Leaving patches: An investigation of a laboratory analogue

Five pigeons were trained on a procedure that has been used as a laboratory analogue to natural patch residence. Trials commenced with two responses available. One of these might provide a reinforcer if the patch was a prey patch; the other ended the residence time in the patch and, after a fixed travel time in blackout, produced another patch that might or might not provide a reinforcer. Patch residence also ended, and was followed by the same travel time, after a reinforcer was obtained or after a fixed maximum time was spent in the patch. The dependent variable was patch residence time, from the commencement of the patch to the time at which the subject emitted a response to exit from the patch or until the maximum patch residence time had elapsed. In Parts 1 to 3, the duration of the imposed travel time was varied from 0.25 to 16 s at three different probabilities (.05, .1, and .2) of food per second (λ) in prey patches. As reported in previous research, both increasing travel time and decreasing probabilities of reinforcers per second increased patch residence time. In Parts 4 to 7, the probability of prey trials (ρ) was varied in an irregular order from .1, through .2, .5, and .7, to .9 for different combinations of λ and travel time. Respectively, these were in Part 4, .05 per second and 0.25 s; in Part 5, .05 per second and 16 s; in Part 6, .2 per second and 0.25 s; and in Part 7, .2 per second and 16 s. A previously offered model, based on optimization assumptions, substantially and consistently underpredicted patch residence time. However, a modification of that model, which assumes that the subjects could not accurately discriminate the residence time that provided the minimum interreinforcer interval, described the data well. The same model also described previously reported residence times in a different species with a uniform distribution of prey-arrival times.     

Residence time in concurrent foraging with fixed times to prey arrival

Five pigeons were trained in a concurrent foraging procedure in which reinforcers were occasionally available after fixed times in two discriminated patches. In Part 1 of the experiment, the fixed times summed to 10 s, and were individually varied between 1 and 9 s over five conditions, with the probability of a reinforcer being delivered at the fixed times always .5. In Part 2, both fixed times were 5 s, and the probabilities of food delivery were varied over conditions, always summing to 1.0. In Parts 3 and 4, one fixed time was kept constant (Part 3, 3 s; Part 4, 7 s) while the other fixed time was varied from 1 s to 15 s. Median residence times in both patches increased with increases in the food-arrival times in either patch, but increased considerably more strongly in the patch in which the arrival time was increased. However, when arrival times were very different in the two patches, residence time in the longer arrival-time patch often decreased. Patch residence also increased with increasing probability of reinforcement, but again tended to fall when one probability was much larger than the other. A detailed analysis of residence times showed that these comprised two distributions, one around a shorter mode that remained constant with changes in arrival times, and one around a longer mode that monotonically increased with increasing arrival time. The frequency of shorter residence times appeared to be controlled by the probability of, and arrival time of, reinforcers in the alternative patch. The frequency of longer residence times was controlled directly by the arrival time of reinforcers in a patch, but not by the probability of reinforcers in a patch. The environmental variables that control both staying in a patch and exiting from a patch need to be understood in the study both of timing processes and of foraging.     

Leaving patches: Effects of travel requirements

Five pigeons were trained in an analogue foraging procedure in which, by completing a travel requirement, they entered a “patch” in which a reinforcer might be available after an unpredictable time. They also had the opportunity, by emitting a defined response, to exit the patch and travel to another patch. Prey availability in a patch was not signaled. Data were collected on the length of time that subjects stayed in patches before exiting (residence times) as a function of various travel requirements: travel for a fixed time in blackout, fixed-interval schedule traveling, fixed-time traveling with an added response required to terminate traveling, and fixed-ratio traveling. For each of these conditions, the required amount of travel (time or responses) was varied over a wide range. As previously reported, residence times increased with increases in fixed-time traveling, as they did with increasing fixed-interval or fixed-ratio traveling. There was no evidence that adding response or work requirements systematically affected residence time except via increased travel time, although 3 of the 5 birds stayed longer in a patch under higher fixed-ratio values. A “threshold-maximization” model described the data well with a single parameter that was consistent across subjects, procedures, and experiments.     

Timing and Foraging: Gibbon's Scalar Expectancy Theory and Optimal Patch Exploitation

We present a study that links optimal foraging theory (OFT) to behavioral timing. OFT's distinguishing feature is the use of models that compute the most advantageous behavior for a particular foraging problem and compare the optimal solution to empirical data with little reference to psychological processes. The study of behavioral timing, in contrast, emphasizes performance in relation to time, most often without strategic or functional considerations. In three experiments, reinforcer-maximizing behavior and timing performance are identified and related to each other. In all three experiments starlings work in a setting that simulates food patches separated by a flying distance between the two perches. The patches contain a variable and unpredictable number of reinforcers and deplete suddenly without signal. Before depletion, patches deliver food at fixed intervals (FI). Our main dependent variables are the times of occurrence of three behaviors: the “peak” in pecking rate (Peak), the time of the last peck before “giving in” (GIT), and the time for “moving on” to a new patch (MOT). We manipulate travel requirement (Experiment 1), level of deprivation and FI (Experiment 2), and size of reinforcers (Experiment 3). For OFT, Peak should equal the FI in all conditions while GIT and MOT should just exceed it. Behavioral timing and Scalar Expectancy Theory (SET) in particular predict a Peak at around the FI and a longer (unspecified) GIT, and make no prediction for MOT. We found that Peak was close to the FI and GIT was approximately 1.5 times longer, neither being affected by travel, hunger, or reinforcer size manipulations. MOT varied between 1.5 and just over 3 times the FI, was responsive to both travel time and the FI, and did not change when the reinforcer rate was manipulated. These results support the practice of producing models that explicitly separate information available to the subject from strategic use of this information.     

Comparing Locomotion With Lever-press Travel In An Operant Simulation Of Foraging

An operant model of foraging was studied. Rats searched for food by pressing on the left lever, the patch, which provided one, two, or eight reinforcers before extinction (i.e., zero reinforcers). Obtaining each reinforcer lowered the probability of receiving another reinforcer, simulating patch depletion. Rats traveled to another patch by pressing the right lever, which restored reinforcer availability to the left lever. Travel requirement changed by varying the probability of reset for presses on the right lever; in one condition, additional locomotion was required. That is, rats ran 260 cm from the left to the right lever, made one response on the right lever, and ran back to a fresh patch on the left lever. Another condition added three hurdles to the 260-cm path. The lever-pressing and simple locomotion conditions generated equivalent travel times. Adding the hurdles produced longer times in patches than did the lever-pressing and simple locomotion requirements. The results contradict some models of optimal foraging but are in keeping with McNair's (1982) optimal giving-up time model and add to the growing body of evidence that different environments may produce different foraging strategies.     

Closed-economy multiple-schedule performance: Effects of deprivation and session duration

Three pigeons responded for food reinforcement on multiple variable-interval schedules in which the total consumption of food was entirely determined by the subjects' interaction with the schedules (a closed economy). The finding of overmatching, where response allocation between components is more extreme than the distribution of reinforcers, was reconfirmed. Generalized-matching sensitivity decreased from overmatching to undermatching values typical of conventional multiple schedules when food deprivation was increased by decreasing session duration, but not when deprivation was increased by decreasing overall reinforcer rate. Sensitivity also increased from undermatching to overmatching as session duration increased from 100 min to 24 hr, while deprivation was held constant by decreasing overall reinforcer rate. These results can be understood in terms of increases in the value of extraneous reinforcers relative to food reinforcers as deprivation decreases or as the economy for extraneous reinforcers becomes more closed. However, no published quantitative expression of the effects of extraneous reinforcers is entirely consistent with the results.     

An experimental analysis of optimal foraging behaviour in patchy environments

A series of experiments was designed to explore the cognitive mechanisms involved in optimal foraging models by using the behavioural controls of operant methodology. Rats were trained to press one of two levers to obtain reinforcement on a progressive variable-interval schedule, which modelled food patch depletion; the schedule was reset by pressing the other lever. Thus both duration (residence time in a patch) and rate-related (interval before and after the final reward) measures were obtained. Experiment 1, which manipulated environmental stability and quality, and Experiment 2, which varied travel time between patches, found results that supported the marginal value theorem (Charnov, 1976) and suggested that rats adjust capture rate to the environment average by monitoring the length of the interval between rewards. Experiment 3 modelled the clumping of food items and found that capture rate was now adjusted by adoption of a fixed giving-up time. Finally, Experiments 4a and 4b ruled out a time expectancy hypothesis by manipulating the number of food clumps and the series of inter-reinforcement intervals. Overall the experiments demonstrate the value of modelling foraging strategies in operant apparatus, and suggest that rats adopt rate predictive strategies when deciding to switch patches.     

Residence time and choice in concurrent foraging schedules

Five pigeons were trained on a concurrent-schedule analogue of the “some patches are empty” procedure. Two concurrently available alternatives were arranged on a single response key and were signaled by red and green keylights. A subject could travel between these alternatives by responding on a second yellow “switching” key. Following a changeover to a patch, there was a probability (p) that a single reinforcer would be available on that alternative for a response after a time determined by the value of λ, a probability of reinforcement per second. The overall scheduling of reinforcers on the two alternatives was arranged nonindependently, and the available alternative was switched after each reinforcer. In Part 1 of the experiment, the probabilities of reinforcement, ρ_red and ρ_green, were equal on the two alternatives, and the arranged arrival rates of reinforcers, λ_red and λ_green, were varied across conditions. In Part 2, the reinforcer arrival times were arranged to be equal, and the reinforcer probabilities were varied across conditions. In Part 3, both parameters were varied. The results replicated those seen in studies that have investigated time allocation in a single patch: Both response and time allocation to an alternative increased with decreasing values of λ and with increasing values of ρ, and residence times were consistently greater than those that would maximize obtained reinforcer rates. Furthermore, both response- and time-allocation ratios undermatched mean reinforcer-arrival time and reinforcer-frequency ratios.     

Time horizons in rats foraging for food in temporally separated patches

An important tenet of optimal foraging theory is that foragers compare prey densities in alternative patches to determine an optimal distribution of foraging behavior over time. A critical question is over what time period (time horizon) this integration of information and behavior occurs. Recent research has indicated that rats do not compare food density in a depleting patch with that in a rich patch delayed by an hour or more (Timberlake, 1984). In the present research we attempted to specify over what time period a future rich patch would affect current foraging. The effect of future food was measured by early entry into the rich patch (anticipation) and by a decrease in food obtained in the depleting patch (suppression). The rats showed anticipation of a rich patch up to an hour distant, but suppressed current feeding only if the rich patch was 16 min distant or less. The suppression effect appeared mediated by competition for expression between anticipatory entries into the rich patch and continued foraging in the depleting patch. These results suggest that optimal foraging is based on a variety of specific mechanisms rather than a general optimizing algorithm with a single time horizon.     

Foraging in a simulated natural environment: There's a rat loose in the lab

Rats were required to earn their food in a large room having nine boxes placed in it, each of which contained food buried in sand. In different phases of the experiment the amount of time allowed for foraging, the amount of food available in each food patch, and the location of the different available amounts were varied. The rats exhaustively sampled all patches each session but seemed to have fairly strong preferences for certain locations over others. If position preferences were for patches containing small amounts of food, the sensitivity to amount available was increased so that when location was compensated for, a pattern of optimal foraging was evident. The importance of environmental constraints in producing optimal behavior and the relation of the observed behavior to laboratory findings are discussed.     

Testing a stochastic foraging model in an operant simulation: Agreement with qualitative but not quantitative predictions

An operant simulation of foraging through baited and empty patches was studied with 4 pigeons. On a three-key panel, side keys were designated as patches, and successive opportunities to complete 16 fixed-ratio 10 schedules on side keys were defined as encounters with feeders. In a random half of the patches in any session, some of the fixed-ratio 10 schedules yielded reinforcement (baited feeders) and the other schedules yielded nonreinforcement (empty feeders). In the other half of the patches, all feeders were empty. Pigeons could travel between patches at any time by completing a fixed-ratio schedule on the center key. An optimal foraging model was tested in Experiments 1 and 2 by varying center-key travel time and number of baited feeders in baited patches. The ordinal predictions that number of feeders visited in empty patches would increase with travel time and decrease as number of baited feeders increased were supported, but pigeons visited far more feeders in empty patches than the optimal number predicted by the model to maximize energy/time. In Experiment 3, evidence was found to suggest that the number of empty feeders encountered before the first baited feeder in baited patches is an important factor controlling leaving empty patches.     

Discrimination learning in a foraging situation

Rats were allowed to forage in a simulated natural environment made up of eight food sources (patches) each containing a fixed number of pellets. Two of the eight contained an extra supply of peanuts. The peanut patches were signaled by an olfactory/visual cue located at the bottom of the ladder leading to the patch. In successive phases the number of sessions per day, height of the patches, and availability of peanuts were manipulated. Subjects showed evidence of discrimination learning under these conditions, although the degree of discriminatory behavior varied as a function of environmental manipulations. Assessment of behavior within foraging sessions showed that subjects systematically changed their patterns of utilization of patches across time. Sampling or exploration, as well as food reinforcement, seem implicated in these results.     

Interactions between the effects of food and water motivating operations on food‐ and water‐reinforced responding in mice

Two experiments examined interactions between the effects of food and water motivating operations (MOs) on the food‐ and water‐reinforced operant behavior of mice. In Experiment 1, mice responded for sucrose pellets and then water reinforcement under four different MOs: food deprivation, water deprivation, concurrent food and water deprivation, and no deprivation. The most responding for pellets occurred under food deprivation and the most responding for water occurred under water deprivation. Concurrent food and water deprivation decreased responding for both reinforcers. Nevertheless, water deprivation alone increased pellet‐reinforced responding and food deprivation alone likewise increased water‐reinforced responding relative to no deprivation. Experiment 2 demonstrated that presession food during concurrent food and water deprivation increased in‐session responding for water relative to sessions where no presession food was provided. Conversely, presession water during concurrent food and water deprivation did not increase in‐session responding for pellets. These results suggest that a) the reinforcing value of a single stimulus can be affected by multiple MOs, b) a single MO can affect the reinforcing value of multiple stimuli, and c) reinforcing events can also function as MOs. We consider implications for theory and practice and suggest strategies for further basic research on MOs.     

Stock optimizing: maximizing reinforcers per session on a variable-interval schedule.

In Experiment 1, 2 monkeys earned their daily food ration by pressing a key that delivered food according to a variable-interval 3-min schedule. In Phases 1 and 4, sessions ended after 3 hr. In Phases 2 and 3, sessions ended after a fixed number of responses that reduced food intake and body weights from levels during Phases 1 and 4. Monkeys responded at higher rates and emitted more responses per food delivery when the food earned in a session was reduced. In Experiment 2, monkeys earned their daily food ration by depositing tokens into the response panel. Deposits delivered food according to a variable-interval 3-min schedule. When the token supply was unlimited (Phases 1, 3, and 5), sessions ended after 3 hr. In Phases 2 and 4, sessions ended after 150 tokens were deposited, resulting in a decrease in food intake and body weight. Both monkeys responded at lower rates and emitted fewer responses per food delivery when the food earned in a session was reduced. Experiment 1's results are consistent with a strength account, according to which the phases that reduced body weights increased food's value and therefore increased subjects' response rates. The results of Experiment 2 are consistent with an optimizing strategy, because lowering response rates when food is restricted defends body weight on variable-interval schedules. These contrasting results may be attributed to the discriminability of the contingency between response number and the end of a session being greater in Experiment 2 than in Experiment 1. In consequence, subjects lowered their response rates in order to increase the number of reinforcers per session (stock optimizing).     

GROUP FORAGING SENSITIVITY TO PREDICTABLE AND UNPREDICTABLE CHANGES IN FOOD DISTRIBUTION: PAST EXPERIENCE OR PRESENT CIRCUMSTANCES?

The ideal free distribution theory (Fretwell & Lucas, 1970) predicts that the ratio of foragers at two patches will equal the ratio of food resources obtained at the two patches. The theory assumes that foragers have "perfect knowledge" of patch profitability and that patch choice maximizes fitness. How foragers assess patch profitability has been debated extensively. One assessment strategy may be the use of past experience with a patch. Under stable environmental conditions, this strategy enhances fitness. However, in a highly unpredictable environment, past experience may provide inaccurate information about current conditions. Thus, in a nonstable environment, a strategy that allows rapid adjustment to present circumstances may be more beneficial. Evidence for this type of strategy has been found in individual choice. In the present experiments, a flock of pigeons foraged at two patches for food items and demonstrated results similar to those found in individual choice. Experiment 1 utilized predictable and unpredictable sequences of resource ratios presented across days or within a single session. Current foraging decisions depended on past experience, but that dependence diminished when the current foraging environment became more unpredictable. Experiment 2 repeated Experiment I with a different flock of pigeons under more controlled circumstances in an indoor coop and produced similar results.     

A temporal limit on the effect of future food on current performance in an analogue of foraging and welfare

Rats obtained access to food twice each 24-hour period. The first session was a work session in which food was available on a progressive-ratio schedule. During the second session, which occurred between 1 and 23 hours after the work session, food was freely available up to a fixed total intake each 24 hours. The situation resembled elements of several real world circumstances, including the choice between continuing to forage in a rapidly depleting patch and waiting for a better patch, and between working now and receiving a guaranteed income later. The purpose of the experiment was to explore the time period over which future access to reward could affect current responding. Contrary to what might be expected from recent theorizing, anticipation of future food delayed by an hour or more after the start of the work session had no effect on current performance. Food intake was high and constant during work sessions except for a prefeeding effect that occurred when the free session closely preceded the next day's work session. Also, an increase in the difficulty of the work schedule increased the amount of work and the maximum price paid for food as if the work session were the only time food was available. The results indicate the importance of considering temporal limits in theories that require animals to integrate input over time to determine the allocation of resources among alternatives.     

Assessment and choice: an operant simulation of foraging in patches

Pigeons were presented with an operant simulation of two prey patches using concurrent random-ratio schedules of reinforcement. An unstable patch offered a higher initial reinforcement probability, which then declined unpredictably to a zero reinforcement probability in each session. A stable patch offered a low but unvarying reinforcement probability. When the reinforcement probability declined to zero in a single step, the birds displayed shorter giving-up times in the unstable patch when the ratio between the initial reinforcement probabilities in the unstable and stable patches was greater and when the combined magnitude of the reinforcement probabilities in the two patches was greater. When the unstable patch declined in two steps, the birds behaved as if their giving-up times were influenced heavily by events encountered during the most recent step of the double-step change. This effect was observed, however, only when the reinforcement probability in that step was .04, not when it was .06. All of these data agree with the predictions of a capture-probability model based on a comparison of the estimated probability of receiving a reinforcer in the current patch with that in alternative patches.     

Time horizons in rats: the effect of operant control of access to future food.

The primary goal of this experiment was to determine whether the addition of an operant requirement for access to a less costly (continuous reinforcement) patch of future food increased the time horizon over which that future patch decreased intake in a currently available depleting (progressive-ratio) patch. Three groups of 4 rats were tested. Each member of the earned-time group was required to cumulate a fixed-time outside the progressive-ratio patch to obtain access to food in the less costly patch; the fixed-time requirement ranged from 2 to 64 min. Rats in the matched-time group received response-independent access to less costly food at the average delay shown by the earned-time group. Rats in the matched-time no-food group were removed from the chamber at the same average delay without receiving access to less costly food. Two of the earned-time rats showed an increased time horizon relative to that shown by the matched-time rats (approaching 40 min for 1 rat). The other 2 earned-time rats markedly increased instrumental responding but showed suppression of intake only when food was less than 20 min away. The matched-time group showed less suppression of intake over a similar range of delay intervals. Surprisingly, the matched-time no-food animals also showed suppression of intake concentrated at the end of the session, possibly reflecting the receipt of their entire daily ration 30 min after the session. The potential importance of time horizons to the foraging process is clear, but experimenters are still working out paradigms for investigation of these horizons.     

A preliminary analysis of adaptive responding under open and closed economies

In the current investigation, we evaluated the effects of open and closed economies on the adaptive behavior of 2 individuals with developmental disabilities. Across both types of economy, progressive-ratio (PR) schedules were used in which the number of responses required to obtain reinforcement increased as the session progressed. In closed-economy sessions, participants were able to obtain reinforcement only through interaction with the PR schedule requirements (i.e., more work resulted in more reinforcer access). In open-economy sessions, participants obtained reinforcers by responding on the PR schedule and were given supplemental (free) access to the reinforcers after completion of the session. In general, more responding was associated with the closed economy.