Generation time, net reproductive rate, and growth in stage-age-structured populations

Intrinsic growth rate and evolution of the Premnotrypes Vorax population using fuzzy information

The white potato worm (Premnotrypes Vorax (Hustache)) is one of the pests that causes the greatest damage to the potato crop and the greatest economic losses to the grower; therefore, knowing its life cycle and estimating its intrinsic growth rate is crucial for selecting an appropriate chemical control method, in order to reduce the environmental impact and ensure a profitable production suitable for consumption. In this article, we present a fuzzy Malthusian model describing the evolution of the white potato worm in the crop, considering that the intrinsic growth rate and the reported initial data on the problem are of fuzzy nature. The main contributions and novelty of this paper are summarized in the following two aspects: first, the estimation of the intrinsic growth rate of the white potato worm, in function of the temperature, by using a Takagi-Sugeno-Kang type fuzzy rule-based model; and second, since in practice the initial white potato worm population in a crop is subjective, imprecise and vague, knowing the intrinsic growth rate, we propose and solve a fuzzy initial value problem to determine the evolution in time of the white potato worm population. In conclusion, given a weekly average temperature, it is possible to know the white potato worm population per unit area oscillating in an interval whose length depends on the degree of inaccuracy of the initial population and the intrinsic growth rate. This study can be relevant for grower decision making in terms of the type and frequency of pest control on his crop.

BatTool: projecting bat populations facing multiple stressors using a demographic model

Bats provide ecologically and agriculturally important ecosystem services but are currently experiencing population declines caused by multiple environmental stressors, including mortality from white-nose syndrome and wind energy development. Analyses of the current and future health and viability of these species may support conservation management decision making. Demographic modeling provides a quantitative tool for decision makers and conservation managers to make more informed decisions, but widespread adoption of these tools can be limited because of the complexity of the mathematical, statistical, and computational components involved in implementing these models. In this work, we provide an exposition of the BatTool R package, detailing the primary components of the matrix projection model, a publicly accessible graphical user interface ( https://rconnect.usgs.gov/battool ) facilitating user-defined scenario analyses, and its intended uses and limitations (Wiens et al., US Geol Surv Data Release 2022; Wiens et al., US Geol Surv Softw Release 2022). We present a case study involving wind energy permitting, weighing the effects of potential mortality caused by a hypothetical wind energy facility on the projected abundance of four imperiled bat species in the Midwestern United States.

Age-specific sensitivity analysis of stable, stochastic and transient growth for stage-classified populations

Sensitivity analysis in ecology and evolution is a valuable guide to rank demographic parameters depending on their relevance to population growth. Here, we propose a method to make the sensitivity analysis of population growth for matrix models solely classified by stage more fine-grained by considering the effect of age-specific parameters. The method applies to stable population growth, the stochastic growth rate, and transient growth. The method yields expressions for the sensitivity of stable population growth to age-specific survival and fecundity from which general properties are derived about the pattern of age-specific selective forces molding senescence in stage-classified populations.

Plastic energy allocation toward life-history functions in a consumer-resource interaction : Analyzing the temporal patterns of the consumer-resource dynamics

Various environmental alterations resulting from the current global change compromise the persistence of species in their habitual environment. To cope with the obvious risk of extinction, plastic responses provide organisms with rapid acclimatization to new environments. The premise of plastic rescue has been theoretically studied from mathematical models in both deterministic and stochastic environments, focusing on analyzing the persistence and stability of the populations. Here, we evaluate this premise in the framework of a consumer-resource interaction considering the energy investment towards reproduction vs. maintenance as a plastic trait according to positive/negative variation of the available resource. A basic consumer-resource mathematical model is formulated based on the principle of biomass conversion that incorporates the energy allocation toward vital functions of the life-cycle of consumer individuals. Our mathematical approach is based on the impulsive differential equations at fixed moments considering two impulsive effects associated with the instants at which consumers obtain environmental information and when energy allocation strategy change occurs. From a preliminary analysis of the non-plastic temporal dynamics, namely when the energy allocation is constant over time and without experiencing changes concerning the variation of resources, both the persistence and stability of the consumer-resource dynamic are dependent on the energy allocation strategies belonging to a set termed stability range. We found that the plastic energy allocation can promote a stable dynamical pattern in the consumer-resource interaction depending on both the magnitude of the energy allocation change and the time lag between environmental sensibility instants and when the expression of the plastic trait occurs.

Temperature sensitivity of pest reproductive numbers in age-structured PDE models, with a focus on the invasive spotted lanternfly

Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health. The recent establishment of the invasive spotted lanternfly in the northeastern United States has proven devastating to farms and vineyards, necessitating urgent development of population dynamical models and effective control practices. In this paper, we propose a stage-age-structured system of PDEs to model insect pest populations, in which underlying dynamics are dictated by ambient temperature through rates of development, fecundity, and mortality. The model incorporates diapause and non-diapause pathways, and is calibrated to experimental and field data on the spotted lanternfly. We develop a novel moving mesh method for capturing age-advection accurately, even for coarse discretization parameters. We define a one-year reproductive number ([Formula: see text]) from the spectrum of a one-year solution operator, and study its sensitivity to variations in the mean and amplitude of the annual temperature profile. We quantify assumptions sufficient to give rise to the low-rank structure of the solution operator characteristic of part of the parameter domain. We discuss establishment potential as it results from the pairing of a favorable [Formula: see text] value and transient population survival, and address implications for pest control strategies.

Reproductive dispersion and damping time scale with life-history speed

Iteroparous species may reproduce at many different ages, resulting in a reproductive dispersion that affects the damping of population perturbations, and varies among life histories. Since generation time ( T c $$ {T}_c $$ ) is known to capture aspects of life-history variation, such as life-history speed, does T c $$ {T}_c $$ also determine reproductive dispersion ( S $$ S $$ ) or damping time ( τ $$ \tau $$ )? Using phylogenetically corrected analyses on 633 species of animals and plants, we find, firstly, that reproductive dispersion S $$ S $$ scales isometrically with T c $$ {T}_c $$ . Secondly, and unexpectedly, we find that the damping time ( τ $$ \tau $$ ) does not scale isometrically with generation time, but instead changes only as T c b $$ {T}_c^b $$ with b < 1 $$ b<1 $$ (also, there is a similar scaling with S $$ S $$ ). This non-isometric scaling implies a novel demographic contrast: increasing generation times correspond to a proportional increase in reproductive dispersion, but only to a slower increase in the damping time. Thus, damping times are partly decoupled from the slow-fast continuum, and are determined by factors other than allometric constraints.

Global warming leads to larger bats with a faster life history pace in the long-lived Bechstein's bat (Myotis bechsteinii)

Whether species can cope with environmental change depends considerably on their life history. Bats have long lifespans and low reproductive rates which make them vulnerable to environmental changes. Global warming causes Bechstein’s bats (Myotis bechsteinii) to produce larger females that face a higher mortality risk. Here, we test whether these larger females are able to offset their elevated mortality risk by adopting a faster life history. We analysed an individual-based 25-year dataset from 331 RFID-tagged wild bats and combine genetic pedigrees with data on survival, reproduction and body size. We find that size-dependent fecundity and age at first reproduction drive the observed increase in mortality. Because larger females have an earlier onset of reproduction and shorter generation times, lifetime reproductive success remains remarkably stable across individuals with different body sizes. Our study demonstrates a rapid shift to a faster pace of life in a mammal with a slow life history.

Warming summers across a 25-year study are linked to larger body sizes in female bats, leading to a switch from a slow-reproducing, long-lived species to a faster pace of life.

Selection on age-specific survival: Constant versus fluctuating environment

According to a classic result in evolutionary biodemography, selection on age-specific survival invariably declines with reproductive age. The result assumes proportional changes in survival and a constant environment. Here, we look at selection on age-specific survival when changes are still proportional but the environment fluctuates. We find that selection may or may not decline with reproductive age depending on how exactly survival is proportionally altered by mutations. However, interpreted in neutral terms, the mathematics behind the classic result capture a general property that the genetics of populations with age structure possess both in a constant and in a fluctuating environment.

Quantifying the effect of genetic, environmental and individual demographic stochastic variability for population dynamics in Plantago lanceolata

Simple demographic events, the survival and reproduction of individuals, drive population dynamics. These demographic events are influenced by genetic and environmental parameters, and are the focus of many evolutionary and ecological investigations that aim to predict and understand population change. However, such a focus often neglects the stochastic events that individuals experience throughout their lives. These stochastic events also influence survival and reproduction and thereby evolutionary and ecological dynamics. Here, we illustrate the influence of such non-selective demographic variability on population dynamics using population projection models of an experimental population of Plantago lanceolata. Our analysis shows that the variability in survival and reproduction among individuals is largely due to demographic stochastic variation with only modest effects of differences in environment, genes, and their interaction. Common expectations of population growth, based on expected lifetime reproduction and generation time, can be misleading when demographic stochastic variation is large. Large demographic stochastic variation exhibited within genotypes can lower population growth and slow evolutionary adaptive dynamics. Our results accompany recent investigations that call for more focus on stochastic variation in fitness components, such as survival, reproduction, and functional traits, rather than dismissal of this variation as uninformative noise.

Microplastics reduce net population growth and fecal pellet sinking rates for the marine copepod, Acartia tonsa

Microplastics (<5 mm) are ubiquitous in the global environment and are increasingly recognized as a biological hazard, particularly in the oceans. Zooplankton, at the base of the marine food web, have been known to consume microplastics. However, we know little about the impacts of microplastics across life history stages and on carbon settling. Here, we investigated the effects of ingestion of neutrally buoyant polystyrene beads (6.68 μm) by the copepod Acartia tonsa on (1) growth and survival across life history stages, (2) fecundity and egg quality, (3) and fecal characteristics. We found that microplastic exposure reduced body length and survival for nauplii and resulted in smaller eggs when copepods were exposed during oogenesis. Combining these life history impacts, our models estimate a 15% decrease in population growth leading to a projected 30-fold decrease in abundance over 1 year or 20 generations with microplastic exposure. In addition, microplastic-contaminated fecal pellets were 2.29-fold smaller and sinking rates were calculated to be 1.76-fold slower, resulting in an estimated 4.03-fold reduction in fecal volume settling to the benthos per day. Taken together, declines in population sizes and fecal sinking rates suggest that microplastic consumption by zooplankton could have cascading ecosystem impacts via reduced trophic energy transfer and slower carbon settling.

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.

Comparing demography inferred from age vs. stage in a perennial plant

Life history theories analyze and predict variation in vital rates, such as survival and reproduction, based on age. The age-from-stage method to derive age-specific vital rates from stage data was developed because age-specific data are rarely obtained for plants. Age-specific vital rates derived by this method might underestimate effects of age on vital rates, because the models assume that vital rates do not vary within stage classes. Consequently, population models and life history summaries relying on these vital rates could be biased against detecting senescence. Here, we perform a comparative study of methods to estimate age-specific vital rates using monitoring data with known age and stage. We derived age-, stage-, and age-and-stage-specific vital rates with demographic data from a long-lived perennial, Silene spaldingii. Then, we derived three age-specific population matrix models (age, age-from-stage, and age-and-stage). For each model, we derived life history summaries commonly used in ecology: population growth rate, net reproductive value, relative reproductive values, stable age distribution, generation time, and sensitivity and elasticity of population growth rate. Many vital rates depended on both age and stage in S. spaldingii. However, this species does not senesce; in fact, the number of flowers increased with age. As expected, the age-from-stage method was not able to accurately recreate the age dependence in some life history summaries, such as relative reproductive value. The age-from-stage model suggested faster reproductive dynamics in S. spaldingii than the models based on known age, i.e., plants started to reproduce earlier, and fertility remained constant thereafter, which may lead to biased predictions about evolutionary consequences of age-dependent life history traits. However, population growth rate, generation time, and net reproductive rate did not differ significantly among the models. Our study demonstrated that some metrics are robust to imprecision in model structure, while others are more sensitive. In spite of these biases, this case study provides another example of the diversity of aging patterns in plants. Age can be essential information when studying senescence in plants, but demographic metrics that were not about age per se were similar across model structures.

Open Science principles for accelerating trait-based science across the Tree of Life

Synthesizing trait observations and knowledge across the Tree of Life remains a grand challenge for biodiversity science. Species traits are widely used in ecological and evolutionary science, and new data and methods have proliferated rapidly. Yet accessing and integrating disparate data sources remains a considerable challenge, slowing progress toward a global synthesis to integrate trait data across organisms. Trait science needs a vision for achieving global integration across all organisms. Here, we outline how the adoption of key Open Science principles-open data, open source and open methods-is transforming trait science, increasing transparency, democratizing access and accelerating global synthesis. To enhance widespread adoption of these principles, we introduce the Open Traits Network (OTN), a global, decentralized community welcoming all researchers and institutions pursuing the collaborative goal of standardizing and integrating trait data across organisms. We demonstrate how adherence to Open Science principles is key to the OTN community and outline five activities that can accelerate the synthesis of trait data across the Tree of Life, thereby facilitating rapid advances to address scientific inquiries and environmental issues. Lessons learned along the path to a global synthesis of trait data will provide a framework for addressing similarly complex data science and informatics challenges.

Drivers of diversity in individual life courses: Sensitivity of the population entropy of a Markov chain

Individuals differ in their life courses, but how this diversity is generated, how it has evolved and how it is maintained is less understood. However, this understanding is crucial to comprehend evolutionary and ecological population dynamics. In structured populations, individual life courses represent sequences of stages that end in death. These life course trajectories or sequences can be described by a Markov chain and individuals diversify over the course of their lives by transitioning through diverse discrete stages. The rate at which stage sequences diversify with age can be quantified by the population entropy of a Markov chain. Here, we derive sensitivities of the population entropy of a Markov chain to identify which stage transitions generate - or contribute - most to diversification in stage sequences, i.e. life courses. We then use these sensitivities to reveal potential selective forces on the dynamics of life courses. To do so we correlated the sensitivity of each matrix element (stage transition) with respect to the population entropy, to its sensitivity with respect to fitness λ, the population growth rate. Positive correlation between the two sensitivities would suggest that the stage transitions that selection has acted most strongly on (high sensitivities with respect to λ) are also those that contributed most to the diversification of life courses. Using an illustrative example on a seabird population, the Thick-billed Murres on Coats Island, that is structured by reproductive stages, we show that the most influential stage transitions for diversification of life courses are not correlated with the most influential transitions for population growth. Our finding suggests that observed diversification in life courses is neutral rather than adaptive, note this does not imply that the life histories themselves are not adaptive. We are at an early stage of understanding how individual level dynamics shape ecological and evolutionary dynamics, and many discoveries await.

Generation Time Measures the Trade-Off between Survival and Reproduction in a Life Cycle

Survival and fertility are the two most basic components of fitness, and they drive the evolution of a life cycle. A trade-off between them is usually present: when survival increases, fertility decreases-and vice versa. Here we show that at an evolutionary optimum, the generation time is a measure of the strength of the trade-off between overall survival and overall fertility in a life cycle. Our result both helps to explain the known fact that the generation time describes the speed of living in the slow-fast continuum of life cycles and may have implications for the extrapolation from model organisms of longevity to humans.

The Equivocal Mean Age of Parents in a Cohort

The mean age at which parents give birth is an important notion in demography, ecology, and evolution, where it is used as a measure of generation time. A standard way to quantify it is to compute the mean age of the parents of all offspring produced by a cohort, and the resulting measure is thought to represent the mean age at which a typical parent produces offspring. In this note, I explain why this interpretation is problematic. I also introduce a new measure of the mean age at reproduction and show that it can be very different from the mean age of parents of offspring of a cohort. In particular, the mean age of parents of offspring of a cohort systematically overestimates the mean age at reproduction and can even be greater than the expected life span of parents.

Age × stage-classified demographic analysis: a comprehensive approach

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.

Generation Time in Structured Populations

Generation time is an intuitively simple concept, but for structured populations there are multiple definitions and no general understanding of how they relate to each other. François Bienvenu and Stéphane Legendre, in their note "A New Approach to the Generation Time in Matrix Population Models," appearing in the June 2015 issue of The American Naturalist, introduced a new measure of generation time T_a, the average time between birth events in an ancestral lineage, and derived the remarkably simple formula [Formula: see text] for any matrix model, where F is the fecundity matrix, v is reproductive value, and w is stable population structure. Here I generalize their formula and interpretations of T_a to a continuous or continuous-discrete population structure and derive similar formulas for three other established generation time measures: average parent age across all births at one time ([Formula: see text]) and mean parent age at birth events for a cohort (μ₁) or generation (T_c). The new formulas reveal that these differently defined measures are unexpectedly often identical in value and clarify when they differ.

Trait level analysis of multitrait population projection matrices

In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits. We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity-fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity-fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population.

Modeling Adaptive and Nonadaptive Responses of Populations to Environmental Change

Understanding how the natural world will be impacted by environmental change over the coming decades is one of the most pressing challenges facing humanity. Addressing this challenge is difficult because environmental change can generate both population-level plastic and evolutionary responses, with plastic responses being either adaptive or nonadaptive. We develop an approach that links quantitative genetic theory with data-driven structured models to allow prediction of population responses to environmental change via plasticity and adaptive evolution. After introducing general new theory, we construct a number of example models to demonstrate that evolutionary responses to environmental change over the short-term will be considerably slower than plastic responses and that the rate of adaptive evolution to a new environment depends on whether plastic responses are adaptive or nonadaptive. Parameterization of the models we develop requires information on genetic and phenotypic variation and demography that will not always be available, meaning that simpler models will often be required to predict responses to environmental change. We consequently develop a method to examine whether the full machinery of the evolutionarily explicit models we develop will be needed to predict responses to environmental change or whether simpler nonevolutionary models that are now widely constructed may be sufficient.

r- and K-selection in fluctuating populations is determined by the evolutionary trade-off between two fitness measures: Growth rate and lifetime reproductive success

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r-selection and K-selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r₀ and the lifetime reproductive success (LRS) R₀ , both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r₀ and average lifetimes are small, whereas R₀ dominates and lifetimes are larger under small noise. Thus, K-selection is closely linked to selection for large R₀ so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r₀ and R₀ ) tend to be maximized at low and high densities, respectively, favoring density-dependent changes in the optimal life history.

The effects of asymmetric competition on the life history of Trinidadian guppies

The effects of asymmetric interactions on population dynamics has been widely investigated, but there has been little work aimed at understanding how life history parameters like generation time, life expectancy and the variance in lifetime reproductive success are impacted by different types of competition. We develop a new framework for incorporating trait‐mediated density‐dependence into size‐structured models and use Trinidadian guppies to show how different types of competitive interactions impact life history parameters. Our results show the degree of symmetry in competitive interactions can have dramatic effects on the speed of the life history. For some vital rates, shifting the competitive superiority from small to large individuals resulted in a doubling of the generation time. Such large influences of competitive symmetry on the timescale of demographic processes, and hence evolution, highlights the interwoven nature of ecological and evolutionary processes and the importance of density‐dependence in understanding eco‐evolutionary dynamics.

Preadult life history variation determines adult transcriptome expression

Preadult determinants of adult fitness and behaviour have been documented in a variety of organisms with complex life cycles, but little is known about expression patterns of genes underlying these adult traits. We explored the effects of differences in egg-to-adult development time on adult transcriptome and cuticular hydrocarbon variation in order to understand the nature of the genetic correlation between preadult development time and premating isolation between populations of Drosophila mojavensis reared in different host cactus environments. Transcriptome variation was analysed separately in flies reared on each host and revealed that hundreds of genes in adults were differentially expressed (FDR P < 0.05) due to development time differences. For flies reared on pitaya agria cactus, longer preadult development times caused increased expression of genes in adults enriched for ribosome production, protein metabolism, chromatin remodelling and regulation of alternate splicing and transcription. Baja California flies reared on organ pipe cactus showed fewer differentially expressed genes in adults due to longer preadult development time, but these were enriched for ATP synthesis and the TCA cycle. Mainland flies reared on organ pipe cactus with shorter development times showed increased transcription of genes enriched for mitochondria and energy production, protein synthesis and glucose metabolism: adults with longer development times had increased expression of genes enriched for adult life span, cuticle proteins and ion binding, although most differentially expressed genes were unannotated. Differences due to population, sex, mating status and their interactions were also assessed. Adult cuticular hydrocarbon profiles also showed shifts due to egg-to-adult development time and were influenced by population and mating status. These results help to explain why preadult life history variation determines subsequent expression of the adult transcriptome along with traits involved with reproductive isolation and revealed previously undocumented connections between genetic and environmental influences over the entire life cycle in this desert insect.

Sex-specific demography and generalization of the Trivers-Willard theory

The Trivers-Willard theory proposes that the sex ratio of offspring should vary with maternal condition when it has sex-specific influences on offspring fitness. In particular, mothers in good condition in polygynous and dimorphic species are predicted to produce an excess of sons, whereas mothers in poor condition should do the opposite. Despite the elegance of the theory, support for it has been limited. Here we extend and generalize the Trivers-Willard theory to explain the disparity between predictions and observations of offspring sex ratio. In polygynous species, males typically have higher mortality rates, different age-specific reproductive schedules and more risk-prone life history tactics than females; however, these differences are not currently incorporated into the Trivers-Willard theory. Using two-sex models parameterized with data from free-living mammal populations with contrasting levels of sex differences in demography, we demonstrate how sex differences in life history traits over the entire lifespan can lead to a wide range of sex allocation tactics, and show that correlations between maternal condition and offspring sex ratio alone are insufficient to conclude that mothers adaptively adjust offspring sex ratio.

Individual heterogeneity in life histories and eco-evolutionary dynamics

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.

The concept of fitness in fluctuating environments

Fitness is a central concept in evolutionary biology, but there is no unified definition. We review recent theoretical developments showing that including fluctuating environments and density dependence has important implications for how differences among phenotypes in their contributions to future generations should be quantified. The rate of phenotypic evolution will vary through time because of environmental stochasticity. Density dependence may produce fluctuating selection for large growth rates at low densities but for larger carrying capacities when population sizes are large. In general, including ecologically realistic assumptions when defining the concept of fitness is crucial for estimating the potential of evolutionary rescue of populations affected by environmental perturbations such as climate change.