A game theoretical interpretation of male combat in the bowl and doily spider (Frontinella pyramitela)

Anita. Behav.,1983, 31, 59-73

A GAME THEORETICAL INTERPRETATION OF MALE COMBAT IN THE BOWL AND DOILY SPIDER (FRONTINELLA PYRAMITELA) BY STEVEN N. AUSTAD

Department of Biological Sciences, Purdue University, West Lafayette, 1N 47907 Abstract. Male bowl and doily spiders (Front&ella pyramitela: Linyphiidae) fight over access to adult

females. The probability of disablement or fatal injury in these contests is a linear function of their duration. Thus the fights fit closely the assumptions of a version of the game theory 'war of attrition'. Because the details of sperm competition are known, female value (expected number of eggs fertilized) to either a copulating male or an intruder can be quantified for any stage of copulation. Using this information, the predictions 0f the war of attrition model were critically examined by experimental manipulation of fighting ability and female value for both web residents and intruders. When female value was equaI for both combatants, the ability to win fights was correlated with body size and the duration of contests was inversely correlated with size difference. The winning percentage of males of specific size differences varied directly with female value. The treatments with the highest percentage of injuries and fatalities were those in which a smaller resident was defending a female of great value to him. In two treatments in which larger web residents were contesting for females of low value, the predictions of the model were seemingly not supported. However, a quantitative analysis of the treatments shows that these apparently anomalous results are in accord with the model. rare alternative strategy (Maynard Smith 1974). Though an ESS approach dictates a specific mode of analysis for any model of conflict, the key to understanding the conflict behaviour itself still lies in detailed and accurate modelling of the particular situation under study. The first generation models developed by this approach (Maynard Smith & Price 1973; Maynard Smith 1974) were necessarily simplified in their assumptions. However, they were nonetheless enlightening in that they suggested possibilities for the evolution of certain counterintuitive behavioural strategies by individual selection. For instance, it was shown theoretically that contests could be resolved without escalated fighting if members of a population respected some asymmetry between contestants, although that asymmetry was unrelated to either relative fighting ability or the value of the disputed resource (Maynard Smith & Parker 1976). Recent models (Hammerstein 1981; Parker & Rubenstein 1981; Hammerstein & Parker 1982) have included more realistic assumptions and subtleties, and are consequently more useful for making general predictions about the incidence, intensity, and outcome of actual contests under a variety of ecological conditions. In this work I quantitatively tested one game theoretical model of conflict, utilizing male bowl and doily spiders (Front&ella pyramitela: Linyphiidae) who were contending for access to females. Not only are the general predictions of

Introduction Until the last decade, the study of animal conflict was dominated by the cataloguing of types of agonistic behaviour and a consideration of the relative importance of internal versus external stimuli in the eruption of overt fighting (e.g. Hinde 1966; Marler & Hamilton 1966). For instance, it was known that dominance relations between the sexes could be l~eversed during certain stages of the breeding season, that the proximity of landmarks or other animals could change dominance status, and that in some species female hormones increase aggressiveness while in others they decrease it (e.g. Hinde 1956; Guhl 1961). However the role of evolution in shaping these disparate phenomena was only vaguely considered. The possibility of a unified predictive theory of animal conflict behaviour arose with the pioneering work of Maynard Smith (1972), who applied game theory mathematics to the problem and developed the concept of the 'evolutionarily stable strategy' or ESS (Maynard Smith 1974). The conceptual advance represented by ESS logic is especially applicable to the evolution of fighting behaviour because instead of merely assigning fixed reproductive costs and benefits to particular behaviours, these costs and benefits are seen to depend upon the action of others. An ESS is defined as a strategy which, if adopted by all members of a population, cannot be invaded and replaced by any initially

59

60

ANIMAL

BEHAVIOUR,

the model fulfilled, but also several otherwise anomalous experimental results are explained, as well.

The War of Attrition One type of animal contest that has been modelled extensively has been called the 'war of attrition' (Maynard Smith & Price 1973; Maynard Smith 1974). In this contest two animals are contending for a resource of value V by mutual display or some kind of continuous struggle whose costs rise linearly with persistence time t. The total cost of the contest then is Kt, where K is a measure of the rate with which costs are incurred. In the simplest case, where both V and K are identical for opponents, the ESS is to select a persistence time randomly from a probability distribution p(t) such that K p(t) = - - exp (--Kt/V) V (Maynard Smith 1974). Norman e t a l . (1977) have generalized this model to include nonlinear costs, while Bishop & Cannings (1978) have explored the case where both costs and benefits depend upon t. Parker & Thompson (1980) have noted that the actual observed distribution of contest durations will not show this distribution even though both contestants are using it. Because the duration of a given contest will be set by whichever contestant picks the lower persistence time, the resulting observed distribution of contest lengths, po(t), will follow the negative exponential distribution 2K

po(t) --

exp (--2Kt/V).

V Bishop et al. (1978) examined a game in which the 'owner' of a resource 'knew' exactly its value, but an intruder 'knew' only the distribution of resource values from which it came. In this case the ESS for the owner is to choose a persistence time for a probability distribution whose mean is directly proportional to the value of the resource, In other words an owner defending a resource of little value will be less persistent than one defending a highly valuable resource. These distributions do not overlap, so that the valuable resource owner will always persist longer than the owner of a poor one. When contestants are assumed to differ in fighting ability (i.e, when KA r K B ) o r the relative value of the resource (VA v~ VB), then

31,

1

Parker & Rubenstein (1981) have shown that K and V interact as a single variable that defines the payoff-relevant asymmetry of the contest. The ESS for this case is: persist indefinitely if A, withdraw immediately when B, when these states are defined by

VA

Vn

KA

KB

This has been called the 'optimal assessor' strategy because it assumes that each combatant has perfect abilities to assess V and K for both himself and his opponent. Even if assessment is perfect, the recurrence of convention-disobeying mutants will ensure that combat will still occasionally occur. However, individuals in role A will always persist longer (i.e. win) than those in role B (Hammerstein & Parker 1982). Furthermore if assessment is less than perfect, then contests will also occur, but individuals in role A wilt persist longer than those in B. The contest lengths are inversely correlated with the accuracy of assessment. Thus as assessment approaches perfection, the 'optimal accessor' strategy will be approached (Hammerstein & Parker, unpublished data).

Combat Among Male Bowl and Doily Spiders Mate bowl and doily spiders merely avoid one another if they meet when off a female web. However, males vigorously defend a female with whom they have not yet finished mating (Austad, personal observation). When males fight they approach one another beneath the web-bowl and spar briefly with the first two pairs of legs, then grapple furiously. Grappling consists of vigorous tugging and twisting after having interlocked jaws and legs. The contest ends either when. one combatant releases his hold and drops into tile web-doily, or else when one is killed. Grapples do not appear to change in intensity as they progress, but are uniformly furious throughout. If the combat loser has already mated, he departs from the web after the fight. If he has not yet copulated, he remains on the web periphery until the victor has finished copulating and then the loser returns to the bowl and mates. In the field several males are frequently found in female webs, and one often sees copulation interrupted by intruding males (Austad, unpublished data). When male web-building spiders mature, they abandon their webs and wander in search of mates. They rarely eat. Therefore the one

AUSTAD: GAME THEORY AND MALE COMBAT IN A SPIDER important resource in their lives, females, is commensurate with reproductive success. Because of the straightforward measurability of these spiders' resources, and because the form of male-male encounters seemed to fit remarkably well the war of attrition model, I used this experimental system to examine whether some general properties predicted by the ESS analysis could in fact be observed. In order to rigorously examine the model, one must measure the rewards of victory and cost of combat in terms of their effect on reproduction. Female Value

The value of a female to a male in evolutionary terms can be defined by the number of potentially fertilizable eggs she contains minus the time, risk, and energy necessary to achieve those fertilizations. In nature, male bowl and doily spiders defend adult and penultimate females (those one moult short of sexual maturity) with whom they have not finished mating. Therefore measuring the females' values entails quantification of the potential number of fertilizations they represent as well as the male copulatory investment necessary to garner those fertilizations for females of all reproductive states. An extensive series of double matings using x-irradiated sterile males and normal fertile males was utilized to determine how copulation interruptions affected the reproductive success of males, and how the reproductive success of a first mate was affected by his replacement by a second male during the course of copulation (see Austad 1982, for methodological details). Bowl and doily spiders exhibit first male sperm priority. That is, the sperm of the first male to mate is used for fertilization before that of subsequent mates, i f allowed to complete mating, the first male transfers enough sperm to fertilize nearly all of the eggs a female will produce, so that subsequent males will fertilize few (less than 5 ~ ) of a female's eggs if they mate immediately alter the first male, and will fertilize no eggs if they mate at least 24 h after the first male (Austad 1982). There is no sperm displacement as a result of takeover. In other words, if the first mate has transferred enough sperm to fertilize 30 ~ of the female eggs, he will fertilize those eggs regardless of whether he is replaced by another male, or whether copulation was terminated for some other reason. Thus a male who is challenged by

61

an intruder during mating will not lose prior fertilizations by losing a fight, but will only lose those he had not yet achieved when the fight began (Austad 1982). Males also perform a 'pre-insemination' phase of mating at the beginning of copulation. They assume the standard copulatory position and accomplish intromission, yet no sperm is transferred. The length of this phase is consistently affected by female reproductive history (Table I), suggesting that males assess female value then (Austad 1982). There is no evidence that males can assess the relative number of eggs contained by females who differ in body size. Female body size is very weakly correlated with fecundity, but laboratory experiments have shown that the overriding variable affecting fecundity is the prey capture rate between maturity and first oviposition (Austad & Kiklevich, unpublished data). Measuring Fighting Ability

Since body size is widely known to be correlated with the ability to win fights in a variety of invertebrates (e.g. Hazlett 1968; Rubenstein & Hazlett 1974; Borgia 1980; Brook 1981), including spiders (Buskirk 1975; Riechert 1978; Christenson & Goist 1979; Vollrath 1980), it seemed likely that combat cost would depend heavily on the relative body size of the combatants. To examine whether this was true for male bowl and doily spiders, 1[ staged 104 encounters between males of known body size, who were simultaneously introduced into females' webs. Methods

All spiders used were collected while immature and reared in the laboratory by methods Table I. Male Mating Behaviour as a Function of Female Reproductive State (Standard Deviations are Shown in Parentheses)

Female reproductive state

N

Virgin

61

17.2 (6.0)

30.7 (10.5)

Recently mated (< 24h) Previously mated (> 24 h)

40

185.3 (100.5)

31.4 (7.1)*

53

25.6 (18.6)

Mean time (rain) spent in: Pre-insemination Insemination

0 (0)

*Only 19 out of 40 males performed any insemination at all. The data shown include only those males that actually transferred sperm.

62

ANIMAL

BEHAVIOUR,

described in Austad (1982). All experimental males were used within 20 days of their ultimate moult, and all were used for only one encounter. All females were adult virgins. Three measurements of body size were recorded: total body length, maximum cephalothorax width, and body weight. Males were anaesthetized with COz and measured for the two linear dimensions using an American Optical Cycloptic Series 58 microscope with an ocular micrometer disc calibrated to 0.03 mm. Linear dimensions were estimated to the nearest 0.01 ram. Repeated observations o n the same individuals revealed a precision of 0.02 m m for body length and 0.03 m m for maximum cephalothorax width. Spiders were weighed on a Mettler H30 analytical balance with a precision of 0.1 mg. Females were induced to build webs upon artificial scaffolding composed of vegetation upon which bowl and doily webs had been found in the field. Males were introduced into the web by allowing them to drop on their own draglines until they contacted the web-tangle, after which they generally proceeded directly to the webbowl where the female was to be found. Grappling and sparring durations were recorded for all contests, as were any obvious injuries such as broken or detached legs or gross abnormality in movement after the fight. All injuries so recorded were sufficiently serious that it is unlikely that the injured male would ever subsequently succeed in reproducing. In three of these encounters grappling occurred in two phases; the males grappled then broke apart, then resumed grappling. In these instances the total duration of both grapples was used.

31,

1

The purpose of this experimental series was twofold: (1) to determine which, if any, measure of body size accurately indicated fighting ability, and (2) to determine whether any behavioural basis for sorting fights into discrete categories based on relative size difference existed. After size measurements were completed, I paired spiders haphazardly so that about one-third of the contests were between individuals of about the same size, one-third between individuals of slightly different sizes, and one-third between individuals of grossly different sizes, according to visual inspection. Results

Body length best predicted the winner of these aggressive encounters (Table II). It was also the only dimension that correctly predicted more than half the contest winners when size was close enough that individuals could not be separated by visual inspection (row 3 of Table II). Winners of fights in which the direction of size-difference was contradictory for two dimensions were predicted equally well by body length and weight. Overall the best predictor of outcome was body length, and because it was also the dimension which was measured with the greatest precision, I chose it as my indicator of fighting ability. After graphing size-difference against grapple duration, I determined by inspection of the data that fights could plausibly be sorted into three categories (Fig. 1). I termed combatants who differed by less than 0.1 m m in length the 'same' size, those who differed by more than 0.1 m m but less than 0.25 m m 'slightly' different, and those differing by more than 0.25 m m 'greatly'

Table H. Body Size Dimensions as Indicators of Fighting Ability (N in Parentheses)

Percentage of fights in which larger size predicted the winner

All fights* Fights with 'contradictory' measures I' Fights with length-difference less than 0.1 mm

Length

Cephalothorax width

Weight

82.5 (103) 77.3 (22)

72.4 (98) 65.2 (23)

77.3 (97) 78.9 (19)

58.6 (29)

44.4 (27)

42.3 (26)

*Total number of fights is less than 104 because of ties in certain body dimensions. tFights with 'contradictory' measures are those in which differences in two dimensions are in opposite directions.

AUSTAD: GAME THEORY AND MALE COMBAT IN A SPIDER

30C

63

g a

eome

.~ 20C

co

10C

"o

o

"is,ghf i II

ame!

9 9 I ' •9 99 9eoe 9 o II

'Great'

j]_~ | 1.s.t~.; 0.1

0.2

0,5

r

,

0.4

0.5

Difference

.'l.m,4~.s,'...~_ 0.6

0,7

0.8

0.9

in b o d y l e n g t h [ m m )

Fig. 1. Grapple duration as a function of size asymmetry. These data are from 104 staged fights between males simultaneously introduced into the webs of virgin females. One outlier (0.05, 604) is not shown. The dotted lines indicate boundaries of the size-difference categories as used in subsequent experiments. These size-differencecategor;.eswere determined by visual inspection of the data. different. Grapples between combatants of the 'same' size lasted 194 s on the average, and size-difference predicted only 59 ~ o f the winners. Males of 'slightly' different size grappled for 24 s on the average, and larger males won 83 of encounters. 'Greatly' different males grappled for an average of 5 s and the larger won 1 0 0 ~ of encounters. Grapple duration was significantly different in all comparisons between these categories (Mann-Whitney U-test, P < 0.0001 for all comparisons).

Examining the War of Attrition Using the previously obtained information on female value and male fighting ability, I examined how the predictions from the 'war of attrition' were fulfilled by the dynamics of male combat.

gories plus four levels of relative female value. Instead of simultaneously entering combatants to the web again to formulate an equal female value treatment, I simply used the data already obtained in the experiments to measure fighting ability (Table III). Each of these 20 treatments consisted of 10 encounters. (Explanation of the particular intrusion points chosen will be 1.C

0.75

a 8, ~ o.5c,.6 g 0.25

Experimental Procedure I manipulated both relative male fighting ability (i.e. body length) and female value (see below). The experimental procedure consisted of choosing two males from a particular sizedifference category, allowing one of them to mate for a predetermined period (Fig. 2), then introducing the second male to the web. Grapple duration, outcome, and the occurrence of injury were recorded. Both variables were manipulated simultaneously. There were five size-difference cate-

99

I 10

I _ 9 20 9 30 Copulation time ( min ]

t A40

I 50

Fig. 2. Proportion of eggs fertilized by copulating males at the different encounter points. Each triangle under the abscissa represents a different encounter point. Significance of the particular interruption points chosen is discussed in the text. The fertilization curve was calculated from extensive sperm competition experiments, the details of which may be found in Austad (1982). Each point represents the reproductive output of between 8 and 11 females.

64

ANIMAL

BEHAVIOUR,

31,

1

Table IlI. Experimental Design and Mean Grapple Duration for Manipulative Examination of the War of Attrition (Grapple Duration is in s, sE is in Parentheses)

Size-difference 'Slight' Encounter point*

'Same'

Simultaneous with first male 1 rain after start of PI End of PI After 7 min of insemination After 21 min of insemination

193.8 (19.4) 235.4 (51.7) 253.4 (59.4) 49.2 (9.3) 29.9 (4.6)

Resident smaller

'Great' Resident larger

24.4 (2.2)I" 55.8 (9.1) 20.4 (3.6) 144.1 (22.9) 44.8 (12.8) 39.2 (7.4) 19.7 (3.7) 12.7 (3.6) 10.7 (3.0)

Resident smaller

Resident larger

5.2 (0.8)t 81.7 (14.2) 10.9 (1.6) 56.9 (7.9) 9.5 (2.6) 19.3 (4.7) 10.6 (1.8) 5.7 (1.5) 6.4 (2.2)

*The significance of these encounter points is discussed in the text. "~Signifiesfights in which the opponents were introduced simultaneously into the web, hence resident and intruder status is not meaningful. discussed below.) The o r d e r o f staged encounters with respect to t r e a t m e n t was r a n d o m i z e d using a p s e u d o r a n d o m n u m b e r function o f a C o m m o d o r e $61 p o c k e t calculator. Calculating Female Value

The value, V, o f the resource to be gained f r o m a contest is the difference between a c o m b a t a n t ' s r e p r o d u c t i v e success if he wins a n d if he loses, ignoring the cost o f the struggle itself ( M a y n a r d S m i t h 1974; P a r k e r 1974). T h e expected lifetime r e p r o d u c t i v e success o f male b o w l a n d doily spiders, assuming no fighting costs, is a function o f the fertilization rate, G, available f r o m the h a b i t a t times male life expectancy, T. I estimated G f r o m a modified version o f an e q u a t i o n used to calculate rate o f energy i n t a k e ( C h a r n o v 1976) o r fitness gain ( P a r k e r & S t u a r t 1976), (filz)Fl G =

consistently, t h o u g h slightly, overestimate the achieved G. However, for the calculations in this p a p e r , m i n o r changes in the a b s o l u t e value o f G will n o t affect a n y conclusions reached. F r o m these p a r a m e t e r s it is estimated t h a t in the absence o f fighting costs, lifetime male expected r e p r o d u c t i v e success is 16.2 eggs ( = GT). I f a male initially finds himself in the web o f a female o f exceptionally high r e p r o d u c t i v e value, however, his expected r e p r o d u c t i v e success will suddenly increase. A s s u m i n g t h a t in the absence o f k n o w l e d g e a b o u t female value, males act u p o n e n v i r o n m e n t a l averages, a male Table IV. Quantities Used in the Computation of V and K (Sources for These Quantities are Anstad 1981, 1982)

Variable fi ( = proportion of webs occupied by females of type i)

(1)

1 + E (filz)t~ where f i is the p r o p o r t i o n o f webs c o n t a i n i n g females o f type i (signifying a specific r e p r o d u c tive state), F i is the average n u m b e r o f fertilizable eggs c o n t a i n e d b y females o f type i, ti is the time required for a m a l e to fertilize those eggs, a n d z is the average m a l e interweb search time. F i a n d ti were d e t e r m i n e d f r o m l a b o r a t o r y d a t a ( A u s t a d 1982); whereas T, f i , a n d x were d e t e r m i n e d f r o m field d a t a o b t a i n e d b y regular censusing o f individually m a r k e d webs a n d l o n g - t e r m following o f i n d i v i d u a l males ( A u s t a d 1981) (Table IV). N o t e t h a t the a b o v e e q u a t i o n assumes there are n o other males in the habitat, a f a c t o r which m e a n s t h a t t h e c a l c u l a t e d G will

Value used (i = ) *plt vir nov oth

= = = =

0.80 0.06 0.08 0.06

F~ ( = average number of fertilizable plt = 40.3 eggs eggs contained by females of vir = 40.3 typei) nov = 1.8 oth = 0.0 h ( = male time investment required to fertilize available eggs in female of type i) T ( = average male reproductive lifetime) z ( = average male interweb travel time)

plt vir nov oth

= 8550 min = 48 = 203 = 24 3 days 2400 min

*pit = penultimate female; vir = virgin female; nov = recently-mated female; oth = other female.

AUSTAD: GAME THEORY AND MALE COMBAT IN A SPIDER initially finding himself in a female web in role r (where the role is defined by the male's information about the reproductive state of the female) has expected reproductive success Sr = ~,fkFk + G ( T - - •fktk),

(2)

where fk is the proportion of females of type k in the habitat from among the possible female types according to male assessment. Thus when a male first enters a web and has not yet contacted the female, fk =.fi. Other parameters in (2) are similarly analogous to those in (1). V can now be calculated for a male that initially finds himself in a female web, Vr = ~fkFl~ - - G ( ~ f k & ) .

(3)

The first term in (3) represents the expected fertilizations from mating with the web resident, and the second term is the expected fertilizations from foraging elsewhere in the habitat for the equivalent amount of time. Vr for a male upon entering a new web will always be the same. However, a male web resident that has assessed something about the reproductive state of the female occupant m a y have either a higher or lower Vr, depending upon what that state is. Thus by allowing the male a given amount of copulation to determine female state, the resident's perceived Vr can be manipulated. Recall that male mating behaviour in the 'pre-insemination' phase differs predictably depending upon female state, so that this assumption about male assessment is plausible. Using (3), I calculated Vr for both resident and intruder at four points of second male introduction, in addition to the original calculation for males introduced simultaneously (Fig. 3), The introduction points are characterized by the following male assessments: Simultaneons. Both males are introduced at the same time. Neither male can have assessed anything about female reproductive state. Vr's are equal. 1 rain after start of PI. Resident has copulated for i min, but has transferred no sperm. Because m a l e s will copulate for about 25 min even with females of no reproductive value to them (see Table I), it is assumed that males cannot tell at this point whether a female has previously mated. However, because intromission occurs during this mating phase, males can presumably determine that a female is mature, because immature females' genitalia are not yet developed enough to allow intromission.

65

End of PI. The resident male has finished pre-insemination. Because the male has now begun to charge his pedipalps with sperm, he has determined that the female is an adult virgin. Note that the only non-virgin adults to whom a male will transfer sperm are those that have mated immediately previously, and in that case the pre-insemination phase lasts much longer (Table I). In the next 31 rain of copulation a male will fertilize about 40 eggs (calculated from Fig. 2 and an average fecundity of 42 eggs, Austad 1981), so the female is now extremely valuable to him. After 7 rain of lnsem. The resident has transferred sperm for 7 min, thus has fertilized about 92 % of the total fertilizable clutch even if he abandons the web and is immediately replaced. In the remaining 24 min of copulation, he will fertilize the remaining 8 % of the clutch. After 21 rain of Insem. The resident has transferred sperm for 21 min, and has now fertilized about 99 % of the fertilizable eggs. Though 10 min of copulation normally remain, little additional fertilization occurs.

Calculating Fighting Cost Although combat cost is often measured in energetic terms (e.g. Rand & Rand 1976; Riechert 1978), calories expended may not always entail a reproductive cost. Unless energy expended could have otherwise been directed to increased reproduction, the expenditure is not important in an evolutionary sense (Brown

/\

40 9 Female volue to resident V ~'

o Expected femo]e voIue fo intruder 1

3o

/

/ \

o

o

.

_[ . . . . . . . . . . .

I

%.

w

eo

10

.

.

.

.

o

#

~ ..........

Simult mlro

1 min otter siorl of P1

I

I

End of P[

After 7 min of insem

__

~'1

After 21 min of insem

Point of encounter

Fig. 3. Relative value of the female to the resident and intruding male. PI == pre-insemination phase, Insem = insemination phase. Calculation of V, and the reason it differs for residertt and intruder are discussed in the text.

ANIMAL

66

BEHAVIOUR,

1978). Seeking to avoid a 'caloric fallacy', I endeavoured to measure the cost of combat in terms of the probability of reduced reproduction as a consequence of disabling or fatal injury. I estimated the cost of fighting by utilizing the slope of a regression line of the probability o f injury as a thnction of grapple duration (Fig. a), the relative probabilities of injury to the larger and smaller combatant, and a male's expected reproductive success if he does not encounter other males (i.e. GT). The probability of injury was compiled from 304 fights. One of the assumptions of the war of attrition model (although see N o r m a n et al. 1977 and Bishop & Cannings 1978) is that costs rise linearly with persistence. This assumption seems to be justified for encounters between male bowl and doily spiders. All regression lines explain more than 90% of the variance in injury probability (Fig. 4). Note that the regression lines represent all injuries incurred, therefore the probability of a given individual being injured is one-half the slope of the line if it is assumed that injuries are distributed equally between the combatants. Both combatants were never seen to be seriously injured, and when a serious injury occurs, the injured individual attempts to flee, although he is often caught and killed by his opponent. Because of the rarity of injury in some of the categories, it was impossible to decompose the lines rigorously into one for the smaller, and one

0 ///./

0.2

/Z

7 ~

/

Kij = qijsjGT,

Table V. Cost of Combat*

= 'Slightly.'dif)~erent-sized - cor'hbata nts

A

(4)

where Kli is the cost of grappling per unit time for a male of relative size i (smaller or larger) in a contest of size difference j; qij is the probability that male i will be injured in a contest of size difference j; sj is the slope of the regression line of injury probability versus grapple duration (Fig. 4), arid G T is again lifetime mate reproductive success. From (4) it is now possible to tabulate the cost of combat in reproductive terms for males contending with any size opponent (Table V).

-'-.'Sams!zedcombo,o', 9

; 0-30

for the larger combatant, within a size-difference category (the width of the grapple duration categories in Fig. 4 was dictated by the desire to have a sample size of at least five for all categories). To decompose the line, I simply weighted the total slope by the relative frequency o f injury to one combatant or the other. For instance, in fights between 'greatly' difl?rentsized opponents, the smaller received 85 % of all injuries. I thus multiplied the slope of the regression line by 0.85 for the smaller, and 0.15 for the larger, combatant. The same procedure holds for 'slight' size-differences in which the smaller combatant received 72~o of the injuries. For 'same' size combatants the slope was simply halved. In actuality the smaller received 55 % of the injuries. To convert the cost of grappling into units of expected fertilizations lost per time spent grappling, I used the equation

The preceding calculations rely on the following simplifying assumptions: (1) Both resident and intruder can accurately assess their respective fighting ability, but only

i_ ~ 0.6

/ / // / / ~

1

I m p l i c i t Assumptions in the C a l c u l a t i o n s

0.8

--04

31,

'Greatly~different- sized

,

31-60 61-90 91420 12H50151-180 >180

Grapple duration (see)

Fig. 4. The cost of grappling. A simple linear regression of grapple duration against probability of disabling or fatal injury explains over 90 ~o of the variance in all cases. Grapple duration class widths were dictated by a desire to have a sample size of at least 5 in each category. Equations for the regression lines--'Same': Y = 0.005X-- 0.10, r 2 = 0.94, P = 0.001; 'Slight': Y = 0.0083X--0.13, r 2 = 0.95, P = 0.006; 'Great': Y = 0.0107X--0.006, r ~ = 0.97, P = 0.003.

Size-difference category

1(-

' Same'

2.75

'Slight' smaller larger

6. I0 2.37

'Great' smaller larger

9.28 1.64

*K represents the expected reduction in lifetime reproductive success per min of grappling. Derivation is discussed in the text.

AUSTAD: GAME THEORY AND MALE COMBAT IN A SPIDER the resident can accurately assess the value of the contested female. The intruder can only respond to habitat averages. (2) The life expectancy of any male is affected only by the risks he runs during intermale combat. (3) Males behave as though the fertilization rate available from the habitat is constant throughout their lifetime. (4) The fertilization rate available from the habitat can be approximated from a disc equation modified to include several types of females, each of whom has a different reproductive history. The first assumption is consistent with what is known about web-building spiders. Although their eyesight is poor, they can recognize complex vibratory cues transmitted through the web, including the size of individual items in the web itself (Witt 1975; Burgess 1979). Because male mating behaviour varies so consistently with female reproductive history (Table I), it is plausible to assume that males can assess females after a certain amount of contact. Because newly arriving males court and mate for a short time with females of no value to them, the assumption that males cannot make a priori evaluations of female value is also plausible. The second assumption is also reasonable. Although the commonest mortality factor among adult male bowl and doily spiders is probably predation (in 361 h of observation of males travelling between webs, six predation events were recorded), predation risk should be independent of male size since most predators, chiefly salticid spiders, are much larger. Therefore male combat probably accounts for most differences in life expectancy between males. The third and fourth assumptions are false simplifying assumptions allowing the calculations. The constant fertilization rate would only be true if males encountered similar type females at a high rate, and even then would only be approximately true. However, because this assumption is only important in calculating the relative value of females, it should not affect the conclusions. Assumption four is not true (Austad 1981). The disc equation (1) somewhat overestimates the rate of egg gain available from the environment, probably because it ignores the presence of other males and the high risk of interweb travel (these issues will be treated at length in subsequent papers). However, the conclusions

67

reached in the remainder of this paper are not sensitive to even moderate Changes in G. Results of the Staged Encounters The results demonstrate unequivocally that males are indeed exhibiting 'assessment strategy' (Parker 1974; Parker & Rubenstein 1981). As previously indicated, grapple duration is inversely correlated with size difference for males introduced simultaneously (Table Ill). This is true whether one examines the three sizedifference categories (Mann-Whitney U-test, P < 0.0001 for all comparisons), or the exact size difference (Spearman rank correlation, P < 0.0001). This reduction in contest length can be attributed to lack of persistence by smaller males, since contest duration is dictated by the loser, and the loser is more frequently the smaller male as size difference increases. Also note that when size difference is essentially zero "(Table VI, first column), the resident (bottom four rows only) wins most often when he has a higher expected gain than the intruder and least often when he has less to gain. Certain other details bear immediate emphasis. Note that there is no advantage in web residence per se (Table VI). In the 200 encounters in which residence was well established, residents won 99 and intruders won 101. When combatants were the 'same' size, residents won 23 of 40 contests, but the wins were skewed dramatically toward certain female value treatments. Thus to the extent that winning or losing could be predicted, it was a result of either relative fighting ability, some aspect of female value, or both. A further point to emphasize is that inspection of the absolute duration of grapples (Table IiI) does not by itself necessarily indicate anything about each opponent's willingness to persist. Contest lengths are determined by the loser. In treatments in which the resident wins nearly all of the time, the observed grapple duration will indicate the willingness o f intruders to persist. Conversely, when intruders usually win, grapple duration will suggest something about resident persistence. For instance, when 'same' size combatants fight and the resident has a greater expected reward, residents win 90 ~ of the fights. Thus the average contest duration will indicate the approximate persis, tence of intruders in such cases. However, for 'same' size individuals simultaneously introduced, grapple duration is difficult to interpret in this context.

68

ANIMAL

BEHAVIOUR,

31,

1

']['able VI. Resident Winning Percentage and Incidence of Injury*

Size Difference 'Slight' Point of 2nd Male introduction Simultaneous with first male++

'Same'

Resident smaller

59 (67)

'Great'

Resident larger

Resident smaller

83 (11)

Resident larger 100 (5)

(70)

(20)

40t

90

(0)

(90)

20

90 (0)

End of PI

90 (60)

60 (90)

100 (10)

20 (60)

90 (10)

After 7 min of insemination

40 (10)

20 (30)

70 (0)

10 (lO)

70 (0)

After 21 min of insemination

10 (lo)

0 (o)

20 (o)

0 (lo)

50

1 min after start of PIw

90

(o)

*Numbers outside parentheses = winning percentage; numbers within parentheses = percentage of fights resulting in disabling or fatal injuries. tTreatments in bold are those in which V and K differ in opposite directions. Significance of these treatments is discussed in the text. ++Noweb residency has been established for these treatments. Winning percentage therefore is for the larger combatant in this row only. w = pre-insemination phase. Although absolute grapple duration is difficult to interpret under some conditions, relative duration may be more easily understood. In these experiments, the intruder should perceive the contest identically, irrespective of his point of introduction. So changes in relative grapple duration within a size-difference category (i.e. contests within the columns of Table III) should reflect changes in the persistence of residents. This is supported by the general trend for the longest contests within a column to occur when the resident has most to gain (second and third rows) and for the shortest to occur when he has least to gain (fifth row). Not only does grapple duration reflect changes in combat persistence as a function of female value, but so does the winning percentage. Every column indicates that residents win most often where the female is worth more to them than to the intruder (second and third rows) and least often where she is worth less (fifth row). One particularly striking result is how persistent smaller residents are against heavy odds when they are contending for a very valuable female. For instance, when female value is equal for opponents and residency is not established, 'slightly' smaller males win 17 ~ of their fights. However, when the female is most valuable to them, 'slightly' smaller residents win 6 0 ~ of

their fights. This difference is statistically significant (z~-test, P < 0.05). Furthermore, fights in this treatment were so severe that 90 of them ended in fatal or disabling injury for one of the participants (Table VI). I f animals behave as predicted by Parker & Rubenstein (1981) and use V/K as the payoffrelevant asymmetry to formulate combat persistence decisions, then escalated contests might be expected not only when V and K are identical, but also when they differ in opposite directions between opponents. There are six treatments in which this occurs (bold figures in Table VI). In four of these (second and third rows, resident smaller), the grapple durations are longer than for any other treatments within that size-difference category (all these differences are statistically significant at P < 0.01 using a t-test, except for the treatment resident 'slightly' smaller, 1 min after start of PI). Moreover although these treatments account for 25 ~ of all fights in which both variables were unequal, they account for 82 ~ of all injuries and deaths (the injury incidence is significantly different again at P < 0.01 using a z2-test, except for the same treatment as before). Whether this treatment which has failed to differ significantly in the e x p e c t e d m a n n e r is in reality anomalous or not, is problematical. The

AUSTAD: GAME THEORY AND MALE COMBAT IN A SPIDER

P < 0.0025 for any c o m p a r i s o n ) , a n d 9 0 ~ o f t h e fights end in serious injury. Thus the results acc o r d well with the theory. One further quantitative p r e d i c t i o n f r o m the w a r o f attrition m o d e l for contests in which fighting ability a n d resource valaaes are s y m m metrical, is t h a t the ESS should result in a negative exponential d i s t r i b u t i o n o f contest lengths ( P a r k e r & T h o m p s o n 1980). This prediction follows f r o m the fact t h a t if there is a c o n s t a n t p r o b a b i l i t y o f s o m e t h i n g h a p p e n i n g in the next small time interval, i n d e p e n d e n t o f the time t h a t has a l r e a d y passed, then the distribution o f times at which t h e event h a p p e n s will b e a negative exponential ( M a y n a r d S m i t h 1974). P a r k e r & T h o m p s o n (1980) f u r t h e r c a l c u l a t e d t h a t the m e a n o f the observed struggle d u r a t i o n s should be V/2K. Caryl (1979), citing d a t a f r o m R a n d & R a n d (1976) on fighting a m o n g female iguanas, f o u n d such a negative exponential. P a r k e r & T h o m p s o n (1980) also r e p o r t finding a g o o d exponential fit for the d i s t r i b u t i o n o f fight d u r a t i o n s between m a l e dungflies contesting for access to females. T h e y continue, however, t h a t the superficial a g r e e m e n t between the m o d e l a n d the d a t a m i g h t be spurious because the negative exponential d i s a p p e a r e d in certain subclasses o f their data. I also find a negative exponential d i s t r i b u t i o n o f fight d u r a t i o n s (Fig. 5). C o m b i n i n g all 304

d a t a differ in the expected direction (i.e. g r a p p l e d u r a t i o n was longer, a n d injury rate was higher), b u t n o t to the p o i n t o f statistical significance. It is t e m p t i n g to p o i n t out t h a t with s a m p l e sizes o f 10 cases per treatment, o n e or two a b e r r a n t animals can m a k e all the difference. However, in fairness it seems best to treat these d a t a as enigmatic, a n d h o p e to p e r h a p s clarify the result in further work. There are two other treatments, on the o t h e r hand, which deviate far f r o m the p r e d i c t i o n o f escalation when V a n d K are ' c o n t r a d i c t o r y ' in direction (resident larger, 21 m i n o f i n s e m i n a t i o n ---Tables I I I a n d VI). I n these, n o t only is g r a p p l i n g abbreviated, b u t also there is n o t a single serious injury. However, the c o m p u t a t i o n o f actual V/K values for all t r e a t m e n t s ( f r o m T a b l e V a n d Fig. 3) reveals t h a t the m o d e l is n o t c o n t r a d i c t e d (Table VII), b u t the results are counter-intuitive. T h e calculations indicate t h a t in these two treatments, a n d only these two, each c o m b a t a n t a p p a r e n t l y perceives the o t h e r as having a greater V/K. T h u s p e r f u n c t o r y c o m b a t w o u l d be p r e d i c t e d f r o m the model. C o n versely, there is one cell (resident smaller, end o f PI) in which each c o m b a t a n t perceives his V/K to be larger. This w o u l d indicate escalated fights should occur. I n d e e d we find t h a t g r a p pling is significantly longer t h a n for any o t h e r cell with o p p o n e n t s o f different sizes (t-test, Table VII. Assessment of

69

V/K for Resident and Intruder* Size-difference category 'Slight'

Intruder introduction points

'Same'

Simultaneous with first malet

2.8 --2.8

1 rain after start of PI

4.8 ~ 2.8 2.8--2.8

End of PI

14.6 +-- 2.8 2.8--2.8

Resident smaller

'Great' Resident larger

1.3 --~ 3.3 2.0 --* 3.3 1.3 ~ 3.3

Resident smaller

Resident larger 0.8 --* 4.9

5.2 +- 1.3 1.3 -~ 4.9 3.3 -,- 1.3 0.8 ~ 4.9

7.8 +. 0.8 4.9 ~ 0.8

6.6 ~-- 3.3 16.9 +- 1.3 4.3 --* 4.9 25.1 4-- 0.8 :~1.3 -~ 3.3 3.3 +. 1.3 0.8 --~ 4.9 4.9 ~-- 0.8

After 7 min of insemination

1.1 --+2.8 2.8 --2.8

0.5 --~3,3 1.3 --~ 3.3

1.3 -- 1.3 0.3 --+4.9 3.3 *-- 1.3 0.8 ~ 4.9

1.9+-0.8 4.9 +- 0.8

After 21 min of insemination

0.1 ~ 2.8 2.8 --2.8

0.05 --~ 3.3 1.3 --~ 3.3

0.4 -+ 1,3 0.03 --+ 4.9 w -,-- 1.3 0.8 --+ 4.9

0.2 ~ 0.8 w ~ 0.8

*Numbers represent V/Kre~--V[Kintas assessed by the resident (upper left of each rectangle) and intruder (lower right). Arrow points in direction of larger V/K. tSince residency status does not exist in this row, numbers represent V/K~m~,ner--V/K~arge~.. +In this treatment both resident and intruder assess their V/K as greater than the opponent. w treatments find both intruder and resident assessing their opponents V]K as greater than their own.

70

ANIMAL

BEHAVIOUR,

fights, the distribution is not significantly different from a negative exponential (linear regression on the transformed data, r 2 == 0.74, P < 0.001). I f I only consider the fights in which there is no resource asymmetry, there is still a negative exponential (Fig. 6, t o p ) (r 2 = 0.44, P < 0.005). The respective means o f these distributions are 59 and 65 s. M y calculated V/2Kfor symmetrical contests is 98 s. Therefore, although the curve shape supports the prediction, the mean makes it suspect. When only those fights which are truly symmetrical for both V and K are examined, both the negative exponential (r 2 = 0.01, P < 0.3) and the mean duration (194 s) no longer fit the prediction even remotely (Fig. 6, bottom). It is not k n o w n how sensitive this prediction is to minute departures from the strict assumptions o f the model, so the significance o f this result is moot. However, it does highlight the fact that both the theory and the experimental system used to examine it are powerful enough to detect superficially concordant, but ultimately discordant, results.

31,

o f injury probability is a linear function o f grapple duration and is specific to different sizedifference categories. Because male spiders have no important resources besides females, this cost is without question related to Darwinian fitness. Results o f staged encounters support the general predictions o f an asymmetric war o f attrition ( M a y n a r d Smith & Parker 1976; Parker & Rubenstein 1981). W h e n opponents are closely matched, there is more prolonged fighting with resulting higher injury rate. Residents who k n o w the value o f the female tend to choose persistence times whose means are directly related to that value (Bishop etal. 1978). When combatants are closely matched in fighting ability, the one with the greater expected reward will tend to win (Parker 1974; Parker & Rubenstein 1981). The relative winning percentage and incidence o f injury in each of the experimental treatments is roughly what would be predicted by calculations o f V/K as perceived by resident and intruder.

Discussion

Male bowl and doily spiders use information on female value and the relative fighting ability o f their opponents to make decisions about persisting in c o m b a t for access to mating. The f o r m o f these fights meets the assumptions o f the war o f attrition model developed by M a y n a r d Smith (1974) and extended by others ( N o r m a n et al. 1977; Bishop & Cannings 1978; Bishop et al. 1978; Parker & T h o m p s o n 1980; Parker & Rubenstein 1981). The cost o f fighting in terms

1

Sizeasymmetrybutno resourceasymmetry

4C 5C 2C

r--L3 i.~

13n

E 7-

125

iI

NO orresource

size asymmetry

~1oo

50 25

75

I

1

I

150 225 300 575 450 525 6oo Grappte dlsmtion ( sec )

75

150

225 300 375 450 525 600 675 Grapple duration ( sec )

Fig. 5. Grapple duration of all 304 fights. The mean duration is 59 s and the general shape fits a negative exponential (r ~ = 0,74, P < 0.001 on the log transformed data). Detailed analysis described in the text indicates this is a spurious fit to the war of attrition prediction on the distribution of fight durations.

Fig. 6. Subclasses of the 304 fights. Top graph depicts the distribution of fights between all size-differences classes that were filtroduced in the web simultaneously. The negative exponential distribution persists (r~ = 0.44, P < 0.005). Mean duration is 65 s. Bottom graph depicts all fights that are truly symmetrical in both variables. Note that the negative exponential has now disappeared. The mean for this subset is 194 s, far greater than predicted by the model in its strict form.

AUSTAD: GAME THEORY AND MALE COMBAT IN A SPIDER It is notable that at least some grappling occurred in nearly all contests. Parker & Rubenstein's (1981) model of assessment strategy in the war of attrition predicts that contests will often be settled without actual engagement of opponents. However, their model assumes that information concerning V and K is perfect and without cost for both participants. This is unlikely to be so in the real world, as they point out in the same paper. In the bowl and doily spider, for instance, knowledge of female value is not available to intruders. Also, body size may not be a perfect index of fighting ability. Thus a brief grapple would give solid evidence of an opponent's strength. These resuIts are compatiable with what is known of combat in other spiders. Size is known to be a critical factor in determining encounter outcome in wolf spiders (Dijkstra 1969), funnelweb spiders (Riechert 1978), orb-weaving spiders (Buskirk 1975; Christenson & Goist 1979; Vollrath 1980), as well as other species in the Linyphiidae (Rovner 1968; Ross 1977). Riechart (1978, 1979) has found that individuals of nearly equal size tend to expend more energy in combat than opponents of greatly different size; she has also reported that fights over valuable web-sites are more escalated than those over poor web-sites for the funnel-weaver Agelenopsis aperta. Crane (1949) reported that male jumping spiders fought more vigorously in the presence of a female than in her absence. Results supporting these general predictions are available from a host of other taxa as well. Escalated fighting between evenly matched opponents has been documented in crayfish (Rubenstein & Hazlett 1974), ghost crabs (Brook 1981), hermit crabs (Hazlett 1968), grapsid crabs (Warner 1970), Siamese fighting fish (Figler t972), and Blennius fish (Gibson 1968). Increased fighting intensity in contests for valuable resources has been reported in crayfish (Hazlett et al. 1975), sunfish (Rubenstein 1977), dungfflies (Parker & Thompson 1980), wasps (Alcock 1979), scorpionflies (Thornhill 1980), mantis shrimp (Caldwell & Dingle 1979), cockroaches (Ewing 1973), Uganda kob (Leuthold 1966), red deer (Clutton-Brock et al. 1979). and house cats (Cole & Sharer 1966). This study has failed to detect any resident advantage even in contests between similar sized individuals. However, if fights had been observed only during the early stages of mating, then a measurable resident's advantage would have appeared. This leads to speculation that

71

perhaps much of the vaunted resident's advantage in territorial disputes may actually be a consequence of resource asymmetries that have gone hitherto undetected. For example, if any investment is necessary to learn the best manner in which to use a territory--learning the richest foraging areas or locating the safest dens--then an interloper would need to learn these factors regardless of which territory is under contest. On the other hand, if an owner wins, he need not make any further investment to learn the vagaries of his territory. Thus the difference between winning and losing is greater for the resident than the intruder. It would be interesting to compare territorial disputes in those species for which time spent in a territory improves its value to the owner with those in which it does not, in order to ascertain whether resident's advantage is more common or pronounced in the former group. The question has been asked 'What can game theory contribute to ethology?' (Caryl 1979). One has only to review the older ethological literature on fighting to realize that the game theoretical analyses have led us from a descriptive to a predictive theory of fighting behaviour. Not only have these analyses allowed the formulation of precise quantitative predictions about behaviour, but the testing of such predictions allows us to identify important variables ignored by the models, distinguish models which overlap in some but not all of their assumptions, and finally to assert with more justification that a behavioural system is, or is not, understood. Acknowledgments My thinking on these matters was considerably clarified by discussions with Rick Howard, Geoff Parker, Susan Riechert, and Peter Waser. An earlier version of this manuscript was improved by the comments of Winston Fulton, Rick Howard, Morry Levy, Fiona Sunquist, Mel Sunquist, Peter Waser and an anonymous reviewer. 1 thank Kerry Rabenold for helping prepare the manuscript, and Terri Werderitsh for typing it mlmerous times. The work was supported in part by a Purdue University David Ross Graduate Student Fellowship and by PurdueUniversity--National Science Foundation Research Initiation and Support Grant SER 77-06731. REFERENCES Alcock, J. 1979. The behavioural consequences of size variation among males of the territorial wasp Hemipepsis ustulata (Hymenoptera: Pompilidae). Behaviour, 71, 322-335.

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185-206. Brook, M. de L. 1981. Size as a factor influencing the ownership of copulation burrows by the ghost crab (Ocypode ceratophthahnus). Z. Tierpsychol., 55, 63-78. Brown, J. L. 1978. Avian communal breeding systems. Ann. Rev. Ecol. Syst., 9, 239-262. Burgess, J. W. 1979. Web-signal processing for tolerance and group predation in the social spider Mallos gregalis Simon. Anita. Behav., 27, 157-164. Buskirk, R. 1975. Aggressive display and orb defence in a colonial spider, Metabus gravidas. Anita. Behav., 23, 560-567. Caldwell, R. L. & Dingle, J. 1979. The influence of size differential on agonistic encounters in the mantis shrimp, Gonodactylus viridis. Behaviour, 69, 255-264. Caryl, P. G. 1979. Communication by agonistic displays: what can game theory contribute to ethology? Behaviour, 68, 136-169. Charnov, E. L. 1976. Optimal foraging: the marginal value theorem. Theor. Pop. Biol., 9, 129-136. Christenson, T. E. & Goist, K. C. Jr. 1979. Costs and benefits of male-male competition in the orbweaving spider, Nephila clavipes. Behav. Ecol. Sociobiol., 5, 87-92. Clutton-Brock, T. H., Albon, S. D., Gibson, R. M. & Guinness, F. E. 1979. The logical stag: adaptive aspects of fighting in red deer (Cervus elaphus L.). Anim. Behav., 27, 211-225. Cole, D. D. & Sharer, J. N. 1966. A study of social dominance in cats. Behaviour, 27, 39-53. Crane, J. 1949. Comparative biology of salticid spiders at Rancho Grande, Venezuela. Part IV. An analysis of display. Zoologica, 34, 159-214. Dijkstra, H. 1969. Comparative research of the courtship behaviour in the genus Pardosa (Arachnida, Araneae): III. Agonistic behavior in Pardosa armentata. Bull. Mus. Nat. Ilist., 41, 91-97. Ewing, L. S. 1973. Territoriality and the influence of females on the spacing of males in the cockroach, Nauphoeta cinerea. Behaviour, 45, 282-303. Figler, M. H. 1972. The relation between elicity stimulus strength and habituation of the threat display in male Siamese fighting fish, Betta splendens. Behaviour, 42, 63-96. Gibson, R. N. 1968. Agonistic behaviour of juvenile Blennius pholis L. (Teleosti). Behaviour, 30, 192-217. Guhl, A. M. 1961. Gonadal hormones and social behavior in infrahuman vertebrates. In: Sex and Internal Secretions (Ed. by W. C. Young), 2rid. ed. pp. 1240-1267. Baltimore: Williams and Wilkins.

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Hammerstein, P. 1981. The role of asymmetries in animal contests. Anita. Behav., 29, 193-205. Hammerstein, P. & Parker, G. A. 1982. The asymmetric war of attrition. J. theor. Biol., 96, 647-682. Hazlett, B. A. 1968. Size relationships and aggressive behaviour in the hermit crab, Clibanarious vittatus. Z. Tierpsychol., 25, 608-614. Hazlett, B. A., Rubenstein, D. I. & Ritschoff, D. 1975. Starvation, aggression, and energy reserves in the crayfish Orconectes virilis. Crustaceana, 28, 11-16. Hinde, R. A. 1956. The biological significance of the territories of birds, lbis, 98, 340--369. Hinde, R. A. 1966. Animal Behavior: A Synthesis of Ethology and Comparative Psychology. New York: McGraw-Hill. Leuthold, W. 1966. Variations in territorial behavior of Uganda kob Adenota kob thomasi (Neumann 1896). Behaviour, 27, 214-258. Marler, P. & Hamilton III, W. J. 1966. Mechanisms of Animal Behavior. New York: John Wiley. Maynard Smith, J. 1972. Game theory and the evolution of fighting. In : On Evolution (Ed. by J. Maynard Smith), pp. 8-28. Edinburgh: Edinburgh University Press. Maynard Smith, J. 1974. The theory of games and the evolution of animal conflict. J. theor. Biol., 47, 209-221. Maynard Smith, J. & Parker, G. A. 1976. The logic of asymmetric contests. Anita. Behav., 24, 159-175. Maynard Smith, J. & Price, G. R. 1973. The logic of animal conflict. Nature, Lond., 246, 15-18. Norman, R. F., Taylor, P. D. & Robertson, R. J. 1977. Stable equilibrium strategies and penalty functions in a game of attrition. J. theor. Biol., 65, 571-578. Parker, G. A. 1974. Assessment strategy and the evolution of fighting behaviour. J. theor. Biol., 47, 223-243. Parker, G. A. & Rubenstein, D. I. 1981. Role assessment, reserve strategy, and acquisition of information in asymmetric animal conflicts. Anita. Behav., 29, 221-240. Parker, G. A. & Stuart, R. A. 1976. Animal behavior as a strategy optimizer: evolution of resource assessment strategies and optimal emigration thresholds. Am. Nat., 110, 1055-1076. Parker, G. A. & Thompson, E. A. 1980. Dung fly struggles: a test of the war of attrition. Behav. EcoL SociobioL, 7, 37-44. Rand, W. M. & Rand, A. S. 1976. Agonistic behaviour in nesting iguanas: a stochastic analysis of dispute settlement dominated by the minimization of energy cost. Z. Tierpsychol., 40, 279-299. Riechert, S. E. 1978. Games spiders play: Behavioural variability in territorial disputes. Behav. Ecol. Sociobiol., 3, 135-162. Riechert, S. E. 1979. Games spiders play. II. Resource assessment strategies. Behav. EcoL SociobioL, 6, 121-128. Ross, J. W. 1977. Evidence for territoriality in the lineweaving spider, Florinda coceinea (Hentz). MS thesis, University of Tennessee. Rovner, J. S. 1968. Territoriality in the sheet-web spider (Linyphia triangularis).Z. Tierpsychol., 25, 232-242. Rubenstein, D. I. 1977. Population density, resource patterning, and mechanisms of competition in the Everglades pygmy sunfish. Ph.D. thesis, Duke University. Rubenstein, D. I. & Hazlett, B. A. 1974. Examination of the agonistic behavior of the crayfish Oreonectes virilis by character analysis. Behaviour, 50, 193-216.

A U S T A D : G A M E THEORY A N D MALE COMBAT I N A SPIDER Thornhill, R. 1980. Competitive, charming males and choosy females: was Darwin correct? Fla. Entomol., 63, 5-30. Vollrath, F. 1980. Male body size and fitness in the webbuilding spider, Nephila clavipes. Z. TierpsychoI., 53, 61-78. Warner, G. F. 1970. Behaviour of two species of grapsid

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crab during intraspecific encounters. Behaviottr, 36, 9-19. Witt, P. N. 1975. The web as a means of communication. Biosci. Communic., 1, 7-23.

(Received 10 November 1981; revised 6 April 1982; MS. number: A2749)