Choice in a successive-encounters procedure and hyperbolic decay of reinforcement

Pigeons responded in a successive-encounters procedure that consisted of a search state, a choice state, and a handling state. The search state was either a fixed-interval or mixed-interval schedule presented on the center key of a three-key chamber. Upon completion of the search state, the choice state was presented, in which the center key was off and the two side keys were lit. A pigeon could either accept a delay followed by food (by pecking the right key) or reject this option and return to the search state (by pecking the left key). During the choice state, a red right key represented the long alternative (a long handling delay followed by food), and a green right key represented the short alternative (a short handling delay followed by food). In some conditions, both the short and long alternatives were fixed-time schedules, and in other conditions both were mixed-time schedules. Contrary to the predictions of both optimal foraging theory and delay-reduction theory, the percentage of trials on which pigeons accepted the long alternative depended on whether the search and handling schedules were fixed or mixed. They were more likely to accept the long alternative when the search states were fixed-interval rather than mixed-interval schedules, and more likely to reject the long alternative when the handling states were fixed-time rather than mixed-time schedules. This pattern of results was in qualitative agreement with the predictions of the hyperbolic-decay model, which states that the value of a reinforcer is inversely related to the delay between a choice response and reinforcer delivery.     

Re-evaluating the extractive foraging hypothesis

In his seminal 1992 paper, Dunbar examined three hypotheses advanced to explain primate intelligence, arguing that whereas his social group size hypothesis was supported, neither of two ecological hypotheses, the extractive foraging and frugivory hypotheses, were supported. Following this, and Dunbar's subsequently elaborated argument, many investigators concluded that primate intelligence arose as social rather than ecological adaptations. This paper questions Dunbar's characterization of extractive foraging and social intelligence as alternative hypotheses, raises sampling issues about Dunbar's brain data, species choice, and measurement of extractive foraging. It summarizes the extractive foraging hypothesis, and counters its critics. It reexamines the hypothesis in light of recent behavioral and brain data, new methodology for quantifying extractive foraging, and a new phylogeny of primate intelligence. It concludes that the extractive foraging hypothesis is now supported by several converging lines of evidence.     

Choice, foraging, and reinforcer duration.

Pigeons were exposed to a foraging schedule characterized by three different states, beginning with a search state in which completion of a variable interval on a white key led to a choice state. In the choice state the subject could, by appropriate responding on a fixed ratio of three, either accept or reject the schedule offered. If the subject accepted the schedule, it entered a handling state in which the appropriate reinforcer amount was presented according to a variable-interval schedule. In Experiment 1 the shorter duration reinforcer was more likely to be accepted the longer the duration of the search state and the shorter the equal durations of the handling states. In Experiment 2 the shorter duration reinforcer was more likely to be accepted the longer the handling time preceding the longer duration reinforcer. All of the results were in qualitative--and some were in quantitative--agreement with those predicted by the delay-reduction hypothesis and the optimal-diet model.     

Choice and foraging

In Experiment 1, six naive pigeons were trained on a foraging schedule characterized by different states beginning with a search state in which completion of a fixed-interval on a white key led to a choice state. In the choice state the subject could, by appropriate responding on a fixed ratio of three, either accept or reject the schedule of reinforcement that was offered (either a variable-interval five-second or a variable-interval 20-second). If the subject accepted the schedule, it entered a “handling state” in which the appropriate variable-interval schedule was presented. Completion of the variable-interval schedule produced food. The independent variable was the fixed-interval value in the search state, and the dependent variable was the rate of acceptance of the long variable-interval in the choice state. Experiment 2 was identical except that the search state required completion of a variable-interval, instead of a fixed-interval, schedule. The rate of acceptance of the long variable-interval schedule in both experiments was a direct function of the length of the search state, in accordance with both optimality theory and the delay-reduction hypothesis.     

Drinking in a patchy environment: the effect of the price of water.

Rats in a laboratory foraging paradigm searched for sequential opportunities to drink in two water patches that differed in the bar-press price of each "sip" (20 licks) of water within a bout of drinking (Experiment 1) or the price and size (10, 20, or 40 licks) of each sip (Experiment 2). Total daily water intake was not affected by these variables. The rats responded faster at the patch where water was more costly. However, they accepted fewer opportunities to drink, and thus had fewer drinking bouts, and drinking bouts were smaller at the more costly patch than at the other patch. This resulted in the rats consuming a smaller proportion of their daily water from the more costly patch. The size of the differences in bout frequency and size between the patches appears to be based on the relative cost of water at the patches. The profitability of each patch was calculated in terms of the return (in milliliters) on either effort (bar presses) or time spent there. Although both measures were correlated with the relative total intake, bout size, and acceptance of opportunities at each patch, the time-based profitability was the better predictor of these intake measures. The rats did not minimize bar-press output; however, their choice between the patches and their bout sizes within patches varied in a way that reduced costs compared to what would have been expended drinking randomly. These data accord well with similar findings for choices among patches of food, suggesting that foraging for water and food occurs on the basis of comparable benefit-cost functions: In each case, the amount consumed is related to the time spent consuming.     

Procurement time as a determinant of meal frequency and meal duration.

Foraging involves the expenditure of both time and effort in the acquisition of food; animals typically modify their meal patterns so as to reduce these expenditures or costs. The contribution of time, as compared with effort, to the overall cost perceived by an animal is not known. We investigated the effect of foraging time as a cost independent of effort by measuring the meal patterns of rats living in a laboratory foraging simulation in which they earned all their daily intake. They pressed a bar once to initiate an interval (procurement interval) leading to the presentation of a large cup of food from which they could eat a meal of any size. As the length of the interval increased from 1 s to 46 hr, meal frequency decreased regularly. Meal size increased in a compensatory fashion, and total daily intake was conserved through an interval of 23 hr. The changes in meal frequency occurred because of changes in the rat's latency to bar press after each meal. The functions relating meal frequency and size to the procurement interval were of the same shape as those seen when cost is the completion of a bar-press requirement, which entails the expenditure of both effort and time. When the bar-press requirement was increased to 10, meal frequency was reduced, but time and effort did not appear to simply add together in the rat's perception of cost. These data reveal that time is preceived to be a cost by rats foraging in this laboratory environment. These results suggest that the time parameters of foraging are different from those of consumption.     

Scaling pigeons' choice of feeds: bigger is better.

Preferences of hungry pigeons among 10 grains and pellets were analyzed using a Thurstone scaling procedure. The recovered scales were positively correlated with size of the feed. The correlations improved when the Thurstonian assumption of equal-sized discriminal dispersions (Case V) was replaced with the assumption of proportional-sized dispersions (Case VI), as entailed by Weber's law. The correlations weakened when the experiments were conducted with the pigeons close to their free-feeding weights, where the probability of sampling alternative grains increased. In the final experiment, exposure to a large pellet shifted the preferences between two smaller pellets.     

Risk-sensitive foraging theory and operant psychology.

Hastjarjo, Silberberg, and Hursh (1990) have presented data on the foraging behavior of rats and discussed it in terms of risk-sensitive foraging theory. Because risk-sensitive foraging theory is comprised of several different models, it does not lead to general predictions about when an organism should prefer a foraging option with high variance to a foraging option with low variance. Any comparison of data with the predictions of the theory must be based on an appropriate model. I draw attention to various experiments that are potentially relevant to the results reported by Hastjarjo et al. and show how the time period over which the organism must survive can influence a model's predictions about risk sensitivity.     

Optimality And Concurrent Variable-interval Variable-ratio Schedules

Despite claims to the contrary, all leading theories about operant choice may be seen as models of optimality. Although melioration is often contrasted with global maximization, both make the same core assumptions as other versions of optimality theory, including momentary maximizing, hill climbing, and the various versions of optimal foraging theory. The present experiment aimed to test melioration against more global optimality and to apply the visit-by-visit analysis suggested by foraging theory. Rats were exposed to concurrent schedules in which one alternative was always variable-ratio 10 and the other alternative was a variable-interval schedule. Although choice relations varied from rat to rat, the overall results roughly confirmed the matching law, a result often taken to support melioration. Pooling the data across sessions and across rats, however, resulted in no increment in unsystematic variance, lending support to the contention by Ziriax and Silberberg (1984) that the choice relation is partly constrained. When the data were analyzed at the level of visits, the results either disconfirmed predictions of melioration or showed regularities about which melioration is silent. Instead, performance tended toward a rough optimization, in which responding favored the variable ratio, but with relatively brief visits to the variable interval. There were no asymmetries in travel or variability that would indicate that different processes were involved in generating visits at the two different schedules. The findings point toward a more global optimality model than melioration and demonstrate the value of per-visit analysis in the study of concurrent performances.     

Meal patterns of cats encountering variable food procurement cost.

The meal patterns of 2 cats in a laboratory habitat with variable foraging costs were examined in a foraging paradigm in which subjects could initiate meals at any time by completing a predetermined number of bar presses (the procurement price) and then could eat any amount. From meal to meal, the procurement price either was fixed or varied among a geometric series of five prices. As the fixed price or the mean of the variable prices increased, meal frequency decreased and meal size increased; daily intake was unaffected. Within variable-price schedules, meal size was not related to the just-paid procurement price. These results suggest that cats respond to the global rather than to the local cost structure of their habitat. They appear to respond to an average of the prices encountered, initiating meals of a frequency and size appropriate to that average. This was true even when the average price was high, meals were infrequent, and thus price encounters were widely separated in time. Therefore, the time window over which the consequences of behavior can affect behavior is longer than often conceived, at least in economies in which the animal controls its intake and the frequency, size, and distribution of its meals.