Fluctuating natural selection accounts for the evolution of diversification bet hedging

Natural environments are characterized by unpredictability over all time scales. This stochasticity is expected on theoretical grounds to result in the evolution of ‘bet-hedging’ traits that maximize the long term, or geometric mean fitness even though such traits do not maximize fitness over shorter time scales. The geometric mean principle is thus central to our interpretation of optimality and adaptation; however, quantitative empirical support for bet hedging is lacking. Here, I report a quantitative test using the timing of seed germination—a model diversification bet-hedging trait—in Lobelia inflata under field conditions. In a phenotypic manipulation study, I find the magnitude of fluctuating selection acting on seed germination timing—across 70 intervals throughout five seasons—to be extreme: fitness functions for survival are complex and multimodal within seasons and significantly dissimilar among seasons. I confirm that the observed magnitude of fluctuating selection is sufficient to account for the degree of diversification behaviour characteristic of individuals of this species. The geometric mean principle has been known to economic theory for over two centuries; this study now provides a quantitative test of optimality of a bet-hedging trait in nature.     

Experimental evolution of bet hedging under manipulated environmental uncertainty in Neurospora crassa

All organisms are faced with environmental uncertainty. Bet-hedging theory expects unpredictable selection to result in the evolution of traits that maximize the geometric-mean fitness even though such traits appear to be detrimental over the shorter term. Despite the centrality of fitness measures to evolutionary analysis, no direct test of the geometric-mean fitness principle exists. Here, we directly distinguish between predictions of competing fitness maximization principles by testing Cohen''s 1966 classic bet-hedging model using the fungus Neurospora crassa. The simple prediction is that propagule dormancy will evolve in proportion to the frequency of ‘bad’ years, whereas the prediction of the alternative arithmetic-mean principle is the evolution of zero dormancy as long as the expectation of a bad year is less than 0.5. Ascospore dormancy fraction in N. crassa was allowed to evolve under five experimental selection regimes that differed in the frequency of unpredictable ‘bad years’. Results were consistent with bet-hedging theory: final dormancy fraction in 12 genetic lineages across 88 independently evolving samples was proportional to the frequency of bad years, and evolved both upwards and downwards as predicted from a range of starting dormancy fractions. These findings suggest that selection results in adaptation to variable rather than to expected environments.     

The role of migration in the evolution of phenotypic switching

Stochastic switching is an example of phenotypic bet hedging, where an individual can switch between different phenotypic states in a fluctuating environment. Although the evolution of stochastic switching has been studied when the environment varies temporally, there has been little theoretical work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here, we explore the interaction of temporal and spatial change in determining the evolutionary dynamics of phenotypic switching. We find that spatial variation in selection is important; when selection pressures are similar across space, migration can decrease the rate of switching, but when selection pressures differ spatially, increasing migration between demes can facilitate the evolution of higher rates of switching. These results may help explain the diverse array of non-genetic contributions to phenotypic variability and phenotypic inheritance observed in both wild and experimental populations.     

Effects of parental survival on clutch size decisions in fluctuating environments

Whereas in constant environments parental survival has no effect on optimal clutch size in the absence of trade-offs between juvenile and parental survival, the situation is drastically different in fluctuating environments. We consider a model in which, with respect to reproduction, parents and offspring are equivalent at the start of the next breeding season. When generations are non-overlapping, the clutch size maximizing geometric mean surviving number of offspring is optimal among all pure clutch size strategies. We prove that, as parental survival increases relative to that of the offspring, the optimal clutch size converges to the arithmetic mean maximizing clutch size (the so-called ‘Lack clutch size’). We also give a numerical procedure for calculating optimal mixed strategies and we show that, as environmental variance increases and/or parental survival decreases, mixed rather than pure strategies become optimal. Furthermore, we explain how to estimate fitness from empirical data under the assumptions of our model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Implicit frequency dependence and kin selection in fluctuating environments

Summary I consider a general model of a fluctuating environment in which the environmental state each year is drawn at random from some given distribution. Each year organisms must choose what action to perform before the environmental state for that year is known. There is no interaction with kin. In this scenario, natural selection will tend to produce organisms which maximize their geometric mean fitness. In this paper I introduce the idea of the profile of a strategy. This function quantifies how the strategy peforms for each environmental state. I show that there is a unique profile such that a strategy is optimal if and only if it has this profile. I then give a characterization of the optimal profile which generalizes previous work by others in this area. The characterization of the optimal profile has a game theoretical interpretation. Motivated by this I introduce a game in which individuals play the field in a constant environment. This game may be interpreted as a cooperative game between kin. The key result of this paper shows that a strategy maximizes geometric mean fitness in the original fluctuating environment problem if and only if it is an evolutionarily stable strategy of the deterministic environment game. It is well known that an optimal strategy in a fluctuating environment may be mixed, involving adaptive coin-flipping. Others have previously noted that this may result in some individuals sacrificing individual reproductive success for the good of the genotype. My analysis shows that one may regain the concept of individual optimization if the quantity maximized is suitably defined. Under an optimal strategy every action taken maximizes the expected number of offspring produced, where this expectation is not calculated using the true distribution of environmental states, but a distribution modified to take account of the actions of kin.     

SPERM‐LIMITED FECUNDITY IN NEMATODES: HOW MANY SPERM ARE ENOUGH?

The Bateman principle, which holds that oocytes are the limiting gamete in reproduction, is violated in a variety of species. Self-fertilizing hermaphrodites of the nematode Caenorhabditis elegans provide an example of a system in which sperm number limits lifetime reproductive output, in this species due to the protandrous nature of sperm production that in turn delays the onset of fertilization. This reproductive delay forms the basis of a trade-off between generation time and total fecundity, in which sperm number plays a pivotal role. I use an age-structured population model to describe the number of sperm that maximize fitness, given larval development time and rates of gamete production. The model predicts the evolution of sperm numbers that are consistent with empirical data for C. elegans provided that precocious larval sperm production is taken into account. Several testable hypotheses follow from the model regarding how natural selection and environmental variation may influence patterns of sperm production among populations or species with a similar mode of reproduction.     

A liquid-based method for the assessment of bacterial pathogenicity using the nematode Caenorhabditis elegans

Caenorhabditis elegans has previously been used as an alternative to mammalian models of infection with bacterial pathogens. We have developed a liquid-based assay to measure the effect of bacteria on the feeding ability of C. elegans. Using this assay we have shown that Pseudomonas aeruginosa strain PA14, Burkholderia pseudomallei and Yersinia pestis were able to inhibit feeding of C. elegans strain N2. An increase in sensitivity of the assay was achieved by using C. elegans mutant phm-2, in place of the wild-type strain. Using this assay,P. aeruginosa PA01 inhibited the feeding of C. elegans mutant phm-2. Such liquid-based feeding assays are ideally suited to the high-throughput screening of mutants of bacterial pathogens.     

Phenotypic plasticity in fluctuating environments: consequences of the lack of individual optimization

I consider the problem of characterizing the optimal plasticresponse when there are large-scale fluctuations in the environmentaffecting all population members. Individuals differ in theirstate, and each makes a reproductive decision before the environmentalconditions are known. An individual's state, its decision, andenvironmental conditions together determine the number of descendantsleft at the next decision epoch. I restrict attention to thesimple problem in which the state of the descendants left atthis epoch does not depend on these three factors. Because theenvironment is fluctuating, there is no individual optimization;instead the best action in one state implicitly depends on thebest action in other states. I characterize an optimal state-dependentstrategy, give a method of computation, and show how behaviorof each individual following the optimal strategy may be reinterpretedas a form of "individual optimization." Concepts are illustratedwith an example of optimal dutch size as a function of territoryquality.     

Bet hedging or not? A guide to proper classification of microbial survival strategies

Bacteria have developed an impressive ability to survive and propagate in highly diverse and changing environments by evolving phenotypic heterogeneity. Phenotypic heterogeneity ensures that a subpopulation is well prepared for environmental changes. The expression bet hedging is commonly (but often incorrectly) used by molecular biologists to describe any observed phenotypic heterogeneity. In evolutionary biology, however, bet hedging denotes a risk-spreading strategy displayed by isogenic populations that evolved in unpredictably changing environments. Opposed to other survival strategies, bet hedging evolves because the selection environment changes and favours different phenotypes at different times. Consequently, in bet hedging populations all phenotypes perform differently well at any time, depending on the selection pressures present. Moreover, bet hedging is the only strategy in which temporal variance of offspring numbers per individual is minimized. Our paper aims to provide a guide for the correct use of the term bet hedging in molecular biology.