Antra. Behav., 1982,30, 719-727
ASPECTS OF RISK-AVERSION IN FORAGING WHITE-CROWNED SPARROWS BY THOMAS CARACO
Department of Biology, University of Rochester, Rochester, New York 14627 Abstract. Two series of aviary experiments with white-crowned sparrows (Zonotrichia leucophrys) are reported. The first series attempts to mimic foraging choices between microhabitats. The second series examines foraging choices made within a single artificial patch, a design intended to resemble dietary selection. In all experiments subjects chose between a constant food reward and a variable reward, the mean of which equalled the constant reward. Each experiment allowed the bird to feed at an overall rate greater than that minimally required for daily energy balance. In both series of experiments, the birds usually preferred the constant reward. Results of the first series do not differ significantly from previously reported preferences of dark-eyed juncos (Junco hyemalis), birds weighing 10 g less than the white-crowned sparrows. Several recent discussions of foraging ecology propose that animals respond not only to the average values, but also to the variances of net benefits associated with strategic options (e.g. Real 1980; Caraco 1981a). One conceptual approach to the study of responses to reward variance considers risk-averse and risk-prone behaviour. Risk-aversion is defined as preference for a probability distribution's mean reward over the distribution itself (Keeney & Raiffa 1976, page 149); risk-proneness implies that a distribution is preferred over its mean reward. These definitions are quite simple, but the difference in preference can lead to quite different foraging strategies (e.g. Oster & Wilson 1978; Caraco 1980). A forager's aversion to, or preference for, variance in benefits and costs may depend on its energy budget (Caraco et al. 1980), Foragers expecting to meet all energy requirements should be risk-averse (Stephens 1981; Pulliam & Millikan, in press). Risk-aversion in this case reduces the probability of an energy deficit, thereby reducing the probability of starvation. Foragers anticipating an energy deficit may, in contrast, be risk-prone. In these circumstances risk-prone behaviour increases the probability of fulfilling daily energy demands and consequently decreases the probability of starvation (Stephens 1981; Pulliam & Millikan, in press). There is substantial evidence that foraging animals' preferences can respond to variance about a given average benefit or cost. The operant psychology literature contains a number of examples (see citations in Lea 1979). Pimm (1978) reports that aggressively dominant hummingbirds prefer more predictable (less
variable) nectar rewards, while Real (1981) and Waddington et al. (1981) demonstrate riskaversion in nectarivorous insects. In the laboratory, yellow-eyed juncos (Junco phaeonotus) foraged in a risk-averse and then in a riskprone manner, and their preferences were consistent with the energy budget argument outlined above (Caraco et al. 1980). Closely corresponding results have been obtained with Junco hyemalis, the dark-eyed junco (Caraco 1981b). MacArthur & Pianka's (1966) seminal paper discussed two aspects of foraging ecology. They pointed out that an animal might economically choose certain patch types from among those available, and might select certain food types from among those found within a single foraging patch. For convenience, I term these respective foraging choices as between-patch and withinpatch decisions. This paper examines b o t h of these choice problems in experiments involving white-crowned sparrows (Zonotrichia leueophrys)'. Section I reports between-patch experiments (conducted as in Caraco 1981b) and compares response to reward variance in the subject sparrows, weighing 29 g, with the behaviour of dark-eyed juncos, which weigh 19 g on average. The small number of subjects constrains the generality of the comparison, but it is reasonable to consider plausible relationships between avian body size and risk-aversion. Section II examines within-patch choices. The design mimics a dietary selection problem. Two food types are made available in a reasonably large spatial array, resembling a single patch. Mean rewards of the food types are equal, but one type is constant while the other is variable; The experiments ask if the sparrows' aversion to 719
risk noted in choices between laboratory microhabitats extends to dietary selection. I. Between-Patch Choice and Body Size Several authors (e.g. Schoener 1969; Taylor 1976) propose that body size can be an important aspect of foraging ecology. Therefore, I thought it worthwhile to investigate the possibility that body size influences risk-aversion. In between-patch experiments with two species of juncos (Caraco et al. 1980; Caraco 1981b), the birds avoided variable rewards when they could expect a positive daily energy budget. The average reward at each trial in those experiments ranged from 1 to 7 millet seeds. There obviously are species of birds for which these rewards, or their energy equivalent in a more appropriate form, would bear little resemblance to the size of food items taken in nature. However, by restricting attention to species that consume grain by husking one seed at a time, one might find an effect of body size when different species experience similar experimental procedures. An argument for a relationship between body weight and risk-aversive foraging can be constructed by drawing on the insights of Calder (1974) and Downhower (1976). Metabolic rate (R) is a power function of body size (w). For both resting and existence metabolism, the exponent is less than unity: R = a w ~, 0 < 3, < i
For given conditions (ambient temperature, etc.), larger birds have greater metabolic requirements than smaller birds. However, larger birds do not need as much energy per gram body weight, since R is a concave function of w. Energy stored as fat (E) constitutes approximately a constant fraction of total body weight in overwintering passerines; E - b w . King & Farner (1966) discuss further aspects of avian fat storage. The length of time (T) a bird ca n persist without food should depend on the ratio of stored energy to metabolic rate: T =
As long as 7 < 1, 8 T / O w > 0. That is, larger birds can survive longer when deprived of food. This capacity might buffer larger birds against short-term variation in foraging benefits and costs. More specifically, the physiological impact of a given deviation below a bird's mean rate of food intake might vary inversely with body size. Therefore, when a larger bird can expect to meet
energy requirements, behavioural aversion to a given level of food reward variance per foraging effort might decline. Of course, this possibility should not be confused with the tendency of a bird of a given size to become risk-prone (or less risk-averse) as its energy budget varies from positive to negative (Caraco 1981b). An alternative hypothesis suggests that any non-breeding forager should be risk-averse whenever (a) energy demand requires efficient foraging (i.e. when different strategies imply real differences in survivorship), and (b) risk-aversion provides a lower probability of starving than does either insensitivity to variance or risk-prone behaviour. The relative advantage of risk-aversion might decrease as weight increases. But response to risk need not necessarily depend on body size, as long as survivorship demands efficient foraging. Foraging sparrows move through a variety of microhabitat patches in any given day. Therefore, I presented white-crowned sparrows (mean weight- 29 g) with a series of between-patch choices nearly identical to experiments in which dark-eyed juncos (mean weight = 19 g) behaved predominantly in a risk-averse manner. The design attempts to isolate reward variance as a factor potentially influencing microhabitat utilization and allows a preliminary comparison of the behaviour of the two species. Methods Three white-crowned sparrows were captured in September I980. Each bird was housed in a separate aviary. All aviaries are equipped with two feeding stations, separated by a large partition. At each station an experimenter, positioned behind a one-way mirror, presented small dishes containing predetermined numbers of seeds. The dishes were attached to sliding trays which were pushed into the aviary through sheet metal sleeves mounted in the wall. The design of the chambers is otherwise as described in Caraco et al. (1980). The birds learned to perch at a point on the midline between the two feeding stations in order to obtain food. To properly document preferences for food rewards, one must guard against an animal's position preference for one side of its enclosure. Each bird was tested for position preference before the experiments began and retested every 3 weeks. The control procedure was accomplished as detailed in Caraco et al. (1980). One bird developed a position preference before being involved in any experiments. After
CARACO: RISK-AVERSE WHITE-CROWNED SPARROWS being moved to a different aviary, this preference disappeared. Thereafter, no significant problems with position preference occurred. When not involved in an experiment, the birds had ad libitum access to millet seed. The food was spread across a tray positioned on the midline between the feeding stations, at a point near the back of the aviary. Grit and water, with avian vitamins added, were always available. Every 2 weeks the birds received a small amount of ground beef to insure proper nutrition. Experimental protocol duplicated that which most often produced risk-aversion in juncos. The subjects were deprived of food for 1 h before an experiment and fed at an average rate of 1 millet seed every 30 s during an experiment. Though several factors govern daily energy budgets, it's sufficient to consider conditions applicable to each experiment reported in this section. Ambient temperature in each aviary is maintained at a constant 10 C. Lights are turned on for exactly 10 h (0730 to 1730 hours) each day. To estimate the amount of food required to meet daily energy costs and maintain body weight, the exact number of seeds that subjects consumed (while feeding ad libitum) during each half hour period (over the course of 10 h) was counted. Known numbers of seeds were provided at the two stationS at the beginning of each time period, and the number remaining 30 min later revealed consumption. These observations were recorded on two days for two of the birds, and on three days for the third bird. The data indicate that over 10 h a subject white-crowned sparrow consumes an average of 872 rni!let seeds (SF~= 34, N = 7). During the first 1.5 h of the foraging day, a bird consumes an average of 162 seeds (SE = 10.6, N = 7). All experiments began after a 1-h deprivation period, which was always initiated at 0900 hours. A subject then needs 710 seeds ( = 872 -- 162) during the remaining 7.5 h, so the minimum required feeding rate is 95 seeds/h. The experimental feeding rate was 120 seeds/h, so the birds could expect to fulfil daily energy requirements. In each of the between-patch experiments, a constant reward (s seeds) was presented at one station, and a variable reward was presented at the other station. The variable reward provided either sl or s2 seeds with equal probability. The expected value of the variable reward always equalled the constant reward; [sl +sz]/2 = s . Since the means were equal, and the variable reward was symmetric about its expectation (no skew), a significant preference for one station
should indicate a response to benefit variance. Before each experiment began, a coin-toss assigned tile constant reward to one station and the variable reward to the other side of the aviary. The same 14 preference tests were completed with each subject between October 1980 and February 1981. Each bird experienced a random sequence of experiments. The birds were released in good condition on April 1, 198l. Most experiments consisted of 24 forcedchoice learning trials, followed by 26 preference trials. The number o f preference trials was reduced to 20 in some of the longest experiments. Only one station provided a food dish at each forced-choice trial. During these learning trials the bird visited each station t2 times in a random order and obtained the same total number of seeds at each station. Learning trials obviously reduce some effects of sampling behaviour during subsequent preference tests, since 24 trials should allow a bird to discriminate reward characteristics in these simple experiments (Krebs et al. 1978; Lea 1979). The subject also can acquire an estimate of its expected energy budget during learning trials, based on its feeding rate (Caraco 1981b). The preference test immediately followed learning trials. The two food dishes were offered simultaneously and the bird selected one at each trial. Caraco et al. (1980) fully explain these procedures. Results of each experiment's preference trials were tested against the null hypothesis of indifference (equal preference), which assumes that the choice probabilities do not differ significantly from 0.5. The analysis of choice probabilities assumes that each preference trial is independent; this was tested by contingency table analysis as discussed in Caraco et al. (1980). For each bird (designated as A, B and C), the data first were categorized by type of result: riskaversion, indifference and risk-proneness. This procedure yielded eight contingency tables, since B never was indifferent. Each calculation indicated that sequential choices were statistically independent. Since the number of seeds provided by the variable reward at each trial was an independent realization of a random variable, a bird could gain no advantage by strategies such as win-stay, lose-shift, etc. Results Table I lists the results of the 42 between-patch experiments. Risk-aversion was recorded 26 times, indifference occurred nine times, and
seven experiments showed risk-prone behaviour. Risk-prone responses appear at relatively low values of the variance-to-mean ratio of the variable reward (designated by 0). The three types o f categorical result occur with nearly equal frequency when 0 ~ 1, but risk-aversion clearly predominates when 0 > 1. I conducted two comparisons o f these data with results obtained in similar experiments involving dark-eyed juncos (see Table l a of Caraco 1981b). The first analysis treats the data categorically; each result is classified as risk-averse, indifferent or risk-prone behaviour. Ten of the 14 experiments listed in Table I previously were conducted with darkeyed juncos. The remaining four values of 0 in Table I n o t included in this analysis are: 0.3, 1.3, 1.5 and 1.8. In the other 30 experiments whitecrowned sparrows were risk-averse 19 times, indifferent five times, and risk-prone six times. In the same experiments dark-eyed juncos were risk-averse 23 times, indifferent five times, and risk-prone twice. Categorical frequencies for the two species do not differ significantly (Z~ = 2.38,
T h e second analysis employs the proportional utilization of the certain reward across preference trials (designated by pc, entered in Table I). T o satisfy assumptions o f the analysis, I t o o k the average pe value for each o f the 14 preference tests and then c o m p a r e d these to m e a n values obtained in 11 tests with each of three dark-eyed juncos (Pc data in Table l a of Caraco 1981b).
Since more than 25 ~o of the values fall in the interval (0.3, 0.7), I transformed the data by the sin -1 method (Sokal & R o h l f 1969, page 386) before conducting an analysis o f covariance. I t o o k the two species as treatments~ The best linear description of the transformed data (p(pe) designates radians) involves functions of In 0. Dark-eyed juncos:
P(Pe) = 0.76+0.24 In 0, r ---- 0.663 F o r white-crowned sparrows: P(Pe) = 0.66+0.27 In 0, r = 0.661 The regression slopes show no significant difference (Fl,z0 = 0.04, NS). Additionally, the intercepts (therefore, the weighted means) do not differ significantly (Fl,m = 0 . 7 6 9 , NS). The analysis implies that mean po values do not differ significantly between treatments, across the observed values of 0. Within the limitations o f the data, the difference in b o d y size between species does not imply a difference in the degree of riskaversion. One other aspect of the data in Table I m a y be noted. There are five preference tests (15 experiments) where a bird chose between s seeds for certain and a variable reward where sl = s - - 3 and s2 = s + 3. The five values of s meeting this criterion are 3, 4, 5, 6 and 7. Since the variance of the variable reward remains a constant (9.0) across five levels of mean reward, one can ask if
Table I. Preference and pc Value, Between-patch Choice
A 0 0.3 0.5 0.8 1.0 1.0 1.3 1.33 1.5 1.8 2.0 2.25 3.0 4.0 5.0
Test 31 (2, 4) (1, 3) P2 5P (3, 7) (0, 2) P1 4P (2, 6) 7I (4, 10) 3P (1, 5) 6P (3, 9) 5I (2, 8) 2P (0, 4) 4P (1, 7) 3P (0, 6) 4P (0, 8) 5P (0, 10)
0.42* 0.04** 1.0 0.16"* 0.88 0.42* 0.77 0.77 0.65* 0.92 0.96 0.92 1.0 0.76
(2, 4) P3 2P (1, 3) (3, 7) P5 (0, 2) P1 4P (2, 6) 7P (4, 10) (1, 5) P3 6P (3, 9) 5P (2, 8) 2P (0, 4) 4P (1,7) 3P (0, 6) 4P (0, 8) 5P (0, 10)
0.27** 0.83 0.25** 0.08** 0.95 0.75 0.15"* 0.95 0.95 0.76 0.92 0.96 0.9 0.85
3I (2, 4) 2I (1, 3) 5I (3, 7) (0, 2) P1 4I (2, 6) 7P (4, 10) 3I (1, 5) 6P (3, 9) 5P (2, 8) 2P (0, 4) 4P (1, 7) 3P (0, 6) 4P (0, 8) 5I (0, 10)
0.62* 0.65* 0.38* 0.04** 0.45* 0.75 0.42* 0.77 0.8 0.76 0.85 0.75 0.85 0.54*
0 is the variance-to-mean ratio of the variable reward, s P(sl, ss) means that s seeds with certainty is preferred significantly over a reward where sl and s2 seeds occur with equal probability. I indicates indifference between the two rewards. (sl, s2)P means the variable reward is preferred significantly, pc is the proportional utilization of the certain reward. A single asterisk (*) after pe indicates indifference. A double asterisk (**) indicates risk-proneness.
CARACO: RISK-AVERSE WHITE-CROWNED SPARROWS risk-aversion in these sparrows is better described as constant or decreasing (Keeney & Raiffa 1976). Constant risk-aversion implies that the response to a given level of variance is independent of the mean reward. Decreasing riskaversion implies that the response to a given level of variance attenuates as the mean reward increases, in these experiments I take Ope/Os = 0 as suggesting constant risk-aversion and 3pe/~3s < 0 as suggesting decreasing risk-aversion. These criteria are not actually sufficient to distinguish the two behaviours in a strict sense. Caraco et al. (1980) discuss conditions required for exact discrimination. Transforming the pe values to radians, I find that p(p~,) and mean reward correlate negatively (r -- -- 0.56, P < 0.05). The data are more completely described by the regression: P(pe) -- 0.72+0.23 s -- 0.032 s 2, R ~ == 0.98 The quadratic term is significant (FI,la - 12.29, P < 0.005), indicating thatpe decreases for s -~ 4 through 7. The conclusion is tentative, but the data appear consistent with decreasing risk aversion, as suggested for yellow-eyed juncos (Caraco et al., 1980). Discussion The experiments demonstrate that whitecrowned sparrows can sense and respond to variance in foraging benefits when they're presented with a choice between two 'patch' types. When the variance of the variable reward exceeds its mean, the birds were usually riskaverse. Consistent risk sensitivity in laboratory experiments implies that response to reward variance could significantly influence behaviour in nature. I failed to find a statistical difference in comparing these results with the behaviour of darkeyed juncos. Risk-aversion and choice probabilities were quite similar, though the larger size of the white-crowned sparrows meant that they required more food per day than the juncos did. The small number of individuals restrains the generality of any comparison at the species level. However, it's not surprising that a moderately stressed bird, which can expect to meet energy requirements, forages risk-aversively. In these experiments body size did not govern the ranking, in terms of survivorship, of behavioural options. Variation in body size should influence behaviour when size differences imply that different constraints on strategy are effective, or when the 'fitness' ranking of behavioural alternatives de-
pends on size (Schoener 1.969; McNaughton & Wolf 1973, page 261). Only two of 42 experiments resulted in exclusive utilization of one of the food sources, Non-exclusive choice occurs commonly in this type of experiment, even though birds usually exhibit distinct preference. For those favouring an 'adaptive' explanation, this allocation of be= haviour might represent selection of a mostpreferred risk lying between the minimal (Pc = 1) and the maximal (pc = 0) variance attainable (Coombs & Huang 1976). Partial preference also might reflect sampling behaviour (Oster & Heinrich 1976; Gill & Wolf 1977; Krebs et al. 1977; Pyke et al. 1977; Real 1981). Animals in temporally varying environments should sample currently non-preferred, but potentially profitable, resources. Though sampling must be important in nature, I think that non-exclusive choice in these egperiments results simply from the inherent stochasticity of the animals' behaviour, and no adaptive explanation need be invoked. II. Within-Patch Choice In addition to choices among patches, MacArthur & Pianka (1966) discuss dietary selection within a patch. Interest in this area generally focuses on predicting how a forager's diet may deviate from the pattern of available food types. Consider a patch where two prey types occur at high density, so that time and energy expended while searching for a potential food item do not influence preference. Suppose that type 1 items cannot escape a forager. Type 2 items are k(k > 1) times as energetically profitable as type 1, but type 2 items are captured in only 1/k of the forager's attempts. The average reward is the same, but type 2 is more variable. A risk-averse forager will prefer type 1 items. In between-patch choices, white-crowned sparrows were most often risk-averse. If they chose a variable reward at a particular trial and received the lower number of seeds, they were required to wait before another choice was offered. This delay allowed some control over the subject's energy budget, and was intended as analogous to the travel time spent moving between patches of microhabitat. In the within-patch situation pictured here, the forager can almost immediately select another item after choosing the variable option and obtaining no reward. Hence, the 'penalty' associated with utilization of the variable reward is reduced, so that risk-aversion
might be less important. But both Real (1981) and Waddington et al. (1981) demonstrate that nectarivorous insects are risk-averse while exploiting two types of artificial flowers within a small experimental patch. Therefore, a roughly similar study was conducted with white-crowned sparrows. The purpose was to ask if birds that foraged risk-aversively in between-patch choices would retain that behaviour in within-patch choices. Methods The three white-crowned sparrows of section I also were subjects in this study. In each experiment in the second series, a number of plastic petri dishes (30 mm diameter) were placed on the f l o o r of the aviary in a random and independent manner. Half of the dishes held a constant number (s) of millet seeds mixed with grit. The dishes were covered with a small piece of construction paper. The colour of the paper over eaeh dish containing s seeds was selected randomly fFom among four possibilities: pink, yellow, blue and white. The other dishes contained variable rewards and some grit, and each was covered by a piece of paper of a single colour chosen randomly from the three remaining. Before any of these experiments were conducted, the birds had learned quickly to remove the paper from the dishes. I did not find a bird with a preference for, or an aversion to, a particular colour. The average of the variable reward was always s seeds. For each bird, experiments involved three levels of average reward (s = 2, 3 and 4) and three levels of predictability (n) of the variable reward. For n -- 1/2 and 1/3, a total of 36 dishes were placed in the aviary; for n = 1/4, 40 dishes were used. Among the variable dishes, a fraction (1 - - g ) contained 0 seeds, and the rest held (s/n) seeds. So, the certain reward provided s seeds with no variance. The variable reward's expectation was s seeds, and its variance was s2[(1 -- ~)/n]. Experiments began at 0930 hours, after the birds had been deprived of food for 30 rain. There were no training trials per so. The dishes were placed in the aviary, and the bird commenced foraging immediately. The subject was allowed to feed until either it had visited half of the dishes or 5 rain had elapsed. Therefore, a pure strategy was possible (though never realized), and relative availability of the two types could not strongly constrain overall choice probabilities. Each 5-rain (or shorter) feeding
period is termed a foraging bout. Each experiment consisted of six bouts, with an inter-bout delay of 10 min. All dishes were removed between bouts, and the seeds were replenished. Procedures allowed the birds to anticipate more than enough food to meet energy costs. During the course of experiments, the minimum required feeding rate was 89 seeds/h, and the average feeding rate achieved was 177 seeds/h. Each visit to a feeding dish was recorded during the course of the six foraging bouts. Occasionally a bird re-visited a dish from which it previously had removed the paper. Since the number of re-visits was small, they are included in the data. Re-visits usually involved a dish with a relatively large number of seeds that the bird had not consumed totally during the first visit. Data froln the six bouts were combined into a single sequence of choices tbr each experiment. The ratio of the number of selections of the certain reward to the number of visits to both types was calculated for the first 10 choices (designated by pl0), the first 15 choices (p15), the first 30 choices (pa0), the 40 choices (p4o), the entire sequence (Pr), and the final 30 choices
Each sequence first was examined to see if the outcome realized when the variable reward was selected influences the next choice (certain or variable). Chi-square indices of heterogeneity were calculated for data sets categorized simultaneously by the following: subject, result based on !7T value (risk-averse, indifferent or riskprone), and predictability. The procedure was carried out for both the first 30 and the last 30 selections. For each subject, heterogeneity also was tested by summing observations across predictability within categorical response to risk, for both the first 30 and the last 30 choices. Neither entire sequences nor combinations of the first and last 30 selections were tested, since choice probabilities varied through time in most experiments. Results The 27 experiments entailed 162 foraging bouts. Of this total, 63 bouts (39~) were terminated before 5 rain had elapsed, since the bird visited half of the dishes in less time. The average number of dishes visited per experiment was 87.5 (SD = 21.6) I conducted 32 heterogeneity tests to detect sequential dependence of choices. Most Chisquare values (30 of 32) revealed that sequential
CARACO: RISK-AVERSE WttITE-CROWNED SPARROWS selections were independent. The two significant heterogeneity values involved bird C. Bird C was risk-prone in two of nine experiments. Data combined from the first 30 trials of these two experiments indicate that C chose certain and variable rewards with essentially equal probability after selecting a variable dish containing some seeds. However, after selecting a variable dish with no food, C tended to choose another variable dish, violating sequential independence ( ~ ~ 4.46, P < 0.05). The other significant heterogeneity value resulted when the data for the last 30 trials in the seven other experiments were combined. Each of these experiments indicated risk-aversion, and heterogeneity resulted from the bird's tendency to choose a certain reward after selecting a variable reward yielding no seeds (;~ = 4.83, P < 0.05). Since heterogeneity was detected only by combining data across experiments with different predictabilities, and since bird C's choice probabilities were overall quite similar to the other two subjects, the sequential dependence may not be important. However, perhaps bird C employed a decision-making process different from that of the other two subjects (see Altmann 1974). Table II lists the p~ values. Risk-aversion occurred 21 times, indifference was noted three times, and three experiments resulted in riskprone behaviour. After transforming the data (sin -1 method) to homogenize variances, a twoway A N O V A was performed. I took subjects as replicates, and the two treatments (mean reward and predictability) each occurred at three levels. I found no significant difference due to reward size (F2,1s = 0.991, NS), predictability ( F 2 , 1 s Table H. PT Values ,Within-patch Choice
0.69 0.49* 0.77
0.64 0.56* 0.33**
0.63 0.61 0.68
A B C
0.38** 0.7 0.62
0.56* 0.6 0.36**
0.72 0.62 0.67
A B C
0.63 0.64 0.69
0.62 0.63 0.74
0.62 0.6 0.69
A B C
Entries are proportional utilization of the certain reward
over all trials. Mean is the average of the variable reward (= certain reward). ~r is the fraction of variable dishes containing seeds. Risk-aversion is the commonest result. Asterisks used as in Table I.
i.628), or their interaction (F4,1s -- 0.951, NS). Overall, the average p'r values for birds A, B and C are, respectively, 0.61, 0.6l and 0.62. The pT values also are independent of the variance-tomean ratio of the variable reward (r == 0.18, 25
dr, Ns). During experiments, the birds learned reward characteristics very quickly. Preferences were evident, if not significant, in the early stages of several experiments. To examine time-dependence of the early stages of the Pi values, choice sequences first were separated into the three categorical responses to risk, based on the statistical significance of the pT values. If a bird is risk-averse, pf might increase in the following rank order: ill0, p15,/)30,/)40, fiT, pL since the impact of sampling should decline through time (Krebs et al. 1978). Observed pi values, ordered from smallest to largest, should positively rank-correlate with this sequence for risk-aversion, should negatively rank-correlate for risk-proneness, and should not significantly rank-correlate with this sequence for true indifference. Table II[ lists the average Pi value for the three types of result. Within the data suggesting risk-aversion, the rank correlation is significantly positive (rs = 1.0, P < 0.0i). Within the data indicating risk-proneness, the rank correlation is not significant (rs = -- 0.43, NS). Experiments resulting in indifference showed, surprisingly, a significantly positive rank correlation (rs = 1.0, P < 0.01). in these experiments, p~ values initially were less than 0.5, but steadily increased through time. Perhaps a greater number of foraging bouts might have yielded evidence of risk-aversion. Table IlL Temporal Sequence of Withln-patch Choice Probabilities
Risk-averse pin p15 p3o p4o PT
0.595 0.603 0.627 0.637 0.658 0.694
Indifferent Risk-prone 0.427 0.467 0.493 0.513 0.536 0.563
0.367 0.357 0.367 0.37 0.357 0.313
Data are separated by categorical result (columns). p~ is the average proportional utilization of the certain reward over the first i choices, pr refers to the entire experiment; p~ refers to only the last 30 choices.
Discussion The second series of experiments were conducted to ask if the response to variation noted in between-patch choices would persist in tests designed to mimic dietary selection. The answer is yes, since 7 8 ~ of the experiments in the second series resulted in risk-aversion. These observations qualitatively agree with those of Real (1981) and Waddington et al. (1981), and lend additional support to the contention that response to stochasticity can be an important element of foraging behaviour. Quantitative comparison of the two series of experiments is not easy, since the deprivation periods, realized feeding rates and reward statistics differed. Risk-aversion did not appear as strong in the second series, but the important result is that the birds consistently avoided variable rewards in both the between and withinpatch experiments. Conclusions Differences in mean rewards can explain a variety of foraging patterns (e.g. Gill & Wolf 1975, 1977; Sih 1980). However, Oaten's (1977) demonstration of the significance of the fundamentally stochastic nature of the foraging process cannot be ignored. In that light, subsequent models have led us to consider that a forager's response to stochasticity may be functionally related to the diversity of its behaviour (Caraco 1980; Real 1980), its energy intake rate (Green 1980), and its probability of starvation (Stephens 1981; Pulliam & Millikan, in press). If foraging strategies in nature respond to stochasticity, a number of interesting questions arise. For example, how do foragers trade off differences in mean rewards against differences in variance ? Variance discounting models (Oster & Wilson 1978; Real 1980) portray the fitness resulting from a behavioural strategy as a linear combination of mean reward and reward variance. These models generally assume constant risk-aversion (or risk-proneness), but can be modified to accommodate decreasing riskaversion. Less general models consider the probability that a forager acquires at least enough food to avoid starvation. If reward distributions are symmetric about their means, these models depict the probability of surviving as a linear combination of the mean and standard deviation (e.g. Stephens 1981). It is not difficult to demonstrate that this condition predicts decreasing risk-aversion. Further, if decreasing risk-aversion accurately portrays fora-
ging behavioar, reductions in mean rewards may be traded off against increases in positive skew (see Arditti 1967). Several stochastic foraging models assume that an animal will attempt to either minimize or maximize reward variance when mean reward is held constant (e.g. Real 1981; Caraco 1981a). However, a forager might most prefer an intermediate level of risk. Data on human decisionmaking have not yet distinguished which prediction is more accurate (Paltatsek & Tversky 1970), though some people apparently favour immediate risk (Coombs & Huang 1976). t suspe.ct that in nature successful foragers are risk-averse. More generally, response to variation may influence a wide range of ecological and evolutionary phenomena, including social organization (Thompson et al. 1974; Baker e t a l . 1981 ; Caraco 1981a), life histories (Schaffer 1974; Templeton & Rothman 1974; Gillespie 1977), community structure (Pimm 1978) and coevolution (Real 1980). Acknowledgments I thank Mitchell Chasin, Irene Kukurudza, Heather McGuire and Sarah Thomas for conducting the experiments. Mary Bayham helped in all phases of the study. I gratefully acknowledge the comments and criticisms of D. H. Janzen, H. R. Pulliam, L. A. Real, F. B. Gill, R. K. Selander, L. L. Wolf, the reviewers, and P. F. Levy. I appreciate the aid provided by NSF grant BNS-8020717 and a USPHS Biomedical Research Support Grant. REFERENCES Altmann, S. A. 1974. Baboons, space, time and energy. Am. Zool., 14, 221-248. Arditti, F. D. 1967. Risk and the required return on equity. J. Finance, 22, 19-36. Baker, M. C., Belcher, C. S., Deutscll, L. C., Sherman, G. L. & Thompson, D. B. 1981. Foraging success in junco flocks and the effects of social hierarchy. Anita. Behav., 29, 137-142. Calder, W. A. 1974. Consequences of body size for avian energetics. In: Avian Energeties (Ed. by R. A. Paynter), pp. 86-144. Cambridge: Nuttall Ornithological Club Publication. Caraco. T. 1980. On foraging time allocation in a stochastic environment. Ecology, 61, 11%128. Caraco, T. 1981a. Risk-sensitivity and foraging groups. Ecology, 62, 52%531. Caraco, T. 1981b. Energy budgets, risk and foraging preferences in dark-eyed juncos (Junco hyemalis). Behav. Ecol. SociobioL, 8, 213-217. Caraco, T., Martindale, S. & Whittam~ T. S. 1980. An empirical demonstration of risk-sensitive foraging preferences. Anim. Behav., 28, 820-830.
CARACO: RISK-AVERSE WHITE-CROWNED SPARROWS Coombs, C. H. & Huang, L. C. 1976. Tests of betweenness property of expected utility. J. Math. Psych., 13, 332-337. Dowrthower, J. F. 1976. Darwin's finches and the evolution of sexual dimorphism in body size. Nature, Lond., 263, 558-563. Gill, F. B. & Wolf, L. L. 1975. Economics of feeding territoriality in the golden-winged sunbird. Ecology, 56, 333-345. Gill, F. B. & Wolf, L. L. 1977. Nourandom foraging by sunbirds in a patchy environment. Ecology, 58, 1284-1296. Gillespie, J. H. 1977. Natural selection for variances in offspring numbers: a new evolutionary principle. Am. Nat., 111, 1010-1014. Green, R. F. 1980. Bayesian birds: a simple example of Oaten's stochastic model of optimal foraging. Theor. Pop. Biol., 18, 244-256. Keeney, R. L. & Raiff~t, H. 1976. Decisions with Multiple Objectives: Preferences and Vahte Tradeoffs. New York: John Wiley. King, J. R. & Farner, D. S. 1966. The adaptive role of winter fattening in the white,crowned sparrow with comments on its regulation. Am. Nat., 100, 403-418. Krebs, J. R., Erichsen, J. T., Webber, M. I. & Charnov, E. L. 1977. Optimal prey selection in the great tit (Parus major). Anim. Behav, 25, 30-38. Krebs, J. R., Kacelnik, A. & Taylor, P. 1978. Test of optimal sampling by foraging great tits. Nature, Loud., 275, 27-31. Lea, S. E. G. 1979. Foraging and reinforcement schedules in the pigeon: optimal and non-optimal aspects of choice. Anim. Behav., 27, 875-886. MacArthur, R. A. & Pianka, E. R. 1966. On optimal use of a patchy environment. Am. Nat., 100, 603-609. McNaughton, S. J. & Wolf, L. L. 1973. General Ecology. New York: Holt, Rinehart & Winston. Oaten, A. 1977. Optimal foraging in patches: a case for stochasticity. Theor. Pop. BioL, 12, 263-285. Oster, G. F. & Heim'ich, B. 1976. Why do bumblebees major?: A mathematical model. Ecol. Mon., 46, 129-133. Oster, G. & Wilson, E. O. 1978. Caste andEcology in the Social Insects. Princeton: Princeton University Press.
Pimm, S. L. 1978. An experimental approach to the effects of predictability on community structure. Am. Zool., 18, 797-808. Pollatsek, A. & Tversky, A. 1970. A theory of risk. J. Math. Psych., 7, 540-553. Pulliam, H. R. & Millikan, G. C. In press~ Social organization in the non-reproductive season. In: Avian Biology, Vol. 6 (Ed. by D. S. Farrier & J. R. King). New York: Academic Press. Pyke, G. H., Pulliam, I-L R. & Charnov, E. L. 1977. Optimal foraging: a selective review of theory and tests. Q. Rev. BioL, 52, 137-154. Real, L. A. 1980. Fitness, uncertainty, and the role of diversification in evolution and behavior. Am. Nat., 115, 623-638. Real, L. A. 1981. Uncertainty and pollinator-plant interactions: the foraging behavior of bees and wasps on artificial flowers. Ecology, 62, 20-26. Schaffer, W. M. 1974. Optimal reproductive effort in fluctuating environments. Am. Nat., 108, 783-790. Schoener, T. W. 1969. Optimal size and specialization in constant and fluctuating environments: an energytime approach. Brookhaven Syrup. Biol., 22, 103-114. Sih, A. 1980. Optimal foraging: partial consumption of prey. Am. Nat., 116, 281-290. Sokal, R. R. & Rohlf, F. J. 1969. Biomet~3,. San Francisco: Freeman. Stephens, D. W. 1981. The logic of risk-sensitive foraging preferences. Anim. Behav., 29, 628-629. Taylor, R. J. 1976. Value of clumping to prey and evolutionary response of ambush predators. Am. Nat., 110, 13-29. Templeton, A. R. & Rothman, E. D. 1974. Evolution in heterogeneous environments. Am. Nat., 108, 409-428. Thompson, W. A., Vertinsky, I. & Krebs, J. R. 1974. The survival value of flocking in birds: a simulation model. J. Anim. Ecol., 43, 785-820. Waddington, K. D., Allen, T. & Heinrich, B. 1981. Floral preferences of bumblebees (Bombus edwardsii) in relation to intermittent versus continuous rewards. Anim. Behav., 29, 77%784.
(Received 10 June I981 ; revised 3 December 1981 ; MS. number: A2671)