Evolution of Size-Dependent Flowering in Onopordum illyricum: A Quantitative Assessment of the Role of Stochastic Selection Pressures

We explore the evolution of delayed, size-dependent reproduction in the monocarpic perennial Onopordum illyricum, using a range of mathematical models, parameterized with long-term field data. Analysis of the long-term data indicated that mortality, flowering, and growth were age and size dependent. Using mixed models, we estimated the variance about each of these relationships and also individual-specific effects. For the field populations, recruitment was the main density-dependent process, although there were weak effects of local density on growth and mortality. Using parameterized growth models, which assume plants grow along a deterministic trajectory, we predict plants should flower at sizes approximately 50% smaller than observed in the field. We then develop a simple criterion, termed the "1-yr look-ahead criterion," based on equating seed production now with that of next year, allowing for mortality and growth, to determine at what size a plant should flower. This model allows the incorporation of variance about the growth function and individual-specific effects. The model predicts flowering at sizes approximately double that observed, indicating that variance about the growth curve selects for larger sizes at flowering. The 1-yr look-ahead approach is approximate because it ignores growth opportunities more than 1 yr ahead. To assess the accuracy of this approach, we develop a more complicated dynamic state variable model. Both models give similar results indicating the utility of the 1-yr look-ahead criterion. To allow for temporal variation in the model parameters, we used an individual-based model with a genetic algorithm. This gave very accurate prediction of the observed flowering strategies. Sensitivity analysis of the model suggested that temporal variation in the parameters of the growth equation made waiting to flower more risky, so selected for smaller sizes at flowering. The models clearly indicate the need to incorporate stochastic variation in life-history analyses.     

Stochastic population dynamics and life-history variation in marine fish species

Abstract We examined whether differences in life-history characteristics can explain interspecific variation in stochastic population dynamics in nine marine fish species living in the Barents Sea system. After observation errors in population estimates were accounted for, temporal variability in natural mortality rate, annual recruitment, and population growth rate was negatively related to generation time. Mean natural mortality rate, annual recruitment, and population growth rate were lower in long-lived species than in short-lived species. Thus, important species-specific characteristics of the population dynamics were related to the species position along the slow-fast continuum of life-history variation. These relationships were further associated with interspecific differences in ecology: species at the fast end were mainly pelagic, with short generation times and high natural mortality, annual recruitment, and population growth rates, and also showed high temporal variability in those demographic traits. In contrast, species at the slow end were long-lived, deepwater species with low rates and reduced temporal variability in the same demographic traits. These interspecific relationships show that the life-history characteristics of a species can predict basic features of interspecific variation in population dynamical characteristics of marine fish, which should have implications for the choice of harvest strategy to facilitate sustainable yields.     

Does environmental stochasticity matter? Analysis of red deer life-histories on Rum

Summary Most life-history theory assumes that short-term variation in an organism's environment does not affect the survivorships and fecundities of the organisms. This assumption is rarely met. Here we investigate the population and evolutionary biology of red deer,Cervus elephas, to see if relaxation of this assumption is likely to make significant differences to the predicted evolutionary biology of this species. To do this we used 21 years of data from a population of deer on Rum, Western Isles, Scotland. Population growth rates in a stochastic environment were estimated using Tuljapurkar's small noise approximation, confirmed by bootstrap simulation. Numerical differentiation was used to see if the selection pressures (i.e. sensitivities of population growth rate to changes in the vital rates) differ between the stochastic and deterministic cases. The data also allow the costs of reproduction to be estimated. These costs, incorporated as trade-offs into the sensitivity analysis, allow investigation of evolutionary benefits of different life-history tactics. Environmentally induced stochastic variation in the red deer vital rates causes a slight reduction ( 1%) in the predicted population growth rate and has little impact on the estimated selection pressures on the deer's life-history. We thus conclude that, even though density-independent stochastic effects on the population are marked, the deer's fitness is not markedly affected by these and they are adapted to the average conditions they experience. However, the selected life-history is sensitive to the trade-offs between current fecundity, survivorship and future fecundity and it is likely that the environmental variance will affect these trade-offs and, thus, affect the life-history favoured by selection. We also show that the current average life-history is non-optimal and suggest this is a result of selection pressures exerted by culling and predation, now much reduced. As the use of stochastic or deterministic methods provide similar estimates in this case, the use of the latter is justified. Thus,r (the annual per capita rate of population growth) is an appropriate measure of fitness in a population with stochastic numerical fluctuations. In a population of constant size lifetime reproductive success is the obvious measure of fitness to use.     

Age-specific fitness components and their temporal variation in the barn owl

Theory predicts that temporal variability plays an important role in the evolution of life histories, but empirical studies evaluating this prediction are rare. In constant environments, fitness can be measured by the population growth rate lambda, and the sensitivity of lambda to changes in fitness components estimates selection on these traits. In variable environments, fitness is measured by the stochastic growth rate lambda(S), and stochastic sensitivities estimate selection pressure. Here we examine age-specific schedules for reproduction and survival in a barn owl population (Tyto alba). We estimated how temporal variability affected fitness and selection, accounting for sampling variance. Despite large sample sizes of old individuals, we found no strong evidence for senescence. The most variable fitness components were associated with reproduction. Survival was less variable. Stochastic simulations showed that the observed variation decreased fitness by about 30%, but the sensitivities of lambda and lambda(S) to changes in all fitness components were almost equal, suggesting that temporal variation had negligible effects on selection. We obtained these results despite high observed variability in the fitness components and relatively short generation time of the study organism, a situation in which temporal variability should be particularly important for natural selection and early senescence is expected.     

Is life‐history buffering or lability adaptive in stochastic environments?

It is commonly thought that temporal fluctuations in demographic parameters should be selected against because of the deleterious impacts variation can have on fitness. A critical underpinning of this prediction is the assumption that changes in environmental conditions map linearly into changes in demographic parameters over time. We detail why this assumption may often break down and why selection should not always favor buffering of demographic parameters against environmental stochasticity. To the contrary, nonlinear relationships between the environment and demographic performance can produce asymmetric temporal variation in demographic parameters that actually enhances fitness. We extend this result to structured populations using simulation and show that 'demographic lability' rather than 'buffering' may be adaptive, particularly in organisms with low juvenile or adult survival. Finally, we review previous ecological work, and indicate cases where 'demographic lability' may be adaptive, then conclude by identifying research that is needed to develop a theory of life-history evolution that encompasses both demographic buffering and lability.     

Seed dormancy and delayed flowering in monocarpic plants: selective interactions in a stochastic environment

We explore the effects of temporal variation in multiple demographic rates on the joint evolution of delayed reproduction and seed dormancy using integral projection models (IPMs). To do this, we extend the standard IPM to include a discrete state variable representing the number of seeds in the seed bank, density-dependent recruitment, and temporal variation in demography. Parameter estimates for Carlina vulgaris and Carduus nutans are obtained from long-term studies. Carlina is relatively long lived and has a short-lived seed bank, whereas most Carduus plants flower in their first year and the seed bank is long lived. Using the evolutionarily stable strategy (ESS) approach, we predict the observed flowering and germination strategies. There is excellent agreement between the predictions and the field observations. The effects of temporal variation on the joint ESS are partitioned into components arising from nonlinear averaging (systematic changes in the mean resulting from the interaction between variability and nonlinearity) and nonequilibrium dynamics (fluctuations in fitness caused by temporal variation). This shows that temporal variation can have substantial effects on the observed flowering and germination strategies and that covariance between demographic processes is important. We extend the models to include spatial population structure and assess the robustness of the results from the nonspatial models.     

From stochastic environments to life histories and back

Environmental stochasticity is known to play an important role in life-history evolution, but most general theory assumes a constant environment. In this paper, we examine life-history evolution in a variable environment, by decomposing average individual fitness (measured by the long-run stochastic growth rate) into contributions from average vital rates and their temporal variation. We examine how generation time, demographic dispersion (measured by the dispersion of reproductive events across the lifespan), demographic resilience (measured by damping time), within-year variances in vital rates, within-year correlations between vital rates and between-year correlations in vital rates combine to determine average individual fitness of stylized life histories. In a fluctuating environment, we show that there is often a range of cohort generation times at which the fitness is at a maximum. Thus, we expect ‘optimal’ phenotypes in fluctuating environments to differ from optimal phenotypes in constant environments. We show that stochastic growth rates are strongly affected by demographic dispersion, even when deterministic growth rates are not, and that demographic dispersion also determines the response of life-history-specific average fitness to within- and between-year correlations. Serial correlations can have a strong effect on fitness, and, depending on the structure of the life history, may act to increase or decrease fitness. The approach we outline takes a useful first step in developing general life-history theory for non-constant environments.     

Offspring fitness in relation to population size and genetic variation in the rare perennial plant species Gentiana pneumonanthe (Gentianaceae)

Seeds were sampled from 19 populations of the rare Gentiana pneumonanthe, ranging in size from 5 to more than 50,000 flowering plants. An analysis was made of variation in a number of life-history characters in relation to population size and offspring heterozygosity (based on seven polymorphic isozyme loci). Life-his-tory characters included seed weight, germination rate, proportion of seeds germinating, seedling mortality, seedling weight, adult weight, flower production per plant and proportion of plants flowering per family. Principal component analysis (PCA) reduced the dataset to three main fitness components. The first component was highly correlated with adult weight and flowering performance, the second with germination performance and the third component with seed and seedling weight and seedling mortality. The latter two components were considered as being maternally influenced, since these comprised life-history traits that were significantly correlated with seed weight. Multiple regression analysis showed that variation in the first fitness component was mainly associated with heterozygosity and not with population size, while the third fitness component was only correlated with population size and not with heterozygosity. The latter relationship appeared to be non-linear, which suggests a stronger loss of fitness in the smallest populations. The second (germination) component was neither correlated with population size nor with genetic variation. There was only a weak association between population size, heterozygosity and the population coefficients of variation for each life history character. Most correlation coefficients were negative, however, which suggests that there is more variation among progeny from smaller populations. We conclude that progeny from small populations of Gentiana pneumonanthe show reduced fitness and may be phenotypically more variable. One of the possible causes of the loss of fitness is a combination of unfavourable environmental circumstances for maternal plants in small populations and increased inbreeding. The higher phenotypic variation in small populations may also be a result of inbreeding, which can lead to deviation of individuals from the average phenotype through a loss of developmental stability.     

Phenotypic selection and covariation in the life‐history traits of elephant seals: heavier offspring gain a double selective advantage

Early developmental conditions contribute to individual heterogeneity of both phenotypic traits and fitness components, ultimately affecting population dynamics. Although the demographic consequences of ontogenic growth are best quantified using an integrated measure of fitness, most analyses to date have instead studied individual fitness components in isolation. Here, we estimated phenotypic selection on weaning mass in female southern elephant seals Mirounga leonina by analyzing individual‐based data collected between 1986 and 2016 with capture–recapture and matrix projection models. In support of a hypothesis predicting a gradual decrease of weaning mass effects with time since weaning (the replacement hypothesis), we found that the estimated effects of weaning mass on future survival and recruitment probability was of intermediate duration (rather than transient or permanent). Heavier female offspring had improved odds of survival in early life and a higher probability to recruit at an early age. The positive link between weaning mass and recruitment age is noteworthy, considering that pre‐recruitment mortality already imposed a strong selective filter on the population, leaving only the most ‘robust’ individuals to reproduce. The selection gradient on asymptotic population growth rate, a measure of mean absolute fitness, was weaker than selection on first‐year survival and recruitment probabilities. Weaker selection on mean fitness occurs because weaning mass has little impact on adult survival, the fitness component to which the population growth of long‐lived species is most sensitive. These results highlight the need to interpret individual variation in phenotypic traits in a context that considers the demographic pathways between the trait and an inclusive proxy of individual fitness. Although variation in weaning mass do not translate to permanent survival differences among individuals in adulthood, it explains heterogeneity and positive covariation between survival and breeding in early life, which contribute to between‐individual variation in fitness.     

Evolutionarily stable dispersal strategies

Using the idea that life-history parameters are subject to natural selection and should approach values that are stable optima, with the population immune to invasion by mutant individuals, we derive an analytic expression for the evolutionarily stable dispersal rate in a stochastic island model with random site extinction. The results provide interesting contrasts between three different optimization criteria: species survival, individual fitness and gene fitness. We also consider the effects of sexual reproduction, and of localized migration (stepping-stone structure).     

Evolution of size-dependent flowering in a variable environment: partitioning the effects of fluctuating selection

In a stochastic environment, two distinct processes, namely nonlinear averaging and non-equilibrium dynamics, influence fitness. We develop methods for decomposing the effects of temporal variation in demography into contributions from nonlinear averaging and non-equilibrium dynamics. We illustrate the approach using Carlina vulgaris, a monocarpic species in which recruitment, growth and survival all vary from year to year. In Carlina the absolute effect of temporal variation on the evolutionarily stable flowering strategy is substantial (ca. 50% of the evolutionarily stable flowering size) but the net effect is much smaller (ca. 10%) because the effects of temporal variation do not influence the evolutionarily stable strategy in the same direction.     

Genotype-by-environment interactions leads to variable selection on life-history strategy in Common Evening Primrose (Oenothera biennis)

Monocarpic plant species, where reproduction is fatal, frequently exhibit variation in the length of their prereproductive period prior to flowering. If this life-history variation in flowering strategy has a genetic basis, genotype-by-environment interactions (G x E) may maintain phenotypic diversity in flowering strategy. The native monocarpic plant Common Evening Primrose (Oenothera biennis L., Onagraceae) exhibits phenotypic variation for annual vs. biennial flowering strategies. I tested whether there was a genetic basis to variation in flowering strategy in O. biennis, and whether environmental variation causes G x E that imposes variable selection on flowering strategy. In a field experiment, I randomized more than 900 plants from 14 clonal families (genotypes) into five distinct habitats that represented a natural productivity gradient. G x E strongly affected the lifetime fruit production of O. biennis, with the rank-order in relative fitness of genotypes changing substantially between habitats. I detected genetic variation in annual vs. biennial strategies in most habitats, as well as a G x E effect on flowering strategy. This variation in flowering strategy was correlated with genetic variation in relative fitness, and phenotypic and genotypic selection analyses revealed that environmental variation resulted in variable directional selection on annual vs. biennial strategies. Specifically, a biennial strategy was favoured in moderately productive environments, whereas an annual strategy was favoured in low-productivity environments. These results highlight the importance of variable selection for the maintenance of genetic variation in the life-history strategy of a monocarpic plant.     

Fluctuating selection on reproductive timing in Digitalis purpurea

Despite recent, strong interest in the modelling of monocarpic perennial flowering strategies, little is known about how variation in demographic rates affects selection on optimal timing of flowering. Temporal variation may yield fluctuating selective pressures, or, if individuals experience time trends, selection for phenotypic plasticity. Here we report the results of a 3-year study in a large field population of the facultative biennial herb Digitalis purpurea , where we use field data on size-dependent growth, survival and fecundity to parameterize an existing optimisation model. We compare results from models using either deterministic or individually varying demographic rates to address the degree of fluctuating selection on the flowering strategy. In addition, we explore whether recent growing conditions influence the size-specific liability to flower. Model results differed widely between years; immediate onset of reproduction was predicted in 1999, strongly delayed reproduction in 2000. This reflected large differences in both growth and survival rates between years. Observed flowering sizes also varied between years, but were larger in 1999 than in 2000, contrary to model predictions. Incorporating individual variation in growth increased predicted optimal flowering sizes compared to models using deterministic growth, whereas the inclusion of individual survival variation had little effect. There was no significant effect of recent growth rate on flowering probability. Taken together, these results indicate highly fluctuating selection on the flowering strategy in D. purpurea , but no evidence of adaptive plasticity in response to current growing conditions. Fluctuating selection may contribute to maintain genetic variation for threshold size for flowering, and may partly explain the large within-season size-variation in flowering individuals found in natural populations of D. purpurea .     

Riding across the selection landscape: fitness consequences of annual variation in reproductive characteristics

Evolutionary models estimating phenotypic selection in character size usually assume that the character is invariant across reproductive bouts. We show that variation in the size of reproductive traits may be large over multiple events and can influence fitness in organisms where these traits are produced anew each season. With data from populations of two orchid species, Caladenia valida and Tolumnia variegata, we used Bayesian statistics to investigate the effect on the distribution in fitness of individuals when the fitness landscape is not flat and when characters vary across reproductive bouts. Inconsistency in character size across reproductive periods within an individual increases the uncertainty of mean fitness and, consequently, the uncertainty in individual fitness. The trajectory of selection is likely to be muddled as a consequence of variation in morphology of individuals across reproductive bouts. The frequency and amplitude of such changes will certainly affect the dynamics between selection and genetic drift.     

Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach

The timing of reproduction is a key determinant of fitness. Here, we develop parameterized integral projection models of size-related flowering for the monocarpic perennial Oenothera glazioviana and use these to predict the evolutionarily stable strategy (ESS) for flowering. For the most part there is excellent agreement between the model predictions and the results of quantitative field studies. However, the model predicts a much steeper relationship between plant size and the probability of flowering than observed in the field, indicating selection for a 'threshold size' flowering function. Elasticity and sensitivity analysis of population growth rate lambda and net reproductive rate R(0) are used to identify the critical traits that determine fitness and control the ESS for flowering. Using the fitted model we calculate the fitness landscape for invading genotypes and show that this is characterized by a ridge of approximately equal fitness. The implications of these results for the maintenance of genetic variation are discussed.     

Spatial data replacing temporal data in population viability analyses: An empirical investigation for plants

In conservation management, there is an urgent need for estimates of population viability and for knowledge of the contributions of different life-history stages to population growth rates. Collection of long-term demographic data from a study population is time-consuming and may considerably delay the start of proper management actions. We examined the possibility of replacing a long-term temporal data set (demographic data from several years within a population) with a short-term spatial data set (demographic data from different populations for the same subset of two continuous years) for stochastic estimates of population viability. Using matrix population models for ten perennial plant species, we found that the matrix elements of spatial data sets often deviated from those of temporal data sets and that matrix elements generally varied more spatially than temporally. The appropriateness of replacing temporal data with spatial data depended on the subset of years and populations used to estimate stochastic population growth rates (log λ_s). Still, the precision of log λ_s estimates measured as variation in the yearly change of logarithmic population size rarely differed significantly between the spatial and temporal data sets. Since a spatiotemporal comparison of matrix elements and their variation cannot be used to assess whether spatial and temporal data sets are interchangeable, we recommend further research on the topic.     

The force of selection on the human life cycle

In this article, I present evidence for a robust and quite general force of selection on the human life cycle. The force of selection acts in remarkably invariant ways on human life histories, despite a great abundance of demographic diversity. Human life histories are highly structured, with mortality and fertility changing substantially through the life cycle. This structure necessitates the use of structured population models to understand human life history evolution. Using such structured models, I find that the vital rates to which fitness is most sensitive are prereproductive survival probabilities, particularly the survival of children ages 0 to 4 years. The fact that the preponderance of selection falls on transitions related to recruitment combined with the late age at first reproduction characteristic of the human life cycle creates a fitness bottleneck out of recruitment. Because of this, antagonistic pleiotropy with any trait that detracts from the constituent transitions to recruitment is expected. I explore the predictors of variation in the force of selection on early survival. High fertility increases the selective premium placed on early survivorship, whereas high life expectancy at birth decreases it.     

The population dynamics of the mangrove Avicennia marina; demographic synthesis and predictive modelling

Population dynamics of the widespread mangrove Avicennia marina was studied over the complete life-history from zygotes through to adults in southeastern Australia. Zygote survival, propagule dispersal, seedling establishment, seedling recruitment and sapling recruitment were examined by demographic censuses over a range of spatial and temporal scales. Hypotheses about factors regulating survival were tested by manipulative field experiments. Life table statistics for survival and fecundity were used to calculate transition probabilities and their variance for seven stages of life history. These parameters were used as the basis of a stochastic model that predicts population structure after small and large scale perturbations.     

Life history in a model system: opening the black box with Arabidopsis thaliana

A broad research programme in Arabidopsis thaliana has provided estimates of selection on specific alleles in specific contexts, and identified geographic patterns of alleles in genes linked to timing of flowering. A closely related field has successfully captured many key axes of the evolution of timing of flowering in other monocarpic species through statistical and demographic modelling of large empirical databases. There has as yet been no synthesis between these two fields. Here we examine ways in which the two fields inform each other, and how this synergy will shape our knowledge of life-history evolution as a whole.     

Interactive life‐history traits predict sensitivity of plants and animals to temporal autocorrelation

Temporal autocorrelation in demographic processes is an important aspect of population dynamics, but a comprehensive examination of its effects on different life‐history strategies is lacking. We use matrix population models from 454 plant and animal populations to simulate stochastic population growth rates (log λ_s) under different temporal autocorrelations in demographic rates , using simulated and observed covariation among rates. We then test for differences in sensitivities, or changes of log λ_s to changes in autocorrelation among two major axes of life‐history strategies, obtained from phylogenetically informed principal component analysis: the fast‐slow and reproductive‐strategy continua. Fast life histories exhibit highest sensitivities to simulated autocorrelation in demographic rates across reproductive strategies. Slow life histories are less sensitive to temporal autocorrelation, but their sensitivities increase among highly iteroparous species. We provide cross‐taxonomic evidence that changes in the autocorrelation of environmental variation may affect a wide range of species, depending on complex interactions of life‐history strategies.