Energy Budget Rule Research Articles

Gender Differences in a Risk-Reduction Model of Sharing.

The current experimental study investigated human sharing within a laboratory task that modeled environmental variability. In particular, it sought to assess the efficacy of a risk-reduction model of sharing, which originated from a risk-sensitive optimization model known as the energy-budget rule. Participants were given the choice between working alone or cooperating and sharing accumulated hypothetical earnings with a fictious partner. Failure to acquire sufficient money resulted in a loss of accumulated earnings. To investigate the effects of economic context on sharing, the difficulty of meeting an earnings requirement was manipulated across conditions by changing the monetary requirement that needed to be met in order to bank earnings, which could later be exchanged for real money. In some conditions sharing was the optimal strategy (positive budget conditions), sometimes working alone was optimal (negative budget conditions), and other times neither option was optimal (neutral budget conditions). Gender differences were examined within this context to determine if males and females differed in their sharing behavior. The results suggested that males chose the sharing option more often in the positive budget condition and showed a stronger preference for the work-alone option in the negative budget condition than females.

Human choices respond to added costs according to the energy budget rule

The energy budget rule is a risk-sensitive optimal foraging model that predicts choice should be risk averse when need levels are relatively easy to meet within a foraging period (positive budget conditions), and risk prone when need levels are more difficult to meet (negative budget conditions). Although research with nonhumans has produced only limited support for the energy budget rule, analogue research with humans has shown that risky choice for monetary outcomes is typically consistent with the model’s predictions. Most human studies have tested the energy budget rule by manipulating minimum requirements, rates of gain, or reserves. The energy budget model also predicts, however, that energy expenditures (costs) can affect risk sensitivity. Two experiments therefore investigated whether monetary costs for choices would affect risk sensitivity. Adults were presented with choices between monetary options in blocks of five trials. Block earnings were paid only if earnings exceeded a minimum amount. Each trial, a monetary cost was subtracted from earnings when a choice was made. Cost magnitude was manipulated across conditions to generate one positive- (cost $0.00) and two negative-budget (cost $0.01 or $0.02) conditions. In Experiment 1, choice options produced the same mean earnings, with one producing a constant amount of money and the other a variable amount. In Experiment 2, both choice options produced the same mean amounts of money but different variances. Similar to previous earnings budget studies, choice varied as a function of budget condition. Trial-by-trial choice patterns were inconsistently predicted by a dynamic optimization model.

A meta-analytical and experimental examination of blood glucose effects on decision making under risk

AbstractPrevious research has shown that short-term changes in blood glucose influence our preferences and may affect decisions about risk as well. However, consensus is lacking about whether and how blood glucose influences decision making under risk, and we conduct two experiments and a meta-analysis to examine this question in detail. In Study 1, using a pecuniary valuation method, we find no effect of blood glucose on willingness to pay for risky products that may act as allergens. In Study 2, using risky gambles, we find that low levels of blood glucose increase risk taking for food and to a lesser degree for non-food rewards. Combining our own and previous findings in a meta-analysis, we show that low levels of blood glucose on average increase risk taking about food. Low blood glucose does not increase risk taking about non-food rewards although this is subject to heterogeneity. Overall, our studies suggest that low blood glucose increases our willingness to gamble on how much food we can get, but not our willingness to eat food that can harm us. Our findings are best explained by the energy budget rule.

An investigation of the probability of reciprocation in a risk-reduction model of sharing

A laboratory study investigated whether reductions in the probability of reciprocation would influence sharing in situations of shortfall risk. Choice in twelve adults was evaluated against the predictions of a risk-reduction model of sharing derived from a risk-sensitive foraging theory (the energy-budget rule). Participants responded on a computer task to earn hypothetical money which could be later exchanged for real money. If participants selected the sharing option, their earnings were pooled and split with a (fictitious) partner. To model shortfall risk, the task was arranged so that participants lost their accumulated earnings if it fell below an earnings requirement. Across conditions the probability that the partner would contribute to the pool was .95, .65, and 0. Choosing the sharing option was optimal under the .95 and .65, but not 0 condition. Although levels of preference for the sharing option were below optimal, participants chose it significantly more in the .95 and .65 conditions than in the 0 condition. Sharing was lower in the .65 condition than .95 condition but the difference was not statically significant. The results are consistent with prior cooperation research and demonstrate that under shortfall risk, reductions in the probability of reciprocation by partners may decrease sharing.

A Risk-Reduction Model of Sharing: Role of Social Stimuli and Inequity

The present study experimentally investigated human cooperation (sharing) in a laboratory foraging task that simulated environmental variability and resource scarcity (shortfall risk). Specifically, it investigated whether a risk-reduction model of food sharing derived from the energy budget rule could predict human cooperative behavior. Participants responded on a computer task for money and were given the choice between working alone or working with others and pooling earnings. Earnings could be kept only if the sum exceeded an earnings requirement (i.e., a need level). The effects of social variables on sharing were investigated to determine whether they constrained optimal decision making. The experiments investigated choice when participants were told the partner was a computer or a (fictitious) partner (Experiment 1) and when the earnings between the participant and partner were inequitable (Experiment 2). The results showed that social variables had no effect on decision making. Instead, sharing patterns were in accord with predictions of the risk-reduction model. These results provide additional evidence that a risk-reduction model of food sharing derived from risk-sensitive foraging models may be useful for predicting human cooperation for monetary outcomes.

Risk-sensitive foraging: changes in choice due to reward quality and delay

Past risk-sensitive foraging studies commonly manipulated delay to reward and reward magnitude, but recent risk-sensitive foraging research revealed that changes in reward quality resulted in changes in a forager's preference for a variable or fixed return. However, no studies have investigated the effects of changes in reward quality and delay to reward on risk sensitivity. Therefore, the current experiment was designed to explore rats' preference for a variable or fixed option when delay to reward and reward quality were manipulated. Using a within-subjects, ABACADA design, rats (N = 10) choose between a variable and constant option that delivered six food pellets but the amount of sugar (i.e. reward quality) and delay to reward differed per condition. In each baseline condition, pellets were 100% sugar and delivered after a 2 s mean delay. Subjects displayed a significant preference for the variable option in all baseline conditions. In condition B, pellets were 20% sugar, delivered after a 2 s mean delay, and rats were risk indifferent. In condition C, rats displayed a significant preference for the variable option when delay was 10 s and reward quality was 100%. Finally, in condition D, subjects showed the strongest variable option responses among all treatments when both reward quality and delay to reward were manipulated (i.e. 20% sugar pellets and 10 s mean delay). Preference was assessed relative to the daily energy budget rule, the scalar utility theory and the sequential choice model. The sequential choice model provided the most comprehensive and accurate prediction of subjects' preferences.

On the origin of risk sensitivity: the energy budget rule revisited

The risk-sensitive foraging theory formulated in terms of the (daily) energy budget rule has been influential in behavioural ecology as well as other disciplines. Predicting risk-aversion on positive budgets and risk-proneness on negative budgets, however, the budget rule has recently been challenged both empirically and theoretically. In this paper, we critically review these challenges as well as the original derivation of the budget rule and propose a `gradual' budget rule, which is normatively derived from a gradual nature of risk sensitivity and encompasses the conventional budget rule as a special case. The gradual budget rule shows that the conventional budget rule holds when the expected reserve is close enough to a threshold for overnight survival, selection pressure being significant. The gradual view also reveals that the conventional budget rule does not need to hold when the expected reserve is not close enough to the threshold, selection pressure being insignificant. The proposed gradual budget rule better fits the empirical findings including those that used to challenge the conventional budget rule.

A changing but not an absolute energy budget dictates risk-sensitive behaviour in the honeybee

Animals are sensitive to risk or the variability of a reward distribution, and the energy budget rule of risk sensitivity theory predicts that it is adaptive for an animal to be risk averse when it is on a positive energy budget and to be risk prone when it is on a negative budget, because the utility of a potential large reward is much higher in the latter case. It has, however, been notoriously difficult to find conclusive empirical support for these predictions. We performed a comprehensive test of the energy budget rule in the honeybee, Apis mellifera, by constructing empirical utility functions and by testing the choice of bees for a constant or variable reward with an olfactory conditioning assay subsequent to manipulating their energy budgets. We demonstrate that a decline in energetic state leads to an increasing choice for a variable reward, while an increase in energetic state leads to an increased choice for a constant reward. We then show that subjects maintained on constant high or low energy budgets are risk indifferent, which suggests that an animal must perceive a change in its energetic state to be risk sensitive. We discuss the challenges of finding empirical evidence for the energy budget rule and the necessity of integrating physiological assays in these tests. Based on our previous results showing that parasitic infections cause an energetic stress in honeybees, we also discuss the possibility of energetic shortfall being responsible for the observed display of risky behaviour in infected bees.

Optimal risky choice in humans: Effects of amount of variability

The present study investigated whether the predictions of an optimal risk-sensitive foraging model (the energy-budget rule) would extend to humans' choices between high- and low-variance monetary response options. In Experiment 1, participants were presented with repeated choices between two options that had the same mean values but different variances across positive- and negative-budget conditions. In Experiment 2, a within-subject comparison was conducted to investigate choice under positive- and negative-budget conditions when the options were either (a) a fixed option and a high-variance option, or (b) a low-variance option and a high-variance option. Session-wide choices were analyzed in relation to the predictions of the energy-budget rule and sequential choices were analyzed with dynamic optimization modeling. When both options were variable choice was generally consistent with predictions of the energy-budget rule and was more risk prone under negative-budget than positive-budget conditions. Sequential choices were sensitive to local budget conditions, but choices were less consistent with optimality when both options were variable, possibly because of the greater similarity in expected earnings for optimal and nonoptimal choices in these conditions. Overall, the results provide further evidence that the energy-budget rule may have broad applicability and that it can extend to human risky choice between multiple variable response options.

Effects of monetary reserves and rate of gain on human risky choice under budget constraints

The energy-budget rule is an optimal foraging model that predicts that choice should be risk averse when net gains plus reserves meet energy requirements (positive energy-budget conditions) and risk prone when net gains plus reserves fall below requirements (negative energy-budget conditions). Studies have shown that the energy-budget rule provides a good description of risky choice in humans when choice is studied under economic conditions (i.e., earnings budgets) that simulate positive and negative energy budgets. In previous human studies, earnings budgets were manipulated by varying earnings requirements, but in most nonhuman studies, energy budgets have been manipulated by varying reserves and/or mean rates of reinforcement. The present study therefore investigated choice in humans between certain and variable monetary outcomes when earnings budgets were manipulated by varying monetary reserves and mean rates of monetary gain. Consistent with the energy-budget rule, choice tended to be risk averse under positive-budget conditions and risk neutral or risk prone under negative-budget conditions. Sequential choices were also well described by a dynamic optimization model, especially when expected earnings for optimal choices were high. These results replicate and extend the results of prior experiments in showing that humans' choices are generally consistent with the predictions of the energy-budget rule when studied under conditions analogous to those used in nonhuman energy-budget studies, and that choice patterns tend to maximize reinforcement.

Risk Reduction and Resource Pooling on a Cooperation Task

Two experiments investigated choice in adult humans on a simulated cooperation task to evaluate a risk-reduction account of sharing based on the energy-budget rule. The energy-budget rule is an optimal foraging model that predicts risk-averse choices when net energy gains exceed energy requirements (positive energy budget) and risk-prone choices when net energy gains fall below energy requirements (negative energy budget). Because sharing can minimize variability in energy gain (i.e., is a risk-averse strategy), the model predicts that sharing should occur under positive but not negative budget conditions. Energy budgets were modeled by substituting money gains for energy gains and earnings requirements for energy requirements. Participants chose between work- alone or work-with-others (sharing) response options. Experiment 1 investigated the effects on choice of manipulating the value of the earnings requirement and the presence of the partner’s money counter. Choice for the sharing option varied as a function of the earnings requirement in a pattern consistent with the predictions of the energy-budget rule. The presence of the partner’s money counter did not influence preference. Experiment 2 replicated Experiment 1 and also showed that under conditions with no earnings requirement (conditions in which the energy-budget rule makes no predictions), subjects often preferred the sharing option over the independent option when sharing increased the partner’s 13arnings, and that subjects often preferred an independent option over the sharing option when the independent option produced a constant earnings amount. Overall, the results replicate and extend the results of earlier earnings-budget studies and further show that laboratory procedures are useful for evaluating the plredictions of risksensitive and social-foraging models.

CONTENTS OF VOLUME

The literature on risk-sensitive foraging theory provides several accounts of species that fluctuate between risk-averse and risk-prone strategies. The daily energy budget rule suggests that shifts in foraging strategy are precipitated by changes in the forager’s energy budget. Researchers have attempted to alter the organism’s energy budget using a variety of techniques such as food deprivation, manipulation of ambient temperatures, and delays to food reward; however, response-effort manipulations have been relatively neglected. A choice preparation using a wheel-running response and rats examined risk-sensitive preferences when both response effort and reward amounts were manipulated. Concurrently available reinforcement schedules (FI/60 and VI/60) yielded equivalent food amounts per unit time in all treatments. Two levels of response effort (20 or 120 g tangential resistance) and two levels of reward amount (three or nine pellets) were combined to form four distinct response–effort/reward–amount pairings. Increasing reward amounts significantly shifted choice toward the FI schedule in both response-effort conditions. The incidence of choice preference and the magnitude of shifts in choice were greater for the high response-effort conditions than for the low response-effort conditions. Implications of the significant interaction between response effort and reward amount are discussed in terms of a general energy-budget model.

Increased effort requirements and risk sensitivity: a comparison of delay and magnitude manipulations.

Reward magnitude and delay to reward were independently manipulated in two separate experiments examining risk-sensitive choice in rats. A dual-running wheel apparatus was used and the tangential force resistance required to displace both wheels was low (50g) for half of the subjects, and high (120g) for the remaining subjects. Concurrent FI30-s and FI60-s schedules delivered equivalent amounts of food reward per unit time (i.e. 5 and 10 pellets of food, respectively), and these conditions served as the baseline treatment for all subjects. Variability, either in reward magnitude or delay, was introduced on the long-delay (60s) schedule during the second phase. All subjects were returned to the baseline condition in the third phase, and variability was introduced on the short-delay (30s) interval schedule during phase four. The subjects were again returned to the baseline condition in the fifth and final phase, ultimately yielding a five-phase ABACA design. Original baseline performance was characterized by a slight short-delay interval preference, and this pattern of performance was recovered with each subsequent presentation of the baseline condition. Overall, the data obtained from the reward magnitude and delay-to-reward manipulations were indistinguishable; subjects experiencing low-response effort requirement behaved in a risk-indifferent manner and subjects experiencing high-response effort requirement preferred the variable schedule. Implications for the daily energy budget rule on risk-sensitive foraging are discussed in light of these findings.

RISK-SENSITIVE FORAGING IN COAL TITS

Current theory of risk-sensitive foraging predicts that foragers should choose feeding sites on the basis of variation in as well as mean reward rate when there is a shortfall in their food supply or a decrease in their energy budget. For a given mean reward delay, they should choose high variance feeding sites if they are running below energy requirement, but low variance sites if they are running above. It has been suggested that the smaller the animal size, the stronger the preference reversion between high and low variable feeding sites. Previous tests of the energy budget rule when there was time variability have used bird species heavier than 80 g. Hence we tested energy budget rule predictions with coal tits Parus ater, a bird of 9 g of body mass, foraging at two feeding sites with high or low variability in food delivering delay. We manipulated energy budgets by controlling air temperature in the laboratory. In one treatment (positive budget), individuals were allowed to eat at the level of their own ad-libitum daily consumption and the air temperature was set to 24°C, while for the other treatment (negative budget), temperature was set to 14°C, and food availability was limited to the maximum daily intake observed in the positive budget treatment. When air temperature was low, daily intake increased but body mass decreased. Birds were also less active in the low temperature treatment, hopping less times every day. Latency to peck decreased as well, pecking for food when it was available sooner than in the high temperature treatment. These results show that coal tits were living in a negative energy budget when air temperature was set to 14°C. Preference for the variable feeding site was greatest in the negative energy budget, as it was predicted by the energy budget rule. Contrary to the energy budget rule, coal tits consistently preferred the variable option also in the positive energy budget. Possible explanations for these results are explored, including alternative foraging models to the energy budget rule.

Risk-sensitive foraging in rats: the effects of response-effort and reward-amount manipulations on choice behavior

The literature on risk-sensitive foraging theory provides several accounts of species that fluctuate between risk-averse and risk-prone strategies. The daily energy budget rule suggests that shifts in foraging strategy are precipitated by changes in the forager’s energy budget. Researchers have attempted to alter the organism’s energy budget using a variety of techniques such as food deprivation, manipulation of ambient temperatures, and delays to food reward; however, response-effort manipulations have been relatively neglected. A choice preparation using a wheel-running response and rats examined risk-sensitive preferences when both response effort and reward amounts were manipulated. Concurrently available reinforcement schedules (FI/60 and VI/60) yielded equivalent food amounts per unit time in all treatments. Two levels of response effort (20 or 120 g tangential resistance) and two levels of reward amount (three or nine pellets) were combined to form four distinct response–effort/reward–amount pairings. Increasing reward amounts significantly shifted choice toward the FI schedule in both response-effort conditions. The incidence of choice preference and the magnitude of shifts in choice were greater for the high response-effort conditions than for the low response-effort conditions. Implications of the significant interaction between response effort and reward amount are discussed in terms of a general energy-budget model.

Energy budgets and risk-sensitive foraging in starlings

The effect of energy budget on risk-sensitive foraging was assessed in a laboratory experiment using starlings (Sturnus vulgaris). Subjects chose between two options offering the same mean amount of food per trial, but differing in variance: a “fixed” option gave 5 units food in every trial, and a “variable” option gave 2 or 11 units food with probabilities 2/3 and 1/3, respectively. We manipulated energy budgets by controlling the cumulative amount of food received by each bird at the end of a day. In one treatment (positive budget) individuals were allowed to eat at the level of their own ad-libitum daily consumption, while for the other (negative budget), food was rationed to provoke a steady drop in body weight during the experimental period. No subject was allowed to drop below 80% of its ad libitum body weight. Contrary to predictions from the “energy budget rule” and contrary to reported results of some other studies, starlings significantly preferred the “fixed” option irrespective of energy budget conditions. Our results support the view that persistent risk aversion for food amounts and risk proneness for food delays are the norm, and shifts in risk attitude according to energy budget are exceptions. Several algorithms, which may have evolved to maximize energetic pay off between variable food sources, can produce this trend as a side effect. We discuss two of these algorithms: (1) maximization of local (per trial) rate as opposed to global rate of gains, with longer handling time for larger rewards, and (2) choosing larger rewards and smaller delays subject to Weber's law in the memory for the parameters of each food supply.

An Introduction to Risk Sensitivity: The Use of Jensen's Inequality to Clarify Evolutionary Arguments of Adaptation and Constraint

Synopsis. I review the basic rationale for risk-sensitive foraging, and present a few of the most common expressions of risk-sensitivity theory. A simple heuristic, the energy-budget rule, and the z-score model are explained. These functional models of risk sensitivity assume or explicitly model fitness as a nonlinear function of an animal's energy state. For such nonlinear relationships, Jensen's inequality predicts that the fitness realized by an animal with a more constant energy state may be higher or lower than the fitness resulting from a variable energy state with the same mean, depending on the shape of the fitness function. Predictive func? tional models of behavior, like the energy-budget rule and the z-score model, depend on specific features of the function relating energy state to fitness, which may or may not be general features for most organisms. While behavioral ecologist have studied the functional significance of animal responses to variation in foraging rewards, psychologists have long studied the psychological mechanisms by which preferences for vari? able or constant rewards are expressed. Jensen's inequality is applied here too; psychologists propose nonlinearities in the perception and processing of information. The growing number of different relationships that might account for risk-sensitive behavior is a potential source of confusion. I advocate returning to the basics, Le., that hypotheses to explain risksensitive behavior should specify precisely the assumed nonlinear rela? tionships.

Risk-sensitive foraging behaviour of the round-eared elephant shrew (Macroscelides proboscideus)

We examined the risk-sensitive foraging behaviour of the round-eared elephant shrew by open-economy choice experiments, in which animals were deprived of food immediately prior to experiments but given food ad libitum afterwards, to test the energy budget rule. The energy budget rule states that if an animal's (daily) energy budget is negative it should behave in a risk-prone manner. A risk-prone elephant shrew should select food from a more variable rather than a constant feeding station, although both feeding stations yield the same average return. The choice of a variable station can indicate the degree to which an animal is an energy-shortfall minimizer. Elephant shrews running below energy requirement did not choose feeding stations in accordance with the rule. Under laboratory conditions, approximating either average summer or winter temperatures, elephant shrews showed risk-averse behaviour. A polycyclic activity profile, the ability to switch the diet, and greater than expected physiological control over energy balance, may favour a continuously foraging animal such that short-term energy deficits are minimized. We argue that, under these conditions, a risk-averse response to reward-size variance is expected, because an elephant-shrew may not reliably perceive those circumstances under which risk-prone behaviour should be adopted.