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.     

Stochastic stable population growth in integral projection models: theory and application

Stochastic matrix projection models are widely used to model age- or stage-structured populations with vital rates that fluctuate randomly over time. Practical applications of these models rest on qualitative properties such as the existence of a long term population growth rate, asymptotic log-normality of total population size, and weak ergodicity of population structure. We show here that these properties are shared by a general stochastic integral projection model, by using results in (Eveson in D. Phil. Thesis, University of Sussex, 1991, Eveson in Proc. Lond. Math. Soc. 70, 411-440, 1993) to extend the approach in (Lange and Holmes in J. Appl. Prob. 18, 325-344, 1981). Integral projection models allow individuals to be cross-classified by multiple attributes, either discrete or continuous, and allow the classification to change during the life cycle. These features are present in plant populations with size and age as important predictors of individual fate, populations with a persistent bank of dormant seeds or eggs, and animal species with complex life cycles. We also present a case-study based on a 6-year field study of the Illyrian thistle, Onopordum illyricum, to demonstrate how easily a stochastic integral model can be parameterized from field data and then applied using familiar matrix software and methods. Thistle demography is affected by multiple traits (size, age and a latent "quality" variable), which would be difficult to accommodate in a classical matrix model. We use the model to explore the evolution of size- and age-dependent flowering using an evolutionarily stable strategy (ESS) approach. We find close agreement between the observed flowering behavior and the predicted ESS from the stochastic model, whereas the ESS predicted from a deterministic version of the model is very different from observed flowering behavior. These results strongly suggest that the flowering strategy in O. illyricum is an adaptation to random between-year variation in vital rates.     

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.     

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.     

Life-history variation in contrasting habitats: flowering decisions in a clonal perennial herb (Veratrum album)

Quantifying intraspecific demographic variation provides a powerful tool for exploring the diversity and evolution of life histories. We investigate how habitat-specific demographic variation and the production of multiple offspring types affect the population dynamics and evolution of delayed reproduction in a clonal perennial herb with monocarpic ramets (white hellebore). In this species, flowering ramets produce both seeds and asexual offspring. Data on ramet demography are used to parameterize integral projection models, which allow the effects of habitat-specific demographic variation and reproductive mode on population dynamics to be quantified. We then use the evolutionarily stable strategy (ESS) approach to predict the flowering strategy-the relationship between flowering probability and size. This approach is extended to allow offspring types to have different demographies and density-dependent responses. Our results demonstrate that the evolutionarily stable flowering strategies differ substantially among habitats and are in excellent agreement with the observed strategies. Reproductive mode, however, has little effect on the ESSs. Using analytical approximations, we show that flowering decisions are predominantly determined by the asymptotic size of individuals rather than variation in survival or size-fecundity relationships. We conclude that habitat is an important aspect of the selective environment and a significant factor in predicting the ESSs.     

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.     

Seed predators and the evolutionarily stable flowering strategy in the invasive plant, Carduus nutans

In plants where reproduction is fatal, seed-feeding insects may have a major impact on the evolutionarily stable reproductive strategy by altering fecundity schedules in a size-dependent manner. We explored this in Carduus nutans, a facultative biennial native to Europe, using two years of data from the South of France. An integral projection model based on detailed statistical models of the demography of Carduus nutans and characteristics of herbivore attack showed that seed predators select for smaller flowering size. An elasticity analysis showed that changes in the slope relating seed herbivore attack rates to plant total receptacle area had a large effect on lifetime reproductive success relative to most other plant demographic rates. Together, these two results indicate that in the absence of seed predators, as is the case in the exotic range of this invasive species, flowering size could evolve to be larger. Further analysis also showed that subsequent introduction of different species of seed-feeders as biocontrol agents could lead to different evolutionary outcomes dependent on the ecological characteristics of the seed-feeders, allowing the direction and magnitude of evolutionary change in flowering size to be predicted based on what seed predators have been introduced where and when. Such data would allow us to distinguish between the effect of seed predators and other hypotheses for size increase in the invasive habitat.     

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.     

Sexual conflict over floral receptivity

In flowering plants, the onset and duration of female receptivity vary among species. In several species the receptive structures wilt upon pollination. Here we explore the hypothesis that postpollination wilting may be influenced by pollen and serve as a general means to secure paternity of the pollen donor at the expense of female fitness. Taking a game-theoretical approach, we examine the potential for the evolution of a pollen-borne wilting substance, and for the coevolution of a defense strategy by the recipient plant. The model without defense predicts an evolutionarily stable strategy (ESS) for the production of wilting substance. The ESS value is highest when pollinator visiting rates are intermediate and when the probability that pollen from several donors arrives at the same time is low. This finding has general implications in that it shows that male traits to secure paternity also can evolve in species, such as plants, where mating is not strictly sequential. We further model coevolution of the wilting substance with the timing of stigma receptivity. We assume that pollen-receiving plants can reduce the costs induced by toxic pollen by delaying the onset of stigmatic receptivity. The model predicts a joint ESS, but no female counter-adaptation when the wilting substance is highly toxic. This indicates that toxicity affects the probability that a male manipulative trait stays beneficial (i.e., not countered by female defense) over evolutionary time. We discuss parallels to male induced changes in female receptivity known to occur in animals and the role of harm for the evolution of male manipulative adaptations.     

THE EVOLUTION OF STRATEGY VARIATION: WILL AN ESS EVOLVE?

Evolutionarily stable strategy (ESS) models are widely viewed as predicting the strategy of an individual that when monomorphic or nearly so prevents a mutant with any other strategy from entering the population. In fact, the prediction of some of these models is ambiguous when the predicted strategy is "mixed", as in the case of a sex ratio, which may be regarded as a mixture of the subtraits "produce a daughter" and "produce a son." Some models predict only that such a mixture be manifested by the population as a whole, that is, as an "evolutionarily stable state"; consequently, strategy monomorphism or polymorphism is consistent with the prediction. The hawk-dove game and the sex-ratio game in a panmictic population are models that make such a "degenerate" prediction. We show here that the incorporation of population finiteness into degenerate models has effects for and against the evolution of a monomorphism (an ESS) that are of equal order in the population size, so that no one effect can be said to predominate. Therefore, we used Monte Carlo simulations to determine the probability that a finite population evolves to an ESS as opposed to a polymorphism. We show that the probability that an ESS will evolve is generally much less than has been reported and that this probability depends on the population size, the type of competition among individuals, and the number of and distribution of strategies in the initial population. We also demonstrate how the strength of natural selection on strategies can increase as population size decreases. This inverse dependency underscores the incorrectness of Fisher's and Wright's assumption that there is just one qualitative relationship between population size and the intensity of natural selection.     

Compensatory responses of vital rates attenuate impacts of competition on population growth and promote coexistence

Competition is among the most important factors regulating plant population and community dynamics, but we know little about how different vital rates respond to competition and jointly determine population growth and species coexistence. We conducted a field experiment and parameterised integral projection models to model the population growth of 14 herbaceous plant species in the absence and presence of neighbours across an elevation gradient (284 interspecific pairs). We found that suppressed individual growth and seedling establishment contributed the most to competition-induced declines in population growth, although vital rate contributions varied greatly between species and with elevation. In contrast, size-specific survival and flowering probability and seed production were frequently enhanced under competition. These compensatory vital rate responses were nearly ubiquitous (occurred in 92% of species pairs) and significantly reduced niche overlap and stabilised coexistence. Our study highlights the importance of demographic processes for regulating population and community dynamics, which has often been neglected by classic coexistence theories.     

Effects of phenological constraints on sex allocation in cosexual monocarpic plants

The effects of two phenological constraints in resource investment to reproduction – resource limitation at the flowering stage and unpredictability of resources gained after flowering – on the resource allocation between male and female functions in monocarpic plants are considered using the ESS (evolutionarily stable strategy) approach. The model predicts that the sex allocation including the seed maturation stage has a female bias, when the quantity of reproductive resources available at flowering is small compared with that which is obtained after flowering, or when the cost of seed maturation relative to ovule production is low. The fluctuation of the quantity of resources available for seed maturation favors overproduction of ovules. As a result, more resources are allocated to female function and less to male function at flowering. The ESS allocation depends on the variability of resources and the cost of seed maturation relative to ovule production. The probability that total resource allocation has a female bias becomes higher than 0.5, and it depends on the cost of seed maturation relative to ovule production rather than resource variability. On the other hand, the probability that resource allocation has a female bias decreases with resource variability if we assume that the floral sex ratio is fixed. Future studies of plant sex allocation would profit by taking account of the phenological process of reproduction such as ovule production or seed maturation.     

Stability in an evolutionary game

A behavior or strategy which is evolutionarily stable must be both optimal and stable. The strategy must be optimal in that it maximizes the expected fitness of all the individuals using it. In addition, the strategy must be resistant to invasion by a mutant. The difference between the Nash solution of game theory and the ESS used in ecology is that the Nash solution only satisfies an optimality criterion and not an evolutionary stability criterion. We extend the ESS definition of Maynard Smith and Price so that it can be applied directly to two-strategy evolutionary games. The concept of a balanced game is introduced, and necessary conditions are derived which are similar to the Nash necessary conditions. The balanced game necessary conditions may be used for direct calculation of ESS candidates. These results are used to examine the optimal flowering time of an annual plant experiencing competition from neighboring plants. The plant competition model is general, and the results may be applied to a wide range of interference competition problems.     

Game theory and evolution: finite size and absolute fitness measures

This article is concerned with the characterization and existence of evolutionarily stable strategies (ESS) in Games against Nature, a class of models described by finite size populations and absolute fitness measures. We address these problems in terms of a new formalism which revolves around the concept evolutionary entropy, a measure of the diversity of options associated with a strategy pure - strategies have zero entropy, mixed strategies positive entropy. We invoke this formalism to show that ESS are characterized by extremal states of entropy. We illustrate this characterization of ESS by an analysis of the evolution of the sex ratio and the evolution of seed size.     

Within‐plant variation in reproductive investment: consequences for selection on flowering time

Variation among the leaves, flowers or fruit produced by a plant is often regarded as a nuisance to the experimenter and an impediment to selection. Here, we suggest that within‐plant variation can drive selection on other plant‐level traits. We examine within‐plant variation in floral sex allocation and in fruit set and predict that such variation generates variation in male success among plants, thereby driving selection on flowering time. We tested this prediction in a simulation model estimating selection on flowering time through male fitness when floral sex allocation and/or fruit set vary directionally among flowers on plants. We parameterized the model through a quantitative literature survey of within‐plant change in sex allocation. As predicted, within‐plant variation in floral sex allocation and in fruit set probability can generate selection on flowering time through male fitness. Declining fruit set from first to last flowers on plants, as occurs in many species, selected for early flowering onset through male fitness. This result was robust to self‐incompatibility and to varying returns on male versus female investment. Selection caused by declining fruit set was strong enough to reverse the selection for late flowering that can be caused by intrafloral protandry. Our model provides testable predictions regarding selection on flowering time through male fitness. The model also establishes the intriguing possibility that within‐plant variation may influence selection on other traits, regardless of whether that variation is under selection itself.     

Climate, size and flowering history determine flowering pattern of an orchid

The flowering pattern of plant species, including orchid species, may fluctuate irregularly. Several explanations are given in the literature to explain that pattern, including: costs associated with reproduction, herbivory effects, intrinsically triggered unpredictable variation of the system, and external conditions (i.e. weather). The influence of age is discussed, but is difficult to determine because relevant long-term field observations are generally absent in the literature. The influence of age, size, reproductive effort and climatic conditions on flowering variability of Himantoglossum hircinum are examined using data collected in a long-term project (1976–2001) in Germany. PCA and multiple regression analysis were used to analyse variability in flowering pattern over the years as a function of size and weather variability. We studied future size after flowering to quantify costs of reproduction. Flowering probability was strongly determined by plant size, while there was no significant influence of age class on flowering probability of the population. Costs associated with reproduction resulted in a decrease in plant size, causing reduced flowering probability of the plants in the following year. The weather explained about 50% of the yearly variation in the proportion of large plants and thus had an indirect, strong influence on the flowering percentage. We conclude that variability in flowering is caused mainly by the variability of weather conditions in the previous and current year, whereby reproductive effort causes further variability in flowering at the individual and, consequently, the population levels.  © 2006 The Linnean Society of London, Botanical Journal of the Linnean Society , 2006, 151 , 511–526.     

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 .     

Between-population variation in size-dependent reproduction and reproductive allocation in Pinguiculavulgaris (Lentibulariaceae) and its environmental correlates

Several important fitness components in herbaceous perennial plants are commonly related to plant size: flowering probability, reproductive allocation and fecundity. However, evidence for such size-dependence of fitness components is mostly anecdotal and unconnected to other life history traits. Here we report size-dependence for flowering probability and reproductive allocation in 11 populations of Pinguicula vulgaris and relate it to environmental factors. Flowering probability was size-dependent in all populations of P. vulgaris , and indicated the existence of a threshold size for reproduction. Populations at low altitudes and in wet soils showed a significantly higher threshold size for reproduction. Reproductive mass was also size-dependent in all populations. We found considerable between-population differences in the slope and the intercept of the regression between plant size and reproductive mass. This variation was weakly related to the environmental factors measured. In general, relationships between different size-dependent fitness components were low. Instead of showing a covariation of traits, in line with interpretations in terms of life history "tactics", P. vulgaris seemed to independently vary each size-dependent fitness component in each locality. In particular, no significant relationship was found between threshold size for reproduction and the slope of size-dependent reproductive allocation, as predicted by previous authors. Neither we found a significant influence of somatic cost of reproduction on size-dependent fitness components.