foraging games - department of biology - mcgill...

8
Foraging Behavior 239 attached to a shrub that was moved to different frequency dependence is an important consequence locations (an unfamiliar foraging site and handling of social foraging, often in combination with den- behavior). Even pigeons and rats pressing keys in sity dependence. a psychologist's operant chamber can come quite Optimality theory can be used to predict forag- close to the predictions of models developed for ing decisionsin relation to the abundance or tactics foraging in the field. of other foragers as with other environmental con- It is likely that the published literature is biased ditions. However, a major difficulty in testing such by the difficulty of publishing negative results and predictions is that the other foragers may also q tendencyfor researchers who obtain negative re- change their behavior in relation to the change in suits to continue searching for additional relevant their foraging environment. Thus, to predict forag- variablesor invalid assumptions.Nevertheless, it is ing behavior in a social context, the results of this clear that the optimality approach has predictive series of mutual interactions must be predicted. power. Evaluation of this power would be im- Game theory provides the mathematical tools for proved if it could be quantified on a common this prediction. See Dugatkin and Reeve (1998) scale. A promising approach comesfrom the math- and Roff (this volume) for summariesof game the- ematical technique of dimensional analysis (Ste- ory in evolutionary ecology. Giraldeau and Caraco phens and Dunbar 1991), which transforms the (2000) provide a detailed recent review along with mathematical relationships of a model into a re- new applications of gametheory to social foraging. duced set of unit-free variables. This unit-free The basic approach of game theory is to find, statement of the decision rule permits different from a given set of decision rules, the rule or mix studies to be compared within the sameframework of rules among the interacting individuals such and revealsthe relative magnitude of discrepancies that no individual using an alternative rule would between observation and prediction. Using this ap- have greater success than the individuals using the proach, a preliminary analysis of patch exploita- established rule or rules. From the perspective of tion studies by Kramer and Giraldeau (unpub- evolutionary genetics,this situation prevents genes lished) confirmed the overall positive relationship for alternative rules from invading the population between proportional patch use and search or and is therefore called an evolutionarily stable travel betweenpatcheswhen scaledto patch "half- strategy (ESS). Evolutionarily stable state is a more life." appropriate term to account for situations in which no single rule is unbeatable but a mix of Foraging Games rules is. The "strategies" in most models tend to be rather simple fixed responses or simple switches An important part of the foraging environment for between two responses based on a single environ- many species is the presenceof other foragers, of mental factor. However, as with applications of the same and sometimes other species, which can optimality theory, in foraging game situations that increaseor decrease foraging success (table 18.3). have actually been studied, the decisions are typi- Sucheffects are most evident when animals forage cally flexible individual responses. in groups, but even "solitary" foragers can affect Game theory is so important because the out- each other, for example, by reducing prey abun- come of games is often strikingly different from dance, alerting prey to the presenceof predators, simple optimal solutions. The selection of foraging or revealing new food sourcesby their foraging ac- sites offers a simple illustration. Consider a choice tivity. Many processes involving interactions with of potential foraging sites that differ only in their other foragers show density dependencebecause food availability and consequently in the foraging their occurrence,magnitude, and sometimesdirec- success they offer. For a single forager, the optimal tion depends on the number of other individuals solution is to forage at the site with the highest present. Density dependenceis often negative, in food availability, and the model does not change that some currency of foraging declines with the the prediction if severalindividuals are considered. number of other individuals, but it may also be If foraging rate is negatively density-dependent, positive (also known as an Allee effect) over at however, and there are many foragers using the least part of the density range. Sometimes, social same set of sites, the foraging rate in the patch with effects may be affected by the proportion of indi- the highest food availability may drop below that viduals making different alternative decisions.This of other unoccupied patches if all go to the site

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Page 1: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

Foraging Behavior 239

attached to a shrub that was moved to different frequency dependence is an important consequencelocations (an unfamiliar foraging site and handling of social foraging, often in combination with den-behavior). Even pigeons and rats pressing keys in sity dependence.a psychologist's operant chamber can come quite Optimality theory can be used to predict forag-close to the predictions of models developed for ing decisions in relation to the abundance or tacticsforaging in the field. of other foragers as with other environmental con-

It is likely that the published literature is biased ditions. However, a major difficulty in testing suchby the difficulty of publishing negative results and predictions is that the other foragers may alsoq tendency for researchers who obtain negative re- change their behavior in relation to the change insuits to continue searching for additional relevant their foraging environment. Thus, to predict forag-variables or invalid assumptions. Nevertheless, it is ing behavior in a social context, the results of thisclear that the optimality approach has predictive series of mutual interactions must be predicted.power. Evaluation of this power would be im- Game theory provides the mathematical tools forproved if it could be quantified on a common this prediction. See Dugatkin and Reeve (1998)scale. A promising approach comes from the math- and Roff (this volume) for summaries of game the-ematical technique of dimensional analysis (Ste- ory in evolutionary ecology. Giraldeau and Caracophens and Dunbar 1991), which transforms the (2000) provide a detailed recent review along withmathematical relationships of a model into a re- new applications of game theory to social foraging.duced set of unit-free variables. This unit-free The basic approach of game theory is to find,statement of the decision rule permits different from a given set of decision rules, the rule or mixstudies to be compared within the same framework of rules among the interacting individuals suchand reveals the relative magnitude of discrepancies that no individual using an alternative rule wouldbetween observation and prediction. Using this ap- have greater success than the individuals using theproach, a preliminary analysis of patch exploita- established rule or rules. From the perspective oftion studies by Kramer and Giraldeau (unpub- evolutionary genetics, this situation prevents geneslished) confirmed the overall positive relationship for alternative rules from invading the populationbetween proportional patch use and search or and is therefore called an evolutionarily stabletravel between patches when scaled to patch "half- strategy (ESS). Evolutionarily stable state is a morelife." appropriate term to account for situations in

which no single rule is unbeatable but a mix ofForaging Games rules is. The "strategies" in most models tend to

be rather simple fixed responses or simple switchesAn important part of the foraging environment for between two responses based on a single environ-many species is the presence of other foragers, of mental factor. However, as with applications ofthe same and sometimes other species, which can optimality theory, in foraging game situations thatincrease or decrease foraging success (table 18.3). have actually been studied, the decisions are typi-Such effects are most evident when animals forage cally flexible individual responses.in groups, but even "solitary" foragers can affect Game theory is so important because the out-each other, for example, by reducing prey abun- come of games is often strikingly different fromdance, alerting prey to the presence of predators, simple optimal solutions. The selection of foragingor revealing new food sources by their foraging ac- sites offers a simple illustration. Consider a choicetivity. Many processes involving interactions with of potential foraging sites that differ only in theirother foragers show density dependence because food availability and consequently in the foragingtheir occurrence, magnitude, and sometimes direc- success they offer. For a single forager, the optimaltion depends on the number of other individuals solution is to forage at the site with the highestpresent. Density dependence is often negative, in food availability, and the model does not changethat some currency of foraging declines with the the prediction if several individuals are considered.number of other individuals, but it may also be If foraging rate is negatively density-dependent,positive (also known as an Allee effect) over at however, and there are many foragers using theleast part of the density range. Sometimes, social same set of sites, the foraging rate in the patch witheffects may be affected by the proportion of indi- the highest food availability may drop below thatviduals making different alternative decisions. This of other unoccupied patches if all go to the site

Page 2: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

240 Behavior

Table 18.3 Social influences on foraging.---

1. Changes in food availability.- Exploitation-removal of food from the foraging area.- Passive interference (also called prey depression)-reducing foraging rates by making prey less available, for

example, by inducing its anti predator defenses.+ Facilitation-making prey more available, for example, by confusing them or making them more visible while

fleeing another forager.+ Risk reduction-lowering the variance of foraging success by sharing food discoveries among individuals.

2, Changes in costs or benefits of search, pursuit, and handling.+ Cooperative hunting-improved pursuit and handling success or decreased pursuit and handling time by groups.+ Increased rate of discovery of shareable prey or patches by foragers in groups.- Scramble competition-animals foraging in groups may have search areas that overlap with those of other forag-

ers and therefore require more search time to discover the same number of prey; they may have to increase theirrate of movement or change other foraging tactics to avoid having other foragers discover or capture the prey ",,;

first. :\'3. Kleptoparasitism-exploiting the search, pursuit, and handling of others. J cO'

+ For the kleptoparasite, more potential victims decrease search, pursuit, or handling time by allowing exploitation .,~:;of prey or patches in which another individual has already invested. :.11',

-/+ For the kleptoparasite, more kleptoparasites may change food availability and change costs and benefits of ~"foraging as in sections 1 and 2. !:

- For the victim, more kleptoparasites result in increased effort in search, pursuit, or handling as a result of losing j';J

prey or all or part of patches, or additional effort to avoid or defend against kleptoparasites, or reduced success "~as a result of choosing prey less vulnerable to kleptoparasitism. '{I

+ For the victim, more victims can improve defense or dilute the impact of kleptoparasites. '~4. Food defense (also called active interference or interference competition)-use of aggressive behavior to reduce the . .,~;1i::

foraging of other individuals on particular prey (food guarding) or specific locations (territoriality). ;1,+ For the defender, increased prey availability as a result of reduced exploitation and passive interference by other ~;.,

. do od I t".

m IVI ua s. 1(';'

+ For the defender, effectiveness of defense may be increased by cooperative defense. ~- For the defender, costs of defense increase with the number of potential intruders. M

+ For intruders, foraging in groups can increase access to defended areas or prey by overcoming the defense. "- For intruders, decreased access to particular prey or foraging sites as a result of effective defense by other individ- ,~;"

uals. ,~- For intruders, increased effort or risk of injury to obtain resources by intruding in locations defended by others. ~;;

",'5. Changes in foraging time availability and risk of attack from predators or conspecifics. ~

,'.

+ Grouping can reduce predation risk during foraging; this may permit less time to be spent on vigilance during {jthe foraging period or the use of sites that would be too dangerous for a solitary individual. ~!!O

- Foraging in groups may attract more predators, increasing predation risk or reducing the areas that are safe to :luse. ;~

+/- ~heno attacks from conspecifics are a threat, groups may either increase or decrease the risk, depending on the isituation i?,;,

. .' . ~:i'6. Foragmg InformatIon. i~\

+ Other individuals can be used to obtain information about beneficial foraging locations, food types, and foraging ';1f;:',f

~",techniques ~\'/jj. ,"",

- I~formation scrounging may reduce the number of accurately informed individuals and provide wrong informa- ,fjtIon. ~:.,- ;&~

Note: Minus and plus signs indicate how each process will affect the foraging success of a focal individual as the number of other "Iforagers increases. ;;~

with highest food availability. The game theory so- dependence in that the best site for anyone forager I

lution, known as the ideal free distribution, is for depends on the distribution of the foragers among ':r~;

individuals to ?ist~ibute themselves a~ong sites so the o~her sites. The i?eal free distribution.is cl~arly ,

that the combInatIon of forager densIty and food too sImple to apply m many real-world sItuatiOns, ~;"'ii

availability results in similar foraging rates in all but it has been repeatedly observed in controlled 'isites, a very different result from the prediction of laboratory studies, where foragers often show an "

simple optimality. This is an example of frequency impressive capacity to adjust quickly to deviations

I f ~"' C

,

,-~

Page 3: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

Foraging Behavior 241

in foraging success. Furthermore, it has formed the place. This decision determines the load size car-basis for a series of more complex models that ried and is part of the foraging process for seed-have strongly affected how behavioral ecologists hoarding rodents, for parental birds provisioningthink of foraging distributions and habitat selec- their young, and for nectar- and pollen-collectingtion. bees and wasps. In this section, I will i.llustrate the

Group size presents a similar problem. For cer- interplay between foraging theory and experi-tain foraging tasks such as the hunting of large mental tests using the load size decision of easternprey by carnivores, it is possible to calculate an op- chipmunks, Tamias striatus. These small (100-g),timal group size that yields the highest rate of for- terrestrial, forest-dwelling sciurid rodents feed pri-aging success per individual. However, group for- marily on the seeds of deciduous trees, though a

. mation constitutes a game: depending on how wide range of plant and animal material is some-;

; groups are formed and how access to groups is times consumed. Food is carried to a burrow fort controlled, groups may form that are much larger both short-term consumption and long-term stor-t' than optimal size with foraging success much age. In the winter, animals hibernate without accu-~ lower than the optimum. This is representative of mulating significant fat reserves, waking periodi-I: a widespread finding in game theory models that cally to feed on stored food. Except for females~ individual success will be lower than that predicted with young, each animal occupies its own burrow,~ by simple optimality. which is vigorously defended against conspecifics.~ A fundamental characteristic of social foraging Although animals chase other individuals near

I: is that the effort of individual foragers creates an food sources and in the vicinity of their burrows,i opportunity for parasitism of that effort by other home ranges overlap extensively. Chipmunks ex-r foragers. Kleptoparasitism, however, is not a via- posed to human presence and provisioning become; ble foraging strategy if all foragers are attempting very tame. At our study site, in the public portion~ to do it and none are looking for their own food. of a university nature reserve, many animals can be, This is another case where frequency dependence observed from a few meters or less without evident

is clearly involved in the success of alternative for- disturbance.ager decisions, such as searching for food patches Our interest in load size decisions arose fromindependently or watching other foragers and at- one of a set of models of central place foragingtempting to join patches that they discover. "Pro- published by Orians and Pearson (1979). This

f ducer-scrounger" models predict the occurrence model is conceptually derived from an influential': and frequency of these alternative foraging deci- model of patch use known as the marginal value; sions. theorem (Charnov 1976). It predicts that, if load-\, Game theory is also relevant to interactions be- ing rate decreases as the size of the load increases,

tween predators and prey and between plants and the optimal load size should increase with distancetheir pollinators and seed dispersal agents. A re- to the central place and with food density. The der-view of such coevolutionary interactions is beyond ivation of this prediction is shown in a step-by-step

r the scope of this chapter (see section "Interspecific analysis in figure 18.1, but an elegant graphical so-; Interactions," this volume). However, recent mod- lution (figure 18.2) improves the intuitive under-[ els of forager distribution are beginning to take standing of the predictions. A decline in loadingr into account distribution games between predators rate with size of the load already accumulated seems

and prey as well as among foragers (e.g., the chap- likely because holding prey could reduce the success\ ter by Sih in Dugatkin and Reeve (1998)). or rate of search, pursuit, and handling of addi-

tional prey, depending on the morphology of the; forager and the type of prey. The trade-off here is1 Case Study between the gain per trip, which is maximized by

~ taking the largest load possible, and the number of; The Load Size Decisions trips per unit of foraging time, which is maximized;, of Chipmunks by taking the smallest load. The rate of food deliv-

ery to the central place is the product of these com-Theory For central place foragers that carry more ponents and is maximized at an intermediate loadthan one prey per trip, one foraging decision is size (figure 18.1C). Note that if the declining load-when to stop loading and return to the central ing-rate constraint is removed so that load size in-

,~t.L

Page 4: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

7A. B.

6 ~ 6 0.012Co ~

"0;,. 5 .S 5 . ~., ~

.~ 4 "3 4 ~ 0.008 V ~ - ~ . R, rate of food deliv"0 5 Q, -.= 3 . 3 .'" - -0 = ... --- co , -'-; 2 ] 2 ~ 0.004 F, trips per unit time

~

;10

20 40 60 80 100 120 20 40 60 80 100 120

L (loading time, s) L (loading time, s)

0.05 0.05., c. + ';j' D. I'"" 0 04 ..- - high density -;:., 0 04 .. short distance

~. r ~ ~. , ~ 0.03 I ~ -- ~ 0.03 I --] low density "0

~ 0.02 I ] 0.02 / I distong ance0 0S 0.01 S 0.01 !', ce ~ (I"c;;: , ~; "

0 20 40 60 s80 100 120 0 20 40 60 80 100 120 t~~~

ii'"L (loading time, s) L (loading time, s) ;;~~t

"'-100 ~;"i',"';;;" E. 6 F. high -'--' ty '!'* ' ~=( ". 0() .0 80 - ....§ 1!" s -- - - ";",

.;; "': low density '. co "V~5 60 -g 4 :,. - ~ :

~'j~ - ,,;.,! -- high -'-- (.ty , 3 t ;"', - -- ~=".. ...c , 40 .,.. ;f"",..J ~ ~:;- ".- ~ 2 ...":= 8 ';if

.S 20 .~ '!,"= ~ I ",~ 0 'fc0 ...'

.,0 0 ,C:'

"0 30 60 90 120 150 180 0 30 60 90 120 150 180 ,:c".

T (travel time, s) T (travel time, s) ,:

\';;:"

Figure 18.1 Orians and Pearson's (1979) load-size/loading-time decision model for a central place for- :;~

ager. The model assumes a currency of gross rate of food delivery to the central place with constraints ~~

as follows: (1) The food density and distance from the central place are fixed by the environment. (2) !:iLoading rate decreases with decreased food density and with the amount of load already acquired; there- ;ifore, the total load increases with loading time, but at a decreasing rate, and approaches the maximum ~load more slowly when food is scarce. Panel A illustrates loading functions for patches of high [W = 6(1 ;~;'

"j.- exp (-O.O4L - 0.02))] and low [W= 6(1 - exp (-0.02L - 0.02))] density, (3) Round-trip travel time ;;

includes the outward and return trip plus unloading time and is a fixed cost for any particular distance; :;,it has a positive value at zero distance because of unloading time and increases linearly with distance.(4) Gross rate of food delivery is the product of food gained per trip (load size) and trips per unit time(l/(loading + travel time)). Panel B shows these values for a high-food-density patch 20 m from theburrow, assuming that T= 50 + 1.6D, where T is travel time (s) and D is distance (m). The animal isfree to cease loading at any time, and the decision rules to be determined relate loading time to traveltime and loading time to food density. For any travel time and food density, food delivery rate can becalculated for all possible loading times. The loading time that provides the maximum delivery rate ispredicted to be the one used by the animal. Panel C compares gain curves for high- and low-densitypatches 20 m from the burrow; panel D compares gain curves for high-density patches at 20 and 80 m.Optimal load sizes are indicated by arrows. The predicted decision rules in panel E relate optimal loadingtime to travel time for high- and low-density patches. In panel F, these are converted to optimal loadsizes, using the loading functions. These show that optimal load sizes are larger in high-density patchesand increase in a curvilinear fashion with travel time.

Page 5: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

Foraging Behavior 243

6

--- 5Oij .. .u 4 .N :.- .'" .

~ 3 :~ . .0 . .

- . .'-' . .~ 2 : .

1

180 160 140 120 100 80 60 40 20 0 20 40 60 80 100 120

, T (travel time, s) L (loading time, s),c",~ Figure 18.2 A graphical formulation of the optimal solution to the load size deci-t sion model based on Orians and Pearson (1979) and using the values for the high-';.. density patch presented in figure 18.1. Load size in relation to loading time in-, creases to the right and travel time increases to the left of the origin. For any travel

time, the optimal loading time and load size are indicated by the tangent to theloading curve. This is because the slope of the loading curve equals the rate of fooddelivery (load divided by loading time + travel time). Any point along the curverepresents a possible decision, but the tangent represents the greatest slope andhence the highest possible food delivery rate. This is illustrated for a short and along travel time. Dotted lines drawn from the points of tangency to the axes indi-cate the optimal loading time and load size.

creases linearly, the optimal load is always the using data from some animals at long distances,maximum (Kramer and Nowell 1980). we were able to estimate the consequences of tak-

ing large loads, even if the animals only took smallTests We chose to make a quantitative, observa- loads when near their burrows. In addition, we de-tional test of the predictive power of the decision termined the round-trip travel time and distance torule relating load size to travel time, under field the burrow for the same trials.conditions (Giraldeau and Kramer 1982). If Orians The data showed clearly that load size increasedand Pearson's model is correct and if chipmunks at a decreasing rate with loading time (figure 18.3A)show a curvilinear loading function, these animals and that travel time increased linearly with dis-could have been selected to take a species-charac- tance. The optimal load size for each travel timeteristic, fixed load size corresponding to the aver- was calculated with the equation T = (((P")/age distance and seed density at which they forage. (' (P")) - P" where ((P") and (' (P") are the load-Our design assumed, however, that individuals can ing function and its derivative evaluated at P", theadjust their load size to recent experience of dis- optimal loading time. (See Giraldeau and Kramertance and loading characteristics, including evolu- 1982 for details.) The result was a prediction for ationarily novel food types and foraging situations. strong increase in load size with increases in travelTo determine the average loading curve for our time over the range of travel times observed (figurestudy population, we recorded the weight of seeds 18.3B).taken in 738 uninterrupted loads and 113 loads in Data from the 738 uninterrupted loads showedwhich the experimenter interrupted the chipmunk that chipmunks did take larger loads when theyearly in the loading process. We used a fixed quan- were farther from their burrows, a finding provid-tity of sunflower seeds (10 g) on a bare tray (23 x ing qualitative support for the predictive capacity24 cm) placed at different distances (0.2-135 m) of the model (figure 18.3B). However, load sizesfrom the burrows of 21 different adult animals. By were considerably smaller than predicted. In addi-

,t.

Page 6: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

. .. . .

20 40 60Loading time (s)

B5 ; ,

;~

'@ 4 , , t t . + + . ~

"-" / t + .,~ / + ++. tN . . ~'m 3 I + + .++.. ~"'0 J. ,cd . T 15"

0 2 'I:~ ~

!'

,11 fi ri

t~~,

0 ~;,0 100 300 i

~Travel time (s) :j~~~

';Figure 18.3 (A) The relationship between load size and loading time for ~eastern chipmunks hoarding sunflower seeds at different distances from ;;

their burrows. Each point represents a different load. The line shows thebest fitting exponential equation, W = 6.0 (1 - exp (-0.018 - 0.023), r =0.56; other curvilinear functions gave a similar fit. (B) The relationshipbetween travel time and load size. The solid circles show observed meanload sizes:f:1 SD, and the dash~d line shows the load size predicted tomaximize the rate of food delivery. (Modified from Giraldeau and Kramer1982, figures 1 and 3.)

Page 7: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

Foraging Behavior 245

tion, instead of a relatively sharp increase in load ity not only to distance but also to several otherthat gradually leveled out size with increasing dis- environmental conditions. These patterns wouldtance, chipmunks showed little change in load size not have been discovered without the a priori the-over the first 50 m, with a sharper increase at ory. Optimality models provide a framework for thegreater distances. In a subsequent study, using a discovery of natural patterns even when they fail touniform spatial array that allowed us to determine predict accurately. To illustrate, I will discuss somethe loading time for each seed, we also found cur- hypotheses to explain why chipmunks take loads

. vilinearity of the loading function and an increase smaller than the predicted optimum. These suggest

of load size with distance (Giraldeau et al. 1994). future studies and ultimately stronger predictions.However, this study also found highly significant First, consider possible limitations in the mod-individual differences, as well as effects of distance el resulting from potentially relevant variables thatand the presence of competitors, on the loading were ignored. When an animal takes smaller loadsfunctions. Travel time was also affected by the pres- than predicted, it makes more trips per unit of for-ence of competitors. Unfortunately, this prevents the aging time than predicted and thus spends moregeneralization of loading curves to predict what ani- time traveling and less time in the patch than itmals would have obtained if they had taken larger would if it took the predicted load sizes. Thus, weloads than the ones observed. Nevertheless, the should consider alternative currencies that woulddata clearly showed that the chipmunks would recognize the benefit of more trips or more travel-have had lower rates of food delivery if they had ing relative to more time loading. Note that smallused loads smaller than those observed, and an ex- loads require more of an explanation than largetrapolation strongly suggested that they would have loads. Consider the rate of gain curves in figuredone better by taking larger loads. In other words, 18.1D and E. An animal taking too large a loadchipmunks in this different test situation were also suffers less of a reduction in gain rate than an ani-very likely to be taking smaller loads than pre- mal taking too small a load. Hence, we might ex-dicted by the Orians and Pearson model. pect less of a cost in responding to variables that

Other researchers have confirmed the qualita- require an increase than a decrease in load.tive increase of load size with distance (Bowers and The most obvious simplification in this modelEllis 1993) and have shown that load sizes also in- is its currency of gross rate of food delivery. Netcrease as a result of delayed access to the food rate of energy gain might seem to be more appro-source, even when distance does not change (Lair priate. However, a 3-g load of sunflower seedset al. 1994). The predicted increase of load size contains about 12 kcal of energy, while loading re-with food density was confirmed qualitatively quires about 0.02 kcaUmin and running requires(Kramer and Weary 1991). A decrease in load size about 0.035 kcaUmin (M. Humphries, personalfrom patches with less canopy cover and presum- communication), so net rate will not differ muchably more risk of aerial predation has been found from gross rate in our study. Furthermore, the en-in some situations (Bowers and Ellis 1993), but not ergy cost of running is higher than the energy costin others (Otter 1994). Furthermore, three studies of lbading, so including energy costs will increasefound a strong, but unpredicted, decrease in load the discrepancy. Predation risk could be a factorsize with increasing trip number (Giraldeau and if loading is more dangerous than traveling or ifKramer 1982; Bowers and Adams-Manson 1993; predation risk increases disproportionately withLair et al. 1994). Because these tests did not mea- larger loads. Intraspecific competition might alsosure the loading curves, it is not clear whether the be a factor. Small loads reduce the rate of foodpatterns arise through differences in loading and delivery, making an animal less effective in scram-travel rates that changed the delivery rate optimum ble competition for a short-lived patch. They alsoor as independent variables that produce devia- reduce time at the foraging site, where a dominanttions from the delivery rate optimum. animal might gain an additional guarding advan-

tage. On the other hand, if the main threat fromImplications The load size decision seems relative- conspecifics is pilferage from the burrow while thely minor in that animals ought to be able to get owner is away, taking smaller loads could improveby quite satisfactorily by simply filling their cheek the guarding of the hoard by increasing the fre-pouches to some constant level on each trip. How- quency with which the burrow is visited. Y den bergever, chipmunks showed rapid short-term flexibil- et al. (1986) developed several models indicating

Page 8: Foraging Games - Department of Biology - McGill Universitybiology.mcgill.ca/faculty/kramer/articles/Kramer_90_part_b.pdf · 240 Behavior Table 18.3 Social influences on foraging.---1

246 Behavior

how animals could use active and passive interfer- research attention. For many other decisions of!ence as competitive tactics to increase their share equal importance, clear general models remain to;fof a limited ephemeral resource. This suggests that be discovered. Furthermore, many interesting mod.'a game theory model of load size taking intraspe- els proposed over the last two decades have re~l 'cific competition into account might have greater ceived little or no testing. This is true even for situ-;',. ;

predictive power. ations where simple optimality approaches apply;!(Having considered possible limitations of the the investigation of social impacts on these deci. ';,

m03el, we should now consider possible limita- sions adds new challenges and should receive a c

tions of the animal. To match the predictions of strong impetus with Giraldeau and Caraco's (2000)the model using behavioral flexibility, an animal book.has to have information about travel time, loading Extending the scope of foraging studies will;rate, and how they are to be integrated. Determin- yield fascinating insights into the links between be- ;\.ing these from recent experience involves complex havior and the neuroscience of information acqui. ~issues such as how many trips to include, how to sition and processing. The field of risk-sensitive "'.weight more recent versus less recent trips, and foraging illustrates these connections. While there .,

how to deal with interruptions such as time vigi- was not space in this chapter to discuss how ani. ' ;

lant, hiding from predators, grooming, or engaged mals deal with variance in foraging and other fit- ;"in aggressive interactions with conspecifics. Fur- ness benefits, this is currently a lively area (see Ka- '.;

therm<;>re, animals may measure time and mass on celnik and Bateson 1996 and other papers in the:a different scale from scientists (Kacelnik and Bate- same symposium). Foraging studies can provide '~!

son 1996). If a chipmunk underestimated loading valuable insights for other areas of physiology. Therate or travel time, its loads would be too small. conceptual framework of foraging is closely relatedMost chipmunks' prior experience would involve to that of the acquisition of water, minerals, andfar lower food densities than what we offered, and oxygen, and these processes can be studied with,optimal loads, therefore, almost always would be similar approaches, even though different physio- ? .,smaller. If the animal used a simple rule of thumb, logical systems are involved. ~it is likely that the food type, location, or mode Optimal foraging arose from questions raisedof presentation did not match the evolutionary or by community ecologists but developed with a fo-developmental environment in which the rule of cus on individual behavior. Our understanding ofthumb had been established. Models that take into foraging is now such that the field can make a realaccount specific mechanisms by which animals de- contribution at the levels of population and com-termine and integrate the foraging parameters munity. Although ecological situations are oftenmight be able to improve the precision of predic- too complex for predictions based on simple be-tions at a considerable loss of generality. havioral theories, the theory and empirical base

provided by foraging studies provide important in-sights into processes of linking behavior and popu-

Future Directions lations.

Acknowledgments I thank the many undergradu-Foraging studies have a long history of providing ate and graduate students and postdoctoral schol-conceptual and methodological advances in behav- ars who have worked with me on chipmunk be-ioral ecology. This field provides an excellent ex- havior at McGill over the past 25 years as well asample of the advantages of integrating quantitative colleagues at many other institutions who have of-theory with rigorous empirical testing. The number fered feedback and made constructive suggestions.of variables influencing the "simple" load size de- D. Gidley, L.-A. Giraldeau, C. Hall, M. Humphries,cision suggests that there are numerous other deci- P. McDougall, C. Schiffer, and H. Young providedsion rules to be discovered, possibly for load size, helpful feedback on an earlier draft. M. Humphriesand certainly for the large number of other deci- and D. Roff provided timely help with the figures.sions involved in foraging. In fact, a few elegant Our research has been funded by NSERC Canadamodels such as prey choice, patch departure (mar- and FCAR Quebec and has been greatly aided byginal value theorem), and spatial distribution (ideal the staff and facilities of the Gault Nature Reservefree distribution) have received disproportionate in St. Hilaire.

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