When should chickadees hoard food? Theory and

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into the adaptive significance of food hoarding. ... (Paridae), species that hoard are typically smaller ... flower seeds under a specific experimental protocol.
Anim. Behav., 1991, 41,579-601

When should chickadees hoard food? Theory and experimental results J E F F R E Y R. L U C A S * t & L Y N N R. W A L T E R ~ *Department o f Biological Science, Purdue University, West Lafayette, IN 47907, U.S.A. ~Department of Biology, College of William & Mary, Williamsburg, VA 23185, U.S.A. (Received 7 May 1990; initial acceptance 25 June 1990; final acceptance 28 August 1990; MS. number: A5792)

Abstract. A dynamic programming model was developed to evaluate conditions that promote food caching. Long-term observations (3-4 months per bird) of caching behaviour by Carolina chickadees, Parus earolinensis, are discussed in the light of the predictions from the model. Two different fitness functions were modelled: net energy-rate maximization and survival-rate maximization. Under most simulated conditions, energy-rate maximizers are predicted to cache at uniformly high rates. Two tradeoffs are important in caching decisions of survival-rate maximizers. (1) When fat le.vels are high, caching decisions should reflect trade-offs between time allocated to foraging and non-foraging behaviour. At the highest fat levels, the expression of non-foraging behaviour should be relatively more valuable than foraging. As a result, caching is not predicted because it increases foraging time and thus reduces time available for alternative behaviour. As fat levels drop below the maximum, foraging requirements become more important and caching rates are predicted to increase. (2) At intermediate to low fat levels, caching decisions should reflect a response to trade-ofls affecting starvation risk. At very low fat levels, the forager should eat any food at the site of discovery to reduce the risk of starvation in the near term. At intermediate fat levels, the forager is not at immediate risk of starvation, so it should cache to reduce starvation risk in the long-term. These mass-dependent trade-offs should also affect diurnal patterns in caching rates: caching rates should be low at dawn, when the forager's fat reserves are at their minimum, and at dusk, when fat reserves are at their peak; caching rates should be highest at midday. The experimental results suggest that chickadees do not maximize net energy intake rates; instead, their behaviour is in broad agreement with the predictions of a survival-rate maximizer. However, one additional prediction was clearly not supported: larger birds cached less than smaller birds. Observed seasonal patterns in caching, retrieval and recaching rates are also discussed. Animal foraging decisions are often sequentially dependent (i.e. decisions vary with success in the foraging period; Houston & McNamara 1982) and generally dependent on the state of the animal (McCleery 1978; relevant state variables include hunger, level of fat reserves and thirst levels). Until recently, these two properties have been difficult to evaluate, and both theoretical and empirical studies have by necessity ignored them. Dynamic optimization techniques have now provided a means of studying dynamic aspects of foraging decisions (e.g. Mangel & Clark 1988), and indeed, have given us a new way to think about decision-making in general. Here we describe an in-depth analysis of food caching, a behaviour pattern that is ideally suited to studying dynamic decision policies. We show that treating caching behaviour as a dynamic tTo whom correspondence should be addressed. 0003 3472/91/040579+23503.00/0

optimization problem provides a unique insight into the adaptive significance of food hoarding. A number of species of birds and mammals 'scatter-hoard' food when foraging on ephemeral resources (for reviews see Smith & Reichman 1984; Sherry 1985). Scatter-hoarded food is stored in spatially separated sites and is not defended (Sherry 1985), making scatter hoards particularly susceptible to pilfering. If food is scatter-hoarded at sufficiently low densities, the forager can reduce pilfering rates by making the caches difficult to locate, thus making searching less profitable for the pilfering animals (Andersson & Krebs 1978; Stapanian & Smith 1978; Clarkson et al. 1986). Since animals are capable of remembering the exact position of cache sites (Sherry 1984; Shettleworth & Krebs 1986; Balda & Kamil 1989), the hoarded food remains profitable to the hoarder; this is a necessary condition for the evolution of scatter-hoarding

9 1991 The Association for the Study of Animal Behaviour 579

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Animal Behaviour, 41, 4

(Andersson & Krebs 1978). However, many species only store at certain times of year (usually winter), so additional advantages must exist peculiar to those times for caching to be favoured over the alternative of simply eating food when it is encountered. At least four factors favouring caching have been discussed in the literature. (1) A caching forager competing for a short-lived food resource may harvest a disproportionate share if the time required to cache food is less than the time required to eat it (Clarkson et al. 1986). In addition, caching may increase harvest rates if foraging time in a patch is limited by dominant individuals or predators, and pilfering rates of cached food are sufficientlylow. In at least one group of animals, the old world tits (Paridae), species that hoard are typically smaller than and subordinate to those that do not hoard (Hinde 1952; Stokes 1962). For these smaller birds, high rates of food removal afforded by caching may compensate for a reduction in the amount of time patches are available (i.e. before dominant birds arrive; Cowie et al. 1981; Shettleworth & Krebs 1982). (2) The risk of starvation may be reduced if caching occurs when food is relatively abundant and retrieval occurs when resources are scarce (Sherry 1985) or when energy requirements are particularly high (VanderWall & Balda 1981). For example, caching tends to be more common in the northern temperate zone than in the tropics; this is presumably because the northern temperate climate is more variable and less productive in winter months (Roberts 1979), although cached food is probably also less perishable in temperate climates. (3) Caching could be an alternative to fat storage in birds. Recent theoretical (Lima 1986) and empirical (Rogers 1987) evidence suggests that fat storage may be a costly way for birds to store energy that might be needed during food shortages. By storing food in caches, birds may be able to reduce fat stores but still ensure a sufficient energy supply in a variable environment. (4) Caching may 'decouple the need for food from the need to forage for it' (Sherry 1985); time can be allocated to eating whenever it is most profitable, for example when predatory risk is low. These four factors are not mutually exclusive: under any given set of conditions, two or more factors may jointly promote the expression of caching behaviour. However, some predictions about which of these factors are most important in the expression of caching behaviour should be possible. For example, decisions consistent with

maximizing harvest rate are often different from decisions consistent with the minimization of starvation risk (Caraco 1979; Stephens & Krebs 1986). Similarly, the relative importance of flexibility in time allocated to eating or caching, as an alternative to fat storage, can be evaluated under specific ecological conditions to give some idea about which factor(s) most strongly influences the amount of caching performed by an animal. In this paper, we present results from a model developed to predict caching rates of Carolina chickadees, Parus carolinensis, foraging for sunflower seeds under a specific experimental protocol. The model treats caching as a sequential, statedependent process. We show that the factors listed above affect the predicted caching behaviour in different ways. The unique predictions from each factor are then evaluated with experimental results from an aviary study of caching by Carolina chickadees.

THE MODEL Caching decisions could potentially be affected by a variety of variables, from food value to the physiological state of the animal. The most important function of our model is to evaluate which of these variables might be important in caching decisions. The model is a variation of the standard technique of dynamic programming (e.g. Mangel & Clark 1988). Dynamic programs predict the expected sequence of decisions that an animal should make, assuming that it starts at some current time and state and ends at some time in the future. The particular dynamic program described here is stochastic, meaning that no single course of action can be predicted; instead, the model describes the probability that any one of many possible sequences is expressed. Any given decision will reflect the immediate costs and benefits of alternative behaviour patterns available to the animal, as well as the effect of the current decision on the future states of the animal. We assume that all cachable food items are found in patches and that these patches are available at predictable times during the day, with the amount of time available for feeding at that patch either a fixed (Appendix I) or random variable (Appendix II). In addition, we assume that the forager is able to search for small non-cachable items at any time during the day. Three alternative behaviour

Lucas & Walter: Caching behaviour patterns are available to the forager at all times: retrieve a seed from a cache site, stop foraging and sit in a shelter safe from predators, or search for non-cachable bits of food. When a food patch is available, the bird can also choose to take a seed from the patch and cache it, or take a seed and eat it immediately. We assume that the patch is large enough for the number of seeds harvested to be limited by time only, and not by the total number of seeds available in the patch. Two state variables, amount of fat storage and cache size (total number of seeds stored), are allowed to vary within fixed boundaries, and the animal is assumed to choose the behaviour pattern, given current fat stores and cache size, that maximizes an expected fitness function. In turn, all behavioural decisions will result in a predictable (but not necessarily deterministic) change in state. In the model, the cache is treated as a state variable with a single dimension, number of seeds stored (see Appendix I). Seeds are cached for at most a few days and are scatter-hoarded in single-seed hoards. Optimal cache density is not included in the model (see Clarkson et al. 1986 and Stapanian & Smith 1978 for models of optimal cache density). Two fitness functions are considered. (1) Harvest rate: we consider the sequence of behaviour that maximizes the long-term net rate of energy intake from foraging. Only one state variable, cache size, is considered for the harvest rate maximizer. (2) Survival rate: caching may function in reducing the risk of starvation. In response to starvation risk, animals might be expected to store as much fat as they are physiologically capable of doing, at least when food is plentiful. It is clear that at least some species of birds do not do this (Rogers 1987), and increased predation risk at higher weights might be the cause (Lima 1986). For this reason, the survival rate fitness function is treated as the product of surviving both starvation and predation (see McNamara & Houston 1982 and Pulliam & Millikan 1982 for a discussion of this fitness function). In the model, starvation probability approximated a cumulative normal distribution about a mean weight at starvation. Following Lima (1986), predation rate is assumed to increase with body mass, although we test the effect of relaxing this assumption. The recurrence equations used in the calculation of the optimal sequence of caching decisions are listed in Appendix I. The model includes eight important parameters likely to influence caching rate under the specified

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conditions. To simplify the analysis, we use one set of conditions as a standard and compare the effect of changes in each parameter against this standard. Assume that the day lasts 7 h, and that the bird starves when its mass falls to 8 g on average. The total amount of time the bird has access to food is 21 min/day, with this access spaced over the day in seven intervals of equal length. Additional parameter values are listed in Appendix I. Harvest Rate Maximizer

There are several time intervals over which a forager could potentially maximize harvest rates. Foragers could attempt to maximize the mean number of seeds taken from a patch during a single visit. Under the standard conditions, the time required to eat a seed is five times longer than the time required to cache a seed. Thus, a forager that maximized the number of seeds harvested from a patch should cache all but the last seed handled. What the bird does with the last seed will have no impact on harvest rate, so the bird should nominally be indifferent with this seed. Alternatively, the forager could attempt to maximize harvest rates over a longer time interval by considering the future use of cached seeds, pilfering and the possibility of forgotten caches in its foraging decisions. The dynamic program estimates the optimal sequence of behaviour over a finite interval of time. The predicted behaviour in the later part of this interval will be affected by the terminal reward function, or the state-dependent payoff the bird receives if it survives to the last interval. As the number of days in the simulation increases, the predicted behavioural sequence in the first few days will come to an equilibrium (i.e. the expected behaviour at any given state and time on day one will be the same as it is at the same state and time on day two) and will be independent of the terminal reward function. This equilibrium solution can be considered to represent the long-term payoffs associated with choosing any of the alternative behaviour (see McNamara & Houston 1986 for a full discussion). In our simulations, all solutions stabilized with a simulation interval of 6 days or less. Thus, to predict the optimal behaviour of long-term harvest rate maximizers, we ran all simulations for 6 days and present the (equilibrium) solution from the first day of the simulation. Under the standard conditions, a bird maximizing the net number of harvested seeds is predicted

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by the model to cache at high rates, independent of time-of-day and independent of the initial cache size. Generally all but the last seed taken from the feeder should be cached, so the proportion of seeds the bird caches under the standard conditions (P~,~h~= 0.85) is lower than the proportion of seeds cached when the feeder is open fewer times (four times) for a longer duration (5 rain each time) (Pc,the = 0'92). Maximum caching rates are predicted under a wide range of parameter values. For example, the results are essentially the same if pilfering rate is increased 100-fold (i.e. if75 % cache loss occurs after 55 min instead of 3.9 days), encounter rate of noncachable seeds increases from 1/3 min to l/2 rain, or the probability of remembering the location of a cached seed decreases from 0-667 to 0-333. However, caching rate should drop to near zero at extreme pilfering rates (5'5 min for 75% loss), high availability of alternative prey (2/3 min) and with very poor memory for cache location (probability of remembering correctly = 0.1). Survival Rate Maximizer

The survival rate maximizer strategy differs from the harvest rate maximizer in two respects. First, predation threat potentially affects caching decisions. In addition, the survival rate maximizer would choose caching strategies that reduce longterm harvest rates if these strategies enhanced the probability of survival. As with the solution for the harvest rate maximizer, a 6-day time interval was used in the model and results from the first day are presented.

Body s&e and cache size effects Unlike harvest rate maximizers, caching rate of survival rate maximizers should change with the level of fat stores, cache size and time-of-day. If the bird starts the day with very low fat levels, the threat of immediate starvation is sufficiently high that the bird is predicted to eat all encountered seeds until its mass is above some threshold (about 8.6 g for the initial conditions, but this will change with cache size; Fig. la). The lighter the bird, the longer it will take the bird to reach this threshold. Thus, the proportion of seeds cached throughout the day will decrease with a lower initial (dawn) body mass if the initial body mass is below the threshold.

At intermediate fat levels, immediate starvation is unlikely but future starvation is a potential problem, so caching rates should be high. At the highest fat levels, starvation risk becomes less relevant and predation risk dominates the solution. Under this condition, the birds should eat any seeds taken from the feeder and should also tend to perch in shelter at other times. This may seem counter-intuitive, because it suggests that under favourable conditions birds with the lowest chance of starvation in the short term should not plan for the future by caching seeds. However, the time horizon of the caching bird is limited by the length of time the cached seed will be available to the cacher. For chickadees and tits, the only available data suggest that this is about 3 days (Cowie et al. 1981; Stevens & Krebs 1986). Under favourable conditions, fat stores may be sufficient to reduce the need for cached seeds within this time window. Also, caching requires that the bird invest extra foraging time caching and retrieving seeds. A fat bird should choose not to invest this time, but instead simply eat seeds when located and spend excess time in the shelter. The result of these three selective pressures is a maximal caching rate at intermediate fat levels. Under the standard conditions, mean body mass is expected to be fairly high (9.35 g; Table I) so caching rate should generally decline with an increase in fat stores (Fig. la). However, the correlation between proportion cached and body mass will weaken and caching rates should remain high with a decrease in the predator arrival rate (Fig. lb) or a decrease in pilferage rate (e.g. 7.7 days to 75% loss). A weak correlation and low caching rates are expected at high predator arrival rates (e.g. 1-67 x 10- 4/min), increased pilferage rate (e.g. 1.3 days to 75% loss) and increased encounter rate of non-cachable food (e.g. 0.5/min; Fig. lc). The opposite correlation (higher caching rates at high fat stores) is expected under a wide range of stressful conditions. For example, an increase in caching rate is predicted at high fat levels iftemperatureis reduced from 20 to 15 or 10~ (Fig. I d), access time is reduced to a total of 10 min during the day, or the amount of non-cachable food is reduced (encounter rate=0.2 instead of 0-333). Surprisingly, the results are not strongly affected by the ability of the bird to memorize cache sites correctly. Virtually the same results are predicted for a 50% error rate and a 0% error rate. The pattern of access to the feeder is expected to have a

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Figure 1. Predicted proportions of seeds that are cached over the course of the day as a function of cache size and body size at dawn. (a) Standard conditions; (b) reduced predator encounter rate: 1.667 • 10- 9/min; (c) increased encounter rate of non-cachable prey: 0.5/min; (d) reduced ambient temperature: 10~ Parameters not listed for b~l are the same as the standard conditions (see text, Appendix I). Simulations assume fixed feeder access times known to the forager.

quantitative effect on caching. Compared with 3 min of access seven times during the day, a bird given 5 min of access four times should cache more at very low and very high weights (compare Fig. la and Fig. 2a). Because the last seed taken from the feeder should generally be eaten, the bird should cache more overall when given less frequent access to the feeder, assuming total access time is the same. The predicted difference at extreme fat levels between 5 min/4 times and 3 min/7 times also fits with the general expected response to stress, because a bird on a 3 min/7 times schedule is predicted to show a slightly higher survival rate than one on a 5 min/4 times schedule. Smaller birds (mass at starvation 6 g instead of 8 g) should cache less, assuming that the only factors that scale with body mass are the probability of escape when a predator is encountered, metabolic rate and the maximal range of fat storage. Time requirements for foraging and weight gained from eaten seeds are assumed to be independent of body size, and physiological constraints that might change with body size (e.g. gut capacity) are

assumed to be unimportant at low prey encounter rates. Two offsetting conditions generate the result. First, larger birds can withstand starvation for longer periods of time because potential fat storage increases with body size (or lean mass) as a constant proportion of mass at starvation, whereas metabolic rate increases at a slower rate (e.g. Ketterson & Nolan 1978). Second, if small birds are as efficient as large birds in converting food to energy (or to fat), then small birds should be able to gain mass more rapidly if they encounter (and can use) the same resources that larger birds encounter. This is because small birds have lower metabolic requirements than large birds, and thus should be more efficient in the expenditure of energy. The first factor causes a decreased starvation risk for large birds; the second factor causes a decreased starvation risk for smaller birds. These two conditions will tend to offset one another, but with the parameter levels simulated here, the second factor is more important. As a result, survival rate of small birds is higher than that of large birds, and this causes a decrease in caching rates.

Animal Behaviour, 41, 4

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Table I. Expected equilibrium body size and cache size for chickadees foraging under aviary conditions* Fixed interval Model parameter Pilfering coefficient ~/ ( x 10-*) 125 250 750 Temperature (~ 10 15 20 25 Encounter rate of non-cachable prey (N/min) 0-20 0.30 0.50 Value of cached seed (g body fat) 0-020 0.027 Cage food (g body fat) 0.00 0.10 0.50 Feeder access time (total min/Nday 1) 10/2 20/1 20/4 21/7 Probability of correctly locating a cached seed 0.500 0-667 0.750 1.000 Predator encounter rate (Nx 10-7/min) 1667 166.7 1.667 0-0167

Random interval

.~ body size

,Ycache size

.~ body size

,~ cache size

8"93 9'35 9.54

37-6 10'0 0-2

8'96 9.49 9.51

35.6 1.7 0"0

7.88 10.10 9.35 9.11

1.1 5.2 I0.0 4.2

7.82 10.09 9.49 9.22

0.2 4.8 1.7 1.3

9.95 9.35 9.04

8.8 10.0 0.2

10.10 9.49 9.06

3.7 1.7 0.0

10.07 9.35

3.6 I0.0

10.13 9.49

1.8 1.7

9.44 9-35 9.35

10.2 10.0 2.6

9.65 9.49 9.21

2.1 1.7 0.5

9.66 9.34 9-38 9.35

0.5 8.7 10.7 10.0

9.52 9.37 9.53 9.49

0.0 1.3 0.8 1.7

9-45 9.35 9.32 9.23

6.8 10.0 11.4 14.4

9.47 9.49 9.50 9.47

0.1 1-7 2.1 3.1

9.02 9-35 10.04 10.67

10.5 10.0 8.6 11.4

9.18 9.49 10.18 10.71

1.6 1.7 1.7 9.9

*Under fixed interval we assume that the birds know exactly when the feeder opens; under random interval we assume that the feeder intervals are normally distributed (see Appendix II). Pilfering is assumed to cause a constant proportional decay in cache size: cache size at time t + At = cache size at time t.exp (-'/At), where At is the time committed to a chosen behaviour. Mean body size and cache size are expected values at dawn.

Caching as an alternative to fa t storage Lima (1986) suggested that fat storage may represent a trade-off between predation risk and starvation risk. Birds with larger fat stores will

suffer lower starvation risk, but they also have higher energy needs and may need to spend more time exposed to predators to satisfy these requirements. Heavier birds may also incur a higher

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Fi ure 2. Predicted proportions of seeds taken from a patch that are cached over the course of the day as a function of cache sizeand body sizeat dawn. (a) Feeder access: 20 min total, four times during the day; (b) probability of escapinga predator (0.1049) independent of body mass; (c) predation rate while inactive is identical to predation while foraging (i.e. no predator-safe haven); (d) random feeder access times (see text, Appendix II). In a--cfixed feeder access times are assumed to be known to the forager. Parameters not listed are the same as the standard conditions (seetext, Appendix I).

predation risk because they are less agile than lighter birds (Lima 1986). This can be evaluated in two ways. If the trade-off is important, mean body mass should increase when starvation risk increases relative to predation risk. The effect of massdependent predation risk can be tested by altering the allometric scaling constant for predation risk. The results show that the relation between body mass and caching predicted by the model is not caused by higher predation risk for birds with large fat stores. If predation risk is independent of fat stores, the predicted caching behaviour is similar to that expected under the standard conditions where fatter birds suffer higher risk (Fig. 2b). Unlike the allometric scaling constant, the presence of a shelter has a strong affect on both the qualitative predictions and on the equilibrium body size. Under the standard conditions, the bird has an option to remain inactive in a predator-safe haven; any other foraging behaviour puts the bird at risk to predation. Thus, inactivity is qualitatively different than foraging. If there is no reduction in predation

threat during inactivity, if inactivity is simply a low cost, low return behaviour pattern, then the predictions change markedly. In general, an increase in caching rate is expected with an increase in fat stores (Fig. 2c); the opposite prediction was derived for the standard conditions. Thus, the predicted reduction in caching rate for fat birds is due to the presence of a predator-safe behaviour, which the bird exhibits when fat stores are high. As starvation risk increases, higher harvest rates become more important than a reduction in predation risk so the bird should tend to cache more at high fat stores. Unless the starvation threat is quite high (e.g. 10~ under these conditions), the birds should also maintain larger fat stores under starvation risk; low temperatures, high pilferage rates, reduced availability of non-cachable food, small seed size, poor memory for cache sites, no 'cage food' (see Appendix I) and short feeder access time will all cause the birds to store more fat (Table I). Birds should also maintain large fat stores und,r lower predation risk (Table I).

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Animal Behaviour, 41, 4

Predation risk should also decrease the mean number of seeds cached (Table I). High pilferage rates should have the same effect (Table I).

Temporal patterns Sherry (1985) suggested that caching may provide more flexibility in an animal's time budget by decoupling search and handling times; caching lets the forager handle prey when and where it is most profitable to do so (see Lima 1985), for example when predators are less active. In the field, predation threat may change over time; however, we assume that the perceived predation threat is constant in the laboratory. In the absence of temporal variation in this factor, caching as a hedge against starvation (factor 2 in the Introduction) and caching as a method of decoupling searching and handling time (factor 4 in the Introduction) become synonymous. Diurnal patterns in diet choice of non-caching birds have been predicted based on changes in starvation threat over the day (Houston & McNamara 1985). Early in the day, a forager should be most concerned with avoiding starvation because of its low weight, especially if the forager has little fat stored. Later in the day, the forager's decisions should reflect metabolic requirements for surviving the night (see also Stephens & Krebs 1986). Caching adds an additional complication, because cachers should also consider diurnal changes in the size of the scatter hoard. Under the standard conditions, changes in body mass and cache size through the day will influence the diurnal caching pattern. The net result of these factors is a decrease in caching rate at dusk, due to a large cache size (stored over the day) and a large fat store (from seeds eaten during the day), and possibly a decrease in caching rate at dawn if the bird is sufficiently light weight (Fig. 3). If the bird has not stored enough fat during the day, it should also cache less and eat more at dusk in an attempt to gain weight rapidly to survive the night. Pilfering also affects the diurnal caching pattern. If pilfering rate is high enough, the value of cached seeds will decrease at dusk because seeds stored over night will be available to pilferers but not to the caching bird. Thus, an increase in pilfering rate will exaggerate diurnal changes in caching behaviour.

Effects of stochastic access times The results listed above assume that the forager knows exactly when the feeder will open and close. In the experiment (see below), the feeder was opened at the same time of day for each feeding schedule. The birds were trained on each schedule for at least 1 week before collecting data on the same schedule for a period of 45 days or more. In short, the birds probably could anticipate when the feeder would open and the duration of access. But an animal is unlikely to be able to measure time intervals without any variance, even if the interval is held constant (Gibbon 1977). From the forager's point of view, this is equivalent to a variable access time. Variation in access time is potentially important because stochastic access time has been shown to alter diet choice predictions (Lucas 1985) and may alter predicted caching behaviour. We simulated variable access time by assuming that the time the feeder opens and closes was approximately normally distributed, with the same mean as the fixed interval simulations (see Appendix II). The predictors for variable feeder access are generally similar to those for fixed access, but some quantitative predictions are affected. Caching rates at high fat stores are generally depressed compared to fixed access times. Thus, under the standard conditions the predicted negative correlation between body mass and caching rate should be stronger for variable access (Fig. 2d). There is also little difference between feeder schedules (3 min access/7 times versus 5 rain access/4 times), whereas with fixed access times, body mass should have only a weak influence on caching rate under the schedule of 5 min access/4 times. As predicted with fixed access times, a positive correlation is expected if the bird is foraging under stress (low temperature, reduced access time, low encounter rate of alternative food or low value of cached food). However, under random access the bird should generally regulate body fat at higher levels than under fixed access (Table I). The increased fat stores are consistent with the prediction that fat stores should be larger with an increase in the threat of starvation (here due to stochastic access to food).

THE EXPERIMENT

Here we describe a test of the predictions of the dynamic programming model discussed above. The

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Figure 3. Predicted decision for the first seed taken from the feeder over the course of the day under the standard conditions. 'Number cached' is 1 if the bird should cache the seed, 0 if the bird should eat it. The feeder is open seven times during the day, so there are at most seven lines in each figure. The predictions are given as a function of initial cache size (X-axis). Each figure represents the expected behaviour of an animal of a given mass. (a) 8.26 g; (b) 8.37 g; (c) 8.48 g; (d) 8.60 g; (e) 9.00 g; (f) 9.24 g; (g) 10.23 g; (h) 10.99 g.

specific predictions tested are listed at the beginning o f each subsection. Results that are directly relevant to these predictions will be described first. To give a

b r o a d e r view o f the caching decisions o f Carolina chickadees, we also discuss patterns in the retrieval and 'recaching' o f seeds and seasonal patterns.

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Animal Behaviour, 41, 4

Recaching is the movement of a cached seed from one cache site to another.

Methods General

Four Carolina chickadees were captured in suburban woodlands of Williamsburg, Virginia, in September 1986. The birds were housed individually in the laboratory, in wire cages measuring 61 • 61 x 91 cm, connected by sliding doors to net aviaries measuring 2.13 • 2" 13 x 2' 13 m. The aviaries were maintained at a constant temperature (20-22~ on a 10:14 h light:dark cycle, with lights on at 0800 hours. The birds were tested in the aviaries for 9 h/day, starting at 0900 hours, where they were fed hulled sunflower seeds from automatic feeders. The feeders consisted of seed trays with sliding covers that limited access to food to certain preset intervals. The feeders were the only source of food available in the aviaries. Each aviary contained three 'trees', approximately 2 m tall and 2.5-10.0 cm in diameter. Eleven to 22 holes (0-5 cm diameter, 1-1.5 cm deep) were drilled into the trees 15-20 cm apart to provide cache sites for the birds, so that 46-50 holes were present in each aviary. Dowel perches were installed 2.5cm below the cache holes. Body mass was recorded each morning. The chickadees were drawn into removable nestboxes ('Kacelnik boxes') and weighed on a triple-beam balance. The birds were given two sources of food during the experiments: sunflower seeds in the aviaries and a mixed diet in their overnight holding cages. We altered the amount of food offered in the holding cages (we call this 'cage-food' below) to vary the body mass of the birds between 100% of normal body mass (as defined by the body mass maintained under ad libitum food availability; mean capture mass was 88 % of normal body mass) and approximately 75% of normal body mass. Overnight diets consisted of the following: 0-3 g sunflower hearts, 1-10 mealworms, 1-10 peanut hearts, 0.625-1.25cm 3 grated carrot, 0-6251-25 cm 3 grated egg and 2-5-7.5 cm 3 dried insect mix (Aleckwa). After an initial feeder training period, the birds were trained to one of two feeder schedules. On schedule 3/7, the birds received 2-95 + 0.17 min of access to hulled sunflower seeds every hour, seven times daily. On schedule 5/4, the birds received

5-18 + 0.17 rain of access to sunflower hearts every 2 hours, four times daily. Total automatic feeder access time for both schedules totalled 20-75+ 0"33 min per day. The birds were trained to each schedule for at least 1 week before data collection began. Two birds were first placed on schedule 3/7, and two birds were first placed on schedule 5/4; after 45-60 days of data collection, they were then switched to the alternate schedule and after another acclimation period of 5-7 days, data were collected for 45-60 more days. We usually tested two birds simultaneously, each in a separate aviary. Data recorded for each feeder opening included handling sequence, handling time, location and fate of each seed taken. Handling time began when a seed was taken from the feeder and ended when the seed was cached, eaten or dropped and not retrieved. If a bird had any cached seeds available, it was observed for at least 45 min/day for retrieval information. Observations of retrievals were conducted in 15-min blocks, one block each for the first, second and third 3-h interval the birds were kept in the aviary. The 15-min blocks were arranged between days so that we had observations for every hour of the day when the data from any given week were combined. Recaching was recorded when a bird retrieved a seed and then cached the seed again in another location without having eaten it. Seeds that were known to have been cached for 5 days were removed ('pilfered'). The experiments were run 7 days/week. The experiment was run from October 1986 to June 1987. For ease of analysis and comparisons, the different schedule runs were assigned a season. A schedule completed before 1 January was designated as an autumn schedule, a schedule completed before t April was designated as a winter schedule, and any schedule that began later than 15 March was designated as a spring schedule. Statistics

Tests of the predicted caching patterns were performed with general linear models using least squares fit (GLM in SAS 1988). For short-term predictions, the dependent variable is the proportion of seeds taken from the feeder, during a single access period, that were cached. The proportion was arcsine transformed (see Sokal & Rohlf 1981) and the total number of seeds taken from the feeder during the access period was used as a weighting

Lucas & Walter: Caching behaviour

factor. In addition to the two primary independent variables, time-of-day and body mass at dawn, the GLM models also included two other variables: day (number of days passed since the start of the experiment, 7 November 1986) and amount of cage-food eaten (see above). Non-linear effects (e.g. reduced caching at dawn and dusk) were tested by adding quadratic terms of all independent variables to the G L M model. Main effects, quadratic terms and two-way interactions between main effects were initially added to the models and non-significant (P>0.05) terms removed in order of increasing F-statistic. Values for dependent variables reported for weight and time-of-day effects are reported as least squares means. These were calculated by dividing the dependent variable into a number of discrete intervals and calculating the least squares means of the transformed proportion of seeds cached for each interval. The use of least squares means allowed us to control for possible confounding effects of alternative variables when we tested the effect of a single variable (e.g. body weight) on caching decisions. We were primarily interested in behaviour at the level of the individual, indeed we were particularly interested in knowing which birds failed to meet the predictions, therefore we tested for the effects of short-term factors (body mass and time-of-day) for each combination of bird and feeding schedule separately. This highlighted individual differences and can provide information about assumptions in the model that should be re-evaluated. The effects of longer-term factors (seasonal effects, schedule effects) were tested by incorporating all data across birds into the model. The dependent variable in these tests was the summed response over the course of the day. Similar analyses were performed for data on retrieval rates and recaching rates. These data were log transformed (In(X+ 1)) to adjust for a right skew.

Results

Harvest rate maximizers

Chickadees took on average 0.25 min to cache a seed and about 1.65 min to eat a seed at the feeder. Thus, the birds could have harvested substantially more seeds from the feeder had they cached all but the last seed (the decision for the last seed will not affect immediate harvest rates). The data show that

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the birds did not use this strategy. In addition, the probability that a bird cached a seed taken from the feeder was significantly correlated with both time-of-day and body mass for all birds (see below). This is also n o t predicted of harvest rate maximizers. Survival rate maximizers: short-term effects Time-of-day. Survival rate maximizers are expected to exhibit peak caching rates at midday, and three of the four birds tested exhibited this pattern under both feeding schedules (Fig. 4); the pattern was significantly non-linear for each (timeof-day coefficients positive and time-of-day2 coefficients negative; P