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Brunner, D., Kacelnik, A., & Gibbon, J. (1996). Memory for inter-reinforcement interval variability and patch departure decisions in the starling,Sturnus vulgaris. Anim. Behav., 51(5), 1025–1045.
Abstract: An experiment with starlings was conducted to investigate the effect of variability in inter-reinforcement intervals on foraging decisions. The experimental design simulated an environment in which food was distributed in patches. Patches contained zero to four food items which could be collected by pecking at a key. All patches ended with sudden depletion. The time elapsed since the last reinforcement was the only way to detect the depletion of the patch. Once a patch was depleted, a new patch could be reached by completion of a travel requirement of 20 flights between two perches. Key pecks within a patch and the time of the last response in a patch (giving-in time) were recorded. The level of variability in the inter-reinforcement intervals was varied between different conditions. An increase in inter-reinforcement interval variability resulted in a flattening of response rate functions and giving-in time distributions, and in more asymmetry of the response functions, but not of the giving-in time distributions. Two theoretical models of decision making are presented, which differ in the assumptions about memory constraints. In one case, all inter-reinforcement intervals are remembered but in the other, only the intervals with extreme values are remembered. Both models accommodate response rates as a function of trial time, but only the second is compatible with the observed departure decision. Our results are compatible with net rate maximization.
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Bateson, M., & Kacelnik, A. (1995). Accuracy of memory for amount in the foraging starling,Sturnus vulgaris. Anim. Behav., 50(2), 431–443.
Abstract: Attempts to include psychological constraints in models of foraging behaviour differ in their assumptions concerning the accuracy of estimation of environmental parameters. Psychologists model estimation error as increasing linearly with the magnitude of a stimulus (Weber's Law), whereas behavioural ecologists either ignore error or assume it to be independent of stimulus magnitude. Studies on the estimation of time intervals have confirmed Weber's Law, but there are few data on the accuracy of estimation of amounts of food. Since the currency of most foraging models is the amount of food acquired per unit of time spent foraging, information on estimation of amount is required. Here, a titration method was used in which starlings chose between two cues. One colour signalled a standard food reward, and the other a reward that adjusted in magnitude according to the birds' choices: it increased when the standard was preferred and decreased when the adjusting option was preferred. There were two standards of 3 and 9 units of food, each of which was delivered at two rates to control for possible effects of rate of reinforcement on discrimination. The observed value of the adjusting option oscillated around a mean value slightly larger than that of the standard. The amplitude and period of these oscillations were larger when the standard was larger, independent of the rate of reinforcement. Also, molecular analysis showed that the probability of choosing the currently larger alternative increased as the relative difference between the adjusting option and standard increased. These results are consistent with Weber's Law applying to starlings' memories for amounts of food.
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Todd, I. A., & Kacelnik, A. (1993). Psychological mechanisms and the Marginal Value Theorem: dynamics of scalar memory for travel time. Anim. Behav., 46(4), 765–775.
Abstract: Abstract. The relation between memory for travel time and foraging decisions was studied experimentally. The temporal properties of two environments with patchily distributed food were simulated in the laboratory using pigeons, Columba livia, as subjects. The two environments differed in mean travel time, while the coefficient of variation of travel time and the decelerated function relating cumulative food gain to time in the patch were held constant within and between environments. Each environment contained a uniform mixture of five travel times experienced in a random order. Two of the five travel times were common in both environments. Effects of travel time were studied by comparing prey collected per patch visit (PPV) after various travel times within each environment, and by comparing patch exploitation after equal travel times between environments. Within the environment with long mean travel time (LMT) PPV was positively correlated with the last and the penultimate travel times but not with travel times before that. The increase in PPV per second of last travel time was six times greater than the increase per second of penultimate travel time, implying very steep memory discounting. In the environment with short mean travel time (SMT), there was no correlation between PPV and previous travel times. However, comparisons between environments of visits following travel times common to both environments (thus removing the effect of the last travel time) showed that substantially more prey were taken after equal travel times in the LMT than in the SMT environment. This difference cannot be accounted for by the within-environment effect of penultimate travel time, implying that there is a different, less steeply devalued, effect of the mixture of travel times. A model of information processing based on combining Scalar Expectancy Theory with the predictions of rate maximization under the Marginal Value Theorem is presented. The model can approximate the results obtained in this and previous experiments and provides a framework for further analysis of memory mechanisms of foraging behaviour.
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Brunner, D., Kacelnik, A., & Gibbon, J. (1992). Optimal foraging and timing processes in the starling, Sturnus vulgaris: effect of inter-capture interval. Anim. Behav., 44(4), 597–613.
Abstract: Laboratory experiments with starlings, Sturnus vulgaris, were conducted to investigate the interaction between timing and cost-benefit considerations. The design simulated an environment in which food was distributed in patches. Patches contained a random number of food items (N=0-4) separated by a fixed inter-capture interval or fixed interval. All patches ended with sudden depletion. The time elapsed since the last prey capture was the only way to detect the depletion of the patch. Once the patch was depleted a new patch could be reached by travelling between two perches. Three measures of timing were taken: (1) rate of working for food as function of `waiting' time in a patch, (2) the time of the last response in a patch or `giving-in' time, and (3) the time at which travel was initiated or `moving-on' time. The fixed interval that characterized patches was varied between conditions. The mean time of the peak in working rate was consistently centred around the fixed interval, while the other two measures of timing kept a roughly linear relation to the fixed interval, with slope greater than one. In accordance with Scalar Expectancy Theory, variability in the three forms of timing was proportional to the magnitude of the fixed interval. The birds seemed to take account of this increase in variability as shown by the mean value of their giving-up criterion. These results imply that information-processing constraints are important for modelling behavioural optimality.
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Caraco, T., Kacelnik, A., Mesnick, N., & Smulewitz, M. (1992). Short-term rate maximization when rewards and delays covary. Anim. Behav., 44(Part 3), 441–447.
Abstract: In nature foragers must exploit resources that vary randomly in both the energy acquired per item (reward) and the time required to pursue, capture and process an item (delay). Furthermore, rewards and delays associated with particular resources may often covary significantly. An analytical model asks how variance-covariance levels for rewards and delays could influence choice of resources when lack of information or cognitive limitation implies that a consumer attempts to maximize its short-term rate of energy gain. Both greater expected reward and reduced expected delay clearly should enhance preference for a resource. The model predicts that increased delay variance and reduced reward-delay covariance should increase a forager's preference for a resource. A forager should be risk-averse towards reward variance when the reward-delay covariance is positive, but should become risk-prone towards reward variance when the reward-delay covariance is negative.
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Kacelnik, A., & Todd, I. A. (1992). Psychological mechanisms and the Marginal Value Theorem: effect of variability in travel time on patch exploitation. Anim. Behav., 43(2), 313–322.
Abstract: The Marginal Value Theorem (MVT) describes the behaviour that maximizes the ratio of expected gain over expected foraging time in a patchy environment. When travel time is variable, the MVT rationale and its predictions are sensitive only to the mean travel time and not to the spread or skew of the distribution. Two mechanistic arguments contradict these predictions. First, tests of the MVT have previously shown that there is a disproportionate influence of the last travel time, and second, psychological models of information processing suggest that memory for time intervals is strongly dependent on the scatter of the distribution experienced. These mechanistic concepts, combined with Jensen's inequality, suggest that patch exploitation should decrease as the scatter of the travel distribution increases. In a Skinner box experiment with pigeons, Columba livia, the problem was examined by simulating three environments with identical patches and the same mean travel time, but different travel time variability. Patch exploitation decreased with increasing variance in travel time. The results are used to argue in favour of the inclusion of realistic psychological properties as constraints in functional models of behaviour. Although both the MVT and the mechanistic models account for some features of the results, none of them can explain all the findings.
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Beauchamp, G., & Kacelnik, A. (1991). Effects of the knowledge of partners on learning rates in zebra finches Taeniopygia guttata. Anim. Behav., 41(2), 247–253.
Abstract: Many interpretations of the adaptive value of group living involve tranfer of knowledge. However, according to learning theory, being in a pair with a knowledgeable partner can have paradoxical consequences. Obtaining food by following a skilled companion may reduce the ability of naive individuals to learn about clues that signal the occurrence of food. This study examined the relation between learning and following in paris of zebra finches. Knowledgeable partners were trained to obtain food from a computer-controlled dispenser by using the information provided by a signal. For non-knowledgeable partners, the signal was irrelevant and could not be used to predict foraging opportunities. The rate of learning about the signal by naive birds that shared the experience of either knowledgeable or nonknowledgeable tutors was then examined. Naive birds learned more slowly as a result of being in a pair with a knowledgeable than a non-knowledgeable partner. Well-informed mates acted as a reliable cue to predict foraging opportunities, and thus overshadowed the independent signal. The knowledge of a partner influences learning rates in naive individuals, but in the opposite direction to that predicted by earlier accounts of learning in social contexts.
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Cuthill, I., & Kacelnik, A. (1990). Central place foraging: a reappraisal of the `loading effect'. Anim. Behav., 40(6), 1087–1101.
Abstract: Animals that provision a central place usually bring back larger loads when foraging far from home. This positive correlation between average load size and distance is typically explained as rate-maximizing behaviour in the face of a trade-off between travel costs and a decelerating rate of prey gain in food patches (the `loading effect'). By using feeders to provide wild parent starlings, Sturnus vulgaris, with constant rates of prey loading, a positive load-distance correlation was shown to exist in the absence of a loading effect (experiment I). However, in a laboratory simulation where no load was transported (experiment II). the average number of prey eaten in patch visits by self-feeding starlings was invariant with travel distance, so the explanation of the load-distance correlation in experiment I must lie in featues peculiar to central place foraging. Bottlenecks in ingestion by chicks and interruption by visual detection of nest disturbance (experiment III) were rejected as causes of the correlation. Risks of dropping prey in flight appeared low, but the risk of kleptoparasitism received weak support. The travel-load size correlation may be an adaptive response to load transport costs, as return travel times increased with the load size being carried (experiment IV).
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Reboreda, J. C., & Kacelnik, A. (1990). On cooperation, tit-for-tat and mirros. Anim. Behav., 40(6), 1188–1189.
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Cuthill, I. C., Kacelnik, A., Krebs, J. R., Haccou, P., & Iwasa, Y. (1990). Starlings exploiting patches: the effect of recent experience on foraging decisions. Anim. Behav., 40(4), 625–640.
Abstract: Laboratory and field experiments have shown that, as predicted by the marginal value model, starlings, Sturnus vulgaris, stay longer in a food patch when the average travel time between patches is long. A laboratory analogue of a patchy environment was used to investigate how starlings respond to rapidly fluctuating changes in travel time in order to find out the length of experience over which information is integrated. When there was a progressive increase in the amount of work required to obtain successive food items in a patch (experiment 1), birds consistently took more prey after long than after short travel times; travel experience before the most recent had no effect on the number of prey taken. Such behaviour does not maximize the rate of energy intake in this environment. The possibility that this is the result of a simple constraint on crop capacity is rejected as, when successive prey were equally easy to obtain up until a stepwise depletion of the patch (experiment 2), birds took equal numbers of prey per visit after long and short travel times: the rate-maximizing behaviour. A series of models are developed to suggest the possible constraints on optimal behaviour that affect starlings in the type of environment mimicked by experiment 1.
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