression to the mean across projection steps. Similarly, we show that inheritance, characterized this way, is inconsistent with a modern understanding of inheritance, and underestimates the degree to which relatives are phenotypically similar. Additionally, we show that the use of a constant biometric inheritance function, particularly with a constant intercept, is incompatible with evolution. Consequently, current implementations of IPMs will predict little or no phenotypic evolution, purely as artifacts of their construction. We present alternative approaches to constructing development and inheritance functions, based on a quantitative genetic approach, and show analytically and through an empirical example on a population of bighorn sheep how they can potentially recover patterns that are critical to evolutionary inference. This article is protected by copyright. All rights reserved.
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In seasonally variable environments, phenotypic plasticity in phenology may be critical for adaptation to fluctuating environmental conditions. Using an 18-generation longitudinal dataset from natural damselfly populations, we show that phenology has strongly advanced. Individual fitness data suggest this is likely an adaptive response towards a temperature-dependent optimum. A laboratory experiment revealed that developmental plasticity qualitatively matches the temperature dependence of selection, partially explaining observed advance in phenology. Expanding our analysis to the macroevolutionary level, we use a database of over 1-million occurrence records and spatiotemporally matched temperature data from 49 Swedish Odonate species to infer macroevolutionary dynamics of phenology. Phenological plasticity was more closely aligned with adaptation for species that have recently colonised northern latitudes, but with higher phenological mismatch at lower latitudes. Our results show that phenological plasticity plays a key role in microevolutionary dynamics within a single species, and such plasticity may have facilitated post-Pleistocene range expansion in this insect clade.
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Community rescue occurs when ecological or evolutionary processes restore positive growth in a highly stressful environment that was lethal to the community in its ancestral form, thus averting biomass collapse in a deteriorating environment. Laboratory evidence suggests that community rescue is most likely in high-biomass communities that have previously experienced moderate doses of sublethal stress. We assessed this result under more natural conditions, in a mesocosm experiment with phytoplankton communities exposed to the ubiquitous herbicide glyphosate. We tested whether community biomass and prior herbicide exposure would facilitate community rescue after severe contamination. We found that prior exposure to glyphosate was a very strong predictor of the rescue outcome, while high community biomass was not. Furthermore, although glyphosate had negative effects on diversity, it did not influence community composition significantly, suggesting a modest role for genus sorting in this rescue process. Our results expand the scope of community rescue theory to complex ecosystems and confirm that prior stress exposure is a key predictor of rescue.
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It is well-known that ecological and evolutionary processes can occur on similar time scales resulting in eco-evolutionary dynamics. One of the main questions in eco-evolutionary dynamics involves the assessment of the relative contribution of evolution, ecology and their interaction in the eco-evolutionary change under study. This has led to the development of several methods aimed to quantify the contributions of ecology and evolution to observed trait change, here referred to as eco-evolutionary partitioning metrics. This study provides an overview on currently-used partitioning metrics with a focus on methods that can quantify evolutionary and non-evolutionary contributions to population and community trait change. I highlight key differences between these metrics found in previous studies. Additionally, I also provide a detailed comparison between the ‘Geber’ method and the reaction norm approach. Next, I provide a guideline for researchers to assess which metrics are best suited for their data, give an overview on the type of data needed for these metrics, and how this data can be collected with a focus on community data.
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Integral projection models (IPMs) are extremely flexible tools for ecological and evolutionary inference. IPMs track the distribution of phenotype in populations through time, using functions describing phenotype-dependent development, inheritance, survival and fecundity. For evolutionary inference, two important features of any model are the ability to (i) characterize relationships among traits (including values of the same traits across ages) within individuals, and (ii) characterize similarity between individuals and their descendants. In IPM analyses, the former depends on regressions of observed trait values at each age on values at the previous age (development functions), and the latter on regressions of offspring values at birth on parent values as adults (inheritance functions). We show analytically that development functions, characterized this way, will typically underestimate covariances of trait values across ages, due to compounding of regression to the mean across projection steps. Similarly, we show that inheritance, characterized this way, is inconsistent with a modern understanding of inheritance, and underestimates the degree to which relatives are phenotypically similar. Additionally, we show that the use of a constant biometric inheritance function, particularly with a constant intercept, is incompatible with evolution. Consequently, current implementations of IPMs will predict little or no phenotypic evolution, purely as artifacts of their construction. We present alternative approaches to constructing development and inheritance functions, based on a quantitative genetic approach, and show analytically and through an empirical example on a population of bighorn sheep how they can potentially recover patterns that are critical to evolutionary inference.
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1.Raising global temperatures are predicted to have strong consequences for ectotherms, as metabolic rates depend directly on external temperatures. To understand consequences for population fitness, a full life‐cycle approach is important because i) temperature can have opposite effects on different vital rates (growth, survival, reproduction), and ii) sensitivities of population growth rate to changes in vital rates can vary in magnitude. Since vital rates are concurrently influenced by other factors, adequately predicting temperature effects requires factors like body size, population density and genetics to be taken into account. 2.The aim of this study was to quantify the role of temperature on all vital rates of Daphnia magna individuals, and their integrated effects on population dynamics. Additionally, we evaluated how clonal lineages differed in their temperature response, both on the vital rate and population‐level. 3.We performed a laboratory experiment, in which we followed 40 populations (five clonal lineages × eight temperatures) during 80 days. Due to our novel setup, we were able to quantify vital rates of individuals within those populations. We identified relations between vital rates and body size, lineage, temperature and population density and used a size‐structured Integral Projection Model to integrate the experimental effects over all vital rates. 4.We found negative density‐dependence in growth and reproduction, resulting in lineage‐specific carrying capacities. Population fitness showed a thermal optimum that differed among genotypes. Interestingly, we found that clones had different life history strategies, optimizing population fitness via different routes. As no lineage outperformed the others in all vital rates, we identified trade‐offs between vital rates, which had strong effects on the dynamics of the population. Moreover, simulations suggest that the genetic composition of mixed populations is temperature‐dependent. 5.Our results underscore the importance of studying individuals within their population when predicting responses to environmental change. The observed density effects, which were as strong as temperature effects but explained considerably more variation in population growth, would have been overlooked in life table experiments. Furthermore, differential temperature responses emphasize the importance of genetic variation in the ability of ectotherm species like Daphnia magna to respond to climate change. This article is protected by copyright. All rights reserved.
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In seasonally-variable environments, phenotypic plasticity in phenology may be critical for adaptation to fluctuating environmental (temperature) conditions. Using an 18-generation longitudinal dataset from natural insect (damselfly) populations, we show that phenology has strongly advanced. Individual fitness data suggest this is likely an adaptive response towards a thermally-dependent fitness optimum. A laboratory experiment revealed that developmental plasticity qualitatively matches environmental-dependence of selection, partially explaining observed phenological advance. Expanding our analysis to the macroevolutionary level, we use a database of over 1-million occurrence records and spatiotemporally-matched temperature data from 49 Swedish Odonate species to infer macroevolutionary dynamics of phenology. Phenological plasticity was more closely aligned with adaptation for species that have recently colonized northern latitudes, with more phenological mismatch at lower latitudes. Our results show that phenological plasticity plays a key role in microevolutionary dynamics within a single species, and such plasticity may have facilitated post-Pleistocene range expansion in this insect clade.
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Harvesting may drive body downsizing along with population declines and decreased harvesting yields. These changes are commonly construed as consequences of direct harvest selection, where small‐bodied, early‐reproducing individuals are immediately favoured. However, together with directly selecting against a large body size, harvesting and body downsizing alter many ecological features, such as competitive and trophic interactions, and thus also indirectly reshape natural selection acting back on body sizes through eco‐evolutionary feedback loops (EEFLs). We sketch plausible scenarios of simple EEFLs in which one‐dimensional, density‐dependent natural selection acts either antagonistically or synergistically with direct harvest selection on body size. Antagonistic feedbacks favour body‐size stasis but erode genetic variability and associated body‐size evolvability, and may ultimately impair population persistence and recovery. In contrast, synergistic feedbacks drive fast evolution towards smaller body sizes and favour population resilience, but may have far‐reaching bottom–up or top–down effects. We illustrate the further complexities resulting from multiple environmental feedbacks using a co‐evolving predator–prey pair, in which case outcomes from EEFLs depend not only on population densities, but also on whether prey sit above or below the optimal predator/prey body‐size ratio, and whether prey are more or less evolvable than their predators. EEFLs improve our ability to understand and predict nature's response to harvesting, but their integration into the research agenda will require a full consideration of the effects and dynamics of natural selection.
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Decomposing variation in population growth into contributions from both ecological and evolutionary processes is of fundamental concern, particularly in a world characterized by rapid responses to anthropogenic threats. Although the impact of ecological change on evolutionary response has long been acknowledged, the converse has predominantly been neglected, especially empirically. By applying a recently published conceptual framework, we assess and contrast the relative importance of phenotypic and environmental variability on annual population growth in five ungulate populations. In four of the five populations, the contribution of phenotypic variability was greater than the contribution of environmental variability, although not significantly so. The similarity in the contributions of environment and phenotype suggests that neither is worthy of neglect. Population growth is a consequence of multiple processes, which strengthens arguments advocating integrated approaches to assess how populations respond to their environments.
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Morphological changes following changes in species' distribution and phenology have been suggested to be the third universal response to global environmental change. Although structural size and body mass result from different genetic, physiological and ecological mechanisms, they are used interchangeably in studies evaluating population responses to environmental change. Using a 22-year (1991-2013) dataset including 1768 individuals, we investigated the coupled dynamics of size and mass in a hibernating mammal, the Alpine marmot (Marmota marmota), in response to local environmental conditions. We (i) quantified temporal trends in both traits, (ii) determined the environmental drivers of trait dynamics, and (iii) identified the life-history processes underlying the observed changes. Both phenotypic traits were followed through life: we focused on the initial trait value (juvenile size and mass) and later-life development (annual change in size [Δsize] and mass [Δmass]). First, we demonstrated contrasting dynamics between size and mass over the study period. Juvenile size and subsequent Δsize showed significant declines, whereas juvenile mass and subsequent Δmass remained constant. As a consequence of smaller size associated with a similar mass, individuals were in better condition in recent years. Second, size and mass showed different sensitivities to environmental variables. Both traits benefited from early access to resources in spring, whereas Δmass, particularly in early life, also responded to summer and winter conditions. Third, the inter-annual variation in both traits was caused by changes in early life development. Our study supports the importance of considering the differences between size and mass responses to the environment when evaluating the mechanisms underlying population dynamics. The current practice of focusing on only one trait in population modelling can lead to misleading conclusions when evaluating species' resilience to contemporary climate change. This article is protected by copyright. All rights reserved.
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Many quantitative traits are labile (e.g. somatic growth rate, reproductive timing and investment), varying over the life cycle as a result of behavioural adaptation, developmental processes and plastic responses to the environment. At the population level, selection can alter the distribution of such traits across age classes and among generations. Despite a growing body of theoretical research exploring the evolutionary dynamics of labile traits, a data‐driven framework for incorporating such traits into demographic models has not yet been developed. Integral projection models (IPMs) are increasingly being used to understand the interplay between changes in labile characters, life histories and population dynamics. One limitation of the IPM approach is that it relies on phenotypic associations between parents and offspring traits to capture inheritance. However, it is well‐established that many different processes may drive these associations, and currently, no clear consensus has emerged on how to model micro‐evolutionary dynamics in an IPM framework. We show how to embed quantitative genetic models of inheritance of labile traits into age‐structured, two‐sex models that resemble standard IPMs. Commonly used statistical tools such as GLMs and their mixed model counterparts can then be used for model parameterization. We illustrate the methodology through development of a simple model of egg‐laying date evolution, parameterized using data from a population of Great tits (Parus major). We demonstrate how our framework can be used to project the joint dynamics of species' traits and population density. We then develop a simple extension of the age‐structured Price equation (ASPE) for two‐sex populations, and apply this to examine the age‐specific contributions of different processes to change in the mean phenotype and breeding value. The data‐driven framework we outline here has the potential to facilitate greater insight into the nature of selection and its consequences in settings where focal traits vary over the lifetime through ontogeny, behavioural adaptation and phenotypic plasticity, as well as providing a potential bridge between theoretical and empirical studies of labile trait variation.
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Individual heterogeneity in life history shapes eco-evolutionary processes, and unobserved heterogeneity can affect demographic outputs characterising life history and population dynamical properties. Demographic frameworks like matrix models or integral projection models represent powerful approaches to disentangle mechanisms linking individual life histories and population-level processes. Recent developments have provided important steps towards their application to study eco-evolutionary dynamics, but so far individual heterogeneity has largely been ignored. Here, we present a general demographic framework that incorporates individual heterogeneity in a flexible way, by separating static and dynamic traits (discrete or continuous). First, we apply the framework to derive the consequences of ignoring heterogeneity for a range of widely used demographic outputs. A general conclusion is that besides the long-term growth rate lambda, all parameters can be affected. Second, we discuss how the framework can help advance current demographic models of eco-evolutionary dynamics, by incorporating individual heterogeneity. For both applications numerical examples are provided, including an empirical example for pike. For instance, we demonstrate that predicted demographic responses to climate warming can be reversed by increased heritability. We discuss how applications of this demographic framework incorporating individual heterogeneity can help answer key biological questions that require a detailed understanding of eco-evolutionary dynamics. © 2015 John Wiley & Sons Ltd/CNRS.
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Many studies have recorded phenotypic changes in natural populations and attributed them to climate change. However, controversy and uncertainty has arisen around three levels of inference in such studies. First, it has proven difficult to conclusively distinguish whether phenotypic changes are genetically based or the result of phenotypic plasticity. Second, whether or not the change is adaptive is usually assumed rather than tested. Third, inferences that climate change is the specific causal agent have rarely involved the testing - and exclusion - of other potential drivers. We here review the various ways in which the above inferences have been attempted, and evaluate the strength of support that each approach can provide. This methodological assessment sets the stage for 11 accompanying review articles that attempt comprehensive syntheses of what is currently known - and not known - about responses to climate change in a variety of taxa and in theory. Summarizing and relying on the results of these reviews, we arrive at the conclusion that evidence for genetic adaptation to climate change has been found in some systems, but is still relatively scarce. Most importantly, it is clear that more studies are needed - and these must employ better inferential methods - before general conclusions can be drawn. Overall, we hope that the present paper and special issue provide inspiration for future research and guidelines on best practices for its execution.
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Cryptic evolution has been defined as adaptive evolutionary change being masked by concurrent environmental change. Empirical studies of cryptic evolution have usually invoked a changing climate and/or increasing population density as the form of detrimental environmental change experienced by a population undergoing cryptic evolution. However, Fisher (1958) emphasized that evolutionary change in itself is likely to be an important component of "environmental deterioration," a point restated by Cooke et al. (1990) in the context of intraspecific competition. In this form, environmental deterioration arises because a winning lineage has to compete against more winners in successive generations as the population evolves. This "evolutionary environmental deterioration" has different implications for the selection and evolution of traits influenced by resource competition than general environmental change. We reformulate Cooke's model as a quantitative genetic model to show that it is identical in form to more recent developments proposed by quantitative geneticists. This provides a statistical framework for discriminating between the alternative hypotheses of environmental change and environmental deterioration caused by evolutionary change. We also demonstrate that in systems where no phenotypic change has occurred, there are many reasonable biological processes that will generate patterns in predicted breeding values that are consistent with what has been interpreted as cryptic evolution, and care needs to be taken when interpreting these patterns. These processes include mutation, sib competition, and invisible fractions.
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1. There is a growing number of empirical reports of environmental change simultaneously influencing population dynamics, life history and quantitative characters. We do not have a well-developed understanding of links between the dynamics of these quantities. 2. 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. 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. 3. 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. 4. 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. We showcase the method through parameterization of a model using data from a well-studied population of Soay sheep Ovis aries. 5. 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. 6. 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. 7. The approach we describe has the potential to explain within and between species patterns in quantitative characters, life history and population dynamics.
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Environmental change has altered the phenology, morphological traits and population dynamics of many species. However, the links underlying these joint responses remain largely unknown owing to a paucity of long-term data and the lack of an appropriate analytical framework. Here we investigate the link between phenotypic and demographic responses to environmental change using a new methodology and a long-term (1976-2008) data set from a hibernating mammal (the yellow-bellied marmot) inhabiting a dynamic subalpine habitat. We demonstrate how earlier emergence from hibernation and earlier weaning of young has led to a longer growing season and larger body masses before hibernation. The resulting shift in both the phenotype and the relationship between phenotype and fitness components led to a decline in adult mortality, which in turn triggered an abrupt increase in population size in recent years. Direct and trait-mediated effects of environmental change made comparable contributions to the observed marked increase in population growth. Our results help explain how a shift in phenology can cause simultaneous phenotypic and demographic changes, and highlight the need for a theory integrating ecological and evolutionary dynamics in stochastic environments.
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Heterogeneity within a population is a pervasive challenge for studies of individual life-histories. Population-level patterns in age-specific reproductive success can be broken down into relative contributions from selective disappearance, selective appearance of individuals into the study population, and average change in performance for survivors (average ontogenetic development). In this article, we provide an exact decomposition. We apply our formula to data on the reproductive performance of a well characterized population of common terns (Sterna hirundo). We show that improvements with age over most of adult life and senescence at old ages are primarily due to a genuine change in the mean among surviving individuals rather than selective disappearance or selective appearance of individuals. Average ontogenetic development accounts for approximately 87% of the overall age-specific population change.
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Best linear unbiased prediction (BLUP) is a method for obtaining point estimates of a random effect in a mixed effect model. Over the past decade it has been used extensively in ecology and evolutionary biology to predict individual breeding values and reaction norms. These predictions have been used to infer natural selection, evolutionary change, spatial-genetic patterns, individual reaction norms, and frailties. In this article we show analytically and through simulation and example why BLUP often gives anticonservative and biased estimates of evolutionary and ecological parameters. Although some concerns with BLUP methodology have been voiced before, the scale and breadth of the problems have probably not been widely appreciated. Bias arises because BLUPs are often used to estimate effects that are not explicitly accounted for in the model used to make the predictions. In these cases, predicted breeding values will often say more about phenotypic patterns than the genetic patterns of interest. An additional problem is that BLUPs are point estimates of quantities that are usually known with little certainty. Failure to account for this uncertainty in subsequent tests can lead to both bias and extreme anticonservatism. We demonstrate that restricted maximum likelihood and Bayesian solutions exist for these problems and show how unbiased and powerful tests can be derived that adequately quantify uncertainty. Of particular utility is a new test for detecting evolutionary change that not only accounts for prediction error in breeding values but also accounts for drift. To illustrate the problem, we apply these tests to long-term data on the Soay sheep (Ovis aries) and the great tit (Parus major) and show that previously reported temporal trends in breeding values are not supported.
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Environmental change, including climate change, can cause rapid phenotypic change via both ecological and evolutionary processes. Because ecological and evolutionary dynamics are intimately linked, a major challenge is to identify their relative roles. We exactly decomposed the change in mean body weight in a free-living population of Soay sheep into all the processes that contribute to change. Ecological processes contribute most, with selection--the underpinning of adaptive evolution--explaining little of the observed phenotypic trend. Our results enable us to explain why selection has so little effect even though weight is heritable, and why environmental change has caused a decline in the body size of Soay sheep.
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The use of regression techniques for estimating the direction and magnitude of selection from measurements on phenotypes has become widespread in field studies. A potential problem with these techniques is that environmental correlations between fitness and the traits examined may produce biased estimates of selection gradients. This report demonstrates that the phenotypic covariance between fitness and a trait, used as an estimate of the selection differential in estimating selection gradients, has two components: a component induced by selection itself and a component due to the effect of environmental factors on fitness. The second component is shown to be responsible for biases in estimates of selection gradients. The use of regressions involving genotypic and breeding values instead of phenotypic values can yield estimates of selection gradients that are not biased by environmental covariances. Statistical methods for estimating the coefficients of such regressions, and for testing for biases in regressions involving phenotypic values, are described.
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1.Integral projection models (IPMs) are an extension of stage-structured population models to continuous classes or traits, such as body size. Recent studies have used age-structured IPMs to investigate the relative contributions of evolutionary versus demographic responses of quantitative traits to environmental change. However, I argue here that evolutionary responses are likely to be underestimated by this approach, because it does not fully capture how phenotypic differences between individuals and genotypes accumulate along life, and are transmitted across generations.2.Trait transitions upon survival and reproduction are treated in IPMs by two classes of functions. First, an ‘inheritance’ function relates the trait of a newborn to that of its adult parent, on the time scale of a reproductive event. And second, growth functions relate the traits of surviving individuals between successive ages. This differs from the quantitative genetic approach, where parent-offspring resemblance is generally quantified for age-specific trait values, and on the time scale of a generation. More importantly, it is unclear to what extent age-structured IPMs account for the fact that phenotypic and genetic variances of adult size are largely caused by differential growth among individuals and genotypes, in multicellular organisms.3.I use simple simulations of growth trajectories to ask what the transition functions from IPMs can tell us about the contribution of genetic evolution to phenotypic change. These simulations illustrate that a flat inheritance function is perfectly compatible with substantial response to selection in adults. They further show that the growth functions from IPMs may obscure genetic differences in body size that accumulate along life owing to genetic variation in growth trajectories.4.IPMs are a powerful tool for investigating age-dependent components of phenotypic selection, and the demographic consequences of plastic responses that act through environmental effects on growth. But using age-structured IPMs to project evolutionary dynamics requires combining them with measurements of age-specific additive genetic variances, and cross-age additive genetic covariances, to accurately describe the accumulation of phenotypic differences across ages, and their transmission across generations.This article is protected by copyright. All rights reserved.
Chapter
This introductory chapter to 'Quantitative Genetics in the Wild' outlines ten big questions which are central to current evolutionary quantitative genetics. It also lists five reasons for addressing these questions in wild populations experiencing natural environments. The application of quantitative genetics analyses to wild populations is a field that has expanded rapidly in recent years, motivated by these questions. The chapters of this book showcase this recent work, and illustrate how quantitative genetic analyses applied to the study of wild populations have improved our understanding of life-history evolution and evolutionary ecology.
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An extension of the selection differential in the Robertson-Price equation for the mean phenotype in an age-structured population is provided. Temporal changes in the mean phenotype caused by transient fluctuations in the age-distribution and variation in mean phenotype among age classes, which can mistakenly be interpreted as selection, will disappear if reproductive value weighting is applied. Changes in any weighted mean phenotype in an age-structured population may be decomposed into between- and within-age class components. Using reproductive value weighting the between-age class component becomes pure noise, generated by previous genetic drift or fluctuating selection. This component, which we call transient quasi-selection, can therefore be omitted when estimating age-specific selection on fecundity or viability within age classes. The final response can be computed at the time of selection, but can not be observed until lifetime reproduction is realized unless the heritability is one. The generality of these results is illustrated further by our derivation of the selection differential for the continuous time age-structured model with general age-dependent weights. A simple simulation example as well as estimation of selection components in a house sparrow population illustrates the applicability of the theory to analyze selection on the mean phenotype in fluctuating age-structured populations.This article is protected by copyright. All rights reserved.
Article
Integral Projection Models (IPMs) use information on how an individual's state influences its vital rates - survival, growth and reproduction - to make population projections. IPMs are constructed from regression models predicting vital rates from state variables (e.g., size or age) and covariates (e.g., environment). By combining regressions of vital rates, an IPM provides mechanistic insight into emergent ecological patterns such as population dynamics, species geographic distributions, or life history strategies. Here, we review important resources for building IPMs and provide a comprehensive guide, with extensive R code, for their construction. IPMs can be applied to any stage-structured population; here we illustrate IPMs for a series of plant life histories of increasing complexity and biological realism, highlighting the utility of various regression methods for capturing biological patterns. We also present case studies illustrating how IPMs can be used to predict species’ geographic distributions and life history strategies. IPMs can represent a wide range of life histories at any desired level of biological detail. Much of the strength of IPMs lies in the strength of regression models. Many subtleties arise when scaling from vital rate regressions to population-level patterns, so we provide a set of diagnostics and guidelines to ensure that models are biologically plausible. Moreover, IPMs can exploit a large existing suite of analytical tools developed for Matrix Projection Models. This article is protected by copyright. All rights reserved.
Article
Predicting the responses to natural selection is one of the key goals of evolutionary biology. Two of the challenges in fulfilling this goal have been the realization that many estimates of natural selection might be highly biased by environmentally induced covariances between traits and fitness, and that many estimated responses to selection do not incorporate or report uncertainty in the estimates. Here we describe the application of a framework that blends the merits of the Robertson-Price Identity approach and the multivariate breeders equation to address these challenges. The approach allows genetic covariance matrices, selection differentials, selection gradients, and responses to selection to be estimated without environmentally-induced bias, direct and indirect selection and responses to selection to be distinguished, and if implemented in a Bayesian-MCMC framework, statistically robust estimates of uncertainty on all of these parameters to be made. We illustrate our approach with a worked example of previously published data. More generally, we suggest that applying both the Robertson-Price Identity and the multivariate breeder's equation will facilitate hypothesis testing about natural selection, genetic constraints, and evolutionary responses. This article is protected by copyright. All rights reserved.
Article
Most plant and animal populations have substantial interannual variability in survival, growth rate, and fecundity. They also exhibit substantial variability among individuals in traits such as size, age, condition, and disease status that have large impacts on individual fates and consequently on the future of the population. We present here methods for constructing and analyzing a stochastic integral projection model (IPM) incorporating both of these forms of variability, illustrated through a case study of the monocarpic thistle Carlina vulgaris. We show how model construction can exploit the close correspondence between stochastic IPMs and statistical analysis of trait-fate relationships in a "mixed" or "hierarchical" models framework. This correspondence means that IPMs can be parameterized straightforwardly from data using established statistical techniques and software (vs. the largely ad hoc methods for stochastic matrix models), properly accounting for sampling error and between-year sample size variation and with vastly fewer parameters than a conventional stochastic matrix model. We show that the many tools available for analyzing stochastic matrix models (such as stochastic growth rate, λS small variance approximations, elasticity/sensitivity analysis, and life table response experiment [LTRE] analysis) can be used for IPMs, and we give computational formulas for elasticity/sensitivity analyses. We develop evolutionary analyses based on the connection between growth rate sensitivity and selection gradients and present a new method using techniques from functional data analysis to study the evolution of function-valued traits such as size-dependent flowering probability. For Carlina we found consistent selection against variability in both state-specific transition rates and the fitted functions describing state dependence in demographic rates. For most of the regression parameters defining the IPM there was also selection against temporal variance; however, in. some cases the effects of nonlinear averaging were big enough, to favor increased temporal variation. The LTRE analysis identified year-to-year variation in survival as the dominant factor in population growth variability. Evolutionary analysis of flowering strategy showed that the entire functional relationship between plant size and flowering probability is at or near an evolutionary stable strategy (ESS) shaped by the size-specific trade-off between the benefit (fecundity) and cost (mortality) of flowering in a temporally varying environment.
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Matrix population models require the population to be divided into discrete stage classes. In many cases, especially when classes are defined by a continuous variable, such as length or mass, there are no natural breakpoints, and the division is artificial. The authors introduce the integral projection model, which eliminates the need for division into discrete classes, without requiring any additional biological assumptions. Like a traditional matrix model, the integral projection model provides estimates of the asymptotic growth rate, stable size distribution, reproductive values, and sensitivities of the growth rate to changes in vital rates. However, where the matrix model represents the size distributions, reproductive value, and sensitivities as step functions (constant within a stage class), the integral projection model yields smooth curves for each of these as a function of individual size. The authors describe a method for fitting the model to data, and they apply this method to data on an endangered plant species, northern monkshood (Aconitum noveboracense), with individuals classified by stem diameter. The matrix and integral models yield similar estimates of the asymptotic growth rate, but the reproductive values and sensitivities in the matrix model are sensitive to the choice of stage classes. The integral projection model avoids this problem and yields size-specific sensitivities that are not affected by stage duration. These general properties of the integral projection model will make it advantageous for other populations where there is no natural division of individuals into stage classes.
Article
A basic principle of natural selection on correlated characters is expressed as an adaptive topography for the vector of mean phenotypes in a population. Under some simple conditions on the pattern of phenotypic and genetic covariation within populations, selection only on body size, certain types of multivariate selection, and random genetic drift in a stochastic phylogeny are each expected to produce allometric evolution, i.e., straight lines or linear regressions on logarithmic coordinates. The orientation of these lines is determined by genetic parameters of the populations. Using this theory, phylogenetic or comparative information can be combined with experimental data on population genetic parameters to test hypotheses about past selective forces. Data from selection experiments on brain and body weights in mice support the conclusions that [1] the short-term differentiation of brain and body sizes in very closely related mammalian forms resulted either from directional selection mostly on body size with changes in brain sizes largely a genetically correlated response, or from random genetic drift; [2] during the long-term allometric diversification within most mammalian orders there has been more net directional selection on brain sizes than on body sizes. It is suggested that encephalization in primates decreased the genetic correlation between brain size and body size within populations, which facilitated further encephalization in the human lineage by avoiding antagonistic selection on brain and body sizes. The evolution of brain:body ontogeny is briefly discussed.
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The inverse of a numerator relationship matrix is needed for best linear unbiased prediction of breeding values. The purpose of this paper to is present a rapid and simple method for computation of the elements of this inverse without computing the relationship matrix itself. The method is particularly useful in non-inbred populations but is much faster than the conventional method in the presence of inbreeding.
Article
1. A mathematical theory of the culling process in dairy cattle has been developed. This was necessary to give a conceptual framework for the discussion of longevity in the dairy herd as a heritable character, of its genetic relationship with milk yield and of the effects of selection on the genetical analysis of yield itself. 2. Culling is assumed to take place at the end of each lactation by truncation selection of a normally distributed variate (the culling variate) of which yield itself is a component. 3. Expressions are then derived for the effect of the culling on various parameters of yield and for survival as a function of yield. 4. The derivation of expressions relevant to progeny groups is dependent on the relative values of the genetic and phenotypic regressions of the culling variate on yield. 5. Because little is known of the actual causes of culling, it is not permissible to predict the genetic gain in yield by multiplying the selection differential by the heritability. This is only justified if the genetic and phenotypic regressions of the culling variate on yield are equal. 6. A direct estimate of the genetic gain by selection can, however, be obtained from the covariance for any character between the mean relative survival of progeny groups and their mean value for the character. 7. The effect of culling on the genetic analysis of yield in later lactations is discussed, as is the effect of later culling on survival to later ages as a function of early yield. It is suggested that the regression coefficient of relative survival of progeny groups on heifer yield will be approximately linear with age whereas that of individuals will probably increase to a limiting value. 8. The heritability of survival to different ages will probably pass through a maximum at the fourth lactation. 9. Longevity itself, as a function of heifer yield, is the sum of the cumulative survival curves to each individual lactation. The regression of length of life on heifer yield, at the individual or at the progeny test level, can be related to the mean phenotypic and genetic selection applied to animals in the herd at any time. 10. Because culling is to a large extent a voluntary action of the farmer, longevity in the dairy herd, though it is under continual selection and may have a significant heritability, need not necessarily increase.
Article
Most population-level studies of eco-evolutionary dynamics assume that evolutionary change occurs in response to ecological change and vice versa. However, a growing number of papers report simultaneous ecological and evolutionary change, suggesting that the eco-evolutionary consequences of environmental change for populations can only be fully understood through the simultaneous analysis of statistics used to describe both ecological and evolutionary dynamics. Here we argue that integral projection models (IPM), and matrix approximations of them, provide a powerful approach to integrate population ecology, life history theory, and evolution. We discuss key questions in population biology that can be examined using these models, the answers to which are essential for a general, population-level understanding of eco-evolutionary change.
Article
Adaptive evolution occurs when fitness covaries with genetic merit for a trait (or traits). The breeder's equation (BE), in both its univariate and multivariate forms, allows us to predict this process by combining estimates of selection on phenotype with estimates of genetic (co)variation. However, predictions are only valid if all factors causal for trait-fitness covariance are measured. Although this requirement will rarely (if ever) be met in practice, it can be avoided by applying Robertson's secondary theorem of selection (STS). The STS predicts evolution by directly estimating the genetic basis of trait-fitness covariation without any explicit model of selection. Here we apply the BE and STS to four morphological traits measured in Soay sheep (Ovis aries) from St. Kilda. Despite apparently positive selection on heritable size traits, sheep are not getting larger. However, although the BE predicts increasing size, the STS does not, which is a discrepancy that suggests unmeasured factors are upwardly biasing our estimates of selection on phenotype. We suggest this is likely to be a general issue, and that wider application of the STS could offer at least a partial resolution to the common discrepancy between naive expectations and observed trait dynamics in natural populations.
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Recent studies have documented rates of evolution of ecologically important phenotypes sufficiently fast that they have the potential to impact the outcome of ecological interactions while they are underway. Observations of this type go against accepted wisdom that ecological and evolutionary dynamics occur at very different time scales. While some authors have evaluated the rapidity of a measured evolutionary rate by comparing it to the overall distribution of measured evolutionary rates, we believe that ecologists are mainly interested in rapid evolution because of its potential to impinge on ecological processes. We therefore propose that rapid evolution be defined as a genetic change occurring rapidly enough to have a measurable impact on simultaneous ecological change. Using this definition we propose a framework for decomposing rates of ecological change into components driven by simultaneous evolutionary change and by change in a non-evolutionary factor (e.g. density dependent population dynamics, abiotic environmental change). Evolution is judged to be rapid in this ecological context if its contribution to ecological change is large relative to the contribution of other factors. We provide a worked example of this approach based on a theoretical predator–prey interaction [Abrams, P. & Matsuda, H. (1997). Evolution, 51, 1740], and find that in this system the impact of prey evolution on predator per capita growth rate is 63% that of internal ecological dynamics. We then propose analytical methods for measuring these contributions in field situations, and apply them to two long-term data sets for which suitable ecological and evolutionary data exist. For both data sets relatively high rates of evolutionary change have been found when measured as character change in standard deviations per generation (haldanes). For Darwin's finches evolving in response to fluctuating rainfall [Grant, P.R. & Grant, B.R. (2002). Science, 296, 707], we estimate that evolutionary change has been more rapid than ecological change by a factor of 2.2. For a population of freshwater copepods whose life history evolves in response to fluctuating fish predation [Hairston, N.G. Jr & Dillon, T.A. (1990). Evolution, 44, 1796], we find that evolutionary change has been about one quarter the rate of ecological change – less than in the finch example, but nevertheless substantial. These analyses support the view that in order to understand temporal dynamics in ecological processes it is critical to consider the extent to which the attributes of the system under investigation are simultaneously changing as a result of rapid evolution.
Article
Heterogeneity is a pervasive problem for analyses in biology and related fields in which it is of interest to get information unbiased by a change in the composition of the population. I show here how a reformulation of the Price equation leads to a decomposition method to address this issue. The derived equation gives the exact contributions of the average change in the surviving individuals and the change due to selective disappearance to the aggregate population change. KeywordsHeterogeneity–Population change–Average change among surviving individuals–Selective disappearance–Price equation
Article
Ecological changes in the phenology and distribution of plants and animals are occurring in all well-studied marine, freshwater, and terrestrial groups. These observed changes are heavily biased in the directions predicted from global warming and have been linked to local or regional climate change through correlations between climate and biological variation, field and laboratory experiments, and physiological research. Range-restricted species, particularly polar and mountaintop species, show severe range contractions and have been the first groups in which entire species have gone extinct due to recent climate change. Tropical coral reefs and amphibians have been most negatively affected. Predator-prey and plant-insect interactions have been disrupted when interacting species have responded differently to warming. Evolutionary adaptations to warmer conditions have occurred in the interiors of species’ ranges, and resource use and dispersal have evolved rapidly at expanding range margins. Observed genetic shifts modulate local effects of climate change, but there is little evidence that they will mitigate negative effects at the species level.
Article
Rapid contemporary evolution due to natural selection is common in the wild, but it remains uncertain whether its effects are an essential component of community and ecosystem structure and function. Previously we showed how to partition change in a population, community or ecosystem property into contributions from environmental and trait change, when trait change is entirely caused by evolution (Hairston et al. 2005). However, when substantial non-heritable trait change occurs (e.g. due to phenotypic plasticity or change in population structure) that approach can mis-estimate both contributions. Here, we demonstrate how to disentangle ecological impacts of evolution vs. non-heritable trait change by combining our previous approach with the Price Equation. This yields a three-way partitioning into effects of evolution, non-heritable phenotypic change and environment. We extend the approach to cases where ecological consequences of trait change are mediated through interspecific interactions. We analyse empirical examples involving fish, birds and zooplankton, finding that the proportional contribution of rapid evolution varies widely (even among different ecological properties affected by the same trait), and that rapid evolution can be important when it acts to oppose and mitigate phenotypic effects of environmental change. Paradoxically, rapid evolution may be most important when it is least evident.
Article
For many organisms, stage is a better predictor of demographic rates than age. Yet no general theoretical framework exists for understanding or predicting evolution in stage-structured populations. Here, we provide a general modeling approach that can be used to predict evolution and demography of stage-structured populations. This advances our ability to understand evolution in stage-structured populations to a level previously available only for populations structured by age. We use this framework to provide the first rigorous proof that Lande's theorem, which relates adaptive evolution to population growth, applies to stage-classified populations, assuming only normality and that evolution is slow relative to population dynamics. We extend this theorem to allow for different means or variances among stages. Our next major result is the formulation of Price's theorem, a fundamental law of evolution, for stage-structured populations. In addition, we use data from Trillium grandiflorum to demonstrate how our models can be applied to a real-world population and thereby show their practical potential to generate accurate projections of evolutionary and population dynamics. Finally, we use our framework to compare rates of evolution in age- versus stage-structured populations, which shows how our methods can yield biological insights about evolution in stage-structured populations.
Article
The effect of ecological change on evolution has long been a focus of scientific research. The reverse—how evolutionary dynamics affect ecological traits—has only recently captured our attention, however, with the realization that evolution can occur over ecological time scales. This newly highlighted causal direction and the implied feedback loop—eco-evolutionary dynamics—is invigorating both ecologists and evolutionists and blurring the distinction between them. Despite some recent relevant studies, the importance of the evolution-to-ecology pathway across systems is still unknown. Only an extensive research effort involving multiple experimental approaches—particularly long-term field experiments—over a variety of ecological communities will provide the answer.
Article
Generalized linear mixed models provide a flexible framework for modeling a range of data, although with non-Gaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distributions that can be evaluated. The R package MCMCglmm implements such an algorithm for a range of model fitting problems. More than one response variable can be analyzed simultaneously, and these variables are allowed to follow Gaussian, Poisson, multi(bi)nominal, exponential, zero-inflated and censored distributions. A range of variance structures are permitted for the random effects, including interactions with categorical or continuous variables (i.e., random regression), and more complicated variance structures that arise through shared ancestry, either through a pedigree or through a phylogeny. Missing values are permitted in the response variable(s) and data can be known up to some level of measurement error as in meta-analysis. All simu- lation is done in C/ C++ using the CSparse library for sparse linear systems.
Article
The breeder's equation, which predicts evolutionary change when a phenotypic covariance exists between a heritable trait and fitness, has provided a key conceptual framework for studies of adaptive microevolution in nature. However, its application requires strong assumptions to be made about the causation of fitness variation. In its univariate form, the breeder's equation assumes that the trait of interest is not correlated with other traits having causal effects on fitness. In its multivariate form, the validity of predicted change rests on the assumption that all such correlated traits have been measured and incorporated into the analysis. Here, we (i) highlight why these assumptions are likely to be seriously violated in studies of natural, rather than artificial, selection and (ii) advocate wider use of the Robertson-Price identity as a more robust, and less assumption-laden, alternative to the breeder's equation for applications in evolutionary ecology.
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Many important questions in ecology and evolutionary biology can only be answered with data that extend over several decades and answering a substantial proportion of questions requires records of the life histories of recognisable individuals. We identify six advantages that long-term, individual based studies afford in ecology and evolution: (i) analysis of age structure; (ii) linkage between life history stages; (iii) quantification of social structure; (iv) derivation of lifetime fitness measures; (v) replication of estimates of selection; (vi) linkage between generations, and we review their impact on studies in six key areas of evolution and ecology. Our review emphasises the unusual opportunities and productivity of long-term, individual-based studies and documents the important role that they play in research on ecology and evolutionary biology as well as the difficulties they face.
Article
Ecology Letters (2010) 13: 1019–1029 Despite decades of research documenting niche differences between species, we lack a quantitative understanding of their effect on coexistence in natural communities. We perturbed an empirical sagebrush steppe community model to remove the demographic effect of niche differences and quantify their impact on coexistence. With stabilizing mechanisms operating, all species showed positive growth rates when rare, generating stable coexistence. Fluctuation-independent mechanisms contributed more than temporal variability to coexistence and operated more strongly on recruitment than growth or survival. As expected, removal of stabilizing niche differences led to extinction of all inferior competitors. However, complete exclusion required 300–400 years, indicating small fitness differences among species. Our results show an ‘excess’ of niche differences: stabilizing mechanisms were not only strong enough to maintain diversity but were much stronger than necessary given the small fitness differences. The diversity of this community cannot be understood without consideration of niche differences.
Article
1. Efforts to understand the links between evolutionary and ecological dynamics hinge on our ability to measure and understand how genes influence phenotypes, fitness and population dynamics. Quantitative genetics provides a range of theoretical and empirical tools with which to achieve this when the relatedness between individuals within a population is known. 2. A number of recent studies have used a type of mixed-effects model, known as the animal model, to estimate the genetic component of phenotypic variation using data collected in the field. Here, we provide a practical guide for ecologists interested in exploring the potential to apply this quantitative genetic method in their research. 3. We begin by outlining, in simple terms, key concepts in quantitative genetics and how an animal model estimates relevant quantitative genetic parameters, such as heritabilities or genetic correlations. 4. We then provide three detailed example tutorials, for implementation in a variety of software packages, for some basic applications of the animal model. We discuss several important statistical issues relating to best practice when fitting different kinds of mixed models. 5. We conclude by briefly summarizing more complex applications of the animal model, and by highlighting key pitfalls and dangers for the researcher wanting to begin using quantitative genetic tools to address ecological and evolutionary questions.