Influence of detectability and ability to escape on

Influence of detectability and ability to escape on natural selection of conspicuous autotomous defenses WILLIAM E. COOPER, JR. Can. J. Zool. Downloaded from www.nrcresearchpress.com by "Institute of Vertebrate Paleontology and Paleoanthropology,CAS" on 06/05/13 For personal use only.

Department of Biology, Auburn University at Montgomery, Montgomery, AL 3611 7 , U.S. A. AND

LAURIE J.

VITT~

Department of Biology, University of California, Los Angeles, CA 90024, U.S.A. Received January 8, 1990 COOPER, W. E., JR., and VITT,L. J. 1991. Influence of detectability and ability to escape on natural selection of conspicuous autotomous defenses. Can. J. Zool. 69: 757-764. Antipredatory adaptations in which a predator's attack is diverted to body parts that may be sacrificed or are less vulnerable sometimes depend upon the conspicuousnessof the body part attacked. The predator's attention is drawn to the emphasized part, which serves as a decoy. Such defenses appear paradoxical in that they increase the probability of detection. However, they simultaneously increase the probability of postdetectional escape enough to decrease the overall probability of being killed. Based on probabilities of detection and of escape following detection, a simple model predicts the conditions in which autotomy and related defenses are favored. For a conspicuous decoy, equilibrium values of the increases in probabilities of detection and of escape following detection are given. Data on the conditional probability of escape after detection are discussed for the scincid lizards Eumeces fasciatus and E. laticeps, which have brightly colored autotomous tails. Versions of the model that split the predator-prey encounter into several successive stages are outlined briefly and illustrated by the data for the two lizard species. Strategies for measuring the probabilities and testing the model's predictions are considered. W. E., JR., et VITT,L. J. 1991. Influence of detectability and ability to escape on natural selection of conspicuous COOPER, autotomous defenses. Can. J. Zool. 69 : 757-764. Les adaptations anti-prkdation par lesquelles l'attaque du prkdateur est dkvike vers des parties du corps qui peuvent Ctre sacrifikes ou qui sont relativement moins vulnkrables dkpendent parfois du caractere frappant de la partie du corps attaquke. L'attention du predateur est attirke vers la partie bien en vue qui sert alors de leurre. Ces systkmes de dkfense peuvent paraitre paradoxaux, puisqu'ils augmentent la probabilitk de dktection. Cependant, en mCme temps ils augmentent pour la proie la probabilitk de pouvoir fuir aprks dktection, suffisamment pour diminuer la probabilitk globable d'Ctre tuk. Un modele simple, qui tient compte a la fois des probabilitks de detection et des probabilitks de fuite apres la dktection, permet de prkdire les conditions dans lesquelles l'autotomie et autres systemes de dkfense semblables sont favorisks. Les valeurs d'kquilibre entre les augmentations de probabilitks de detection et de fuite aprks dktection lorsque le > est bien visible ont kt6 mesurkes. On trouvera ici des donnkes sur la probabilitk conditionnelle de fuite apres detection chez des lkzards scincidks Eumeces fasciatus et'E. laticeps qui portent tous deux une queue bien visible capable d'autotomie. Les versions du modkle qui divisent la rencontre prkdateur-proie en plusieurs ktapes successives sont rksumkes brievement et illustrkes par les donnees sur les lkzards. Les stratkgies de mesure des probabilitks et les tests propres a kprouver les prkdictions du modele sont examines. [Traduit par la redaction]

Introduction ~ ~ fmarkings l ~and behavioral ~ ~ idisplays ~ are ~ beneficial because they distract predators from body structures that are vulnerable and direct attacks to those that may be sacrificed or are relatively impervious to attack (Edmunds 1974). Although deflectionhas obvious benefits, the distracting feature may be so conspicuous as to cause the prey to be discovered by predators that othenuise would not have noticed them. The apparent paradox of an antipredatory mechanism that increases the probability of being observed and attacked is readily resolved by considering the trade-off between increased probability of being detected and enhanced ability to avoid capture once detected. Bright coloration of an expendable body part or activity drawing attention to it can simultaneously increase the likelihood of being detected by a predator and of surviving its attack. The qualitative validity of this reasoning is widely accepted (e. g ., Cott 1940; Edmunds 19-74), but its quantitative implications for the natural selection of antipredatory mechanisms have been largely ignored. ' ~ e ~ r i requests nt should be sent to the following address: Reprint SC 29801, Depaament, SavannahRiver Ecology Laboratory, U.S.A. 2~resent address: Oklahoma Museum of Natural History, University of Oklahoma, Norman, OK 73019, U.S .A.

Rinted in Canada I lmprimk au Canada

An example of such an apparently paradoxical defense is autotomy ofconspicuous body parts. ~ u t o t o m i z i ndispensable ~ parts when attacked increases the probability escape in diverse taxa (Cott l940; Robinson et al. 1970; Greene 1973; Morton 1973; Edmunds l974; Maiorana 1977; Amold 1984; 985). autotomizinga grasped a predator a if the lizard can greatly increase its chances predator's attention is diverted from the body (Amold 1984, 1988). Rapid thrashing of the autotomized tail increases the probability that the predator's attention will be attracted to the tail while the lizard escapes (Clark 1971; Dial and Fitzpatrick often enhancethe effectivenessof autotomy l983). Prey to the autotomizable pan drawing Lizards (e.g., COngdOnet al. 1974) and the (BrOdie 1977) may wave Or The efficacy of caudal autotomy might be greatly enhanced if lizards could induce predators to direct attacks to the intact tail rather than to other body parts. Lizards appear to do this in three ways: by waving the tail (Congdon et al. 1974; Arnold 1984), by having brightly colored tails, or both (Cott 1940; Arnold 1984; cooper and ~ i t 1985; t Vitt and Cooper 1986b). Juveniles of lizard 'pecies of the genus Eumeces have bright blue or orange tails that contrast markedly with the color of the body, which in most species is black with narrow yellow stripes. They rely heavily on autotomy of the tail as a last-ditch -

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defense (Cooper and Vitt 1985; Vitt and Cooper 1986b). The tail's brightness enhances the ability of juvenile E. fasciatus and E. laticeps to survive by increasing the proportion of predatory attacks directed to the tail (Cooper and Vitt 1985). The bright coloration is not aposematic and does not function as a social signal (Cooper and Vitt 1985). Thus, it is very likely an adaptation that evolved because it increases the probability that a predator will attack the lizard's tail rather than its body. In this paper, we present a simple model specifying the conditions required for bright coloration of autotomous lizard tails to be favored. Laboratory data provide estimates of the increase in postdetectional escape probability attributable to bright tail coloration in juvenile E. fasciatus and E. laticeps. Selectively stable end points are considered and the model is extended to include effects of antipredatory benefits operating at postdetection stages of predator-prey encounters. Because the model is not genetic, the degree of response to natural selection and its time course are not predicted. However, it is clear that the influence of natural selection on heritable variation in the model's major variables could lead to evolution of the favored defenses. The high energetic (Congdon et al. 1974; Vitt et al. 1977; Dial and Fitzpatrick 1981; Daniels 1984), social (Fox and Rostker 1982), and locomotory (e.g. , Ballinger er al. 1979; Punzo 1982; Arnold 1984) costs of tail loss largely restrict the use of tail autotomy by lizards to an escape mechanism of last resort during close encounters with predators, i. e., during the subjugation or resistance phase of predator-prey encounters (Holling 1966). In contrast, bright tail coloration and other conspicuous features that are static or expressed intermittently without regard to the presence of predators may affect predator-prey encounters then and throughout the detection and escape phases. We present separate estimates of the benefits of . bright tail coloration in juvenile Eumeces during the escape and resistance phases.

Methods In developing the model we favored simplicity over realism, stripping predator-prey encounters to the barest essentials. We began testing by estimating model parameters for laboratory encounters between hatchling blue-tailed skinks, E.fasciatus and E . laticeps , and saurophagous scarlet king snakes, Lampropeltis triangulum elapsoides. Some of the data used for this estimation were published previously in a different context (Cooper and Vitt 1985; Vitt and Cooper 19866). In our previous experimental studies on the effects of bright tail coloration, no control was included for the effects of painting tails to artificially darken them. In August 1988, we conducted additional encounters (identical with those described previously; Cooper and Vitt 1985) to increase the sample size for estimating the model's parameters and to control for possible effects of painting. In each encounter, a single hatchling E. fasciatus was placed in a clear plastic arena (3 1 X 17 X 8 cm) containing a scarlet king snake. Attacks, their outcomes (misses and bites), body part bitten (tail versus body), autotomy, and success of escape attempts after being bitten were recorded. Two types of lizard were presented: those with tails painted blue and those with tails painted black. Testor's model paints were used to match the natural blue tail and black body coloration. Whenever possible, encounters were stopped before the snake could swallow potentially toxic paint. All encounters for lizards with tails painted blue were stopped when the snake seized the lizard. After the tail was removed, the snake was allowed to eat the lizard. Snakes were allowed to consume all but the tails of lizards with blackened tails. This difference in procedure was adopted for the new group to prevent any aversive reaction to the tails. This was not a problem for lizards with blackened tails because none were bitten on the tail. Insufficient

hatchlings were available in 1988 to test lizards with tails not painted blue, but these tests were comparable to previous ones. Differences between groups were examined by means of Fisher's exact probability tests.

Results The model Conditionsfavoring conspicuous defenses In an encounter with a predator, a prey may or may not be discovered. If discovered, it may or may not be killed. Let the probability of being detected be Pd and the probability of escaping once detected be P,. It is assumed that Pd and P, are independent. The probability of being captured is Suppose that a population includes individuals with a cryptically colored, or at least inconspicuously colored, expendable structure such as an autotomizable tail. Let the probabilities in eq. 1 apply. For an individual with a brightly colored tail, the probability of being detected is increased by an amount a , so that its total probability of being detected equals Pd + a . However, the probability of escape following detection is increased by an amount P, giving a total conditional probability of escape of P, + P. For the conspicuous individual, the probability of being captured is Natural selection favors conspicuousness if PC> PC!,i .e., if This leads to the inequality

Inequality [4] indicates that natural selection of bright tails is favored if (i) P is large, (ii) the probability of detection for an inconspicuous individual is large, (iii) a is small relative to P and Pd, and (iv) the probability of capture following detection (i.e., 1 - P,) is small. Points i and iii are obvious: a large increase in probability of escape with little or no increase in probability of being detected is beneficial. Point ii emphasizes that if Pd is very high, a is necessarily low, which increases the overall benefit from any increment in P. For antipredatory mechanisms to operate in the escape or resistance phases, prey must sometimes avoid being killed after being attacked. Point iv indicates this quantitatively: the greater the probability of escape after detection without bright coloration, the smaller the increment in escape ability required to favor increasing brightness. In the limiting case, in which all inconspicuous individuals are captured if detected (P, = O), conspicuousness can be selectively favored if

At the other extreme, in which all prey escape, no increase in ability to escape can occur because P, plus P cannot exceed 1.O (i.e., P,, = 1.O - P,). Conspicuousness in this case is free to increase to its maximum possible value, a,,, = 1 - Pd, without cost, but there is no selection for such increase by predation. As P, increases at intermediate values, the magnitude of p necessary to favor increasing brightness becomes less, but there is a simultaneous decrease in the maximum p attainable (Fig. I).

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The zone of a and P values favorable to the evolution of bright tail coloration varies with P, and Pd. Each section of Fig. 1 shows the curve

for a fixed P, and several Pd values. At a given P,, the minimum favorable P for a given a value increases as Pd decreases. As Pd increases, the area of the favorable zone of a and P values shrinks. This effect occurs because a,,, decreases. If the predator cannot ever detect the prey, then P > (1 - P,) = P,, a contradiction. Conspicuousness is not favored when prey are undetectable. Even if Pd > 0, any decoy having a positive P value but not increasing detectability ( a = 0) will be favored (inequality [5] becomes p > 0). Any antipredatory benefit, no matter how small, would be favored because it would have no antipredatory cost. This simple formulation ignores any energetic or physiological costs that could reduce the overall contribution to fitness of increasing ability to escape. Given the broad range of adaptive joint increments in detectability and escape ability, what values of a and P would be stable under natural selection? Equilibrium conditions (derived in the Appendix) are given by

where N is an exponent of a in a simple power function relating a and p (see Appendix). Because stability at equilibrium has not been analyzed, the biological significance of this equilibrium is unknown. Sequential probabilities The model can be extended to account for effects of conspicuousness in an arbitrary number of sequential stages of encounters, each stage having a conditional probability. For example, the prey has a probability of being captured following detection and a separate probability of being killed after being captured. Let Pcldbe the probability of being captured once detected and Pklcthe probability of being killed after capture. Let p, and Pk be the improvements in probability of avoiding being captured and killed, respectively, conferred by a conspicuous trait. Using the same logic as in the original model, we now have and Rearrangement of inequality [9] to a form equivalent to inequality [4] gives

FIG.1. In each graph, the areas lying above the curves and bounded by the lines a,,, = 1 - Pd, Pmax = 1 - P,, and a = 0 represent adaptive zones in which the evolution of conspicuousness is favored. The minimum adaptive P value for a given a value decreases as Pd decreases and as P, increases. However, because P,,, = 0 when P, = 1, at least a minimal finite risk of capture is required for conspicuousness to be beneficial. The Pd axis has two interpretations. First, the values shown are those used to construct the curves (0.0, 0.25,0.50,0.75, 1.0). Second, each value of Pd determines a corresponding a,,, value directly below it on the a axis.


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Inequalities [4] and [lo] are identical except that f3 of [4] is replaced by three terms expressing the combined effects of PC and Pk, which, in sum, equal 1 - P e l - PcldPklc. Favorable regions could be plotted with a , PC, and Pk axes for various levels of P, and Pd, as in Fig. 1, but it would be necessary to specify values of PCldand Pklc. Conditionsfavoring crypsis and related defenses Several important defenses, including crypsis, immobility, and anachoresis (reclusiveness, see Edmunds 1974), are effective because they decrease the likelihood of being detected. Selection favors inconspicuous defense when PC< PC!.Solving a reversed inequality [3] for a , we have

This is likely to occur when predators are inefficient at detecting prey (Pd small), when conspicuousness does not greatly enhance ability to escape (P small), and, importantly, when the predator captures a high proportion of detected prey (P, + P small). When perfect crypsis is achieved, Pd = 0. Starting from a reversed inequality [4], we then obtained P < 1 - P,. Only if P = Pmaxare crypsis and conspicuousness equally effective. Thus, conspicuousness cannot be selectively favored when the prey is undetectable.

'

Defenses inconspicuou; before detection but conspicuous thereafter Some antipredatory mechanisms render the prey very conspicuous, but only after detection. With Pd = 1 and a = 0, a rearranged inequality [4] becomes P/(.l - P,) > 0. This suggests that either f3 > 0 or P, = 1. In the latter case the inequality is undefined. Thus, the model reduces to the expected result that conspicuous defenses that do not affect the probability of detection can be favored by natural selection if they enhance the probability of escape even slightly. Shifts in selective balance Changes in either detectability or ability to escape subsequent to detection may alter the direction of inequality [4], changing either the favored mode of defense or the features required to achieve it. Suppose that a population is suddenly rendered conspicuous by a change in the environment or predators. If the population had been protected by crypsis and gained no increase in ability to escape as a result of becoming conspicuous ( p = 0), selection would operate against conspicuousness. Selection will favor decreased conspicuousness when inequality [3] is reversed, i.e., when P C< PC!.With P = 0, a reversed inequality [4] becomes 1121 0 < a ( l - P,) Therefore, as long as some prey are captured and a is positive, selection will favor decreasing conspicuousness. Estimation of parameters All nine juveniles with blackened tails were bitten on the body anterior to the tail and were consumed. Of lizards with tails painted blue, six were bitten on the tail and eight on the body. Five of nine with tails not painted blue were bitten on the tail base and escaped while the snake ate the autotomized tail. The other four were bitten on the body and eaten. Painting the tail blue had no effect on frequency of attack on the tail (painted blue versus not painted blue: P > 0.10). Importantly, lizards with tails painted blue were attacked on the tail in a significantly

FIG. 2. Possible equilibrium values of P for various levels of a , given the assumptions that Pd = P , = 0.5 and P = aaN.

higher proportion of trials than those with blackened tails ( P = 0.03). If data for lizards with blue tails, whether painted or unpainted, are pooled, the frequency of attacks on tails is significantly greater than for black-tailed lizards at the 0.01 level. Painting reduced the flexibility of the tail, but the results indicate that this did not alter the probability that strikes were directed to the tail. Based on data for lizards with unpainted blue tails and with tails painted black, P = Pel - P, = 0.56 - 0 = 0.56. The corresponding estimates for lizards with tails painted blue and for the pooled blue-tailed groups are 0.43 and 0.48. The estimates are preliminary because they include only the final outcome of encounters. Each trial was run until a successful strike occurred, but trials often included multiple attacks. Because a higher proportion of strikes at the tail (0.42) than at the body (0.06) missed altogether (see Vitt and Cooper 1986b for E. fasciatus, E. inexpectatus, and E. laticeps), data on all attacks or initial attacks only are needed to calculate P accurately. Data for E. laticeps (Table 1) allow better estimation of P in staged encounters with L. triangulum elapsoides, similar to those described for E. fasciatus (Vitt and Cooper 1986b) but in which all attacks were recorded. The snakes attempted to strike a higher percentage of blue- than black-tailed hatchlings on the tail (X2= 9.69, df = 1, P < 0.01). Analysis of combined data for attacks on all hatchlings demonstrates that a higher percentage of strikes at the tail than at the body miss, 16.0 vs. 4 1.7, but this difference is not significant ( P > 0.10, Fisher test). If colorful tails cause increased misses by deflecting strikes to the relatively small target presented by the tail, bright coloration may increase the probability of escape without autotomy. Whatever the mechanisms involved, blue-tailed hatchlings had a significantly greater probability of escape than black-tailed hatchlings (x2 = 4.98, df = 1, P < 0.05). For E laticeps, f3 = 0.600 - 0.235 = 0.365. Increments to the sequential conditional probabilities of being captured after detection and being killed after capture (PC and Pk) were estimated for E. laticeps (Table 1) by calculating the probabilities of successful strikes and of kills after strikes for black-tailed and blue-tailed lizards, and their differences. Because Pd = 1.O, a = 0.0 and P c l dis the number of successful strikes divided by the total number of strikes on black-tailed

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TABLE1. Results of predation encounters between scarlet king snakes and hatchling broad-headed skinks with blue and black tails

Total no. of strikes % total hits % total misses %strikesattail % tail hits % tail misses % body strikes % body hits % body misses % captures % escapes

Blue- tailed skinks

Black-tailed skinks

20 70.0 (14120) 30.0 (6120) 55.0(11/20) 54.5 (6111) 45.4(5/11) 45.0 (9120) 88.9 (819) 11.1 (119) 40.0 (8120) 60.0 (12120)

17 82.4 (14117) 17.6 (3117) 5.9(1/17) 100.0 (111) o.o(o/ij 94.1 (161 17) 81.2 (13116) 18.8 (3116) 76.5 (13117) 23.5 (4117)

NOTE:Numbers in parentheses show numbers of trials.

lizards. Thus, Pcld= 0.824 and PC= 0.824 - 0.700 = 0.124. Because all lizards bitten on the tail escaped and all lizards bitten anterior to the tail were killed, P k l cis the number of successful strikes on the body divided by the sum of successful strikes to the body and successful strikes to the tail on black-tailed lizards. For blue-tailed skinks, 8 of 14 hits were on the body, and for black-tailed shinks, 13 of 14. This gives Pklc= 0.929 and Pk = 0.929 - 0.57 1 = 0.358. Using these estimates, eq. 10 becomes 0.366Pdl/a > 0.766. Thus, for an overall increase in escape ability of 0.366 and (1 - P,) = 0.766, conspicuousness is favored for all values of P d labove the line P d t= 2.090~or above Pd = 1.090~.

Discussion

Adaptive conspicuousness Bright tail coloration and other conspicuous defenses can be adaptive in a broad range of conditions. Comparisons of adaptive zones for different escape abilities reveal that the selectively beneficial areas become larger for a given Pd value as P, decreases (Fig. 1). This does not indicate that a low P, value favors adaptive conspicuousness: it is clear from inequality [4] that a high P, value favors conspicuousness. The most important trend is that as P, increases, the minimum selectively beneficial value of P decreases for a given combination of a and Pd. Thus, for equal detectability, a smaller enhancement of predation avoidance is needed to evolve conspicuousness when the probability of escape is already high. The preliminary estimates of P for E. fasciatus and E. laticeps greatly exceed the minimum values needed to induce selection for brightness. Such high values of P would favor tail brightness except at very low P,, low Pd, and high a values. The estimates of p are somewhat inflated and those of P, are too low because in the field, lizards sometimes detect predators and escape before a strike is possible, whereas in the staged encounters complete avoidance was impossible. Thus, the P estimates cannot be considered representative of natural conditions. Because the tail provides substantial protection even in species lacking bright tail coloration (e.g . , Congdon et al. 1974; Dial and Fitzpatrick 1983), the probability of escape may have been fairly high when evolution of increased conspicuousness began. Present data are insufficient to reconstruct the evolution of bright tail coloration in Eumeces, but its broad features are fairly clear. The probability of detection is relatively high because these skinks forage actively on trees and forest litter (Fitch 1954;

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Vitt and Cooper 1 9 8 6 ~ ) .Both the increased probability of escape afforded by autotomy and high detectability favored evolution of brightness. However, no estimates of Pd or a are available because the predator readily detected all prey in the small cage used in our study. The model presumably applies to several other defenses that entail conspicuousness prior to detection. Among such defenses that render palatable prey conspicuous before detection are predetectional flight, preemptive attack, and behavioral displays that appear to deter pursuit by signallling the predator that it has been detected (Woodland et al. 1980; Craig 1982; Bildstein 1983; Dial 1986). Predetection displays may increase detectability, but more than compensate by reducing the probability of being attacked once detected. Evolution of conspicuous defenses in distasteful or noxious species may often require kin or "green beard" selection (Guilford 1988) or strong frequency-dependent selection (Huheey 1988). Thus, our model does not account for the evolution of aposematism, Batesian mimicry, or Mullerian mimicry. However, regardless of their selective mode and evolutionary trajectory, inequality [4] must be satisfied for these defenses to be favored. Among the defensive adaptations that are conspicuous only after detection are deflective color patterns that operate only at close range and deflective behavioral displays emitted after detection. Deflection involving color patterns occurs in numerous butterflies, especially lycaenids (e.g . , Cott 1940; Robbins 1981). In experimental encounters between blue jays (Cyanocitta cristata) and European cabbage butterflies (Pieris rapae), butterflies having wings painted with various components of false head markings escaped more often when attacked than did unpainted controls (Wourms and Wasserman 1985). The butterflies were released in an enclosure where all were detected. The probability of escape for individuals with false head markings (0.206) was greater than for unpainted butterflies (0.096), giving an estimate of P = 0.107. Because the butterflies had already been detected, any positive value of P would be favored. Experimental data indicate an increased escape rate (a positive p value) for these and several defenses that are conspicuous only after detection. Such data show that the defenses can be maintained by natural selection, but do not reveal their initial mode of evolution (Huey and Bennett 1986). Detection versus escape in the major defenses The major antipredatory mechanisms of animals may be categorized according to stage of operation in an encounter with a predator and the degree of conspicuousness and increase in ability to escape required. Defenses listed in Table 2 follow Edmunds' (1974) classification supplemented by mechanisms listed recently by Endler (1986). Endler (1986) discussed defense mechanisms operating in five stages of predator-prey encounters: detection, identification, approach, subjugation, and consumption. In our model, effects of detection and identification are lumped in Pd; those in the remaining stages are lumped in P, of the simplest version of our model, but are separated in the sequential versions. Stage of operation in Table 2 refers to both the periods in which the defense is effective and those in which detectability is affected. Major defense mechanisms that decrease detectability of prey are crypsis, anachoresis, and immobility. Cryptic and immobile prey may be relatively vulnerable following discovery. Although its p value is listed as zero, immobility might actually decrease the likelihood of escape after detection. A larger decrease in detectability would then be needed to favor immobility. The P

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TABLE2. When a defense is used strongly affects the relative importance of conspicuousness and of ability to escape after being detected Defense mechanism

Stage of operation

Crypsis Immobility Anachoresis Thanatosis Retaliation Noxiousness Flash coloration Deimatic (startle) behavior Deflective behavior Deflective coloration or predetection display Aposematism Batesian mimicry Mullerian mimicry Flight Preemptive attack

Predetection Predetection Pre- and post-detection Postdetection Postdetection Postdetection Postdetection Postdetection Postdetection

Parameters

Pre- and post-detection Pre- and post-detection Pre- and post-detection Pre- and post-detection Pre- and post-detection Pre- and post-detection

value for anachoresis is shown as greater than zero because anachoretic prey may be difficult to capture in refuges. Several other defense mechanisms, including flash coloration, deimatic (= frightening or startling) behavior, retaliation, deflective behavior, thanatosis, and flight after detection, do not affect detectability and operate only after detection. Selection favors such adaptations only if they confer an increase in escape probability. Flash coloration is of particular interest. Although conspicuous during emission, it allows the prey to remain inconspicuous at other times (Cott 1940). It could evolve in otherwise cryptic forms, but might in certain cases evolve secondarily to aposematic coloration to reduce a . The remaining antipredatory mechanisms potentially increase detectability. These defenses, including deflective coloration and displays performed before detection, flight occurring prior to detection, aposematism, Batesian mimicry, Mullerian mimicry, and preemptive attack, are most interesting because their feasibility depends on the probabilities described by the model. Related work and sequential probabilities A related model was developed by SillCn-Tullberg and Bryant (1983) to account for evolution of aposematism by individual selection. Their model includes a term for the probability of detection, but differs in that conditional probabilities of being captured once detected, and of being killed once captured, are treated separately, whereas we include only a probability of being killed once detected (but see below). Thus, 1 - P, in our model is equal to the product of the two conditional probabilities in theirs. A major difference in the models is that Sillkn-Tullberg and Bryant (1983) assume that there is a negative linear relationship between the probability of being captured once detected and the probability of being detected. A similar assumption is made in our model regarding a positive corelation between a and p, but not between Pd and P,. The models are equivalent in this regard only if all captured prey are killed and 1 - P, = e - f ~ d where , e and f-are regression coefficients of a linear relationship between Pd and P,. An important difference is that our model includes separate terms for increments in detectability and ability to escape. This complicates algebraic comparisons among defenses, but is an important advantage because quantitative predictions can be generated about relative levels of detectability and escape

ability. The emphasis on differences between inconspicuous and conspicuous defenses also focuses attention on readily manipulated features. The added terms allow explicit consideration of the changes from the current state required to favor conspicuousness. Our sequential model accounts for effects of conspicuousness on the separate conditional probabilities in the model of Sillkn-Tullbergand Bryant (1983). For tail autotomy in juvenile Eumeces, the overall increase in probability of escape consists of separate increases in ability to avoid being captured once detected and ability to avoid being killed after capture. The ability to avoid capture is enhanced because snakes are more likely to miss completely when attempting to strike the tail rather than the body (Vitt and Cooper 1986b). A larger increase in ability to escape once seized is conferred by the autotomous tail. The sequential model described above is appropriate when the defense operates primarily before the prey is seized. However, deterrent displays may provide their greatest benefit by preventing the predator from attacking at all. Predators that do attack may do so with reduced accuracy or may attack tentatively so that weakly grasped prey may escape. Only a minor modification of the model expressed in eqs. 8, 9, and 10 is needed to include these possibilities (see Appendix). Shifts in selective balance Industrial melanism is a classic case of an environmentally induced change in the balance between detection and escape. The typical form of the moth Lasiocampa quercus was detected and eliminated by gulls on heather at a much higher probability (0.864 for males, 0.895 for females) than was a more cryptic melanic form (0.182, 0.000), giving a values of 0.682 for the typical males and 0.895 for the typical females (estimated from data in Kettlewell et al. 197 1). The differential rate of elimination of cryptic and noncryptic morphs of the peppered moth, Biston betularia, was over 0.70 (Kettlewell 1956). In these studies the cryptic forms had higher survival rates, demonstrating that many moths were captured (P, < 1) and that a < 0 by a substantial margin for the cryptic morphs. Ontogenetic changes in color and behavior may be defensively adaptive if growth results in the prey becoming invulnerable to some predators and attractive to others having different abilities to detect and capture prey. This may explain the changes in the South African lizard Eremias lugubris, which is a black and white behavioral mimic of a noxious carabid beetle as a juvenile but has concealing coloration as an adult (Huey and Pianka 1977). It appears that adults are too large to be successful beetle mimics. Changes in favored defenses also may accompany changes in physiological state. Gravid female lizards, for example, may be so slowed by the mass of their clutches that their ability to escape is greatly impaired. This impairment may be responsible for a shift to cryptic behaviour by gravid female Lacerta vivipara (Bauwens and Thoen 1981). Many such changes in defense mechanisms may be explained by changes in conditions leading to shifts in the directionality of eqs. 4 and 11. Measurements, predictions, and limitations Beta can be readily measured for many antipredatory adaptations in addition to blue tail coloration in skinks. Any conspicuous trait can be experimentally rendered inconspicuous or the conspicuous behavior suppressed in the field or laboratory. Alternatively, conspicuousness might be increased artificially. P,, a , or any of the postdetection conditional probabil-


COOPER AND VITT

ities can be measured following such manipulations. Natural opportunities for such tests may be found in populations dimorphic or polymorphic for the conspicuous trait or in closely related, similar species that differ in degree of conspicuousness. Studies of a require more complex environments than we used. Tests of the predictions regarding favorability of conspicuousness are straightforward. For a given P, and Pd, P must achieve a predicted minimum for any given a value. Historical considerations, nondefensive adapive constraints, and the absence of appropriate mutations may prevent evolution of conspicuous traits when they might be beneficial. However, P should be in the favorable zone in a stable predator-prey situation. If p is below the minimum favorable value for a , it should be possible to find evidence of current selection for decreased conspicuousness. Owing to its simplicity, the model fails to account for some important effects. For example, because brightness attracts predatory attack to a skink's tail, its effectiveness may be determined at very close range when the predator attempts to grasp the prey. In contrast, Pd and a are presumably decreasing functions of distance. Beta may be constant with respect to distance for autotomy, but may increase with distance for other defenses. For example, a predator that has learned to avoid noxious prey may be less likely to attack if it views the prey from

763

a distance (Guilford 1986). Variation in a,P, Pd, and P, with distance is not reflected in the equations given earlier. Although the present model assumes independence of Pd and P,, predators good a detecting prey may also be good at capturing them. If Pd and 1 - P, were positively correlated, conspicuous decoys would be more difficult to evolve. The relationship is determined by substituting for either Pd or P, in inequality [3]. To offset the increase in probability of capture following detection, higher P values, lower a values, or both, would be required. Another important factor, not directly considered in the present model, might be learning by the predator. After repeated exposure, some predators might learn to bite the body rather than the bright tail.

This work was supported by contract DE-AC09-76SR008 19 between the U.S. Department of Energy and the University of Georgia through the Savannah River Ecology Laboratory, by Oak Ridge Associated Universities, the Department of Biology of the University of California at Los Angeles, and by a grant-in-aid from Auburn University at Montgomery. The paper was substantially improved by comments made by Bob Jaeger, Ray Semlitsch, and Reid Harris.

b

Appendix Equilibrium values of a and P Stable values of detectability and escape ability occur when the derivative of the probability of capture, PC!,with respect to a is zero. To solve for explicit values, it is necessary to assume a functional relationship between a and P. The increments in detectability and escape ability may be positively correlated in numerous defenses. For example, bright tail coloration in juvenile lizards (E. laticeps) appears to simultaneously increase detectability and escape ability (Cooper and Vitt 1985). Because a = 0 when P = 0, the intercept term of a linear relationship must be 0. To include a wider range of possible relationships than a linear one, assume that P = aaN. Then [All P c ~ = P d ( l - P e ) + a ( l - P e ) - ~ d a a N - a a N + l and

Equilibrium, obtained by setting eq. A2 equal to 0, is given by

Equilibrium solutions for a vary with P,, Pd, N, and a , a constant. Holding P,, Pd, and N constant, it is possible to solve for a in terms of a . For a linear relationship between a and P, i.e., N = 1,

and

By substituting @/aN) for a in eq. A3, at equilibrium we obtain

There is a unique equilibrium point for each combination of P,, Pd, a , and N. For each combination of P, and Pd, there is a family of curves, one curve for each value of the detectability exponent, N. Each point on a particular curve represents the equilibrium point for a specific value of the constant a . This is illustrated in Fig. 2 for Pd = P, = 0.5.


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CAN. J. ZOOL. VOL. 69. 1991

Sequential attack, seizure, a n d killing 1n the sequential model described in the text, two distinct stages were lumped in Pcld. First, predators may be deterred from attacking at all by aposematic coloration and various other sorts of alerting displays (e.g., Cophosaurus texanus; Dial 1986), warning displays, and subterfuges. Thus, it may be necessary in many cases to consider separate conditional probabilities of being attacked following detection, Paid, and of being captured if attacked, P c I a .If these probabilities are used in place of P c l d ,with increments Pa and PCreplacing the original PC, inequality [ 1 l ] becomes

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