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  • Journal of lnsect Behavior, Vol. 9, No. 1, 1996

    Factors Regulating Predation by First-Instar Spined Assassin Bugs [Sinea diadema (Fabricius)] (Hemiptera: Reduviidae)

    J. R. Taylor I and J. M. Schmidt 1'2

    Accepted July 11, 1994; revised September 12, 1995

    Selected nutritional and developmental factors regulating the predatory behavior of first-instar spined assassin bugs Sinea diadema (Fabricius) (Hemiptera: Redu- viidae) were investigated. The longevity of unfed nymphs provided with free water, bean pod sections, or glucose solutions was not significantly greater than that of unfed nymphs which were not provided with a source of water. First- instar S. diadema that were provided with larvae of Ephestia kuehniella Zeller (Lepidoptera: Pyralidae) as prey began feeding 1.9 (+0.9) days after hatching. In contrast, first-instar S. diadema that were provided with conspecifics of the same age did not begin feeding until they were 3.9 (+0.9) days old. These results suggest that the potential nutritional benefits to be gained from feeding equal or outweigh the risk of attacking prey capable of effective self-defense only when nymphs have not fed for 4 days after hatching. Providing the nymphs with water or glucose solutions significantly delayed the onset of conspecific predation. Additional data are presented which demonstrate that first-instar S. diadema are not restrained from preying on siblings by kin recognition:

    KEY WORDS: Reduviidae; interspecific predation; intraspecific predation; nutrition; kin recog- nition.

    INTRODUCTION

    According to optimal foraging theory, a predator should select prey that maxi- mize its net energy gain (see Pyke et al., 1977; Krebs, 1978). The handling'

    ' Department of Environmental Biology, University ofGuelph, Guelph, Ontario, Canada N 1G 2W 1. 2To whom correspondence should be addressed.

    23

    0892-755319610100-0023509.5010 9 1996 Plenum Publishing Corporation

  • 24 Taylor and Schmidt

    time required for a specific prey species is an important factor in prey selection because handling time can be costly in terms of energy expenditure by the predator. The reaction of the prey when it is attacked may be a deciding factor in prey selection, especially for a generalist predator that attacks many different types of prey. Handling time is greatly affected by the time it takes a predator to subdue the prey (Molles and Pietruszka, 1983) and prey with vigorous defen- sive reactions are often rejected by satiated predators (Marston et al., 1978; Evans 1982). The physiological state of the predator may also influence prey selection. Hunger can often prompt a predator to increase the range of prey species that it will accept (Pastorok, 1980; Molles and Pietruszka, 1987). In addition, hunger can alter an animal's response to the risk of predation (Croy and Hughes, 1991). Conversely, animals that have recently fed, or have nutrient reserves, may be less likely to attack prey that are capable of counterattack.

    In this study, we investigated the effect that different foods have on intra- specific predation by first instars of a predatory bug. Sinea diadema (Fabricius) (Hemiptera: Reduviidae) is a common North American predatory bug that feeds on a wide variety of prey species (Readio, 1924). It employs a sit-and-wait strategy for capturing prey with its raptorial forelegs. Prey encountered in the field by S. diadema nymphs include various soft-bodied insects such as lepi- dopteran and coleopteran larvae. In addition, the nymphs are likely to encounter a variety of predatory arthropods that are both potential prey and predators, including spiders, nabid bugs and other reduviid nymphs. In a series of four experiments we determined some of the factors that regulate the response of S. diadema nymphs to potentially hazardous prey. The hazardous prey used in these experiments were conspecific nymphs of the same age and similar nutri- tional status.

    In our first experiment we tested the effect of different diets on nymphal survival in order to establish the relative value of water, glucose solutions and conspecific prey. In the second experiment first-instar S. diadema were offered two types of prey: the soft-bodied larvae of Ephestia kuehniella Zeller (Lepi- doptera: Pyralidae) and conspecific nymphs. The larvae of E. kuehniella are the usual food fed to S. diadema in our laboratory. Conspecifics of the same age and size were chosen as the second prey species because they are representative of prey with similar aggressive qualities and defensive capabilities. Furthermore, cannibalism occurs frequently under laboratory conditions (Readio, 1924). If a predator does alter its behavior according to its nutritional status, particularly the likelihood of continuing an attack on an aggressive prey, then it must use physiological cues associated with recent feeding activity to regulate its behav- ior. In our third experiment we evaluated whether the availability of water or glucose solution delayed cannibalism among first instars.

    Since female S. diadema lay their eggs in clutches, cannibalism among siblings possibly occurs in the field. To control for any affect this may have on

  • Predation by Spined Assassin Bugs 25

    predatory behavior observed in the experiment, we conducted an additional test to determine whether individuals cannibalize kin less readily than they canni- balize nonkin.

    MATERIALS AND METHODS

    Experiment 1: Development and Life Span of First Instars Fed Different Diets

    Sinea diadema egg clutches were collected from captive adults every 2 to 3 days. The eggs were kept in petri dishes until the time of hatching. In all tests, nymphs less than 16 h old were placed individually in 5-cm-diameter petri dishes. Every 24 h, nymphal mortality and development were recorded. Obser- vations ceased when a nymph either had died or had developed to the second stadium. There were 20-25 replicates of each treatment. Three diets were tested.

    Test 1. Bean vs. No Bean. (a) Each nymph was provided with a section of green bean pod (Phaseolus vulgaris) which was replaced with a fresh section every 2 days. Nothing else was provided. (2) Each nymph was provided with neither food nor water.

    Test 2. Water vs. No Water. (1) Each nymph was provided with a 1-cm 2 piece of absorbent 3M Supersorb material moistened with water. More water was added as needed every 2 days. (2) Each nymph was provided with a dry 1-cm 2 piece of absorbent 3M Supersorb material.

    Test 3. Variable Amounts of Prey. In this test, nymphs were allowed to consume a fixed number of prey. Nymphs were provided with a 1-cm 2 piece of absorbent 3M Supersorb material moistened with water, Prey consisted of con- specifics that had been killed by freezing. On the day of hatching, each nymph was provided with one prey item. Twenty-four hours later, each prey was checked for indications that it had been fed upon (i.e., sucked out). If the prey had been fed upon, the nymph was recorded as consuming a prey item. Each day prey were replaced with freshly killed nymphs regardless of whether they had been fed upon. This procedure was repeated every day until the nymph had consumed its allotment of prey. The nymphs were fed a total of either 2, 3, 4, 5, or 6 conspecifics.

    In addition, 20 newly emerged nymphs were divided into two groups of 10 nymphs each. One group was provided with water, while the other group was not provided with water. When the nymphs were 3 days old they were weighed and the average weight of a nymph was calculated.

    For tests 1 and 2, the Mann-Whitney U test was performed to test the significance of the observed difference between the lifespans of treatment nymphs and control nymphs.

  • 26 Taylor and Schmidt

    Experiment 2: Occurrence of Predation and Cannibalism

    All nymphs were less than 16 h old and unfed at the beginning of the experiment. One or three nymphs were placed in a 5-cm-diameter petri dish with a section of green bean pod. There were three treatments.

    (1) A single nymph was provided with four 2-week-old E. kuehniella lar- vae that were replaced every 48 h with fresh larvae.

    (2) A group of three nymphs was not provided with any prey. (3) A single nymph was not provided with any prey.

    Treatment 3 was used to determine the age at which the nymphs died of hunger.

    Each dish was checked every 24 h. In treatment 1, nymphs were checked for distended abdomens, which indicated that a nymph had fed. Observations of each nymph continued until the nymph had fed. In treatment 2, occurrences of cannibalism were recorded. Cannibalism was assumed to have occurred if there was at least one dead nymph in the dish and one, or both, of the remaining nymphs had distended abdomens. Observations of each group of nymphs con- tinued until the first incidence of cannibalism. In treatment 3, nymphal mortality was recorded. Observations of each nymph continued until the nymph died. There were 20-25 replicates of each treatment.

    The Mann-Whitney U test was performed to test the significance of the observed difference between the age at which nymphs began feeding on E. kuehnieUa larvae in treatment 1, and the age at which cannibalism began in treatment 2. The Mann-Whitney U test was also performed to test the signifi- cance of differences between the mortality distribution of nymphs maintained in groups in treatment 2 and the mortality distribution of single nymphs in treat- ment 3.

    Experiment 3: The Effect of the Availability of Water and Glucose on the Life Span and on the Age at Which First Instars Begin to Cannibalize

    On the day that nymphs hatched, one or three nymphs were placed in a 5-cm-diameter petri dish. Liquids were presented by moistening two 0.5-cm 2 pieces of absorbent 3M Supersorb material with water or with a 20 % glucose solution. Diets were refreshed every 48 h. The following six treatments were tested for their effects on either the life span of nymphs or the age at which nymphs began to cannibalize.

    (1) A single nymph was provided with water only. (2) A single nymph was provided with water and a 20 % glucose solution.

  • Predation by Spirted Assassin Bugs 27

    (3) A single nymph was provided with neither water nor glucose (control). (4) A group of three nymphs was provided with water only. (5) A group of three nymphs was provided with water and a 20% glucose

    solution. (6) A group of three nymphs was provided with neither water nor glucose

    (control).

    Every 24 h, nymphal mortality and development in treatments 1, 2 and 3 and occurrences of cannibalism in treatments 4, 5 and 6, were recorded. Can- nibalism was assumed to have occurred if there was at least one dead nymph in the dish and one, or both, of the remaining nymphs had distended abdomens. In treatments 1, 2 and 3, observations ceased when a nymph had either died, or had developed to the second stadium. In treatments 4, 5 and .6, observations ceased when one of the three nymphs was dead..There were 34 replicates of each treatment.

    A Kruskal-Wallis test was performed to test for significant differences in the age at which nymphs begin to cannibalize among treatments with grouped nymphs. It was also used to test for differences in the lifespan of nymphs among treatments with single nymphs. Pairwise comparisons were performed using the Mann-Whitney U test.

    Experiment 4: Selective Cannibalism of Unrelated Nymphs

    Animals collected from the same area may be closely related. To obtain animals that were not related, animals were collected from three different pop- ulations at sites at least 10 km apart.

    To ensure that offspring were full siblings, virgin females were paired with a single male. Each pair was kept in a 5 x 7-cm plastic bottle from which egg clutches were collected every two days. The parentage of each clutch was noted.

    Three nymphs were placed in each petri dish. The three nymphs consisted of a pair of full sibling nymphs (kin) and one nymph from an egg clutch produced by adults collected from a different area (nonkin). Nymphs were marked with a dab of acrylic paint on the back of the head for identification. Nymphs were checked daily for cannibalism. Cannibalism was assumed to have occurred if one nymph was dead and one, or both, of the remaining nymphs had distended abdomens. There was a total of 35 replicates. Replicates in which two nymphs were dead were omitted from the final analysis.

    If nymph s do not discriminate between kin and nonkin, then the nonkin nymph should be the first nymph killed in one-third of the replicates. A one- tailed G test for goodness of fit (Sokal and Rohlf, 1981) was performed to test the null hypothesis that nymphs do not discriminate between kin and nonkin.

  • 28 Taylor and Schmidt

    RESULTS

    Experiment 1: Development and Life Span of First Instars Fed Different Diets

    In the first test, none of the first-instar S. diadema provided with only green bean pod developed into second instars. The availability of green bean pod also had no significant effect on the mean life span of the first instars (P > 0.10; Mann-Whitney U test) (Table I). In the second test, the availability of free water also had no significant effect on the life span of first instars (Table I) (P > 0.10; Mann-Whitney U test). In the third test, the proportion of nymphs developing into second instars increased with the quantity of conspecifics con- sumed (Table II).

    Nymphs that had been provided with water weighed 0.32 mg on average when they were 3 days old, while nymphs that had been deprived of water weighed only 0.24 mg on average.

    Experiment 2: Occurrence of Predation and Cannibalism

    Nymphs began feeding on E. kuehniella larvae 1.9 (+0.9) days after hatch- ing. In contrast, nymphs began feeding on conspecifics 3.9 (+0.9) days after hatching (P < 0.05; Mann-Whitney U test) (Table III). The life span of nymphs that were kept individually and were not provided with prey was 6.0 (+1.0) days.

    Experiment 3: The Effect of the Availability of Water and of Glucose on the Life Span and on the Age at Which First Instars Begin to Cannibalize

    First instars that were kept individually and that were provided with water, and with water and glucose solution, survived 5.2 (+0.9) and 5.6 (+ 1.6) days,

    Table I. Mean Life Span (+SD) of First Instars Provided Either with a Section of Green Bean Pod or with No Food and Water; Also, the Mean Life Span (+SD) ot First Instars Provided with

    Either Water or with No Food and Water"

    Bean h No bean Wate/' No water

    Life span (days) 6.0 + 1.0 5.5 -I- 1.0 6.7 + 1.4 6.2 + 1.4 (n) (24) (25) (25) (22)

    "Nymphal mortality was recorded approximately every 24 h. bTreatment mean was not significantly different from control mean (P > 0.10; Mann-Whitney U test).

  • Predation by Spined Assassin Bugs 29

    Table H. The Number of First Instars, Fed 2, 3, 4, 5, or 6 Dead Conspeeifics, to Complete Development to Second Instar"

    No. of dead conspeeifics provided to first instars 2 3 4 5 6

    No. of first instars to develop to second instar 0 6 10 14 16

    Percentage of first instals to develop to second instar 0 30 50 70 80

    I l l l

    ~ = 20 for each column. Data are also presented as the percentage of nymphs to complete development.

    respectively. These nymphs did not live significantly longer than nymphs that were not provided with water (4.9 -t- 1.1 days) (P > 0.10; Kruskal-Wal l is test) (Table IV). However, nymphs provided with water or with a glucose solution began to cannibalize when they were significantly older (4.0 ___ 1.0 and 4.5 + 1.3 days, respectively) than nymphs that were not provided with water (3.2 + 0.7 days) (P < 0.05; Mann-Whitney U tests) (Table IV). The age at which cannibalism began among nymphs provided with water was not significantly different from those provided with a glucose solution (P > 0.10; Mann-Whitney U test) (Table IV).

    Experiment 4: Selective Cann iba l i sm of Unre lated Nymphs

    Twenty-nine replicates were used in the analysis. In nine, or 31%, of the observations, the nonkin nymph was the first nymph to be killed. There is no evidence that first-instar S. diadema prefer to cannibalize nonkin rather than kin (P > 0.10; G test for goodness of fit).

    Table i l l Mean Age (+SD) at Which Nymphs Began Feeding on Nonconspecific and Conspecific Prey and the Lifespan of Nymphs Kept Individually

    Age at which nymphs began feeding (days)

    Single nymphs provided with Grouped nymphs provided with Life span of single nymphs E. kuehniella larvae no prey" provided with no prey

    1.9 + 0.9 3.9 + 0.9 6.0 + 1.0 (n = 25) 01 = 20) (n = 24)

    "Age at which nymphs began feeding on larvae was significantly different from the life span of single nymphs provided with no prey (P < 0.05; Mann-Whitney U tests).

  • 30 Taylor and Schmidt

    Table IV. Mean Life Span (4-SD)of Nymphs that Were Maintained Individually and the Mean Age (+SD) at Which First Instars Kept in Groups of Three Began to Cannibalize (n = 34 for

    Each Treatment): Three Diets Were Testf, d ~

    Diet

    Water Water & 20% glucose No water provided solution provided provided

    Single nymphs--lifespan b (days) 5.2 + 0.9 5.6 + 1.6 4.9 + 1.1 Three nymphs--age at first

    incidence of cannibalism c (days) 4.0 + 1.0 b 4.5 4- 1.3 b 3.2 4- 0.7 c

    "Nymphal mortality was recorded approximately every 24 h. ~'Life span of single nymph and age at which first inslars began to cannibalize were significantly different for each diet (P < 0.05; Mann-Whitney U tests).

    CMeans within roW followed by the same letter (superscript) were not significantly different (P < 0.05; Mann-Whitney U tests).

    DISCUSSION

    Nutritional Factors Regulating the Predatory Behavior of First-lnstar S. diadema

    As shown in Experiments 1 and 3, first-instar S. diadema did not develop into second instars when provided with only water, bean pod, or a glucose solution. The life spans of nymphs provided With moisture sources were not si'gnificantly greater than those of nymphs reared without a source of water. Therefore, first-instar S. diadema cannot obtain sufficient nutrients from these substances to complete development or 'prolong survival. Comparable results have been obtained with Sinea confusa, Zelus renardii Kolenati, and Z. tetra- canthus (Stoner et al., 1975). Even the availability of high-protein plant food, such as dandelion pollen, did not sustain the development of first-instar S. complexa, S. confusa, Z. renardii, and Z. tetracanthus, although their life spans were five to nine times greater than the life spans of nymphs provided only with water (Stoner et al., 1975).

    In contrast, several predatory hemipterans have been found to develop to second instar on a diet of only plant food and water. Podisus maculiventris (Say) (Hemiptera: Pentatomidae) developed into second instars when fed potato foli- age and water (Ruberson et al., 1986); Geocoris punctipes (Say) (Hemiptera: Lygaediae) developed into second instars when fed bean pods (Naranjo and Stimac, 1985; Stoner, 1970); and Orius insidiosus (Say) (Hemiptera: Antho- coridae) (Kiman and Yeargan, 1985) and O. tristicolor White (Salas-Aguilar and Ehler, 1977) developed into second instars when fed bean pod and water.

  • Predation by Spined Assassin Bugs 31

    Podisus maculiventris and G. punctipes are predatory members of primarily phytophagous families (Cobben, 1979). In contrast, the Reduviidae are com- prised solely of predators and arc probably descendants of a much older carniv- orous offshoot (Sweet, 1979). The different evolutionary origins oftbese families may.account for their differing abilities to use plant food. Podisus'maculiventris and G. punctipes may. still possess physiological adaptations that allow them to fully use plant nutrients. For instance, amylase activity was detected in the saliva of P. maculiventris, 'but not in the saliva of Zelus renardii, Sinea confusa, or G. punctipes (Cohen, 1990).

    Reduviids appear to require animal protein for development. The only nymphs of S. diadema to complete development among Tests 1, 2, and 3 in Experiment 1 were those that fed on dead conspecifics. Parker (1965) noted that the occurrence of molting in first instars of the reduviid, Psilius tipuliformis, was closely linked with the supply of insect food. Edwards (1962a) found that the reduviid, Rhinocoris carmelita, required at test one meal of prey for moulting to occur. These results demonstrate that prey is essential for development. Fur- thermore, as shown in Experiment 1, Test 3, the probability of successfully developing to the next stadium increases with the quantity of prey ingested.

    Experiments 1 and 3 also raise questions about the purpose of drinking in reduviids. First-instar S. diadema drank readily when either free water or bean was provided (personal observation). Edwards (1962b) studied the drinking behavior of Rhinocoris carmelita, Platymeris rhaidamanthus, and Reduvius per- sonatus (Linnaeus) and found that drinking was stimulated by contact between water and the tibial pads of the forelegs and midl.egs, the tips of the antennae, or the beak. Moreover,. when drinking, the reduviids could discriminate between ionic solutions of different concentrations. These observations suggest that drink- ing is a common behavior, and therefore nymphs must derive some benefit from it. ,However, in Experiment 1 water availability did not increase the survival of S. diadema nymphs. Moreover, S. diadema nymphs did not need to drink water prior to killing and feeding on prey (personal observation). Thus, the signifi- cance of drinking behavior in reduviids is not clear. Possibly, it facilitates feeding by decreasing the time required to paralyze and ingest the prey. Large amounts of fluid may increase the production of saliva. Saliva contains the toxins and proteolytic enzymes needed for the paralysis and preoral digestion of the prey (Smith, 1985). Moreover, large amounts of dilute saliva are neded to form a temporary suspension of the digested tissue which: is then ingested (Smith, 1985). A comparison of the time required for the onset.of paralysis of prey and ingestion of prey by nymphs that are provided with water and nymphs that are not provided with water, is neded to test this hypothesis.

    Nymphs that were provided with E. kuehniella larvae did not begin feeding until they were 2 days old. Edwards (1966) noted that when emerged Zelus exsanguis Stal (Hemiptera: Reduviidae) nymphs are "maintained at high humid-

  • 32 Taylor and Schmidt

    ity they will not take prey for three to four days." Sinea diadema nymphs and Z. exsanguis nymphs must be sustaining themselves for the first few days after emergence on nutrient reserves persisting from the egg stage.

    When conspecifics were the only prey available to first-instar S. diadema, feeding did not begin until nymphs were nearly 4 days old. It is possible that E. kuehniella larvae are more active and therefore encounter nymphs more frequently. However, differences in encounter rates between nymphs and larvae and between nymphs and conspecifics were considered negligible because of the simplicity and small size of the experimental arenas and relatively long time period over which the experiment was conducted.

    The reaction of the prey during encounters is probably the major factor in prey selection. In response to being attacked by a nymph, the E. kuehniella larvae thrashed their bodies for about 30 s, until the injected salivary toxin paralyzed them. In contrast, S. diadema nymphs reacted to being attacked by posturing and striking with their raptorial forelegs. Sinea diadema nymphs had a more vigorous defensive behavior than E. kuehniella larvae and were thus more successful at repelling attacks. The defensive behavior of the prey may also communicate to the predator the degree of risk associated with attacking. There is little risk of injury to a S. diadema nymph attacking an E. kuehniella larva. However, a nymph that is attacking a conspecific of the same age and size is at significant risk of being injured and even killed. Thus, it appears that conspecifics are attacked and killed only when a nymph is compelled by hunger to persist in the attack, such as after a prolonged period of food deprivation. This suggests that when nymphs are four days old and have not fed, the nutri- tional benefits to be gained from feeding on a conspecific equal or outweigh the handling costs and risk of attacking that prey.

    Interactions between recently hatched nymphs and between older, starved nymphs do not differ significantly in duration, however, the behaviors displayed do change markedly with age. During interactions between 2-day-old, unfed nymphs the predominant behaviors are posturing and striking with the forelegs. The nymphs rarely hold or grapple with each other with their forelegs. In con- trast, 5-day-old, starved nymphs interact at close quarters, often grappling with each other while attempting to insert their stylets (Talyor and Schmidt, 1994). Grappling was observed in only 18% of the interactions between 2-day-old nymphs. In contrast, 67% of the interactions between 5-day-old nymphs con- tained grappling. Cannibalism occurs only in interactions during which grap- pling occurs (Taylor and Schmidt, 1994).

    The observation that the consumption of conspecifics is delayed compared to consumption of E. kuehniella larvae suggests that S. d iadem nymphs may have information concerning their own nutritional status. This information may regulate the likelihood that a nymph will grapple with, and attempt to immobilize an aggressive prey. Physiological cues that may be involved include distension

  • Predation by Spined Assassin Bugs 33

    of the digestive tract, tissue dehydration, hemolymph volume, and the concen- tration of specific hemolymph components such as trehalose. In Experiment 3, nymphs that were not supplied with water began to cannibalize at a significantly younger age than nymphs that were provided with either water or a glucose solution. Again, this result is surprising as water availability did not increase the survival of first instars in Experiment 1. Assuming that the age at which nymphs begin to cannibalize is an indication of their motivation to feed, and hence their hunger level, then nymphs that were not provided with water were "hungrier" than nymphs of the same age that were provided with water. When water is available, nymphs can consume substantial amounts. First instars that had water available since hatching weighed 0.32 mg on average when they were 3 days old. In comparison, nymphs that had been deprived of water weighed only 0.24 mg on average when they were 3 days old. Possibly, distension of the gut stimulated stretch receptors of the abdominal wall, indicating to the nymph that its gut was partially full. Distension of the gut has been shown to stimulate stretch receptors which control intake of food in flies (Dethier, 1976) and the reduviid Rhodnius prolixus (Wigglesworth, 1965). Still, ingesting so much water that it lowers a nymph's motivation to feed appears counteradaptive. In fact, nymphs that do not drink appear to have an advantage since they are more aggressive and are more likely to capture prey than nymphs that do drink. Further research is needed to understand the behavioral and physiological impli- cations of drinking.

    Kin Recognition and Cannibalism

    There was no evidence that S. diadema nymphs behave differently toward kin and nonkin. This is not surprising since kin recognition among conspecifics engaged in cannibalism is relatively rare outside of the eusocial insects (Wilson, 1987). There is no evidence of kin recognition in land snail larvae (Baur, 1987), acarid mites (Radwan, 1993), several species of waterstriders (Nummelin, 1989; Carcamo and Spence, 1993), and lace bugs (Tallamy and TaUamy, 1993).

    Cannibalism has been cited as a significant obstacle to mass-rearing pred- atory insects for biological control (DeBach and Rosen, 1991). However, our results indicate that the risks and possibility of effective counter attack associated with preying on conspecifics may delay or reduce the incidence of cannibalism. If predators such as S. diadema are provided with adequate supplies of lower risk prey, losses due to cannibalism can be reduced.

    ACKNOWLEDGMENTS

    This research was supported by the Natural Sciences and Engineering Research Council of Canada. The authors thank H. Nadel for helpful discussion.

  • 34 Taylor and Schmidt

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