Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations

Unraveling population trends in Italy (1921-2021) with spatial econometrics

Testing density-dependence and path-dependence in long-term population dynamics under differentiated local contexts contributes to delineate the changing role of socioeconomic forces at the base of regional disparities. Despite a millenary settlement history, such issue has been rarely investigated in Europe, and especially in highly divided countries such as those in the Mediterranean region. Using econometric modeling to manage spatial heterogeneity, our study verifies the role of selected drivers of population growth at ten times between 1921 and 2021 in more than 8000 Italian municipalities verifying density-dependent and path-dependent dynamics. Results of global and quantile (spatial) regressions highlight a differential impact of density and (lagged) population growth on demographic dynamics along the urban cycle in Italy. Being weakly significant in the inter-war period (1921-1951), econometric models totalized a high goodness-of-fit in correspondence with compact urbanization (1951-1981). Model's fit declined in the following decades (1981-2021) reflecting suburbanization and counter-urbanization. Density-dependence and path-dependence were found significant and, respectively, positive or negative, with compact urbanization, and much less intense with suburbanization and counter-urbanization. A spatial econometric investigation of density-dependent and path-dependent mechanisms of population dynamics provided an original explanation of metropolitan cycles, delineating the evolution of socioeconomic (local) systems along the urban-rural gradient.

Life history complementarity and the maintenance of biodiversity

Life history, the schedule of when and how fast organisms grow, die and reproduce, is a critical axis along which species differ from each other^1-4. In parallel, competition is a fundamental mechanism that determines the potential for species coexistence^5-8. Previous models of stochastic competition have demonstrated that large numbers of species can persist over long timescales, even when competing for a single common resource^9-12, but how life history differences between species increase or decrease the possibility of coexistence and, conversely, whether competition constrains what combinations of life history strategies complement each other remain open questions. Here we show that specific combinations of life history strategy optimize the persistence times of species competing for a single resource before one species overtakes its competitors. This suggests that co-occurring species would tend to have such complementary life history strategies, which we demonstrate using empirical data for perennial plants.

Seasonal timing on a cyclical Earth: Towards a theoretical framework for the evolution of phenology

Phenology refers to the seasonal timing patterns commonly exhibited by life on Earth, from blooming flowers to breeding birds to human agriculture. Climate change is altering abiotic seasonality (e.g., longer summers) and in turn, phenological patterns contained within. However, how phenology should evolve is still an unsolved problem. This problem lies at the crux of predicting future phenological changes that will likely have substantial ecosystem consequences, and more fundamentally, of understanding an undeniably global phenomenon. Most studies have associated proximate environmental variables with phenological responses in case-specific ways, making it difficult to contextualize observations within a general evolutionary framework. We outline the complex but universal ways in which seasonal timing maps onto evolutionary fitness. We borrow lessons from life history theory and evolutionary demography that have benefited from a first principles-based theoretical scaffold. Lastly, we identify key questions for theorists and empiricists to help advance our general understanding of phenology.

Evolution of class-structured populations in periodic environments

What is the influence of periodic environmental fluctuations on life-history evolution? We present a general theoretical framework to understand and predict the long-term evolution of life-history traits under a broad range of ecological scenarios. Specifically, we investigate how periodic fluctuations affect selection when the population is also structured in distinct classes. This analysis yields time-varying selection gradients that clarify the influence of the fluctuations of the environment on the competitive ability of a specific life-history mutation. We use this framework to analyse the evolution of key life-history traits of pathogens. We examine three different epidemiological scenarios and we show how periodic fluctuations of the environment can affect the evolution of virulence and transmission as well as the preference for different hosts. These examples yield new and testable predictions on pathogen evolution, and illustrate how our approach can provide a better understanding of the evolutionary consequences of time-varying environmental fluctuations in a broad range of scenarios.

Density-dependent selection and the maintenance of colour polymorphism in barn owls

The capacity of natural selection to generate adaptive changes is (according to the fundamental theorem of natural selection) proportional to the additive genetic variance in fitness. In spite of its importance for development of new adaptations to a changing environment, processes affecting the magnitude of the genetic variance in fitness-related traits are poorly understood. Here, we show that the red-white colour polymorphism in female barn owls is subject to density-dependent selection at the phenotypic and genotypic level. The diallelic melanocortin-1 receptor gene explained a large amount of the phenotypic variance in reddish coloration in the females ([Formula: see text]). Red individuals (RR genotype) were selected for at low densities, while white individuals (WW genotype) were favoured at high densities and were less sensitive to changes in density. We show that this density-dependent selection favours white individuals and predicts fixation of the white allele in this population at longer time scales without immigration or other selective forces. Still, fluctuating population density will cause selection to fluctuate and periodically favour red individuals. These results suggest how balancing selection caused by fluctuations in population density can be a general mechanism affecting the level of additive genetic variance in natural populations.

The Importance of Noise Colour in Simulations of Evolutionary Systems

Simulations of evolutionary dynamics often employ white noise as a model of stochastic environmental variation. Whilst white noise has the advantages of being simply generated and analytically tractable, empirical analyses demonstrate that most real environmental time series have power spectral densities consistent with pink or red noise, in which lower frequencies contribute proportionally greater amplitudes than higher frequencies. Simulated white noise environments may therefore fail to capture key components of real environmental time series, leading to erroneous results. To explore the effects of different noise colours on evolving populations, a simple evolutionary model of the interaction between life-history and the specialism-generalism axis was developed. Simulations were conducted using a range of noise colours as the environments to which agents adapted. Results demonstrate complex interactions between noise colour, reproductive rate, and the degree of evolved generalism; importantly, contradictory conclusions arise from simulations using white as opposed to red noise, suggesting that noise colour plays a fundamental role in generating adaptive responses. These results are discussed in the context of previous research on evolutionary responses to fluctuating environments, and it is suggested that Artificial Life as a field should embrace a wider spectrum of coloured noise models to ensure that results are truly representative of environmental and evolutionary dynamics.

Global patterns of resilience decline in vertebrate populations

Maintaining the resilience of natural populations, their ability to resist and recover from disturbance, is crucial to prevent biodiversity loss. However, the lack of appropriate data and quantitative tools has hampered our understanding of the factors determining resilience on a global scale. Here, we quantified the temporal trends of two key components of resilience-resistance and recovery-in >2000 population time-series of >1000 vertebrate species globally. We show that the number of threats to which a population is exposed is the main driver of resilience decline in vertebrate populations. Such declines are driven by a non-uniform loss of different components of resilience (i.e. resistance and recovery). Increased anthropogenic threats accelerating resilience loss through a decline in the recovery ability-but not resistance-of vertebrate populations. These findings suggest we may be underestimating the impacts of global change, highlighting the need to account for the multiple components of resilience in global biodiversity assessments.

The Alignment of Natural and Sexual Selection

Sexual selection has the potential to decrease mean fitness in a population through an array of costs to nonsexual fitness. These costs may be offset when sexual selection favors individuals with high nonsexual fitness, causing the alignment of sexual and natural selection. We review the many laboratory experiments that have manipulated mating systems aimed at quantifying the net effects of sexual selection on mean fitness. These must be interpreted in light of population history and the diversity of ways manipulations have altered sexual interactions, sexual conflict, and sexual and natural selection. Theory and data suggest a net benefit is more likely when sexually concordant genetic variation is enhanced and that ecological context can mediate the relative importance of these different effects. Comparative studies have independently examined the consequences of sexual selection for population/species persistence. These provide little indication of a benefit, and interpreting these higher-level responses is challenging.

Slower environmental cycles maintain greater life-history variation within populations

Populations in nature are comprised of individual life histories, whose variation underpins ecological and evolutionary processes. Yet the forces of environmental selection that shape intrapopulation life-history variation are still not well-understood, and efforts have largely focused on random (stochastic) fluctuations of the environment. However, a ubiquitous mode of environmental fluctuation in nature is cyclical, whose periodicities can change independently of stochasticity. Here, we test theoretically based hypotheses for whether shortened ('Fast') or lengthened ('Slow') environmental cycles should generate higher intrapopulation variation of life history phenotypes. We show, through a combination of agent-based modelling and a multi-generational laboratory selection experiment using the tidepool copepod Tigriopus californicus, that slower environmental cycles maintain higher levels of intrapopulation variation. Surprisingly, the effect of environmental periodicity on variation was much stronger than that of stochasticity. Thus, our results show that periodicity is an important facet of fluctuating environments for life-history variation.

Variation in generation time reveals density regulation as an important driver of pace of life in a bird metapopulation

Generation time determines the pace of key demographic and evolutionary processes. Quantified as the weighted mean age at reproduction, it can be studied as a life-history trait that varies within and among populations and may evolve in response to ecological conditions. We combined quantitative genetic analyses with age- and density-dependent models to study generation time variation in a bird metapopulation. Generation time was heritable, and males had longer generation times than females. Individuals with longer generation times had greater lifetime reproductive success but not a higher expected population growth rate. Density regulation acted on recruit production, suggesting that longer generation times should be favoured when populations are closer to carrying capacity. Furthermore, generation times were shorter when populations were growing and longer when populations were closer to equilibrium or declining. These results support classic theory predicting that density regulation is an important driver of the pace of life-history strategies.

An Evolutionary and Ecological Community Model for Distribution of Phenotypes and Abundances among Competing Species

AbstractHere, we propose a theory for the structure of communities of competing species. We include ecologically realistic assumptions, such as density dependence and stochastic fluctuations in the environment, and analyze how evolution caused by r- and K-selection will affect the packing of species in the phenotypic space as well as the species abundance distribution. Species-specific traits have the same matrix G of additive genetic variances and covariances, and evolution of mean traits is affected by fluctuations in population size of all species. In general, the model produces a shape of the distributions of log abundances that is skewed to the left, which is typical of most natural communities. Mean phenotypes of the species in the community are distributed approximately uniformly on the surface of a multidimensional sphere. However, environmental stochasticity generates selection that deviates species slightly from this surface; nonetheless, phenotypic distribution will be different from a random packing of species. This model of community evolution provides a theoretical framework that predicts a relationship between the structure of the phenotypic space and the form of species abundance distributions that can be compared against time series of variation in community structure.

A simple completion of Fisher's fundamental theorem of natural selection

Fisher's fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher's original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher's concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.

Density-Dependent Adaptive Topography in a Small Passerine Bird, the Collared Flycatcher

AbstractAdaptive topography is a central concept in evolutionary biology, describing how the mean fitness of a population changes with gene frequencies or mean phenotypes. We use expected population size as a quantity to be maximized by natural selection to show that selection on pairwise combinations of reproductive traits of collared flycatchers caused by fluctuations in population size generated an adaptive topography with distinct peaks often located at intermediate phenotypes. This occurred because r- and K-selection made phenotypes favored at small densities different from those with higher fitness at population sizes close to the carrying capacity K. Fitness decreased rapidly with a delay in the timing of egg laying, with a density-dependent effect especially occurring among early-laying females. The number of fledglings maximizing fitness was larger at small population sizes than when close to K. Finally, there was directional selection for large fledglings independent of population size. We suggest that these patterns can be explained by increased competition for some limiting resources or access to favorable nest sites at high population densities. Thus, r- and K-selection based on expected population size as an evolutionary maximization criterion may influence life-history evolution and constrain the selective responses to changes in the environment.

An extended stochastic Allee model with harvesting and the risk of extinction of the herring population

Overexploitation of commercially beneficial fish is a serious ecological problem around the world. The growth profiles of most of the species are likely to follow density regulated theta-logistic model irrespective of any taxonomy group [Sibly et al., Science, 2005]. Rapid depletion of population size may cause reduced fitness, and the species is exposed to Allee phenomena. Here sustainability is addressed by modelling the herring population as a stochastic process and computing the probability of extinction and expected time to extinction. The models incorporate an Allee effect, crowding effect which reduce birth and death rates at large populations, and two possible choices of harvesting models viz. linear harvesting and nonlinear harvesting. A seminal attempt is made by Saha [Saha et al., Ecol. Model, 2013] for this economically beneficial fish, but ignored the vital phenomena of harvesting. Moreover, in this model, the demographic stochasticity is introduced through the white-noise term, which has certain limitations when harvesting is introduced into the system. White noise is appropriate for such a system where immigration and emigration are allowed, but a harvesting model is rational for a closed system. The demographic stochasticity is introduced by replacing an ordinary differential equation model with a stochastic differential equation model, where the instantaneous variance in the SDE is derived directly from the birth and death rates of a birth-death process. The modelling parameters are fit to data of the herring populations collected from Global Population Dynamics Database (GPDD), and the risk of extinction of each population is computed under different harvesting protocols. A threshold for handling times is computed beneath which the risk of extinction is high. This is proposed as a recommendation to management for sustainable harvesting.

The Price equation and reproductive value

The Price equation is widely recognized as capturing conceptually important properties of natural selection, and is often used to derive versions of Fisher's fundamental theorem of natural selection, the secondary theorems of natural selection and other significant results. However, class structure is not usually incorporated into these arguments. From the starting point of Fisher's original connection between fitness and reproductive value, a principled way of incorporating reproductive value and structured populations into the Price equation is explained, with its implications for precise meanings of (two distinct kinds of) reproductive value and of fitness. Once the Price equation applies to structured populations, then the other equations follow. The fundamental theorem itself has a special place among these equations, not only because it always incorporated class structure (and its method is followed for general class structures), but also because that is the result that justifies the important idea that these equations identify the effect of natural selection. The precise definitions of reproductive value and fitness have striking and unexpected features. However, a theoretical challenge emerges from the articulation of Fisher's structure: is it possible to retain the ecological properties of fitness as well as its evolutionary out-of-equilibrium properties? This article is part of the theme issue 'Fifty years of the Price equation'.

The Demographic Buffering Hypothesis: Evidence and Challenges

In (st)age-structured populations, the long-run population growth rate is negatively affected by temporal variation in vital rates. In most cases, natural selection should minimize temporal variation in the vital rates to which the long-run population growth is most sensitive, resulting in demographic buffering. By reviewing empirical studies on demographic buffering in wild populations, we found overall support for this hypothesis. However, we also identified issues when testing for demographic buffering. In particular, solving scaling problems for decomposing, measuring, and comparing stochastic variation in vital rates and accounting for density dependence are required in future tests of demographic buffering. In the current context of climate change, demographic buffering may mitigate the negative impact of environmental variation and help populations to persist in an increasingly variable environment.

Cyclical environments drive variation in life-history strategies: a general theory of cyclical phenology

Cycles, such as seasons or tides, characterize many systems in nature. Overwhelming evidence shows that climate change-driven alterations to environmental cycles-such as longer seasons-are associated with phenological shifts around the world, suggesting a deep link between environmental cycles and life cycles. However, general mechanisms of life-history evolution in cyclical environments are still not well understood. Here, I build a demographic framework and ask how life-history strategies optimize fitness when the environment perturbs a structured population cyclically and how strategies should change as cyclicality changes. I show that cycle periodicity alters optimality predictions of classic life-history theory because repeated cycles have rippling selective consequences over time and generations. Notably, fitness landscapes that relate environmental cyclicality and life-history optimality vary dramatically depending on which trade-offs govern a given species. The model tuned with known life-history trade-offs in a marine intertidal copepod Tigriopus californicus successfully predicted the shape of life-history variation across natural populations spanning a gradient of tidal periodicities. This framework shows how environmental cycles can drive life-history variation-without complex assumptions of individual responses to cues such as temperature-thus expanding the range of life-history diversity explained by theory and providing a basis for adaptive phenology.

Contrasting patterns of density-dependent selection at different life stages can create more than one fast-slow axis of life-history variation

There has been much recent research interest in the existence of a major axis of life-history variation along a fast-slow continuum within almost all major taxonomic groups. Eco-evolutionary models of density-dependent selection provide a general explanation for such observations of interspecific variation in the "pace of life." One issue, however, is that some large-bodied long-lived "slow" species (e.g., trees and large fish) often show an explosive "fast" type of reproduction with many small offspring, and species with "fast" adult life stages can have comparatively "slow" offspring life stages (e.g., mayflies). We attempt to explain such life-history evolution using the same eco-evolutionary modeling approach but with two life stages, separating adult reproductive strategies from offspring survival strategies. When the population dynamics in the two life stages are closely linked and affect each other, density-dependent selection occurs in parallel on both reproduction and survival, producing the usual one-dimensional fast-slow continuum (e.g., houseflies to blue whales). However, strong density dependence at either the adult reproduction or offspring survival life stage creates quasi-independent population dynamics, allowing fast-type reproduction alongside slow-type survival (e.g., trees and large fish), or the perhaps rarer slow-type reproduction alongside fast-type survival (e.g., mayflies-short-lived adults producing few long-lived offspring). Therefore, most types of species life histories in nature can potentially be explained via the eco-evolutionary consequences of density-dependent selection given the possible separation of demographic effects at different life stages.

A continuum of biological adaptations to environmental fluctuation

Bet-hedging-a strategy that reduces fitness variance at the expense of lower mean fitness among different generations-is thought to evolve as a biological adaptation to environmental unpredictability. Despite widespread use of the bet-hedging concept, most theoretical treatments have largely made unrealistic demographic assumptions, such as non-overlapping generations and fixed or infinite population sizes. Here, we extend the concept to consider overlapping generations by defining bet-hedging as a strategy with lower variance and mean per capita growth rate across different environments. We also define an opposing strategy-the rising-tide-that has higher mean but also higher variance in per capita growth. These alternative strategies lie along a continuum of biological adaptions to environmental fluctuation. Using stochastic Lotka-Volterra models to explore the evolution of the rising-tide versus bet-hedging strategies, we show that both the mean environmental conditions and the temporal scales of their fluctuations, as well as whether population dynamics are discrete or continuous, are crucial in shaping the type of strategy that evolves in fluctuating environments. Our model demonstrates that there are likely to be a wide range of ways that organisms with overlapping generations respond to environmental unpredictability beyond the classic bet-hedging concept.

The influence of fluctuating population densities on evolutionary dynamics

The causes and consequences of fluctuating population densities are an important topic in ecological literature. Yet, the effects of such fluctuations on maintenance of variation in spatially structured populations have received little analytic treatment. We analyze what happens when two habitats coupled by migration not only differ in their trade‐offs in selection but also in their demographic stability—and show that equilibrium allele frequencies can change significantly due to ecological feedback arising from locally fluctuating population sizes. When an ecological niche exhibits such fluctuations, these drive an asymmetry in the relative impact of gene flow, and therefore, the equilibrium frequency of the locally adapted type decreases. Our results extend the classic conditions on maintenance of diversity under selection and migration by including the effect of fluctuating population densities. We find simple analytic conditions in terms of the strength of selection, immigration, and the extent of fluctuations between generations in a continent‐island model. Although weak fluctuations hardly affect coexistence, strong recurrent fluctuations lead to extinction of the type better adapted to the fluctuating niche—even if the invader is locally maladapted. There is a disadvantage to specialization to an unstable habitat, as it makes the population vulnerable to swamping from more stable habitats.

Life-history evolution under fluctuating density-dependent selection and the adaptive alignment of pace-of-life syndromes

We present a novel perspective on life-history evolution that combines recent theoretical advances in fluctuating density-dependent selection with the notion of pace-of-life syndromes (POLSs) in behavioural ecology. These ideas posit phenotypic co-variation in life-history, physiological, morphological and behavioural traits as a continuum from the highly fecund, short-lived, bold, aggressive and highly dispersive 'fast' types at one end of the POLS to the less fecund, long-lived, cautious, shy, plastic and socially responsive 'slow' types at the other. We propose that such variation in life histories and the associated individual differences in behaviour can be explained through their eco-evolutionary dynamics with population density - a single and ubiquitous selective factor that is present in all biological systems. Contrasting regimes of environmental stochasticity are expected to affect population density in time and space and create differing patterns of fluctuating density-dependent selection, which generates variation in fast versus slow life histories within and among populations. We therefore predict that a major axis of phenotypic co-variation in life-history, physiological, morphological and behavioural traits (i.e. the POLS) should align with these stochastic fluctuations in the multivariate fitness landscape created by variation in density-dependent selection. Phenotypic plasticity and/or genetic (co-)variation oriented along this major POLS axis are thus expected to facilitate rapid and adaptively integrated changes in various aspects of life histories within and among populations and/or species. The fluctuating density-dependent selection POLS framework presented here therefore provides a series of clear testable predictions, the investigation of which should further our fundamental understanding of life-history evolution and thus our ability to predict natural population dynamics.