Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris

Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.     

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.     

Genetic Variation in a Heterogeneous Environment. II. Temporal Heterogeneity and Directional Selection

The maintenance of genetic variation is investigated in a finite population where selection at an autosomal locus with two alleles varies temporally between two environments and the heterozygote has an intermediate fitness value. When there is additive gene action and equal selection in both environments, the autocorrelation between subsequent environments must be negative for more maintenance of genetic variation than for neutrality. The maximum maintenance occurs when there is equal selection in the two environments and the autocorrelation approaches ^-1.0 (for a stochastic model), or when there is short repeating cycle such as one related to seasons. Also comparison of the effects of stochastic variation in selection in finite and infinite populations is made by using Monte Carlo simulation. One situation was found where temporal environmental variation maintains genetic variation very effectively even in a small population and that is when there is evolution of dominance, i.e., the heterozygote is closer in fitness to the favored homozygote than the other homozygote. An important conclusion is that in a finite population genetic tracing of environmental change, particularly when there is a positive autocorrelation between environments or a long environmental cycle, leads to an increased loss of genetic variation making such a response undesirable in the long term, a result different from that in infinite populations.     

Self-fertilization and the escape from pollen limitation in variable pollination environments

Seed production in many plants is pollen limited, likely because of unpredictable variation in the pollinator environment. One way for plants to escape the consequences of pollinator variability is to evolve mating systems, such as autonomous selfing, that assure reproduction without relying on pollinators. We explore this hypothesis through the construction and analysis of heuristic models of plant population dynamics in seed- or site-limited populations. Our analysis suggests several important points: the familiar rule that inbreeding depression greater than 0.5 maintains outcrossing significantly underestimates the threshold required under pollen limited conditions with prior selfing; variability in the pollination environment erodes the ability of inbreeding depression to maintain outcrossing; and variable pollination environments can result in stable intermediate rates of prior selfing. The results reflect the importance of geometric mean fitness (which in a variable environment is less than the arithmetic mean) in the face of temporal variation.     

Variation in natural selection for growth and phlorotannins in the brown alga Fucus vesiculosus

Directional selection for plant traits associated with resistance to herbivory tends to eliminate genetic variation in such traits. On the other hand, balancing selection arising from trade-offs between resistance and growth or spatially variable selection acts against the elimination of genetic variation. We explore both the amount of genetic variation and variability of natural selection for growth and concentration of phenolic secondary compounds, phlorotannins, in the brown alga Fucus vesiculosus. We measured variation in selection at two growing depths and two levels of nutrient availability in algae that had faced two kinds of past growing environments. Genetic variation was low for growth but high for phlorotannins. The form and strength of selection for both focal traits depended on the past growing environment of the algae. We found strong directional selection for growth rate in algae previously subjected to higher ultraviolet radiation, but not in algae previously subjected to higher nutrient availability. Stabilizing selection for growth occurred especially in the deep growing environment. Selection for phlorotannins was generally weak, but in some past-environment-current-environment combinations we detected either directional selection against phlorotannins or stabilizing selection. Thus, phlorotannins are not selectively neutral but affect the fitness of F. vesiculosus. In particular, there may be a fitness cost of producing phlorotannins, but the realization of such a cost varies from one environment to another. Genetic correlations between selective environments were high for growth but nonexistent for phlorotannins, emphasizing the high phenotypic plasticity of phlorotannin production. The highly heterogeneous selection, including directional, stabilizing, and spatially variable selection as well as temporal change in selection due to responses to past environmental conditions, probably maintains a high amount of genetic variation in phlorotannins. Such variation provides the potential for rapid evolutionary response of phlorotannins under directional selection.     

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.     

Buffering and plasticity in vital rates of oldfield rodents

1. Under the hypothesis of environmental buffering, populations are expected to minimize the variance of the most influential vital rates; however, this may not be a universal principle. Species with a life span <1 year may be less likely to exhibit buffering because of temporal or seasonal variability in vital rate sensitivities. Further, plasticity in vital rates may be adaptive for species in a variable environment with reliable cues. 2. We tested for environmental buffering and plasticity in vital rates using stage-structured matrix models from long-term data sets in four species of grassland rodents. We used periodic matrices to estimate stochastic elasticity for each vital rate and then tested for correlations with a standardized coefficient of variation for each rate. 3. We calculated stochastic elasticities for individual months to test for an association between increased reproduction and the influence of reproduction, relative to survival, on the population growth rate. 4. All species showed some evidence of buffering. The elasticity of vital rates of Peromyscus leucopus (Rafinesque, 1818), Sigmodon hispidus Say & Ord, 1825 and Microtus ochrogaster (Wagner, 1842) was negatively related to vital rate CV. Elasticity and vital rate CV were negatively related in Peromyscus maniculatus (Wagner, 1845), but the relationship was not statistically significant. Peromyscus leucopus and M. ochrogaster showed plasticity in vital rates; reproduction was higher following months where elasticity for reproduction exceeded that of survival. 5. Our results suggest that buffering is common in species with fast life histories; however, some populations that exhibit buffering are capable of responding to short-term variability in environmental conditions through reproductive plasticity.     

Adaption,neutrality and life-course diversity

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non-genetic and also non-environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non-genetic, non-environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life-course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non-genetic non-environmental variation.     

Correctly estimating how environmental stochasticity influences fitness and population growth

Increased temporal variance in life-history traits is generally predicted to decrease individual fitness and population growth. We show that a widely used result of stochastic sensitivity analysis that bolsters this generality is flawed because it ignores the effects of correlations between vital rates. Considering the effects of these correlations (although ignoring autocorrelations), we show that the apparently simple relationship between vital rate variance and fitness can be considerably more complex than previously thought. In particular, the previously estimated negative sensitivities of fitness or population growth to variance in a vital rate can be either enhanced by positive correlations between rates or reversed by negative correlations, even to the point that variability in a rate can increase fitness or population growth. We apply this new sensitivity calculation to data from the desert tortoise and discuss its interpretation in light of the factors generating vital rate correlations.     

Quantification and decomposition of environment‐selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait‐absolute fitness relationship remains constant. We apply and extend a regression‐based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment‐selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait‐fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.     

Environmental uncertainty, autocorrelation and the evolution of survival

Survival is a key fitness component and the evolution of age- and stage-specific patterns in survival is a central question in evolutionary biology. In variable environments, favouring chances of survival at the expense of other fitness components could increase fitness by spreading risk across uncertain conditions, especially if environmental conditions improve in the future. Both the magnitude of environmental variation and temporal autocorrelation in the environment might therefore affect the evolution of survival patterns. Despite this, the influence of temporal autocorrelation on the evolution of survival patterns has not been addressed. Here, we use a trade-off structure which reflects the empirically inspired paradigm of acquisition and allocation of resources to investigate how the evolutionarily stable survival probability is shaped in variable, density-dependent environments. We show that temporal autocorrelation is likely to be an important aspect of environmental variability that contributes to shaping age- and stage-specific patterns of survival probabilities in nature.     

Sensitivity of the population growth rate to demographic variability within and between phases of the disturbance cycle

For species in disturbance-prone ecosystems, vital rates (survival, growth and reproduction) often vary both between and within phases of the cycle of disturbance and recovery; some of this variation is imposed by the environment, but some may represent adaptation of the life history to disturbance. Anthropogenic changes may amplify or impede these patterns of variation, and may have positive or negative effects on population growth. Using stochastic population projection matrix models, we develop stochastic elasticities (proportional derivatives of the long-run population growth rate) to gauge the population effects of three types of change in demographic variability (changes in within- and between-disturbance-phase variability and phase-specific changes). Computing these elasticities for five species of disturbance-influenced perennial plants, we pinpoint demographic rates that may reveal adaptation to disturbance, and we demonstrate that species may differ in their responses to different types of changes in demographic variability driven by climate change.     

Maintenance of sexually dimorphic preadult traits in Marchantia inflexa (Marchantiacae)

Marchantia inflexa, a dioecious thallose liverwort, is sexually dimorphic in clonal expansion traits. We used selection analyses to measure the magnitude and direction of selection on clonal fitness to uncover possible mechanisms for the maintenance of preadult sexually dimorphic characters. We planted replicates of genotypes of female and male M. inflexa in two light environments in a greenhouse and measured morphological and phenological characters associated with growth and asexual reproduction. Timing to onset of asexual reproduction and plant size early in development were under sex-specific selection in a low light environment. Additionally, females exhibited a sex-specific cost of plasticity in the timing of their onset of asexual reproduction in high light. Selection on asexual fitness tended to shift traits toward monomorphism rather than sexual dimorphism, whereas the expressed phenotype of females was congruent with patterns of selection acting on sexual fitness. We detected negative trade-offs between asexual and sexual fitness components in females in one light environment. Opposing selective forces acting on asexual and sexual fitness components may explain how sexual dimorphisms persist in the face of selection for monomorphism in the preadult phase.     

Natural selection on age-specific fertilities in human females: comparison of individual-level fitness measures.

Lifetime reproductive success and timing of reproduction are key components of life-history evolution. To understand the evolution of reproductive schedules, it is important to use a measure of fitness that is sensitive both to reproductive quantity and reproductive timing. There is a contradiction between the theory, which mainly focuses on the rate measures of fitness (r and lambda), and empirical studies, which mainly use lifetime reproductive success (LRS), or some of its correlates, as a fitness measure. We measured phenotypic selection on age-specific fertilities in three pre-modern human populations using individually estimated finite rate of increase, er (lambda). We found that lambda and lifetime reproductive success ranked individuals differently according to their fitness: for example, a female giving birth to four children at a young age may actually have a higher fitness than a female giving birth to six children at a greater age. Increase in fertility at the young age classes (15-19 years) was favoured by selection, but the intensity of selection on fertility was higher in the older age classes (20-30 years), where the variance in fertility was highest. Hence, variation in fertility in the older age classes (20-30) was actually responsible for most of the observed variation in fitness among the individuals. Additionally, more than 90% of variation in fitness (lambda) was attributable to individual differences in LRS, whereas only about 5% of all variation in fitness was due to differences in the reproductive schedule. The rate-sensitive fitness measure did not significantly challenge the importance of total fertility as a component of fitness in humans. However, the rate-sensitive measure clearly allowed more accurate estimation of individual fitness, which may be important for answering some more specific questions.     

Environmental Uncertainty and Variable Diapause

We analyze a stage-structured model of a population that displays variable diapause in a randomly varying environment. The ruggedness of the environment is measured by the extent of random variation in per-capita reproductive success. We show how variable diapause and environmental characteristics affect the population′s stochastic growth rate. In rugged unpredictable environments, phenotypes that show some tendency to diapause are found to have a higher growth rate than nondiapausing phenotypes. In harsh rugged environments, some tendency to diapause may be all that permits population persistence. Positive serial autocorrelation causes the optimal diapause fraction to decrease, while negative autocorrelation causes that fraction to increase. The structured model behaves very differently from a scalar model for large diapause fractions even in uncorrelated environments, and in many cases predicts a broad optimum. The difference between models is due to the extreme variability of stage structure in populations subject to even small variability when diapause tendency is high.     

Timing in a fluctuating environment: environmental variability and asymmetric fitness curves can lead to adaptively mismatched avian reproduction

Adaptation in dynamic environments depends on the grain, magnitude and predictability of ecological fluctuations experienced within and across generations. Phenotypic plasticity is a well-studied mechanism in this regard, yet the potentially complex effects of stochastic environmental variation on optimal mean trait values are often overlooked. Using an optimality model inspired by timing of reproduction in great tits, we show that temporal variation affects not only optimal reaction norm slope, but also elevation. With increased environmental variation and an asymmetric relationship between fitness and breeding date, optimal timing shifts away from the side of the fitness curve with the steepest decline. In a relatively constant environment, the timing of the birds is matched with the seasonal food peak, but they become adaptively mismatched in environments with temporal variation in temperature whenever the fitness curve is asymmetric. Various processes affecting the survival of offspring and parents influence this asymmetry, which collectively determine the 'safest' strategy, i.e. whether females should breed before, on, or after the food peak in a variable environment. As climate change might affect the (co)variance of environmental variables as well as their averages, risk aversion may influence how species should shift their seasonal timing in a warming world.     

Life history evolution and demographic stochasticity

Summary Can demographic stochasticity bias the evolution of life history traits? Under a neutral version of the Cole-Charnov-Schaffer model, variance in offspring number for both annuals and perennials depends on the precise values of fitness components. Either annuals or perennials may have the larger variance (for equal ), depending on the importance of random survivalversus fixed reproduction. By extension, the variance in offspring number should generally depend on whether is mainly composed of highly variable elements or elements with limited variation. Thus, data about the variability of demographic parameters may be as important as data about their mean values.This result concerns only one source of demographic stochasticity, the probabilistic nature of demographic processes like survival. The other source of demographic stochasticity is the fact that populations are composed of whole numbers of individuals (integer arithmetic). Integer arithmetic without probabilistic demography (or environmental variation) can make it difficult for rare invaders to persist in populations even when selection would favour the invaders in a deterministic model. Integer arithmetic can also cause population coexistence when the equivalent deterministic model leads to exclusion. This effect disappears when demography is probabilistic, and probably also when there is environmental variation. Thus probabilistic demography and environmental variation may make some population patterns more, rather than less, understandable.     

An integrated analysis of phenotypic selection on insect body size and development time

Most studies of phenotypic selection do not estimate selection or fitness surfaces for multiple components of fitness within a unified statistical framework. This makes it difficult or impossible to assess how selection operates on traits through variation in multiple components of fitness. We describe a new generation of aster models that can evaluate phenotypic selection by accounting for timing of life‐history transitions and their effect on population growth rate, in addition to survival and reproductive output. We use this approach to estimate selection on body size and development time for a field population of the herbivorous insect, Manduca sexta (Lepidoptera: Sphingidae). Estimated fitness surfaces revealed strong and significant directional selection favoring both larger adult size (via effects on egg counts) and more rapid rates of early larval development (via effects on larval survival). Incorporating the timing of reproduction and its influence on population growth rate into the analysis resulted in larger values for size in early larval development at which fitness is maximized, and weaker selection on size in early larval development. These results illustrate how the interplay of different components of fitness can influence selection on size and development time. This integrated modeling framework can be readily applied to studies of phenotypic selection via multiple fitness components in other systems.     

Stochastic demography and population dynamics in the red kangaroo Macropus rufus

1.  Many organisms inhabit strongly fluctuating environments but their demography and population dynamics are often analysed using deterministic models and elasticity analysis, where elasticity is defined as the proportional change in population growth rate caused by a proportional change in a vital rate. Deterministic analyses may not necessarily be informative because large variation in a vital rate with a small deterministic elasticity may affect the population growth rate more than a small change in a less variable vital rate having high deterministic elasticity.
2.  We analyse a stochastic environment model of the red kangaroo ( Macropus rufus ), a species inhabiting an environment characterized by unpredictable and highly variable rainfall, and calculate the elasticity of the stochastic growth rate with respect to the mean and variability in vital rates.
3.  Juvenile survival is the most variable vital rate but a proportional change in the mean adult survival rate has a much stronger effect on the stochastic growth rate.
4.  Even if changes in average rainfall have a larger impact on population growth rate, increased variability in rainfall may still be important also in long-lived species. The elasticity with respect to the standard deviation of rainfall is comparable to the mean elasticities of all vital rates but the survival in age class 3 because increased variation in rainfall affects both the mean and variability of vital rates.
5.  Red kangaroos are harvested and, under the current rainfall pattern, an annual harvest fraction of c . 20% would yield a stochastic growth rate about unity. However, if average rainfall drops by more than c . 10%, any level of harvesting may be unsustainable, emphasizing the need for integrating climate change predictions in population management and increase our understanding of how environmental stochasticity translates into population growth rate.