The evolution of alarm calling: a cost-benefit analysis

Anim. Behav., 1990, 39, 86(~868

The evolution of alarm calling: a cost-benefit analysis R O B E R T J. T A Y L O R , D A V I D F. B A L P H & M A R T H A

H. B A L P H

Department of Fisheries and Wildlife, Utah State University, Logan, Utah 84322-5200, U.S.A.

Abstract. Three arguments for the likelihood of alarm calling in colonial animals are presented. The first, a game-theoretic portrait, predicts that alarm calling should be less probable per animal in larger groups and also that actual fitness benefits and costs are not quantitatively important in determining the evolutionarily stable probability of calling in large populations. The second is a geometric model of the dependence of risk upon position within a colony of sedentary animals. The two models are integrated to form a third, which predicts that the probability that an animal gives an alarm call is independent of both group size and the ratio of benefits to costs, above some minimum group size. Some of the available data are consistent with the models, and some are not.

When a predator approaches a group of prey, one or more prey individuals may give a call that alerts the group. This act would seem to draw the predator's attention to the caller, thus creating problems in dealing with the behaviour as a product of individual selection. Since the mid-1960s, attention has been directed toward identifying the selective benefits and costs of apparently altruistic alarm calling. The fitness benefits may be immediate and obvious, such as saving the lives of animals with whom the caller bears genes in common (Hamilton 1964; Maynard Smith 1965; Sherman 1977; Hoogland 1983). They may be indirect, such as preserving mates (Witkin & Fitkin 1979) or other group members in circumstances where group living is beneficial (Smith 1986). Benefits may be considerably delayed. For example, animals might call in anticipation of future reciprocity, or by calling they may forestall predators learning to hunt in the vicinity of the group (Trivers 1971). Some explanations of alarm calling offer arguments that minimize the costs of the act, suggesting perhaps that confusion following the call makes it difficult for the predator to single out one prey animal (Sherman 1985) or that the caller's alarmed-but-disoriented conspecifics may actually distract the predator away from the caller (Charnov & Krebs 1974). The originators of all these arguments suggest circumstances in which the benefit to an individual of giving a call exceeds its cost; such a qualitative relationship must exist for the behaviour to be selectively advantageous. But discriminating among these alternative hypotheses would appear to require a more quantitative understanding of how alarm calling depends upon benefits and costs. Is, for 0003-3472/90/050860+09 $03.00/0

example, the high value of kin protection necessary, or would alarm calling remain advantageous in a population of unrelated individuals? The evolution of alarm calling is clouded further by the conspicuous frequency dependence of its fitness value. While the benefit to an animal of giving a call may exceed its cost, that animal may profit even more by remaining silent if others around it call. The appropriate frame of reference for the evolution of a behaviour, the fitness of which is frequency dependent, is game theory. We define the question of whether or not to call more precisely as what is the best probability of calling per predator sighted, and then, using game theory, we search for an evolutionarily steady state (ESS) in the probability of calling. This is done first for spatially homogeneous groups, groups where positions of individuals vary rapidly and are unpredictable. Then, we treat the extreme case of spatial organization, where position within the group is fixed. Although the second was by far the more difficult case to develop, we were forced to it by the importance to this question of empirical research on ground-dwelling sciurids. A game-theoretic approach requires that one accept the assumption that natural selection generates optimum solutions to environmental problems. The truth of this assumption cannot be addressed empirically. Since there exist an infinite number of optimality arguments, the rejection of any single one cannot be construed as reflecting directly upon the premise of optimality. We see no problems with this assumption and offer the standard rationale for such reasoning, namely (1) the assumption of optimality is not prima facie

9 1990 The Association for the Study of Animal Behaviour 86O

861

T a y l o r et al.: A l a r m calling Animal 2 Call

B-C/2

B

p * = ( B - C ) / ( B - C/2)

(1)

Not call

B-C

0

Figure 1. Payoffmatrix for animal 1 engaged in an alarmcallinggame with animal 2. B is the fitnessbenefitof a call and C is its cost. incompatible with evolution by natural selection and (2) the assumption of optimality can lead to novel, unintuitive hypotheses that are (3) frequently quite vulnerable to empirical test. Since hypotheses of this sort are valuable and not common in behavioural ecology, the optimality assumption seems justified, if only on the grounds of utility. SPATIAL HOMOGENEITY We begin with the simplest case, where the spatial relationships among potential callers is not precisely predictable. This would be true, for example, of flocks of birds, herds of ungulates and groups of foraging primates. A Game Between Two Animals In this category of models, the smallest functional population is comprised of two animals. The payoff matrix for one of these animals appears in Fig. 1. The net benefit to animal 1 when neither calls is defined to be zero. A call by a single animal benefits both equally. When both call, they split the risk or fitness cost; when only one calls, however, it must bear all the cost. Examination of Fig. 1 reveals that if cost (C) exceeds benefit (B), the pure strategy of never calling is evolutionarily stable. IfB > C, however, then neither pure strategy is an ESS. If animal 2 calls, animal 1 is best off not calling; if animal 2 fails to call, then animal 1 finds it more profitable to call. This suggests that the ESS is a mixed strategy, namely call with probably p* where

(e.g. Bishop & Cannings 1978). Obviously p* is sensitive to the relative values of B and C. This first look at the problem is interesting but fragile, requiring as it does that the effective population consists of only two animals. Since the matrix formulation is not useful for games against a larger population, we develop next a general model.

A Game Against the Field A general model requires an expression for the fitness ofa singlep-strategist invading a population ofp*-strategists. Because the number of animals in a group is usually both limited and variable, we treat this as an n-person game. The first issue to consider in describing this game is the dependence upon group size of the costs and benefits of an alarm call. The cost of giving a call is presumably increased risk of predatory attack. In the usual circumstance, where only one group member is attacked, it seems reasonable that this risk be partitioned among all callers. For simplicity's sake, we choose to partition it equally. How group size affects the benefit of calling is much less clear. In many circumstances, the benefit does not depend upon group size. If, for example, the potential caller is closely related to all group members, then the loss of any animal to a predator would be an equal fitness loss, regardless of the size of the group. Or if Trivets' (1971) arguments about predator learning hold, then the benefit of a call lies in preventing a successful attack upon any group member and is again independent of the number of animals at risk. On the other nan& circumstances might arise when a group member would garner different fitness benefits by calling in a larger group than in a smaller. If, for example, the group were newly constituted and only a few of its members were kin, then the probability that the victim of the next attack is a relative should vary with the number of animals in the group. And in those few circumstances where a predator's probability of successful attack increases with group size, we expect that the benefit to an individual of a call should be greater in larger groups than in smaller. Alternatively, if larger groups are less vulnerable, animals in small groups might resist the loss of another animal more strongly. If the benefits of grouping lie primarily in more effective surveillance, then a small group might be at substantially

Animal Behaviour, 39, 5

862 ['0

0.8

0,6 & 0.4

0.2

= ,

2

5

4

5

6

7

8

9

10

II

12

N

Figure 2. Dependence of the equilibrium probabilityof calling upon group size for five values of B/C, in the case when B is independent of group size. greater risk following the capture of one of its members. Because all of these circumstances are possible, we adopt the initial position that the benefits of calling, B(N), should be a general function of group size. The Appendix details the derivation of an ESS probability of giving an alarm call for a population of size N + 1. The solution is a polynomial of degree N ~] (n + I)!(N -- n)! \1 -- p*l

n=0

C

(2)

For N = 1 and B(N)=B, a constant, equation (2) simplifies to equation (1) as expected. Equation (2) can be solved explicitly in some cases (small values of N), but even where it is insoluble it yields quite easily to numerical procedures. We used a commercial software package which employs the method of steepest-descent. All numerical searches resulted in one and only one positive real value for p*. In Fig. 2 we plot the dependence of p* on N for three values of B/C under the circumstance where B is independent of group size, the circumstance we consider most general. The upper and lower lines represent extreme parameter combinations, the upper where benefits grossly exceed costs and the lower where benefits barely exceed costs. The three intermediate curves represent more realistic combinations of parameters. All of these combinations predict that the probability an individual will call should be highest in small populations and diminish as N gets large. Examination of equation (2) suggests that this must be true in general. If simultaneously N is allowed to approach infinity and the

sum of the series is required to converge to a constant, B/C, then p* must converge to zero. In other words the envelope for all solutions converges to zero as N grows large. In addition, Fig. 2 suggests that within a reasonable range, the precise values of B and C seem not to matter a great deal for large populations, only that B > C. Among other things, this implies that the results of the two-person game do not generalize to a larger n-person game. This describes the behaviour of an individual member of the population. For the population as a whole, the probability that no animal gives an alarm call can also be calculated. This probability, which equals (1 _p.)N+ 1, appears to converge to a constant value (Fig. 3). We have not been able to prove this conjecture but speculate that it may be a size-insensitive feature of a group's behaviour. The circumstance where the value of a call depends upon group size is obtained by setting B(N) = bN ~.The parameter b represents the benefit derived from a call when only one other group member is at risk; the exponential constant, s, is a shape parameter and would most likely be in the range - 1 < s < 1. Equation (2) yields the predicted values of p* in Fig. 4 for the three cases o f s = - 1/2, 0, + 1/2. The functional form of B(N) would seem to be important for small populations. These simple game-theoretic portraits of alarm calling generate several predictions. First among them is that the evolutionarily stable probability of an individual giving a call is sensitive to population size. If this pattern does exist, then it would be worth discovering its functional basis. Since an individual animal might find itself in groups of

863

Taylor et al.: Alarm calling

0,4

0-2

U

I

A

I0 N

I

I~5

2O

Figure 3. Relationship of the probability that no alarm call is given to group size.

I'0 0'8[

o.o 0.4-

0

9 (C)

2

3

4

,

I

5

6

I

N

7'

I

8

I

9

I

I

[0

II

12

Figure 4. Dependence of the probability of calling upon group size when B(N) = bNL Curve (a) represents s = 1/2. Curve (b) represents s=0, as in Fig. 2. Curve (c) represents s= - 1/2. In all three cases B/C=2.0. dramatically different sizes within the course of a single day, a genetic or developmental proximate mechanism is inappropriate. O n the other hand it seems somewhat far-fetched to suggest that all animals that give alarm calls continually and accurately count the number in their groups. The decreasing importance, as colony size increases, of the actual differences between the benefit of calling and its cost suggests that one need not be overly concerned with precise values of the two variables, only their rank. As a consequence, we feel comfortable with the various low-value explanations; nepotism may be a sufficient benefit of alarm calling but is hardly a necessary one. In a practical sense this is a helpful result; the benefit of calling is a difficult parameter to estimate directly, both for h u m a n observers and for the animals

involved (Altmann 1979). The costs of calling, by comparison, are immediate and easy to assess. We should expect prey animals to be able to estimate rather precisely the risk they take in drawing attention to themselves and to alter their calling behaviour accordingly. The most likely measure of risk is the distance between the predator and prey. We treat next the problem of spatial variation of risk within the colony and how it might influence alarm-calling behaviour. SPATIAL

STRUCTURE

A Consideration of Geometry Alone Assume that a colony of prey animals is circular in shape and that individual animals are spaced uniformly within its boundaries. G o o d reasons

864

Animal Behaviour, 39, 5

~

1.0 Predator 0.8

o

o 0'6

Danger zone

o.

0-2 Figure 5. Geometry of overlap of the danger zone with the colony. Variables definedin text. 0

exist for assuming circularity in a homogeneous environment (Taylor 1988). A predator approaching the periphery of the colony will carry with it a zone of danger. This area, centred on the predator, is a region within which it can capture a prey animal. The idea that space is divided sharply between areas of risk and areas of security may seem unreasonable at first glance but is in fact a well-established result of the theory of differential pursuit games (Isaacs 1965). The shape of this zone of danger will not in general be radially symmetric; predators can neither detect nor move rapidly toward prey equally well in all directions relative to their orientation. But if one assumes that the predator is moving directly toward the colony, then the interesting fraction of the zone is that in front of the predator, and that portion should approximate an arc of a circle. The radius of this zone reflects the probability that an animal can get to its burrow before capture and should relate to the relative speeds of the prey and predator9 The geometry of the problem is suggested in Fig. 5, in which the zone of danger overlaps a portion of the colony. Discovery of the fraction of the colony in danger is straightforward. The origin of the coordinate system is placed at the centre of the colony, with the X-axis aligned along the line connecting the centre and the predator. The predator is a distance d from the origin when sighted. The radius of the colony is re, and the radius of the zone of danger is r d. The area of overlap of the two circles is found by integration from d - r d to r c (Appendix). The proportion of the total colony this area forms is D = B/~z+

a_(r~d~2 ~z\ r ~ /

(3)

1 2~zrc2

/4d2re2_ (d2_rd2 +re2)2

0'4

0"8 1"2 1"6 Radius of the danger zone

2"0

Figure 6. Proportion of the colony not calling as a function of the radius of the danger zone relative to the radius of the colony. In this example d= 1.2. where a is the angle from the X-axis to a line connecting the centre of the colony and the point of intersection of the two circles and fl is the angle from the X-axis to a line connecting the predator and the intersection of the two circles. If animals always called when safe and never called if in immediate danger, equation 3 would comprise a prediction of the proportion of the colony that would call. Figure 6 shows this proportion as a function of r d, the radius of the zone of danger. The relationship is sigmoid, showing the least variation in response to changes in r d at extreme values and the most at intermediate values. If the parameter r d is proportional to the relative speeds of the predator and prey, as seems reasonable, then Fig. 6 suggests that slow predators should elicit many more alarm calls than moderately fast predators. Very fast predators should elicit almost none. This assumes that predators are sighted a constant distance from the colony, regardless of speed. It also assumes that hearing is equally important to all predators, which is not true in general. A question that arises consequent to this argument is whether all animals not at immediate risk will automatically call. The logic of the spatially homogeneous model suggests that they will not. A Geometric Game

If one assumes that colony members within an approaching predator's zone of danger find that the cost of a call exceeds its benefit, then the alarmcalling game will be restricted to those animals within the zone of relative security. This makes the

Taylor et al.: Alarm calling 1,0

(o) 0'75 BIG 0"50

:

:

=

3"0

=2.0 1"33

=

0'25

I'0~

(b)

865

diferent speeds. As plotted, p* is the ESS probability of calling for an individual animal averaged over the entire colony not just the fraction out of immediate danger. The conspicuous feature of Fig. 7 is that the ratio B/C makes even less difference to p* than in the spatially homogeneous case. The lack of smoothness in Fig. 7a, b derives from the rounding off process in step 3 above. The differences between the two graphs reflect primarily variation in the vulnerability of small colonies to attacks by predators of different speeds.

0"75

0-50

~

B/C =3"0 =2"0 = 1"33

0"2

2

3 4

5 6

7

8 9 /V

[0 II

12

Figure 7. Dependence of the ESS probability of alarm calling upon colony size in the geometric game; (a) represents a relatively slow predator (ra = 0.1); (b) represents a relatively fast predator (rd= 1.0). dependence of p* upon group size somewhat more complicated than in the simple, spatially homogeneous game. An increase in group size implies an increase in colony area and a consequent decrease in the fraction of the colony close to the predator. The consequence of fusing the geometric and game-theoretic arguments can be discovered with the following recipe. (1) Assume that density in a colony, 5, is constant so that the number of animals is proportional to the colony's area. Then N = 5nrc 2 or (4)

rc = ~/(N/Sn)

(2) Insert equation (4) into equation (3) and solve for S = l - D , the proportion of animals with B > C in any single attack. (3) Solve, forp', a modified form of equation (2) u,

N'!

.70 (n + I)!(N'

(

p'

y = B(N)(5)

- n)! \ 1 - p ' J

C

where N' is the nearest integer to SN. Substitution of N' for N is not made in B(N), since the benefit should reflect the size of the entire colony. (4) Find p* =p'N'/N. In Fig. 7 we show the dependence of p*, calculated in this way, upon group size for predators of two

DISCUSSION Three arguments are proposed for the evolution of alarm calling. The first, a spatially homogeneous analysis of an n-person game, predicts that the evolution of alarm calling should result in a mixed ESS, that the evolutionarily stable frequency of calling should decline to zero as the number of potential callers grows large, and that the rate of decline should reflect the functional relationship between the benefit of a call and the size of the group. The probability that at least one call is given may prove to be relatively independent of, group size. The second argument considers only the geometry of risk within spatially structured colonies and ignores the game-theoretic approach. It leads to the conclusion that the fraction of animals calling will depend upon the relative speeds of the predator and the prey. We synthesize these two into a third argument that supposes the following. If an animal is within the predator's zone of danger, then the cost of drawing attention to itself is quite high; in few cases will the benefits of calling exceed the cost for that animal. In such a circumstance, the ESS is the pure strategy of not calling. But if the prey is outside the zone of danger, its costs drop dramatically, possibly to well below the benefit of a call. In this case, the ESS is mixed, and the results of the gametheoretic analysis apply. However, the size of the population against which that animal should expect to play is no longer the number within view, only that portion of the exposed population outside the zone of danger. The third model predicts that differences in the 9 e~ benefit-cost ratio have only very minor influences on the ESS probability of giving an alarm call. This means that discrimination among alternative

866

Animal Behaviour, 39, 5

evolutionary scenarios will not be achieved merely by measuring the tendency to give alarm calls. The geometric game differs fundamentally from the spatially homogeneous gam~ in partitioning the population into a subset that will potentially call and a subset that will not. In principle it seems reasonable to accept that not all animals will participate in the game. But once one accepts that a population can be partitioned with respect to likelihood of calling, the question arises as to what is the best criterion by which to make that partition. We suggest that it makes a great deal more sense to study first variation in risk rather th~/n variation in relatedness to other members of the colony. Variation in risk is an inevitable consequence of spatial structure within a colony. The observation that both social and kinship status , can influence alarm calling may be of little importance and may even reflect a spurious correlation with physical location. The line of reasoning in the geometric game suggests that if the predator is fast, the fraction of the group out of danger is both small and located on the most distant margin of the colony. These animals should call with high probability. If, on the other hand, the predator is slow, then most of the colony is secure. Members of this more numerous group should each call with a lower probability. The simultaneous operation of these two decision processes is compensatory, resulting in stabilization of p* at a non-zero value. The influence of the predator's speed will still be felt; fast predators will generate high variance in the probability of calling in relation to position and slow predators will generate low variance. Given the need for nearly instantaneous response to danger, the predator's maximum speed is probably the primary information upon which an animal bases the decision to call. The systematic data needed to reflect critically upon all these ideas have not been published. One can point to a number of intriguing observations in the literature. The probability that birds give an alarm call can vary and may depend upon the composition of the group (Sullivan 1985). Ground squirrels also vary in their tendencies to give alarm calls (Schwagmeyer 1980). Some of our own observations on Uinta ground squirrels, Spermophilus armatus, suggest risk-sensitivity in alarm-calling behaviour. These are sedentary animals that live in aggregations (Balph 1984) and readily give alarm calls in response to predators (Balph & Balph

1966). Within the area occupied by a study population, males are usually scattered in closed habitats where there are few other squirrels or escape burrows (Slade & Balph 1974). Males, therefore, derive relatively little benefit and may suffer substantially increased risk by calling. In contrast, females and their young commonly live in open habitats where the densities of both squirrels and burrows are high; these animals are conspicuous to predators. As expected, females engage in alarm calling a great deal more frequently than do males, an observation that seems to apply to some other ground-dwelling sciurids as well (e.g. Sherman 1977; Hoogland 1983). In an experimental analysis of Uinta ground squirrel alarm calls, Cherry (1979) found that when a red fox, Vulpesfulva, suddenly appeared within 10 m of squirrels in an arena with escape burrows, the squirrels typically became motionless and remained silent. As the fox moved about and happened to approach the squirrels, they fled to their burrows. Of those that gave alarm calls with a fox in pursuit, 81% did so just as they approached or disappeared into the burrow. Under the controlled conditions of this experiment, sex, age and season had no significant effects upon the probability of calling. These results are consistent with the strategy to be silent when risk is high (i.e. when the fox was nearby and had yet to see the squirrels) and to call when safe (i.e. upon nearing or entering the burrow). F o r this ground squirrel, evidence seems to support the theory. On the other hand, Sherman (1985) has data on Belding's ground squirrel, Spermophilus beldingi, which appear inconsistent with the theory. He flew tame hawks, Parabuteo unicinctus, over a closely watched colony in the Sierra Nevada Mountains of California. The more likely callers were animals in exposed positions, closer to the hawk, and further from hiding places. This result seems counterintuitive, but perhaps hawks rely little on hearing and a squirrel is not made more conspicuous by calling. In fact, Sherman noted a variety of differences in his squirrels' responses to mammalian and avian predators. The role sound plays in alerting raptors to the presence of squirrels is unknown; none the less, it is unlikely that striking raptors, with the exception of harriers, rely much upon sound. If calling does indeed prove to be functionally without cost in the face of hawk attacks, then the logic employed irt this paper will need to be restricted to predators that rely more heavily upon hearing.

Taylor et al,: Alarm calling Finally, Latane' et al. 0981) reviewed a large number of experiments investigating the influence of group size on helping behaviour in humans. They considered the following result to be the single most reliable in the field of social psychology With very few exceptions, individuals faced with a sudden need for action exhibit a mark-

867

edly reduced likelihood of response if other people actually are, or are believed to be, available to act. (Page 290) This phenomenon can be attributed to several causes, prominent among which is 'diffusion of responsibility', essentially the same mechanism developed here in the game-theoretic treatment.

APPENDIX Derivation of Equation (2)

In a population consisting of N individuals, each calling with probability p*, the probability that n animals call is a binomial random variable Pr(ncallslN.p,)=(N)p,,(1

_p,)N-,

(4)

The fitness of a single p-strategist invading this population is w(p,p*) = p

p'n(1 - - p * ) S - n ( B ( N ) -- C/n + 1) + (1 +p)[1 -- (1 - p * ) S ] B ( N ) n

(5)

0

The derivative of equation (5) at equilibrium is ~, n

p*"(1 - p * ) N - " ( B ( N )

- C/n + 1) = B ( N ) - B(N)(1 _ p , ) N

(6)

0

which simplifies to C~

p*"(1 - p * ) ~ - " ( 1 / n + 1) = B ( N ) (1 _ p , ) N

(7)

n=0

This in turn reduces to equation (2). Derivation of Equation (4)

The equation for the colony's perimeter is y = _+ ~

-- x 2

(8)

The equation for the zone of danger around the predator is y=

_+X/rd 2 - ( x - d )

2

(9)

The overlap of these two circles extends over the range d - r a ~
J~ -

X/rd 2 _ (X _ d) 2 dx + 2 1 ,c x//~-~2_ x 2 dx rd

where/, the point of intersection of the circles, is ( d - r d 2 + rr

(10)

dI

Solving equation (10) yields

A = ard 2 + flrd 2 - (1/2)~/4d2r~ 2 - (d2 - rd2 + r~2)2 Equation (3), the proportion of the colony within the zone of danger, is A/~zre 2.

(I 1)

Animal Behaviour, 39, 5

868

REFERENCES Altmann, S. A. 1979. Altruistic behaviour: the fallacy of kin deployment. Anim. Behav., 27, 958-959. Balph, D. F. 1984. Spatial and social behavior in a population of Uinta ground squirrels: interactions with climate and annual cycle. In: The Biology of Grounddwelling Squirrels (Ed. by J. O. Murie & G. R. Mitchener),pp. 336-352. Lincoln, Nebraska: Nebraska University Press. Balph, D. M. & Balph, D. F. 1966. Sound communication of Uinta ground squirrels. J. MammaL, 47, 440450. Bishop, D. T. & Cannings, C. 1978. A generalized war of attrition. J. theor. Biol., 70, 85-124. Charnov, E. L. & Krebs, J. R. 1974. The evolution of alarm calls: altruism and manipulation. Am. Nat., 109, 107 112. Cherry, M. B. 1979. Alarm cells of captive Uinta ground squirrels (Spermophilus armatus). M.S. thesis, Utah State University. Hamilton, W. D. 1964. The genetical evolution of social behaviour. I and II. J. theor. Biol., 7, 1 16, 17-32. Hoogland, J. L. 1983. Nepotism and alarm calling in the blacktailed prairie dog (Cynomys ludovicianus). Anim. Behav., 31,472-479. Isaacs, R. 1965. Differential Games. New York: John Wiley. Latane', B., Nida, S. A. & Wilson, D. W. 1981. The effects of group size on helping behavior. In: Altruism and Helping Behavior: Social, Personality and Developmental Perspectives (Ed. by J. P. Rushton & R. M. Sorrentino), pp. 287-314. Hillsdale, New Jersey: Erlbaum.

Maynard Smith, J. 1965. The evolution of alarm calls. Am. Nat., 99, 59~53~ Schwagmeyer, P. L. 1980. Alarm calling behavior of the thirteen-lined ground squirrel, Sphermophilus tridecemlineatus. Behav. Ecol. Sociobiol., 7, 195-200. Sherman, P. W. 1977. Nepotism and the evolution of alarm calls. Science, N. Y., 197, 1246-1253. Sherman, P. W. 1985. Alarm calls of Belding's ground squirrels to aerial predators: nepotism or selfpreservation? Behav. Ecol. SociobioL, 17, 313 323. Slade, N. A. & Balph, D. F. 1974. Population ecology of Uinta ground squirrels. Ecology, 55, 989-1003. Smith, R. J. F. 1986. Evolution of alarm signals: role of benefits of retaining group members or territorial neighbors. Am. Nat., 128, 604610. Sullivan, K. 1985. Selective alarm calling by downy woodpeckers in mixed-species flocks. Auk, 102, 184~187. Taylor, R. J. 1988. Territory size and location in animals with refuges: influence of predation risk. Evol. Ecol., 2, 95 101. Trivers, R. L. 1971. Tile evolution of reciprocal altruism. Q. Rev. Biol., 46, 35-57. Williams, G. C. 1966. Adaptation and Natural Selection. Princeton, New Jersey: Princeton University Press. Witkin, S. R. & Fitkin, M. S. 1979. Chickadee alarm calls: does mate investment pay dividends? Anita. Behav., 27, 1275-1276.

(Received 6 February 1989; initial acceptance 29 March 1989;final acceptance 8 June 1989; MS. number: A5484)