Population management requires predictions of extinction risk based on a general understanding of these risks and on system-specific modelling. Life tables, available for numerous populations and species, permit calculating population growth and the construction of multi-type branching process models which predict population survivorship and ultimate extinction probabilities. We exemplify this approach and tailor it to an experimental model to predict extinction probabilities per unit of time. In age-structured populations, founders from different age classes lead to different predicted extinction probabilities. Age effects interact with environmental effects such as culling levels, which influence population growth rates. We assess the accuracy of predictions based on an age-structured matrix model, in an extinction experiment over an eight-week period on the springtail Folsomia candida, with crossed founder age and culling level treatments. Using parameter estimates from an accessory experiment, the fit of model predictions to observed extinction probabilities was generally good. A modified branching process model which allowed culling events between and at observations reduced prediction error. However, additionally maximizing the likelihood of observed extinction probabilities based on survival and fecundity parameters, or on a parameter which concentrated fecundity within a subinterval, did not significantly reduce prediction error according to the AICc. Our study shows that satisfactory predictions of establishment probabilities and of the initial persistence of small populations can be made using multi-type branching processes and available parameter estimates. Predictions can be improved by integrating knowledge of when events occur within intervals. This can be done without additional parameter estimation. ### Competing Interest Statement The authors have declared no competing interest.

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.

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.

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.

The evolutionary significance of introgression has been discussed for decades. Questions about potential impacts of transgene flow into wild and weedy populations brought renewed attention to the introgression of crop alleles into those populations. In the past two decades, the field has advanced with considerable descriptive, experimental, and theoretical activity on the dynamics of crop gene introgression and its consequences. As illustrated by five case studies employing an array of different approaches, introgression of crop alleles has occurred for a wide array of species, sometimes without significant consequence, but on occasion leading to the evolution of increased weediness. A new theoretical context has emerged for analyzing empirical data, identifying factors that influence introgression, and predicting introgression's progress. With emerging molecular techniques and analyses, research on crop allele introgression into wild and weedy populations is positioned to make contributions to both transgene risk assessment and reticulate evolution.

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.

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.

The floodplains of the West-African Sahel region have experienced extensive habitat transformation during the past four decades, coinciding with an impoverishment of raptor populations. We investigated foraging patterns of Palaearctic migratory Eurasian Marsh Harriers Circus aeruginosus, Pallid Harriers C.macrourus and Montagus Harriers C.pygargus on a floodplain system in northern Cameroon to assess species, sex- and age-related habitat preferences. Sex and age have rarely been incorporated into general studies of raptor habitat associations, despite clear evidence of intrasexual and age-related differences in foraging strategies and diet composition, potentially carrying strong conservation implications. We found evidence of sexual differences in foraging preference related to land use, particularly in the most sexually dimorphic Pallid Harrier, and evidence that juveniles used different habitats to adults. This constitutes the first quantitative documentation of such differentiation by Palaearctic raptors on African wintering grounds, indicating that general patterns of habitat use in wintering raptors may obscure sex- and age-specific preferences. Contrary to expectations, we found limited evidence for interspecific foraging segregation. Food partitioning by prey mass was related to harrier body mass and facilitated by a diverse availability of prey on human-transformed floodplains. Anticipated further large-scale conversion of floodplain habitat into predominantly desiccated grasslands raises concerns about the survival of wintering harriers.

Summary Serotiny, the retention of mature seeds in closed fruits within the canopy for over a year, is a common trait in fire‐prone environments. When competition with adult plants prevents seedling establishment between fire events and in the absence of post‐release soil seed dormancy, strong serotiny, i.e. the retention of all seeds until the next fire, appears as the best strategy. Despite the low levels of inter‐fire seed recruitment for several species in both Australian and South African fire‐prone environments, considerable variation in the duration of fruit retention is nevertheless observed among species. Our aim is to predict optimal age‐specific reproductive schedules in a perennial, serotinous species, when cone maintenance is costly. We focus on species where adults are killed by fire, without a soil seed‐bank. We explicitly consider a trade‐off between growth (which determines plant survival), seed production and seed maintenance. In our model recruitment relies upon fire events. We use dynamic programming to determine, for given fire regimes, the optimal pattern of resource allocation. We further study the effect of changes in fire regime on the viability of populations adapted to some historical fire regime. We find that, whenever maximal plant survival probability is low, the optimal strategy consists in reducing resource allocation to seed maintenance while increasing resource allocation to annual seed production. This illustrates a trade‐off between current and future reproduction. A low rather than a strong level of serotiny should evolve whenever the variance of fire intervals is large and the mean fire interval is low. Low levels of serotiny could constitute a bet‐hedging strategy with decreasing predictability of the arrival of fire. Once adapted to some historical fire regime, serotinous populations are highly sensitive to a change in mean fire frequency and to an increase in the variance of fire intervals. Populations adapted to a historically high level of variance in fire return are more robust to changes in fire regime. Synthesis: Life‐history trade‐offs and low predictability of fire intervals may favour low rather than strong levels of serotiny even when recruitment essentially occurs just after fire events.

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.

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.

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.

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.

This chapter contains section titled: Introduction Patch Depletion by a Single Female: the Marginal Value Theorem (MVT) Competitive Patch Depletion without Superparasitism Competitive patch Depletion with Superparasitism Discussion Acknowledgments References

Chapter 18 Statistical Tools for Analyzing Data on Behavioral Ecology of Insect Parasitoids Éric Wajnberg, Éric WajnbergSearch for more papers by this authorPatsy Haccou, Patsy HaccouSearch for more papers by this author Éric Wajnberg, Éric WajnbergSearch for more papers by this authorPatsy Haccou, Patsy HaccouSearch for more papers by this author Book Editor(s):Éric Wajnberg, Éric WajnbergSearch for more papers by this authorCarlos Bernstein, Carlos BernsteinSearch for more papers by this authorJacques van Alphen, Jacques van AlphenSearch for more papers by this author First published: 07 April 2008 https://doi.org/10.1002/9780470696200.ch18Citations: 12 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Summary This chapter contains section titled: Introduction An Introduction to Generalized Linear Models (GLMs) Non-Independent data Pseudoreplication Unbalanced Set-Ups Conclusion References Citing Literature Behavioral Ecology of Insect Parasitoids: From Theoretical Approaches to Field Applications RelatedInformation

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.