Taking the rough with the smooth: foraging for particulate food in continuous time.

This paper describes the development of the general dynamical model of foraging developed by Ollason (1980, Theoret. Popul. Biol. 18, 44-65) to predict foraging for particulate food in three different types of environment. In an environment containing particles of different types of food, the model predicts the selection of an approximately optimal diet; in an environment in which the particles occur in patches, the model predicts a time budget of patch occupancy that approximates to the optimal time budget; and in an environment containing patches of particles that regenerate by the addition of particles of food at constant rates, the model predicts that animals will dispose themselves among the patches approximately as predicted by the ideal free distribution. Where the predictions of the model depart from the predictions of optimal foraging theory, they are qualitatively similar to the observed departures of the behaviour of real animals from the predictions of optimal foraging theory. The model provides a general representation of the foraging decisions of animals whether they feed strictly continuously or discontinuously on particles of food, and does so without explicit reference to optimization processes.

The approximately ideal, more or less free distribution.

We present the minimum set of requirements necessary and sufficient to represent the foraging behaviour of an animal, and its utilisation of food, in order to explore the emergent properties of behaviour that allow animals to reduce their hunger. We present an individual-based model of foraging that provides a simple quantification of the requirements, which is sufficiently simple to yield some analytical results. Complex interactions beyond the scope of analysis have been explored through simulating animals foraging in regenerating patchy environments. In most cases the populations pass into equilibrium distributions which appear to be stable. The equilibria always approximate closely to the ideal free distribution, although typically with a small degree of undermatching. (Undermatching is the term applied to the departure from the ideal free distribution caused by a smaller proportion of the population than expected occupying areas with a higher than average regeneration rate). The model therefore implies that the distribution, hitherto accounted for in terms of ESSs may, in fact, be simply an effect of the animal's utilization of the food it collects to reduce its hunger. The model defines a specific feeling rate, v, the rate at which an animal can feed on a unit of food. This is a function of three parameters, v1, the specific feeding rate when alone, v(infinity), the rate, possibly zero, at which it can feed in the presence of an indefinitely large number of conspecifics, and n1/2, the number of conspecifics that cause v to take the value (v1+v(infinity)/2. Exploitation competition in the absence of interference is represented by setting v1 = v(infinity). Differences in competitive ability in exploitation have been represented by simulating animals with a range of values of v1, those with the larger values, feeding more rapidly, being the more effective competitors, and those with the lower values being the less effective. Interference competition is represented by setting v1 > v(infinity) and social facilitation by v1 < v(infinity). Individual differences in the strength of interaction are represented by different values of n(1/2). In competition, the animals with the larger values of n(1/2) are the more effective competitors: in facilitation, they are the less effective facilitators. The addition of physiological and behavioural detail makes very little alteration to the emergent equilibria, always close to the ideal free distribution, almost always showing undermatching.

Trail-laying and recruitment to sugary foods by foraging red wood-ants Formica aquilonia Yarrow (Hymenoptera: Formicidae).

The use of trail communication by red wood-ants, Formica aquilonia Yarrow, foraging to sugar baits, was investigated by providing a laboratory colony with aqueous sucrose at two novel feeding sites, with a third site, providing no food, as a control. During trials, the sites were connected to the nest by paper bridges which were replaced between treals. One of the sites providing food was reached by a two-way bridge, as was the control. The second baited site was reached by a one-way bridge: this site had a one-way exit from which returning foragers dropped to the nest. Hence, if returning foragers laid a trail from a bait, they would do so on the two-way bridge, but not on the one-way bridge by which foragers did not return, nor on the bridge to the unbaited site. This would lead to a greater increase in foraging traffic on the two-way bridge, relative to that on the other two bridges, during a given trial. Each trial was preceded by a 30-min counting session with no baits present, to establish the mean number of ants arriving per minute on each bridge through random exploration. After provision of food, ants arriving on each bridge per minute were counted in four separate 30-min sessions: each count was then converted to a proportion of the original mean traffic on that bridge, and the change in traffic with time was compared between bridges using analysis of variance. The increase in traffic was significantly greater on the two-way bridge than on the control and one-way bridges, indicating that replete ants returning from the bait left a trail on the homeward route, which other ants subsequently followed.

Site fidelity in foraging wood-ants Formica aquilonia yarrow and its influence on the distribution of foragers in a regenerating environment.

The proportions of the population of red wood-ants Formica aquilonia Yarrow, foraging for sucrose at two artificial feeding sites in the laboratory, approximated to those predicted by the ideal free distribution (Lamb and Ollason, 1993). It was assumed that, for the foraging population to attain the ideal free distribution, each individual would visit and assess the availability of food at both feeding sites and distribute its foraging effort in proportion to the rate of regeneration of food. In order to demonstrate this, large samples of foragers at each of the feeding sites were colour-marked according to site. It was expected that the marked sample of foragers would in time become distributed as predicted by the ideal free distribution; instead, the distribution of marked ants was biased toward the site where they had been marked. Hence some individuals are not continually visiting and feeding at both patches, and such individuals will not be able directly to assess their feeding rates at each patch. There is, in principle, no way that such individuals can distribute themselves as predicted by the ideal free distribution, and as the site-faithful ants form a large proportion of the population, it appears that there is no way that the members of such a population can become so distributed. One resolution of this apparent paradox is provided by the behaviour of the mobile ants, the existence of which is demonstrated by observations of marked ants foraging at the site other than that at which they were marked. If the mobile members of the population assess the quality of both patches and distribute themselves to maximise their rates of feeding, the whole population will become distributed as predicted by the ideal free distribution. A modification of Ollason's (1987) model shows how this distribution could develop. It emerges that there is a minimum proportion of mobile ants in a population, below which the ideal free distribution will not develop, and that the distribution of foragers will depart from the ideal free distribution increasingly as the discrepancy between the regeneration rates of the patches of food increases.

Foraging wood-ants Formica aquilonia yarrow (hymenoptera: formicidae) tend to adopt the ideal free distribution.

Three colonies of red wood-ants were established in the laboratory; each colony was provided with two feeding sites, each one metre from the nest. An aqueous solution of sucrose (7% w/v) was pumped at a defined rate to each site, where it dropped on filter paper for collection by foraging ants. The distribution of foragers between sites was compared daily with the distribution of delivery rates of sucrose between sites. Ratios of delivery rates between sites were 1:1, 2:1, or 3:1; each distribution was maintained for eight days, and in the 2:1 and 3:1 conditions the delivery rates were exchanged between sites after eight days so that the richer of a pair of sites was impoverished and the poorer was enriched. Foragers came to approximate the ideal free distribution within two or three days of an exchange of delivery rates; their distribution then remained stable until the next exchange of rates. The adoption of the ideal free distribution suggests that individual ants used movement rules which maintained the maximum possible rate of feeding: this behaviour would ensure that the foraging population as a whole maintained the fastest rate of intake of food possible from a given environment.

Diet selection by common shrews Sorex araneus in a depleting environment.

Common shrews (Sorex araneus L.) were presented with two prey types at various densities in a depleting environment. Observed diet choice was compared to predictions of the classical optimal diet model and of "shrew-specific" simulations incorporating patch depletion. Two strategies were simulated: expansion of the diet from taking only profitable prey to taking both types, and fixed partial preference. The simulations predict partial preference over a narrow range of initial densities of profitable prey. However, within this range, energetic benefits are relatively insensitive to diet composition. Shrews preferred more profitable prey and were more selective when encounter rate with profitable prey was higher, broadly as predicted by all the models. Partial preference was observed, but neither of the mechanisms simulated was strongly supported by results for the shrews. Univariate and multivariate analyses were used to identify cues involved in selecting prey. Instantaneous measures of encounter rates and encounters per unit search distance were the best predictors of subsequent prey choice, but decisions appear to have been made on a probabilistic basis.