Establishment versus population growth in spatio-temporally varying environments.

We consider situations where repeated invasion attempts occur from a source population into a receptor population over extended periods of time. The receptor population contains two locations that provide different expected offspring numbers to invaders. There is demographic stochasticity in offspring numbers. In addition, temporal variation causes local invader fitnesses to vary. We show that effects of environmental autocorrelation on establishment success depend on spatial covariance of the receptor subpopulations. In situations with a low spatial covariance this effect is positive, whereas high spatial covariance and/or high migration probabilities between the subpopulations causes the effect to be negative. This result reconciles seemingly contradictory results from the literature concerning effects of temporal variation on population dynamics with demographic stochasticity. We study an example in the context of genetic introgression, where invasions of cultivar plant genes occur through pollen flow from a source population into wild-type receptor populations, but our results have implications in a wider range of contexts, such as the spread of exotic species, metapopulation dynamics and epidemics.

High-Resolution Gene Flow Model for Assessing Environmental Impacts of Transgene Escape Based on Biological Parameters and Wind Speed.

Environmental impacts caused by transgene flow from genetically engineered (GE) crops to their wild relatives mediated by pollination are longstanding biosafety concerns worldwide. Mathematical modeling provides a useful tool for estimating frequencies of pollen-mediated gene flow (PMGF) that are critical for assessing such environmental impacts. However, most PMGF models are impractical for this purpose because their parameterization requires actual data from field experiments. In addition, most of these models are usually too general and ignored the important biological characteristics of concerned plant species; and therefore cannot provide accurate prediction for PMGF frequencies. It is necessary to develop more accurate PMGF models based on biological and climatic parameters that can be easily measured in situ. Here, we present a quasi-mechanistic PMGF model that only requires the input of biological and wind speed parameters without actual data from field experiments. Validation of the quasi-mechanistic model based on five sets of published data from field experiments showed significant correlations between the model-simulated and field experimental-generated PMGF frequencies. These results suggest accurate prediction for PMGF frequencies using this model, provided that the necessary biological parameters and wind speed data are available. This model can largely facilitate the assessment and management of environmental impacts caused by transgene flow, such as determining transgene flow frequencies at a particular spatial distance, and establishing spatial isolation between a GE crop and its coexisting non-GE counterparts and wild relatives.

Quantifying stochastic introgression processes in random environments with hazard rates.

Introgression is the permanent incorporation of genes from the genome of one population into another. Previous studies have found that stochasticity in number of offspring, hybridisation, and environment are important aspects of introgression risk, but these factors have been studied separately. In this paper we extend the use of the hazard rate which we previously used to study effects of demographic stochasticity with repeated invasion attempts, to incorporate temporal environmental stochasticity. We find that introgression risk varies much in time, and in some periods it can be much enhanced in such environments. Furthermore, effects of plant life history parameters, such as flowering and survival probabilities, on hazard rates depend on characteristics of the environmental variation.

Repeated triggering of sporulation in Bacillus subtilis selects against a protein that affects the timing of cell division.

Bacillus subtilis sporulation is a last-resort phenotypical adaptation in response to starvation. The regulatory network underlying this developmental pathway has been studied extensively. However, how sporulation initiation is concerted in relation to the environmental nutrient availability is poorly understood. In a fed-batch fermentation set-up, in which sporulation of ultraviolet (UV)-mutagenized B. subtilis is repeatedly triggered by periods of starvation, fitter strains with mutated tagE evolved. These mutants display altered timing of phenotypical differentiation. The substrate for the wall teichoic acid (WTA)-modifying enzyme TagE, UDP-glucose, has recently been shown to be an intracellular proxy for nutrient availability, and influences the timing of cell division. Here we suggest that UDP-glucose also influences timing of cellular differentiation.

Quantifying introgression risk with realistic population genetics.

Introgression is the permanent incorporation of genes from the genome of one population into another. This can have severe consequences, such as extinction of endemic species, or the spread of transgenes. Quantification of the risk of introgression is an important component of genetically modified crop regulation. Most theoretical introgression studies aimed at such quantification disregard one or more of the most important factors concerning introgression: realistic genetical mechanisms, repeated invasions and stochasticity. In addition, the use of linkage as a risk mitigation strategy has not been studied properly yet with genetic introgression models. Current genetic introgression studies fail to take repeated invasions and demographic stochasticity into account properly, and use incorrect measures of introgression risk that can be manipulated by arbitrary choices. In this study, we present proper methods for risk quantification that overcome these difficulties. We generalize a probabilistic risk measure, the so-called hazard rate of introgression, for application to introgression models with complex genetics and small natural population sizes. We illustrate the method by studying the effects of linkage and recombination on transgene introgression risk at different population sizes.

Quantifying time-inhomogeneous stochastic introgression processes with hazard rates.

Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It is currently of particular concern as a possible mechanism for the spread of modified crop genes to wild populations. The hazard rate is the probability per time unit that such an escape takes place, given that it has not happened before. It is a quantitative measure of introgression risk that takes the stochastic elements inherent in introgression processes into account. We present a methodology to calculate the hazard rate for situations with time-varying gene flow from a crop to a large recipient wild population. As an illustration, several types of time-inhomogeneity are examined, including deterministic periodicity as well as random variation. Furthermore, we examine the effects of an extended fitness bottleneck of hybrids and backcrosses in combination with time-varying gene flow. It is found that bottlenecks decrease the hazard rate, but also slow down and delay its changes in reaction to changes in gene flow. Furthermore, we find that random variation in gene flow generates a lower hazard rate than analogous deterministic variation. We discuss the implications of our findings for crop management and introgression risk assessment.

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.

Stochasticity in the adaptive dynamics of evolution: the bare bones.

First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics.

Quantifying stochastic introgression processes with hazard rates.

Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It can have large environmental consequences, such as the spread of insecticide or herbicide resistant genes, the escape of transgenes from genetically modified crops, and the invasion of exotic genes into new habitats. Introgression usually involves strong random components, such as rare hybridization and backcrossing events, and demographic variation in reproduction and survival. Most introgression studies ignore these random effects, and consequently fail to accurately assess the risk of introgression. This paper presents a methodology for quantifying stochastic introgression processes, based on multitype branching process models. We derive a quantity called the hazard rate, which can be used to investigate how the risk of introgression depends on crop management and life history.

Evolution of cannibalism and female's response to oviposition-deterring pheromone in aphidophagous predators.

1. Egg cannibalism by larvae is common in Coccinellidae and is known to be advantageous for the cannibals. Furthermore, larvae of aphidophagous ladybirds usually produce an oviposition-deterring pheromone (ODP), which inhibits oviposition by adult females. It has been proposed that the response to ODP has evolved because of the high costs of cannibalism. However, this has never been formally proved. 2. In this paper, we study the theoretical evolution of this system. We first look at the conditions under which cannibalism and the response to ODP can evolve. Subsequently, we examine the occurrence of polymorphism both in the production of larval tracks and in the sensitivity of females to specific pheromones. 3. The models predict that the amount of cannibalism should not depend on prey density and that evolution should lead to a continuous increase in cannibalism, and consequently larvae should always cannibalize eggs when possible. In response to the cost of cannibalism, ODP recognition can evolve, so that females avoid laying eggs in patches of prey already occupied by conspecific larvae. The result is an arms race between larvae and adult females, which favours a diversification of ODP pheromones. Our models show that: (i) females should be able to recognize mixtures of hydrocarbons rather than a single molecule; and (ii) females should be more sensitive to the tracks of their own offspring than those of non-related larvae.

Introgression of resistance genes between populations: a model study of insecticide resistance in Bemisia tabaci.

Introgression is a key process in conservation biology, genetic modification of (crop) species and in the evolutionary ecology of many species. Here we consider the case of introgression of insecticide resistance in the whitefly, Bemisia tabaci. B. tabaci is a species complex consisting of a range of biotypes, known to have a high degree of inter-biotype reproductive isolation. In areas where insecticide resistant and susceptible biotypes of B. tabaci coexist, introgression of the resistance gene will have considerable consequences for whitefly control. Using a stochastic branching process model we calculate the relative importance of life-history traits in determining the probability of introgression given that a hybridization event has occurred. We show that a fitness cost expressed through the average number of eggs laid, has the largest effect on the introgression probability as compared to fitness costs expressed through other life-history parameters. These results change when we consider a reproductive isolation mechanism, for which we show that the fitness cost expressed through the male survival and mating probability have the largest effect on the probability of introgression.

Dynamics of escape mutants.

We use multi-type Galton-Watson branching processes to model the evolution of populations that, due to a small reproductive ratio of the individuals, are doomed to extinction. Yet, mutations occurring during the reproduction process, may lead to the appearance of new types of individuals that are able to escape extinction. We provide examples of such populations in medical, biological and environmental contexts and give results on (i) the probability of escape/extinction, (ii) the distribution of the waiting time to produce the first individual whose lineage does not get extinct and (iii) the distribution of the time it takes for the number of mutants to reach a high level. Special attention is dedicated to the case where the probability of mutation is very small and approximations for (i)-(iii) are derived.

Optimal conservation strategy in fluctuating environments with species interactions: resource-enhancement of the native species versus extermination of the alien species.

Alien species are often a major threat to native species. We consider optimal conservation strategies for a population whose viability is affected both by an alien species (such as a competitor, a predator, or a pathogen) and by random fluctuations of the environment (e.g. precipitation, temperature). We assume that the survivorship of the native population can be improved by providing resources such as food and shelter, and also by an extermination effort that decreases the abundance of the alien species. These efforts decrease the extinction probability of the native population, but they are accompanied by economic costs. We search for the optimal strategy that minimizes the weighted sum of the extinction probability and the economic costs over a single year. We derive conditions under which investment should be made in both resource-enhancement and extermination, and examine how the optimal effort levels change with parameters. When the optimal strategy includes both types of efforts, the optimal extermination effort level turns out to be independent of the density and economic value of the native species, or the variance of the environmental fluctuation. Furthermore, the optimal resource-enhancement effort is then independent of the density of the alien species. However, the parameter dependencies greatly change if one of the efforts becomes zero. We also examine the situation in which the impact of the alien species is uncertain. The optimal extermination effort increases with the uncertainty of this impact except when the cost of extermination is very high.

The effect of autocorrelation in environmental variability on the persistence of populations: an experimental test.

Despite its significance regarding the conservation and management of biological resources, the body of theory predicting that the correlation between successive environmental states can profoundly influence extinction has not been empirically validated. Identical clonal populations from a model experimental system based on the collembolan Folsomia candida were used in the present study to investigate the effect of environmental autocorrelation on time to extinction. Environmental variation was imposed by variable implementation (present/absent) of a culling procedure according to treatments that represented six patterns of environmental autocorrelation. The average number of culling events was held constant across treatments but, as environmental autocorrelation increased, longer runs of both favourable and unfavourable culling tended to occur. While no difference was found among the survival functions for the various treatments, the time taken for 50% of the component populations to become extinct decreased significantly with increasing environmental autocorrelation. Similarly, analysis of all extinct populations demonstrated that time to extinction was shortened as environmental autocorrelation increased. However, this acceleration of extinction can be fully offset if sequential introduction is used in place of simultaneous introduction when founding the populations.

Multiple-year optimization of conservation effort and monitoring effort for a fluctuating population.

We consider optimal conservation strategies for an endangered population. We assume that juvenile survival is affected by unpredictable environmental fluctuation and can be improved by costly conservation effort. The initial population size is not accurately known at the time that the conservation effort level is chosen, but the uncertainty of its estimate can be reduced by a costly monitoring effort. In a previous paper, we analysed the optimal management strategy that minimizes a weighted sum of extinction probability and economic costs when only a single year is considered. Here we examine the case in which the conservation period lasts for several years by dynamic programming with incompletely observed process states. We study the optimal levels of the conservation and the monitoring efforts, and their dependence on the length of the conservation period and other parameters. The main conclusions are: (1) The optimal conservation effort in the first year depends on the accuracy of the information on the population size in the first year, but is almost independent of the accuracy of the information in later years. (2) When the risk of population extinction is small, the optimal conservation effort increases with the uncertainty of the population size. In contrast when the population is endangered, the optimal conservation effort decreases with the uncertainty of the population size. (3) The optimal conservation and monitoring efforts both increase with the length of the conservation period, provided that the population is relatively safe. However, if the population is endangered, both types of effort become smaller when the conservation period increases.

Learning and colonization of new niches: a first step toward speciation.

Learning processes potentially play a role in speciation but are often ignored in speciation models. Learning may, for instance, play a role when a new niche is being colonized, because the learning of niche features may cause niche-specific assortative mating and a tendency to produce young in this niche. Several animal species learn about their environmental features that may be important in finding or attracting mates. We use a gene-culture coevolutionary model to look into the effect of such learning on the colonization of new niches and on the genetic divergence between groups using different niches, which are steps necessary in achieving speciation. We assume that density is regulated separately in each of the two niches and that the viability of an individual depends on its genotype as well as on which niche it exploits. Our results show that genetic adaptation to the new niche is enhanced by a high female fecundity and a low viability selection against heterozygotes. Furthermore, when initial colonization (without genetic adaptation) fails, genetic divergence is more difficult when the mating preference is stronger. In contrast, when colonization without genetic adaptation is successful, a stronger mating preference makes genetic divergence easier. An increase in the number of egg-laying mistakes by females can have a positive or negative effect on the success of genetic adaptation depending on other parameters. We show that genetic divergence can be prevented by a niche shift, which can occur only if viabilities in the two niches are asymmetrical.

Modes of reproduction and the accumulation of deleterious mutations with multiplicative fitness effects.

Mutational load depends not only on the number and nature of mutations but also on the reproductive mode. Traditionally, only a few specific reproductive modes are considered in the search of explanations for the maintenance of sex. There are, however, many alternatives. Including these may give radically different conclusions. The theory on deterministic deleterious mutations states that in large populations segregation and recombination may lead to a lower load of deleterious mutations, provided that there are synergistic interactions. Empirical research suggests that effects of deleterious mutations are often multiplicative. Such situations have largely been ignored in the literature, since recombination and segregation have no effect on mutation load in the absence of epistasis. However, this is true only when clonal reproduction and sexual reproduction with equal male and female ploidy are considered. We consider several alternative reproductive modes that are all known to occur in insects: arrhenotoky, paternal genome elimination, apomictic thelytoky, and automictic thelytoky with different cytological mechanisms to restore diploidy. We give a method that is based on probability-generating functions, which provides analytical and numerical results on the distributions of deleterious mutations. Using this, we show that segregation and recombination do make a difference. Furthermore, we prove that a modified form of Haldane's principle holds more generally for thelytokous reproduction. We discuss the implications of our results for evolutionary transitions between different reproductive modes in insects. Since the strength of Muller's ratchet is reduced considerably for several forms of automictic thelytoky, many of our results are expected to be also valid for initially small populations.

Establishment success and extinction risk in autocorrelated environments.

We consider establishment success (and extinction risk of small populations) in fluctuating environments, by means of an inhomogeneous branching process model. In this model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period individuals reproduce independently and have random numbers of offspring. Expected numbers of offspring vary over reproduction periods due to random environmental changes. Previous simulation results indicated that there is a positive autocorrelation between the establishment probabilities of invaders in successive reproduction periods when environmental states are independently distributed. This result was never formally proved. In this paper we prove that this is indeed true, regardless of the form of the distribution of environmental states or the offspring distribution (under a monotonicity condition, which holds for biologically realistic models). Furthermore, we prove that it is also true for positively autocorrelated environmental states. We show by a counterexample that in environments with a strong negative autocorrelation establishment probabilities can be negatively autocorrelated. This was further examined through simulations. Our results imply that in independent, positively autocorrelated and weakly negatively autocorrelated environments the probability of success of invasion in different independently varying sites is the highest, followed by sequential invasion. For environments with a strong negative autocorrelation, sequential invasion has the highest probability of success. Effects of autocorrelation were further examined with simulations. From the results it appears that the expected length of 'runs of bad luck' is the most crucial factor for establishment success.

Patch leaving strategies and superparasitism: an asymmetric generalized war of attrition.

When several competitors deplete a patch, it can be advantageous for each of them to stay provided that others leave, whereas, on the other hand, staying longer decreases the expected payoff for everyone. This situation can be considered as a generalized war of attrition. Previous studies have shown that optimal patch leaving strategies become stochastic and the expected leaving time is much larger than predicted by the marginal value theorem when competitors interfere. The possibility of superparasitism, as occurs for example in parasitoids, induces such interference. In addition, it gives several complications. First, the payoff of females that have left the patch is affected by the ovipositions of the remaining individuals. Second, differences in the arrival time of females cause payoff-relevant asymmetries, since females that arrived early on have parasitized more hosts in a patch at the moment superparasitism starts than those that arrived later. We show that this can be modelled as an asymmetric generalized war of attrition, and derive global characteristics of the ESS for simultaneous decisions on when to start superparasitism and when to leave a patch.

Conservation effort and assessment of population size in fluctuating environments.

We consider optimal conservation strategies for endangered populations. We assume that the survival of the population is affected by unpredictable environmental fluctuation and can be improved by conservation effort. Furthermore, the exact value of the initial population size is assumed to be unknown. The conservation strategy involves two aspects: investment of assessment effort, to improve the estimate of the initial population size and investment of conservation effort. Both types of effort imply economic costs. The optimal management strategy is assumed to minimize the weighted sum of extinction probability and the economic cost of the conservation and the assessment effort. (1) We first analyse the optimal conservation effort when the current population size is known accurately. (2) Next, we consider the situation in which there is limited information (i.e. a cue) on population size. (3) We subsequently discuss the cases where the cue accuracy can be improved by assessment of the population. We study the optimal level of the assessment effort and discuss its dependence on various parameters.