Revisiting the “fallacy of averages” in ecology: Expected gain per unit time equals expected gain divided by expected time

Fitness is often defined as the average payoff an animal obtains when it is engaged in several activities, each taking some time. We point out that the average can be calculated with respect to either the time distribution, or to the event distribution of these activities. We show that these two averages lead to the same fitness function. We illustrate this result through two examples from foraging theory, Holling II functional response and the diet choice model, and one game-theoretic example of Hamilton’s rule applied to the time-constrained Prisoner’s dilemma (PD). In particular, we show that in these models, fitness defined as expected gain per unit time equals fitness defined as expected gain divided by expected time. We also show how these fitnesses predict the optimal outcome for diet choice and the prevalence of cooperation in the repeated PD game

The effect of fight cost structure on fighting behaviour

A common feature of animal populations is the stealing by animals of resources such as food from other animals. This has previously been the subject of a range of modelling approaches, one of which is the so called "producer-scrounger" model. In this model a producer finds a resource that takes some time to be consumed, and some time later a (generally) conspecific scrounger discovers the producer with its resource and potentially attempts to steal it. In this paper we consider a variant of this scenario where each individual can choose to invest an amount of energy into this contest, and the level of investment of each individual determines the probability of it winning the contest, but also the additional cost it has to bear. We analyse the model for a specific set of cost functions and maximum investment levels and show how the evolutionarily stable behaviour depends upon them. In particular we see that for high levels of maximum investment, the producer keeps the resource without a fight for concave cost functions, but for convex functions the scrounger obtains the resource (albeit at some cost)

Nonlinear and Multiplayer Evolutionary Games

Classical evolutionary game theory has typically considered populations within which randomly selected pairs of individuals play games against each other, and the resulting payoff functions are linear. These simple functions have led to a number of pleasing results for the dynamic theory, the static theory of evolutionarily stable strategies, and the relationship between them. We discuss such games, together with a basic introduction to evolutionary game theory, in Sect. 5.1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Sect. 5.2 we discuss various ways in which nonlinearity can appear in evolutionary games, including pairwise games with strategy-dependent interaction rates, and playing the field games, where payoffs depend upon the entire population composition, and not on individual games. In Sect. 5.3 we consider multiplayer games, where payoffs are the result of interactions between groups of size greater than two, which again leads to nonlinearity, and a breakdown of some of the classical results of Sect. 5.1. Finally in Sect. 5.4 we summarise and discuss the previous sections

Anti-predator defence and the complexity–stability relationship of food webs

The mechanism for maintaining complex food webs has been a central issue in ecology because theory often predicts that complexity (higher the species richness, more the interactions) destabilizes food webs. Although it has been proposed that prey anti-predator defence may affect the stability of prey–predator dynamics, such studies assumed a limited and relatively simpler variation in the food-web structure. Here, using mathematical models, I report that food-web flexibility arising from prey anti-predator defence enhances community-level stability (community persistence and robustness) in more complex systems and even changes the complexity–stability relationship. The model analysis shows that adaptive predator-specific defence enhances community-level stability under a wide range of food-web complexity levels and topologies, while generalized defence does not. Furthermore, while increasing food-web complexity has minor or negative effects on community-level stability in the absence of defence adaptation, or in the presence of generalized defence, in the presence of predator-specific defence, the connectance–stability relationship may become unimodal. Increasing species richness, in contrast, always lowers community-level stability. The emergence of a positive connectance–stability relationship however necessitates food-web compartmentalization, high defence efficiency and low defence cost, suggesting that it only occurs under a restricted condition

Intra-seasonal Strategies Based on Energy Budgets in a Dynamic Predator-Prey Game

We propose a game-theoretical model to describe intra-seasonal predator-prey interactions between predatory mites (Acari: Phytoseiidae) and prey mites (also called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees. Its parameters have been instantiated based on laboratory and field studies. The continuous-time dynamical model comprises predator and prey densities, along with corresponding energy levels, over the length of a season. It also includes time-dependent decision variables for the predator and the prey, representing the current portions of the predator and prey populations that are active, as opposed to diapausing (a state of physiological rest). Our aim is to find the optimal active/diapausing ratio during a season of interaction between predatory mites and prey mites: this is achieved by solving a dynamic game between predator and prey. We hereby extend our previous work that focused solely on the optimal strategy for the prey. Firstly, we analyze the optimal behavior of the prey. Secondly, we show that the optimal strategy for the predator is to stay active for the entire season. This result corresponds to biological observations

Predicting distributions of Wolbachia strains through host ecological contact—Who's manipulating whom?

Reproductive isolation in response to divergent selection is often mediated via third-party interactions. Under these conditions, speciation is inextricably linked to ecological context. We present a novel framework for understanding arthropod speciation as mediated by Wolbachia, a microbial endosymbiont capable of causing host cytoplasmic incompatibility (CI). We predict that sympatric host sister-species harbor paraphyletic Wolbachia strains that provide CI, while well-defined congeners in ecological contact and recently diverged noninteracting congeners are uninfected due to Wolbachia redundancy. We argue that Wolbachia provides an adaptive advantage when coupled with reduced hybrid fitness, facilitating assortative mating between co-occurring divergent phenotypes—the contact contingency hypothesis. To test this, we applied a predictive algorithm to empirical pollinating fig wasp data, achieving up to 91.60% accuracy. We further postulate that observed temporal decay of Wolbachia incidence results from adaptive host purging—adaptive decay hypothesis—but implementation failed to predict systematic patterns. We then account for post-zygotic offspring mortality during CI mating, modeling fitness clines across developmental resources—the fecundity trade-off hypothesis. This model regularly favored CI despite fecundity losses. We demonstrate that a rules-based algorithm accurately predicts Wolbachia infection status. This has implications among other systems where closely related sympatric species encounter adaptive disadvantage through hybridization