When to come out from a refuge: risk-sensitive and state-dependent decisions in an alpine lizard

Prey often respond to predator presence by increasing theiruse of refuges. However, unfavorable thermal conditions in refugesmight entail physiological costs for an ectothermic prey. Thus,the decision of when to come out from a refuge should be optimizedby considering the expected fitness effects of diminution ofpredation risk with time, but also by considering the cost of theloss of time spent at optimal body temperature maximizing physiological functions.The model of Ydenberg and Dill describes the trade-off betweenrisk and cost for a prey fleeing to a refuge. We present a specialcase of this model to predict how emergence time from the refugein lizards or other ectotherms should vary as a function ofrisk of predation and thermal costs of refuge use. The analysesof the variation in emergence time from a refuge of Lacertamonticola lizards in the field under two different predation risklevels supported the predictions of the model. As predicted,time spent in the refuge was longer when the threat of the initialattack had been higher, and therefore the subsequent diminutionof risk was slower, but only when lizards emerged at the sameplace where they hid. When initial body temperature was high,some lizards decreased emergence time by emerging from a differentplace. In addition, the effects of thermal costs were more relevant inthe high-risk situation. Time spent in the refuge under highrisk increased when thermal conditions of the refuge were moresimilar to thermal conditions outside (i.e., physiological costsof refuge use were lower). We conclude that optimization ofrefuge-use strategies might help lizards cope with changes in predationrisk without incurring excessive physiological costs.     

Wall Lizards Modulate Refuge Use through Continuous Assessment of Predation Risk Level

Prey species might use several possible ways to assess predation risk when encountering a predator. Animals may consider the risk level estimated in a first encounter to remain unchanged across subsequent encounters (fixed risk response), or they may update and change their responses across encounters in accordance with short‐term changes in risk levels (flexible risk response). We examined in the field how wall lizards assess risk level by analyzing time spent in refuges after simulated predator attacks. We first examined how risk was assessed when multiple consecutive sources of risk were present simultaneously. The results suggest that wall lizards assess risk based on multiple cues, such as approach speed, directness, and persistence (measured as the distance of the predator to their refuge after an attack). When risk was high lizards remained longer in their refuges. The first decision to appear partly from the refuge depended on both approach speed and persistence, whereas the decision to emerge completely depended only on persistence and not on approach speed. This suggests that wall lizards update information on predator threat and adjusted their emergence accordingly. In a second experiment, we analyzed how short‐term changes in risk level of successive attacks affected refuge use. Successive emergence times varied as a function of current risk level of each repeated attack, independently of the risk level of previous attacks. This indicated that lizards could track short‐term changes in risk level through time and modify their initial responses when required. Fine adjustments of refuge use may help lizards to minimize costs of refuge use in unfavorable and variable environments where antipredatory responses are costly.     

Can Wall Lizards Combine Chemical and Visual Cues to Discriminate Predatory from Non‐Predatory Snakes Inside Refuges?

The ability to use multiple cues in assessing predation risk is especially important to prey animals exposed to multiple predators. Wall lizards, Podarcis muralis, respond to predatory attacks from birds in the open by hiding inside rock crevices, where they may encounter saurophagous ambush smooth snakes. Lizards should avoid refuges with these snakes, but in refuges lizards can also find non‐saurophagous viperine snakes, which lizards do not need to avoid. We investigated in the laboratory whether wall lizards used different predator cues to detect and discriminate between snake species within refuges. We simulated predatory attacks in the open to lizards, and compared their refuge use, and the variation in the responses after a repeated attack, between predator‐free refuges and refuges containing visual, chemical, or visual and chemical cues of saurophagous or non‐saurophagous snakes. Time to enter a refuge was not influenced by potential risk inside the refuge. In contrast, in a successive second attack, lizards sought cover faster and tended to increase time spent hidden in the refuge. This suggests a case of predator facilitation because persistent predators in the open may force lizards to hide faster and for longer in hazardous refuges. However, after hiding, lizards spent less time in refuges with both chemical and visual cues of snakes, or with chemical cues alone, than in predator‐free refuges or in refuges with snake visual cues alone, but there were no differences in response to the two snake species. Therefore, lizards could be overestimating predation risk inside refuges. We discuss which selection pressures might explain this lack of discrimination of predatory from similar non‐predatory snakes.     

Costs of Refuge Use Affect Escape Decisions of Iberian Rock Lizards Lacerta monticola

Theoretical models of anti-predator escape behaviour suggest that prey may adjust their escape response such that the optimal flight distance is the point at which the costs of staying exceed the costs of fleeing. Anti-predatory decisions should be made based also on consequences for long-term expected fitness, such as the costs of refuge use. For example, in lizards, the maintenance of an optimal body temperature is essential to maximize physiological processes. However, if unfavourable thermal conditions of refuges can decrease the body temperature of lizards, their escape decision should be influenced by refuge conditions. Analyses of the variation in flight distances and emergence latency from a refuge for the lizard Lacerta monticola under two different predation risk levels, and their relationship with the thermal environment, supported these predictions. When risk increased, lizards had longer emergence latencies, and thus costs of refuge use increased (a greater loss of time and body temperature). In the low-risk situation, lizards that were farther from the refuge had longer flight distances, whereas thermal conditions were less important. When risk increased, lizards had longer flight distances when refuges were farther off, but also when the external heating rate and the refuge cooling rate were lower. The results suggest that, in addition to the risk of predation, expected long-term fitness costs of refuges can also affect escape decisions.     

Wall lizards combine chemical and visual cues of ambush snake predators to avoid overestimating risk inside refuges

The threat sensitivity hypothesis assumes that multiple cues from a predator should contribute in an additive way to determine the degree of risk-sensitive behaviour. The ability to use multiple cues in assessing the current level of predation risk should be especially important to prey exposed to multiple predators. Wall lizards, Podarcis muralis, respond to predatory attacks from birds or mammals by hiding inside rock crevices, where they may encounter another predator, the smooth snake, Coronella austriaca. We investigated in the laboratory whether chemical cues may be important to wall lizards for detection of snakes. The greater tongue-flick rate and shorter latency to first tongue-flick in response to predator scents indicated that lizards were able to detect the snakes' chemical cues. We also investigated the use of different predatory cues by lizards when detecting the presence of snakes within refuges. We simulated successive predator attacks and compared the propensity of lizards to enter the refuge and time spent within it for predator-free refuges, refuges containing either only visual or chemical cues of a snake, or a combination of these. The antipredatory response of lizards was greater when they were exposed to both visual and chemical cues than when only one cue was presented, supporting the threat sensitivity hypothesis. This ability may improve the accuracy of assessments of the current level of predation risk inside the refuge. It could be especially important in allowing lizards to cope with threats posed by two types of predators requiring conflicting prey defences.     

When to Come Out from a Refuge: Balancing Predation Risk and Foraging Opportunities in an Alpine Lizard

Prey often respond to predator presence by increasing their use of refuges, but because this strategy may be costly, the decision regarding when to come out from a refuge should be optimized. The loss of foraging opportunities may be one of the main costs when safer microhabitats (i.e. refuges) are also the poorest in terms of their foraging profitability. We present the results of an experimental field study to test whether emergence times from a refuge of the Iberian rock lizard, Lacerta monticola, vary as a function of expected foraging opportunities and level of satiation of the lizard. As predicted, short‐term fluctuations in availability of food influenced emergence times; when a lizard had just detected some food in the recent past, emergence times decreased greatly, because the loss of opportunities for foraging increased costs of refuge use. Furthermore, the characteristics and success of the encounter with food, nutritional state of lizards, and the added possibility of capturing new food items influenced the duration of hiding times. Therefore, foraging requirements and avoidance of predators may be conflicting demands that L. monticola lizards balance by modifying the duration of time spent in refuges.     

Pregnant female lizards Iberolacerta cyreni adjust refuge use to decrease thermal costs for their body condition and cell-mediated immune response

Lizards often respond to increased predation risk by increasing refuge use, but this strategy may entail a loss of thermoregulatory opportunities, which may lead to a loss of body condition. This may be especially important for pregnant oviparous female lizards, because they need to maintain optimal body temperatures as long as possible to maximize developmental embryos rate until laying. However, little is known about how increased time spent at low temperatures in refuges affects body condition and health state of pregnant female lizards. Furthermore, it is not clear how initial body condition affects refuge use. Female Iberian rock lizards forced to increase time spent at low temperatures showed lower body condition and tended to show lower cell-mediated immune responses than control females. Therefore, the loss of thermoregulatory opportunities seems to be an important cost for pregnant females. Nevertheless, thereafter, when we simulated two repeated predatory attacks, females modified refuge use in relation to their body condition, with females with worse condition decreasing time hidden after attacks. In conclusion, female lizards seemed able to compensate increased predation risk with flexible antipredatory strategies, thus minimizing costs for body condition and health state.     

Effect of Risk on Aspects of Escape Behavior by a Lizard, Holbrookia propinqua, in Relation to Optimal Escape Theory

Prey must balance gains from activities such as foraging and social behavior with predation risk. Optimal escape theory has been successful in predicting escape behavior of prey under a range of risk and cost factors. The optimal approach distance, the distance from the predator at which prey should begin to flee, occurs when risk equals cost. Optimal escape theory predicts that for a fixed cost, the approach distance increases as risk increases. It makes no predictions about approach distance for prey in refuges that provide only partial protection or about escape variables other than approach distance, such as the likelihood of stopping before entering refuge and escape speed. By experimentally simulating a predator approaching keeled earless lizards, Holbrookia propinqua, the predictions of optimal escape theory for two risk factors, predator approach speed and directness of approach were tested. In addition, predictions that the likelihood of fleeing into refuge without stopping and the speed of escape runs increase with risk, in this case predator approach speed, and that lizards in incompletely protective refuges permit closer approach than lizards not in refuges were also tested. Approach distance increased with predator approach speed and directness of approach, confirming predictions of optimal escape theory. Lizards were more likely to enter refuge and ran faster when approached rapidly, verifying that predation risk affects escape decisions by the lizards for escape variables not included in optimal escape theory. They allowed closer approach when in incompletely protective refuges than when in the open, confirming the prediction that risk affects escape decisions while in refuge. Optimal escape theory has been highly successful, but testing it has led to relative neglect of important aspects of escape other than approach distance.     

You can’t run but you can hide: refuge use in frog tadpoles elicits density-dependent predation by dragonfly larvae

The potential role of prey refuges in stabilizing predator–prey interactions is of longstanding interest to ecologists, but mechanisms underlying a sigmoidal predator functional response remain to be fully elucidated. Authors have disagreed on whether the stabilizing effect of prey refuges is driven by prey- versus predator-centric mechanisms, but to date few studies have married predator and prey behavioural observations to distinguish between these possibilities. We used a dragonfly nymph–tadpole system to study the effect of a structural refuge (leaf litter) on the predator’s functional response, and paired this with behavioural observations of both predator and prey. Our study confirmed that hyperbolic (type II) functional responses were characteristic of foraging predators when structural cover was low or absent, whereas the functional response was sigmoidal (type III) when prey were provided with sufficient refuge. Prey activity and refuge use were density independent across cover treatments, thereby eliminating a prey-centric mechanism as being the genesis for density-dependent predation. In contrast, the predator’s pursuit length, capture success, and handling time were altered by the amount of structure implying that observed shifts in density-dependent predation likely were related to predator hunting efficiency. Our study advances current theory by revealing that despite fixed-proportion refuge use by prey, presence of a prey refuge can induce density-dependent predation through its effect on predator hunting strategy. Ultimately, responses of predator foraging decisions in response to changes in prey availability and search efficiency may be more important in producing density-dependent predation than the form of prey refuge use.     

Experimental manipulation reveals the importance of refuge habitat temperature selected by lizards

Refuges provide shelter from predators, and protection from exposure to the elements, as well as other fitness benefits to animals that use them. In ectotherms, thermal benefits may be a critical aspect of refuges. We investigated microhabitat characteristics of refuges selected by a heliothermic scincid lizard, Carlia rubrigularis, which uses rainforest edges as habitat. We approached lizards in the field, simulating a predator attack, and quantified the refuge type used, and effect of environmental temperatures (air temperature, substrate temperature and refuge substrate temperature) on the amount of time skinks remained in refuges after hiding (emergence time). In respone to our approach, lizards were most likely to flee into leaf litter, rather than into rocks or woody debris, and emergence time was dependent on refuge substrate temperature, and on refuge substrate temperature relative to substrate temperature outside the refuge. Lizards remained for longer periods in warmer refuges, and in refuges that were similar in temperature to outside. We examined lizard refuge choice in response to temperature and substrate type in large, semi‐natural outdoor enclosures. We experimentally manipulated refuge habitat temperature available to lizards, and offered them equal areas of leaf litter, woody debris and rocks. When refuge habitat temperature was unmanipulated, lizards (85%) preferred leaf litter, as they did in the field. However, when we experimentally manipulated the temperature of the leaf litter by shading, most skinks (75%) changed their preferred refuge habitat from leaf litter to woody debris or rocks. These results suggest that temperature is a critical determinant of refuge habitat choice for these diurnal ectotherms, both when fleeing from predators and when selecting daytime retreats.     

Optimal time to emerge from refuge

Factors affecting emergence by prey that enter refuges when approached by predators have been studied intensively, but only two theoretical models predict how long prey should remain in a refuge before emerging. We argue that prey can make better decisions than allowed by one model; the other model describes cases in which predators wait for prey to emerge. We present optimality models that permit prey to select a time to emerge that maximizes fitness. When in a refuge, a prey cannot obtain benefits outside; emerging too soon can be catastrophic, but delaying emergence entails loss of fitness. If predators resume foraging quickly rather than engaging in strategic waiting games, current theory suggests that prey emerge when the costs of remaining in a refuge and of emerging are equal. However, prey often can do better by emerging at the time maximizing fitness rather than when benefits equal costs (i.e. when prey break even). Optimal emergence time depends on initial fitness, benefits lost by remaining in refuge, and the decay rate of predation risk. Benefits lost if a prey is killed are modelled separately from benefits that contribute to lifetime fitness, even if the prey is killed (individual reproduction, altruism). Fitness of prey emerging at the optimal emergence time may be greater than, equal to or less than initial fitness. Break-even and optimality models base predictions on the opposing effects of risk and loss of benefits. Thus, many empirically verified predictions are identical at the ordinal level although differing quantitatively. Optimality models provide novel testable predictions for the effects of initial fitness, benefits, and, for ectotherms, the rate of cooling in refuge. They predict earlier emergence for equal retainable benefits than for those lost upon death.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 375–382.     

食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。     

Plesiomorphic Escape Decisions in Cryptic Horned Lizards (Phrynosoma) Having Highly Derived Antipredatory Defenses

Escape theory predicts that the probability of fleeing and flight initiation distance (predator–prey distance when escape begins) increase as predation risk increases and decrease as escape cost increases. These factors may apply even to highly cryptic species that sometimes must flee. Horned lizards (Phrynosoma) rely on crypsis because of coloration, flattened body form, and lateral fringe scales that reduce detectability. At close range they sometimes squirt blood‐containing noxious substances and defend themselves with cranial spines. These antipredatory traits are highly derived, but little is known about the escape behavior of horned lizards. Of particular interest is whether their escape decisions bear the same relationships to predation risk and opportunity costs of escaping as in typical prey lacking such derived defenses. We investigated the effects of repeated attack and direction of predator turning on P. cornutum and of opportunity cost of fleeing during a social encounter in P. modestum. Flight initiation distance was greater for the second of two successive approaches and probability of fleeing decreased as distance between the turning predator and prey increased, but was greater when the predator turned toward than away from a lizard. Flight initiation distance was shorter during social encounters than when lizards were solitary. For all variables studied, risk assessment by horned lizards conforms to the predictions of escape theory and is similar to that in other prey despite their specialized defenses. Our findings show that these specialized, derived defenses coexist with a taxonomically widespread, plesiomorphic method of making escape decisions. They suggest that escape theory based on costs and benefits, as intended, applies very generally, even to highly cryptic prey that have specialized defense mechanisms.     

Can protective attributes of artificial refuges offset predation risk in lizards?

Artificial refuges are often used to supplement habitat in areas where natural shelters have been degraded or removed. Although artificial refuges are intended to support particular species, they may be equally attractive and accessible to others, including predators. We explored the influence of snake predation risk and shelter attributes on the overnight use of different artificial refuges (timber, tiles, and iron) using the predator‐prey relationship between Boulenger's skink, Morethia boulengeri and the curl snake, Suta suta. We collected adult M. boulengeri from two bioregions in south‐eastern Australia: the Riverina, where the two species co‐occur, and the South Western Slopes, where S. suta does not occur. Two adult S. suta were collected for use as chemical donors. We conducted four experiments on overnight refuge choice to determine: (i) predator‐scent avoidance, (ii) artificial refuge preferences, (iii) a trade‐off between a preferred refuge and predator‐avoidance, and (iv) the effect of gap height on refuge preference. We found that skinks avoided predator‐scented refuges in favour of identical, but unscented refuges. Skinks preferred timber refuges, and most skinks maintained this preference when predator‐scent was added. However, when gap height was manipulated, skinks shifted to the refuge with the smallest gap. Skinks displayed complex regional variation in behaviour; skinks from both bioregions avoided predator‐scent, but in the trade‐off experiment, skinks from the South Western Slopes were less likely to avoid predator‐scented timber refuges than those from the Riverina. Our findings suggest that protective refuge attributes, such as small gap height, can offset the risk implied by predator‐scent within a refuge. This study highlights the need to consider predator‐prey interactions when designing and using artificial refuges for habitat restoration or biological monitoring.     

Magnitude of food reward affects escape behavior and acceptable risk in Balearic lizards, Podarcis lilfordi

During encounters with predators, prey must balance the degreeof risk against the loss of fitness-enhancing benefits suchas feeding and social activities. Most studies of tradeoffsbetween risk and cost of escaping have measured flight initiationdistance and time to emerge from refuge, for which theory providesrobustly supported predictions. Tradeoffs involving other aspectsof encounters, including distance fled and time between escapeand return to a food source, have received little theoreticalor empirical attention. By adapting models of flight initiationdistance and time between entry into refuge and emergence, wepredict effects of predation risk and cost on distance fledand time to return to a source of benefit after fleeing. Actingas simulated predators that approached at a fixed speed, weconducted an experimental field study to test the hypothesesthat flight initiation distance, distance fled, and time toreturn to food by Balearic lizards (Podarcis lilfordi) decreasewith the presence and amount of insect food. Predictions ofthe models were strongly supported, including those for distancefled and return time, but predictions for other cost factorsand predation risk factors remain to be tested.     

Differential Avoidance of Snake Odours by a Lizard: Evidence for Prioritized Avoidance Based on Risk

Most studies of predator avoidance behaviours have focussed on single‐predator systems, despite the fact that prey often are confronted with predator rich environments. In the presence of more than one predator, prey may have to choose between avoiding one predator over another. How prey cope with exposure to several enemies simultaneously remains largely untested. In this study I set out to investigate if skinks showed preferential avoidance of snake odours based on the relative predation risk posed by different snake species. This relative predation risk was estimated using information on density, diet specificity and foraging habit of each snake species. I tested retreat‐site selection in two‐choice tests, where lizards chose between different combinations of control and snake treated retreat‐sites as well as two retreat‐sites treated with different snake species odours. Lizards preferred control–treated retreat‐sites to those treated with snake odours and showed a differential avoidance response to refuges treated with odours from different snake species. There was strong evidence to suggest that lizards preferentially avoided refuges with the odours of the snake that posed the greatest predation risk, the white‐lipped snake (Drysdalia coronoides). Naïve juvenile lizards were also tested and their response was similar to the adults demonstrating that the behaviour is innate and not the result of higher encounter rates of more common snake odours. To my knowledge this is one of the first studies to demonstrate that prey can prioritize avoidance to a single most dangerous predator in the face of several predators and conflicting avoidance responses.     

Prey refuges as predator hotspots: ocelot (Leopardus pardalis) attraction to agouti (Dasyprocta punctata) dens

We tested the hypothesis that prey refuges attract predators, leading to elevated predator activity in the vicinity of refuges. We used camera traps to determine whether the spatial activity of a predator, the ocelot (Leopardus pardalis), was biased toward refuge locations of its principal prey, the agouti (Dasyprocta punctata). We radio-tracked agoutis at night to locate active refuges and compared the activity of ocelots between these refuges and surrounding control grid locations. We found that ocelots visited the area near agouti refuges significantly more often and for longer periods of time than control locations, and that they actively investigated the refuge entrances. Both occupied and unoccupied refuges were visited, but the duration of inspection was longer at occupied refuges. As the ocelots could probably not see the agoutis within the refuges, olfaction likely cued foraging ocelots. Two refuges were repeatedly visited by the same ocelots on different days, suggesting spatial memory. Overall, our results suggest that predators can be attracted to prey refuges or refuging prey. The benefits to prey of staying nearby a refuge would thus be counterbalanced by higher likelihoods of predator encounter. This should stimulate prey to use multiple refuges alternatingly and to not enter or exit refuges at times of high predator activity.     

Balancing predation risk,social interference,and foraging opportunities in backswimmers,<Emphasis Type="Italic"> Notonecta maculata</Emphasis>

Loss of foraging opportunities and intraspecific competition for prey may be important costs of using refuges, because a hiding animal is unable to use or defend its foraging area from conspecific intrusions. Thus, animals should balance antipredator demands with other requirements in deciding when to come out from a refuge after a predators unsuccessful attack. Observations on foraging and social interactions of backswimmers Notonecta maculata suggest that foraging may be costly in terms of intraspecific agonistic interactions. When prey density is low, increasing the probability of finding a prey may require active exploration of a larger area, but this also increases the probability of encountering a competitor. After simulated exposure to predators, unfed bugs resumed feeding positions after a significantly shorter hiding period than recently fed bugs. We hypothesized that hiding time may also be reduced by recent interactions with conspecific competitors, due to an increased perceived need to defend feeding opportunities. Thus, when a predator attack occurred immediately after an agonistic conspecific interaction, backswimmers resumed feeding positions more quickly, and closer to the original position from which they were disturbed, suggesting short-term defense of particular positions. We conclude that when foraging, backswimmers balance the benefits of finding prey with the costs of predation risk and social interference in deciding their foraging strategy.Communicated by P.K. McGregor     

Consequences of refuge for the functional response of Dermestes ater (Coleoptera: Dermestidae) to Musca domestica (Diptera: Muscidae)

It is well known that a predator has the potential to regulate a prey population only if the predator responds to increases in prey density and inflicts greater mortality rates. Predators may cause such density-dependent mortality depending on the nature of the functional and numerical responses. Yet, few studies have examined the relationship between the addition of refuges and the characteristic of functional response fits. We investigated whether addition of a refuge changed the type of functional response exhibited by Dermestes ater on Musca domestica, comparing the inherent ability of D. ater to kill houseflies in the absence and in the presence of refuge. An additional laboratory experiment was also carried out to assess handling and searching times exhibited by D. ater. Logistic regression analyses revealed a type III functional response for predator–prey interaction without refuge, and results were described by the random predator equation. The mean number of prey killed did not differ between experimental habitats, indicating that the addition of refuge did not inhibit predation. However, predators that interacted with prey without refuge spent less time searching for prey at higher densities, increasing predatory interaction. We concluded that this interaction may be weak, because data from experiments with refuge fitted poorly to models. However, the high variability and the nonsignificance of the data from the experiment with refuge show the importance of refuge for promoting spatial heterogeneity, which may prevent prey extinction.     

Choosing among alternative refuges: Distances and directions

Many prey flee to refuges to escape from approaching predators, but little is known about how they select one among many refuges available. The problem of choice among alternative refuges has not been modeled previously, but a recent model that predicts flight initiation distance (FID = predator–prey distance when escape starts) for a prey fleeing to a refuge provides a basis for predicting which refuge should be chosen. Because fleeing is costly, prey should choose to flee to the refuge permitting the shortest FID. The model predicts that the more distant of two refuges can be favored if it is not too far and if the prey's trajectory to the farther refuge is more away from the predator than the direction to the nearer refuge. The difference in predicted FID between the farther and nearer refuges increases curvilinearly as the interpath angle for the farther refuge increases. The difference in predicted FID between the farther and nearer refuges increases linearly as the distance to the farther refuge increases. An isocline describing where nearer and farther refuges are equally favored shows a negative curvilinear relationship between interpath angle and prey distance to the farther refuge. In the region below the isocline, the farther refuge is favored, whereas above the isocline the prey should flee to the nearer refuge.