A general version of optimal foraging theory: The effect of simultaneous encounters

Optimal foraging theory is extended so as to treat cases where a choice between several options is required. A new version of optimal foraging theory is derived under this assumption of simultaneous encounters of prey species and proved by using a set-theoretic approach. On the basis of this new version, it is demonstrated that, in general, no unique ranking of food types can be specified only from knowledge of the intrinsic properties of the food types. It is demonstrated that a food type may become less frequent in the diet as a result of becoming more abundant in the environment; that an increase in the abundance of a food type represented in the diet may have the effect that new food types enter the diet; and that an increase in the overall food abundance may imply that new types are included and/or old ones are excluded.     

Seasonality, optimal foraging, and prey coexistence

Several empirical studies suggest that herbivores may promote coexistence between plants by relaxing the strength of resource competition. In contrast, recent mathematical models predict that food-limited herbivory instead cause exclusion through apparent competition, regardless of whether herbivore selectivity is constant or density dependent. This study extends existing theory to consider a strongly seasonal system. Herbivores with fixed diet preferences have the same effect regardless of seasonality, but there is a marked difference when the diet selectivity of herbivores conforms to a simple optimal-foraging model. An optimally foraging herbivore in a seasonal environment is able to promote plant coexistence among many species. The mechanism involves diet switching, occurring over narrow density intervals. For this to have an effect in a nonseasonal model, equilibrium resource densities must be in this interval, which requires close parameter fitting. In seasonal environments, resource densities change through the year and may frequently move across narrow regions in which diet changes occur. The potential of gray-sided voles to promote coexistence between two arctic dwarf shrubs is evaluated in terms of the model. For this system, it is shown that vole herbivory has the potential to reverse competitive dominance.     

The optimal foraging theory, crowding and Swedish grouse hunters

Hunters that have options to hunt in different areas should evaluate their previous hunting success when they decide where to hunt. Following optimal foraging theory for non-human predators, we investigated if hunting success and density of other hunters on the hunting area will affect the probability of return to the same area, and if such behavioural changes will result in a higher hunting success compared to hunters that change to a new area. For this purpose, we used detailed information about willow grouse (Lagopus lagopus) hunters on state-owned land in Sweden. We found support for the optimal foraging theory application on grouse hunters’ behavioural changes according to hunting success. The return rate increased with increasing hunting success, and hunters that returned to the same area also increased their success compared to hunters that changed to a new area. Only one third of the hunters returned to the same area the subsequent year. We also found a negative effect of density of hunters in an area on hunters’ return rates and their hunting success, suggesting crowding among Swedish grouse hunters.     

Visual perception and social foraging in birds

Birds gather information about their environment mainly through vision by scanning their surroundings. Many prevalent models of social foraging assume that foraging and scanning are mutually exclusive. Although this assumption is valid for birds with narrow visual fields, these models have also been applied to species with wide fields. In fact, available models do not make precise predictions for birds with large visual fields, in which the head-up, head-down dichotomy is not accurate and, moreover, do not consider the effects of detection distance and limited attention. Studies of how different types of visual information are acquired as a function of body posture and of how information flows within flocks offer new insights into the costs and benefits of living in groups.     

Age-specific optimal diets and optimal foraging tactics: A life-historic approach

By linking optimal foraging theory and optimal life history theory, we demonstrate that optimal diets, in general, may depend on the individual's age even when everything else remains the same. Older individuals (i.e., individuals with lower reproductive values) are predicted to have diets composed of highly nutritious food types that are possibly dangerous to pursue.     

Imperfect optimal foraging and the paradox of enrichment

We show that the paradox of enrichment can be theoretically resolved in a flexible predator–prey system in which the predator practices imperfect optimal foraging. A previous study showed that perfect optimal foraging can mitigate increases in the amplitude of population oscillations associated with enrichment, but it did not show a stabilization pattern. Our results show that imperfect optimal foraging can stabilize the system and resolve the paradox of enrichment under nonequilibrium dynamics. Furthermore, the degree of stabilization with enrichment was stronger when the imperfection of optimal foraging was larger.     

Integrating optimal foraging and optimal oviposition theory in plant–insect research

The current approach for studying host selection by phytophagous insects is mainly based on optimal oviposition theory, i.e. the preference–performance hypothesis. Almost no attention has been given to optimal foraging theory. However, recent papers and additional evidence given in this work illustrate that also optimal foraging may shape host preference patterns of phytophagous insects. Therefore and because optimal foraging and optimal oviposition may oppose conflicting needs to phytophagous insects, we plea for an integration of optimal foraging and optimal oviposition in plant–insect research. We argue how this may improve our understanding of plant–insect interactions.     

Testing optimal foraging models for air-breathing divers

Models of diving optimality qualitatively predict diving behaviours of aquatic birds and mammals. However, none of them has been empirically tested. We examined the quantitative predictions of optimal diving models by combining cumulative oxygen uptake curves with estimates of power costs during the dives of six tufted ducks, Aythya fuligula. The effects of differing foraging costs on dive duration and rate of oxygen uptake (V_O2up) at the surface were measured during bouts of voluntary dives to a food tray. The birds were trained to surface into a respirometer after each dive, so that changes in V_O2up over time could be measured. The tray held either just food or closely packed stones on top of the food to make foraging energetically more costly. In contrast to predictions from the Houston & Carbone model, foraging time (t_f) increased after dives incorporating higher foraging energy costs but surface time (t_s) remained the same. While optimal diving models have assumed that the cumulative oxygen uptake curve is fixed, V_O2up increased when the energy cost of the dive increased. The optimal breathing model quantitatively predicted ts in both conditions and oxygen consumption during foraging (m₂t_f) in the control condition, for the mean of all ducks. This offers evidence that the ducks were diving optimally and supports the fundamentals of optimal diving theory. However, the model did not consistently predictt_s or m₂t_f for individual birds. We discuss the limits of optimal foraging models for air-breathing divers caused by individual variation. Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.      

Host-plant selection,diet diversity,and optimal foraging in a tropical leafcutting ant

Summary A month-long study was conducted on the comparative foraging behavior of 20 colonies of the leafcutting ant, Atta cephalotes L. in Santa Rosa National Park, Guanacaste Province, Costa Rica. The study was conducted during the middle of the wet season, when trees had mature foliage and the ants were maximally selective among species of potential host plants. The colonies always gathered leaves from more than a single tree species but on average one species constituted almost half the diet with the remaining species being of geometrically decreasing importance. Colonies exhibited greater diversity in their choice of leaves and lower constancy of foraging when the average quality of resource trees was lower, as predicted by elementary optimal foraging theory. Furthermore, the ants were more selective of the species they attacked at greater distances from the nest. However, the ants sometimes did not attack apparently palatable species, and often did not attack nearby individuals of species they were exploiting at greater distances.A classical explanation for why leafcutting ants exploit distant host trees when apparently equally good trees are nearer, is that the ants are pursuing a strategy of conserving resources to avoid long-term overgrazing pressure on nearby trees. We prefer a simpler hypothesis: (1) Trees of exploited species exhibit individual variation in the acceptability of their leaves to the ants. (2) The abundance of a species will generally increase with area and radial distance from the nest, so the probability that at least one tree of the species will be acceptable to the ants also increases with distance. (3) The ants forage using a system of trunk-trails cleared of leaf litter, which significantly reduces their travel time to previously discovered, high-quality resource trees (by a factor of 4- to 10-fold). (4) Foragers are unware of the total pool of resources available to the colony. Therefore once scouts have chanced upon a tree which is acceptable, the colony will concentrate on harvesting from that tree rather than searching for additional sources of leaves distant from the established trail.     

An optimal foraging and migration model for juvenile plaice

Summary A state-dependent model has been used to predict daily and tidal patterns of migration, feeding and inactivity in juvenile plaice (Pleuronectes platessa L.) in their intertidal and shallow subtidal nursery areas. Vertical position, quantity of energy reserves and fullness of the gut characterized the state of individual fishes. If feeding is visually mediated, the model predicts that, by night, plaice should move to areas of low predation risk and become inactive, whereas by day, plaice should migrate to feed in areas of high prey encounter rate. Vertical zones adopted by day and night and, hence, patterns of migration, should depend on the distributions of predators and prey. When prey are more abundant in the intertidal zone, plaice should move onshore to feed as the tide rises and when prey are more abundant offshore, plaice should move offshore to feed by day. If predators are equally abundant in all zones, the fish should behave as if no predators were present, having no effective refuge. An increase in the abundance of predators with depth results in the restriction of plaice activities to shallower vertical zones, depending on the magnitude of the predation threat. Zones adopted thus depend on the trade-off between energy intake and predation risk. Concordance between predicted behaviour and observed patterns is evident in contrasting habitats. Migration and feeding in the Wadden Sea, where prey are more abundant on intertidal flats, is dominated by the tidal component, whereas on impoverished exposed beaches of the west coast of Scotland, the diurnal component is dominant. Tidally related behaviour persists in the latter environment, not predicted by the model and may be a consequence of using endogenous rhythms to approach optimal behavioural patterns.     

A mathematical framework for optimal foraging of herbivores

The aim of this paper is to study a model of optimal foraging of herbivores (with special reference to ungulates) assuming that food distribution is arbitrary. Usually the analysis of foraging of herbivores in the framework of optimal foraging theory is based on the assumption of a patchy food distribution. We relax this assumption and we construct more realistic models. The main constraint of our model is the total amount of food which the animal may eat and the currency is the total foraging time. We represent total foraging time as a variational expression depending on food eaten and the length of the path. We prove that there exists a threshold for food acquisition. More explicitly, it exists a positive real number such that, at any point x of the path, the animal either eats till the density of food is decreased to the value or, if the density of food at x is less than , there it does not eat. We discuss the results and emphasize some biologically important relationships among model parameters and variables. Finally, we try to give a sound biological interpretation of our results.     

Snowshoe hare optimal foraging and its implications for population dynamics

The results of an optimal foraging model using linear programming with constraints for feeding time, digestive capacity, sodium requirements, and energy requirements indicate that snowshoe hare (Lepus americanus) may forage as energy maximizers. The solution provides the quantities of major food classes (leaves, herbs, fungus, twigs) included in the diet. The species composition of each diet class also is determined using a simultaneous search model based upon the probability of encounter, the probability of sufficient item size, and the probability of sufficient quality. The results also indicate that hare life history parameters (weaning size, size at first reproduction, average adult size) and potential demographic changes in hare populations may be controlled by foraging considerations.     

Descriptions of superparasitism by optimal foraging theory,evolutionarily stable strategies and quantitative genetics

Many parasitoids superparasitize, in which an insect attacks a previously parasitized host, laying an egg in the host even though only one offspring will emerge from the host. In this paper superparasitism is considered from the perspectives of optimal foraging theory, evolutionarily stable strategies, and quantitative genetics. The focal question is: at what point in its life should an individual parasitoid begin attacking previously parasitized hosts? Each of the three theoretical methods can be used to answer the question and by doing so, we see how the three methods are connected. Qualitative, empirical predictions based on the theories are described.     

Inheritance of optimal foraging behaviour in Columbian ground squirrels

Summary I examined the potential inheritance of the ability of Columbian ground squirrels (Spermophilus columbianus) to select an optimal diet. I calculated the diet that would maximize daily energy intake for each of 21 adult females and their litters, using a linear programming optimization model for each individual. The absolute value of the difference between an individual's predicted optimal diet and observed diet (deviation from an optimal diet) was used as a measure of an individual's foraging ability. The foraging ability of individuals was consistent over time and in different foraging environments, so I considered foraging ability to be a potentially heritable trait.Inheritance was determined from correlations of mother and offspring foraging ability. I experimentally removed some mothers just as they weaned their offspring so that offspring could not be influenced by their mother while learning to forage, while leaving the other mothers to raise their litters normally. In both cases, offspring strongly resembled their mother in foraging ability. However, offspring with mothers absent exhibited significantly larger deviations from their optimal diet. Offspring with mothers absent appeared to imitate their mother's diet during lactation, and this tendency partially explained their greater deviation. Consequently, offspring appear to inherit the ability to forage optimally from their mother, perhaps through observational learning or imitation. There may also be a genetic basis to foraging ability, but uncontrolled maternal effects in the experiment prevent a proper test for it.     

Modeling hunter-gatherer decision making: complementing optimal foraging theory

While optimal foraging theory has been of considerable value for understanding hunter-gatherer subsistence patterns, there is a need for a complementary approach to human foraging behavior which focuses on decision-making processes. Having made this argument, the paper proposes the type of modeling approach that should be developed, using decision making during encounter foraging as an example. This model concerns the individual decision maker attempting to improve his foraging efficiency, rather than maximize it, under the constraint of limited information and with conflicting goals. This is illustrated by applying it to the Valley Bisa hunters using computer simulation.     

Decisions of cattle herdsmen in Burkina Faso and optimal foraging models

Models of optimal foraging theory are used to evaluate the decisions of a sedentary herdsman and his family in Burkina Faso concerning the movement of his cattle from pasture to pasture. Generally, such models describe exploitation at the patch level, but are inadequate at higher levels. The herdsmen in the study area are generally sedentary, and their strategy of exploitation appears to be characterized by planning at least in terms of a whole day and minimizing daily travel time among fields. In conjuction with this conclusion a modified optimization model is proposed. We conclude that optimal foraging models are useful in interpreting and understanding the rules governing the movements of traditional West African herdsmen when so modified, but that more data are needed to develop and test these models further.