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When an opportunistic predator is looking for a given type of prey and encounters another one from different species, it tries to utilize this random opportunity. We characterize the optimal levels of this opportunism in the framework of stochastic models for the two prey-one predator case. We consider the spatial dispersal of preys and the optimal diet choice of predator as well. We show that when both preys have no handling time, the total opportunism provides maximal gain of energy for the predator. When handling times differ with prey, we find a conditional optimal behavior: for small density of both prey species the predator prefers the more valuable one and is entirely opportunistic. However, when the density of the more valuable prey is higher than that of the other species, then the predator prefers the first one and intentionally neglects the other. Furthermore, when the density of the less valuable prey is high and that of the other one is small, then predator will look for the less valuable prey and is therefore totally opportunistic. We demonstrate that prey preference is remunerative whenever the advantage of a proper prey preference is larger than the average cost of missed prey preference. We also propose a dynamics which explicitly contains two sides of shared predation: apparent mutualism and apparent competition, and we give conditions when the rare prey goes extinct.

## Summary

The paper deals with two bee species collecting nectar from two plant species. It is assumed that the nectar stock is reduced but not exhausted by the nectar collection, each individual's pay-off depends linearly on its own foraging strategy (i.e., on the probability of a visit to a plant species) and on the average strategies of both species. For the corresponding matrix game model, it is shown that evolutionary stability of a totally mixed equilibrium foraging strategy pair is only determined by the efficiency parameters of nectar collection. The latter parameters depend on morphological characteristics of all involved species, determined by the long-term evolutionary processes. The evolutionarily stable foraging strategy is locally asymptotically stable with respect to the corresponding replicator dynamics.

## Abstract

Functional responses measure the trophic interactions between species, taking into account the density and behavior of the interacting species. In predator-prey interactions, the prey preference of the predator and the antipredator behavior of the prey together determine the feeding rate of the predator and the survival rate of the prey. Consequently, the behavior dependent functional responses make it possible to establish dynamic ecological models providing insight, among others, into the coexistence of predator and prey species and the efficiency of agents in biological pest control. In this paper the derivation methods of functional responses are reviewed. Basically, there are three classes of such methods: heuristic, stochastic and deterministic ones. All of them can take account of the behavior of the predator and prey. There are three main stochastic methods for the derivation of functional responses: renewal theory, Markov chain and the Wald equality-based method. All these methods assume that during the foraging process the prey densities do not change, which provides a mathematical basis for heuristic derivation. There are two deterministic methods using differential equations. The first one also assumes that during the foraging process the prey densities do not change, while the second one does not use that assumption. These derivation methods are appropriate to handle the behavior dependent functional responses, which is essential in the derivation of ecological games, when the payoff of prey and predator depends on the strategies of the prey and predator at the same time.

Insect parasitoids have been widely studied, particularly due to their ecological implications through the study of the special relationships observed among this kind of species, as well as to their expression in mathematical models. However, there are still scarce studies on parasitoid relationships and their expression in more realistic mathematical models. The present work is aimed at deepening into competition relationships among parasitoids. Bearing this purpose in mind, the system shaped by two parasitoids was chosen: *Trichogramma brassicae* (idiobiont egg parasitoid) and *Chelonus oculator* (koinobiont egg-larval parasitoid). Both species compete against each other for the same host species (Lepidoptera). The results obtained in the laboratory point out that *T. brassicae* may be considered a better competitor than *Ch. oculator*. This is the result of the extrinsic competition due to the substances injected by the female during parasitization. However, our results show this classification into better and worse competitors inaccurate. Thus, these interspecific competition influences are detrimental to both parasitoid species. This is the first time that the effect of this competition is mentioned regarding parasitoid functional response. Our results and their ecological implications are reported and discussed.

Population dynamics models suggest that the over-all level of resource productivity plays an important role in community dynamics. One such factor of resource productivity is the quality of the host plant, which can determine the effectiveness of entomophagous (predatory and parasitoid) species by altering the growth rate of the phytophagous population via effects on fecundity, survival, and rate of development. These effects have been studied in relation to the distribution of host plants and their physiological state. However, few studies have considered the differences among plant cultivars. The objective of this study was to identify a continuous-time dynamic model, to describe the effects of different tomato cultivars on a one predatortwo prey model. The experiment was carried out under greenhouse conditions using ten tomato cultivars, with the predatory species *Nesidiocoris tenuis* (Reuter) (Insecta, Hemiptera, Miridae) and two prey species: the phytophagous species *Bemisia tabaci* (Gennadius) (Insecta, Hemiptera, Aleyrodidae) and the parasitoid species *Trichogramma achaeae* (Nagaraja & Nagarkatti) (Insecta, Hymenoptera, Trichogrammatidae); the latter was used as the intraguild-prey. Using the software SIMFIT, we found that a three-dimensional Lotka-Volterra type system could be well fitted to the data, estimating the phytophagous species´ growth rate, the parasitoid and predator mortality rates, the predation and parasitism rates, and the parasitoid emergence rate according to the cultivar type. The results showed an important effect of the host plant quality, by cultivar, on intraguild predation, resulting in important changes in the dynamics of phytophagous populations. These results are also discussed in relation to their importance in the biological control of pest species in greenhouse crops.

Cannibalism is a common phenomenon among insects. It has raised considerable interest both from a theoretical perspective and because of its importance in population dynamics in natural ecosystems. It could also play an important role from an applied perspective, especially when using predatory species in biological control programmes. The present paper aims to study the cannibalistic behaviour of *Nabis pseudoferus* Remane and the functional response of adult females. In a non-choice experiment, adult females showed clear acceptance of immature conspecifics as prey, with relatively high mortality values (51.89 ± 2.69%). These values were lower than those occurring for heterospecific prey, *Spodoptera exigua* Hübner, under the same conditions (80.00 ± 2.82%). However, the main result was that the rate of predation on heterospecific prey was reduced to 59.09 ± 7.08% in the presence of conspecific prey. The prey-capture behaviour of adult females differed when they hunted conspecific versus heterospecific prey. This was shown in the average handling time, which was 23.3 ± 3.3 min in the first case (conspecific) versus 16.6 ± 2.5 min in the second (heterospecific). Furthermore, the values increased in the former case and declined in the latter according to the order in which the prey were captured. The difference in handling time was not significant when adjusting the adult female functional response to conspecific nymphs. We argue that these results likely indicate risk aversion and a fear of reprisal among conspecifics.