No abstract

We present a handy mechanistic functional response model that realistically incorporates handling (i.e., attacking and eating) and digesting prey. We briefly review current functional response theory and thereby demonstrate that such a model has been lacking so far. In our model, we treat digestion as a background process that does not prevent further foraging activities (i.e., searching and handling). Instead, we let the hunger level determine the probability that the predator searches for new prey. Additionally, our model takes into account time wasted through unsuccessful attacks. Since a main assumption of our model is that the predator's hunger is in a steady state, we term it the steady-state satiation (SSS) equation.The SSS equation yields a new formula for the asymptotic maximum predation rate (i.e., asymptotic maximum number of prey eaten per unit time, for prey density approaching infinity). According to this formula, maximum predation rate is determined not by the sum of the time spent for handling and digesting prey, but solely by the larger of these two terms. As a consequence, predators can be categorized into two types: handling-limited predators (where maximum predation rate is limited by handling time) and digestion-limited predators (where maximum predation rate is limited by digestion time). We give examples of both predator types. Based on available data, we suggest that most predators are digestion limited.The SSS equation is a conceptual mechanistic model. Two possible applications of this model are that (1) it can be used to calculate the effects of changing predator or prey characteristics (e.g., defenses) on predation rate and (2) optimal foraging models based on the SSS equation are testable alternatives to other approaches. This may improve optimal foraging theory, since one of its major problems has been the lack of alternative models.

The functional response of a consumer is the relationship between its consumption rate and the abundance of its food. A functional response is said to be of type I if consumption rate increases linearly with food abundance up to a threshold level at which it remains constant. According to conventional wisdom, such type I responses are more frequent among filter feeders than among other consumers. However, the validity of this claim has never been tested. We review 814 functional responses from 235 studies, thereby showing that type I responses are not only exceptionally frequent among filter feeders but that they have only been reported from these consumers. These findings can be understood by considering the conditions that a consumer must fulfil in order to show a type I response. First, the handling condition: the consumer must have a negligibly small handling time (i.e. the time needed for capturing and eating a food item), or it must be able to search for and to capture food while handling other food. Second, the satiation condition: unless its gut is completely filled and gut passage time is minimal, the consumer must search for food at a maximal rate with maximal effort. It thus has to spend much time on foraging (i.e. searching for food and handling it). Our functional response review suggests that only filter feeders sometimes meet both of these conditions. This suggestion is reasonable because filter feeders typically fulfil the handling condition and can meet the satiation condition without losing time, for they are, by contrast to non-filter feeders, able simultaneously to perform foraging and non-foraging activities, such as migration or reproduction.

An increasing number of studies demonstrate phenotypic and genetic changes in natural populations that are subject to climate change, and there is hope that some of these changes will contribute to avoiding species extinctions (‘evolutionary rescue’). Here, we review theoretical models of rapid evolution in quantitative traits that can shed light on the potential for adaptation to a changing climate. Our focus is on quantitative-genetic models with selection for a moving phenotypic optimum. We point out that there is no one-to-one relationship between the rate of adaptation and population survival, because the former depends on relative fitness and the latter on absolute fitness. Nevertheless, previous estimates that sustainable rates of genetically based change usually do not exceed 0.1 haldanes (i.e., phenotypic standard deviations per generation) are probably correct. Survival can be greatly facilitated by phenotypic plasticity, and heritable variation in plasticity can further speed up genetic evolution. Multivariate selection and genetic correlations are frequently assumed to constrain adaptation, but this is not necessarily the case and depends on the geometric relationship between the fitness landscape and the structure of genetic variation. Similar conclusions hold for adaptation to shifting spatial gradients. Recent models of adaptation in multispecies communities indicate that the potential for rapid evolution is strongly influenced by interspecific competition.

The large body of theory on speciation with gene flow has brought to light fundamental differences in the effects of two types of mating rules on speciation: preference/trait rules, in which divergence in both (female) preferences and (male) mating traits is necessary for assortment, and matching rules, in which individuals mate with like individuals on the basis of the presence of traits or alleles that they have in common. These rules can emerge from a variety of behavioral or other mechanisms in ways that are not always obvious. We discuss the theoretical properties of both types of rules and explain why speciation is generally thought to be more likely under matching rather than preference/trait rules. We furthermore discuss whether specific assortative mating mechanisms fall under a preference/trait or matching rule, present empirical evidence for these mechanisms, and propose empirical tests that could distinguish between them. The synthesis of the theoretical literature on these assortative mating rules with empirical studies of the mechanisms by which they act can provide important insights into the occurrence of speciation with gene flow. Finally, by providing a clear framework we hope to inspire greater alignment in the ways that both theoreticians and empiricists study mating rules and how these rules affect speciation through maintaining or eroding barriers to gene flow among closely related species or populations.

We present a handy mechanistic functional response model that realistically incorporates handling (i.e., attacking and eating) and digesting prey. We briefly review current functional response theory and thereby demonstrate that such a model has been lacking so far. In our model, we treat digestion as a background process that does not prevent further foraging activities (i.e., searching and handling). Instead, we let the hunger level determine the probability that the predator searches for new prey. Additionally, our model takes into account time wasted through unsuccessful attacks. Since a main assumption of our model is that the predator's hunger is in a steady state, we term it the steady state satiation (SSS) equation. The SSS equation yields a new formula for the asymptotic maximum predation rate (i.e., asymptotic maximum number of prey eaten per unit time, for prey density approaching infinity). According to this formula, maximum predation rate is determined not by the sum of the time spent for handling and digesting prey, but solely by the larger of these two terms. As a consequence, predators can be categorized into two types: handling‐limited predators (where maximum predation rate is limited by handling time) and digestion‐limited predators (where maximum predation rate is limited by digestion time). We give examples of both predator types. Based on available data, we suggest that most predators are digestion limited. The SSS equation is a conceptual mechanistic model. Two possible applications of this model are that (1) it can be used to calculate the effects of changing predator or prey characteristics (e.g., defenses) on predation rate and (2) optimal foraging models based on the SSS equation are testable alternatives to other approaches. This may improve optimal foraging theory, since one of its major problems has been the lack of alternative models.

No abstract

Adaptation lies at the heart of Darwinian evolution. Accordingly, numerous studies have tried to provide a formal framework for the description of the adaptive process. Of these, two complementary modeling approaches have emerged: While so-called adaptive-walk models consider adaptation from the successive fixation of de novo mutations only, quantitative genetic models assume that adaptation proceeds exclusively from preexisting standing genetic variation. The latter approach, however, has focused on short-term evolution of population means and variances rather than on the statistical properties of adaptive substitutions. Our aim is to combine these two approaches by describing the ecological and genetic factors that determine the genetic basis of adaptation from standing genetic variation in terms of the effect-size distribution of individual alleles. Specifically, we consider the evolution of a quantitative trait to a gradually changing environment. By means of analytical approximations, we derive the distribution of adaptive substitutions from standing genetic variation, that is, the distribution of the phenotypic effects of those alleles from the standing variation that become fixed during adaptation. Our results are checked against individual-based simulations. We find that, compared to adaptation from de novo mutations, (i) adaptation from standing variation proceeds by the fixation of more alleles of small effect and (ii) populations that adapt from standing genetic variation can traverse larger distances in phenotype space and, thus, have a higher potential for adaptation if the rate of environmental change is fast rather than slow.