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Vigilance while feeding by female Dall’s sheep (Ovis dalli dalli Nelson, 1884): interactions among predation… Frid, Alejandro 1994

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VIGILANCE WHILE FEEDING BY FEMALE DALL'S SHEEP (Ow's dalli dalli Nelson, 1884): INTERACTIONS AMONG PREDATION RISK FACTORS by ALEJANDRO FRID B.Sc. The Evergreen State College, 1988 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Animal Science)  We accept this thesis as conforming to the required)Sjtandard  THE UNIVERSITY OF BRITISH COLUMBIA September 1994 ©Alejandro Frid, 1994  In presenting this thesis  in partial fulfilment  of  the  requirements  for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of department  or  by  his  or  her  representatives.  It  is  understood  that  copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  /+vuvn<A/TWivn^V  3  ->c\-ewo C\-ewc<^  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  Q,\  5/fh  ii ABSTRACT I proposed and tested the Interactive Risk Factors Hypothesis (IRFH), in which predation risk factors have an interactive (multiplicative) rather than an independent (additive) effect on vigilance while feeding. Four predictions were tested on adult female Dall's sheep (Ovis dalli dalli) in the wild: 1) Vigilance increases with decreasing group size, but the magnitude of this response becomes smaller as (a) distance to cliffs decreases, and/or (b) distance to obstructive cover increases. 2) Vigilance increases with increasing distance to cliffs, but the magnitude of this response becomes smaller as (a) group size increases, and/or (b) distance to obstructive cover increases. 3) Vigilance increases with decreasing distance to obstructive cover, but the magnitude of this response becomes smaller as (a) group size increases, and/or (b) distance to cliffs decreases. 4) The magnitude of any of the above responses will be greater for mothers with neonates than for adult females within 2 months prior to the lambing season. Predictions 1a, 2a, and 4 were supported, implying that when risk is low due to other conditions, animals may increase vigilance very little or not at all in response to a particular factor that would otherwise have a strong effect. A priori analysis showed that distance to obstructive cover had no effect on vigilance (predictions 1 b, 2b and 3), which neither rejects nor supports the hypothesis. This result, however, was probably due to incomplete field measurements and a  iii posteriori analysis suggested that distance to obstructive cover does have an interactive effect on vigilance. The IRFH is a general hypothesis that should be able to handle any other factors that affect risk, and is potentially applicable to any terrestrial prey. Testing for interactions among predation risk factors may provide a more realistic approach to understanding vigilance than merely assuming that such factors have independent effects.  iv  TABLE OF CONTENTS  Abstract  ii  Table of Contents  iv  List of Tables  v  List of Figures  vi  Acknowledgments  vii  INTRODUCTION  1  METHODS Study Site Characteristics Reproductive Class and Group Size Criteria Recording Behaviour Statistical Analyses RESULTS Effects of Group Size and Distance to Cliffs Effects of Distance to Cover Effects of Reproductive Class Position in Group: a Non-Effect? Predator Records  6 6 8 11 14 17 17 22 23 23 25  DISCUSSION  26  REFERENCES  32  APPENDIX A: Summary of Terrestrial Predators  37  V  LIST OF TABLES  TABLE 1. Reduced regression model estimating vigilance responses of pre-lambing females  18  TABLE 2. Reduced regression model comparing vigilance responses between pre-lambing females and mothers  21  vi LIST OF FIGURES FIGURE 1: Interactive versus independent risk factors models  4  FIGURE 2: Estimated response of vigilance to the interaction of group size and distance to cliffs for pre-lambing females  19  FIGURE 3: Response of vigilance to the interaction of reproductive status and distance to cliffs for adult females  24  VII  ACKNOWLEDGMENTS David Shackleton, Lee Gass, Alton Harestad, Gail Lotenberg, Wes Hochachka, Andrea Byrom, Karen Hodges, Kim Cheng, Mark O'Donoghue, Marco Scaife, Matt Kirchhoff, C.J. Krebs, A.R.E. Sinclair and Manfred Hoefs critically read earlier drafts of this manuscript. I am particularly indebted to Gail for doing half of the field work and most of the thinking, to Wes for the constant fire of his statistical e-mails, and to Mark for relaying Wes' messages via walkietalkie while I stood in pre-dawn, winter darkness on the roof of my Yukon cabin. Extra special thanks are also due to two of my committee members, David and Lee, both outstanding teachers and great folks who gave constant support and advice. Manfred Hoefs also shared his knowledge of the study area, both published and unpublished. The Kluane Boreal Forest Ecosystem Project shared unpublished data, and provided a surrogate campus in the Yukon. Alistair Blachford programmed the event recorder and taught me AWK programming (no small feat of patience). Jasper Stephens and Karen Hodges assisted in data collection. Dick Repasky, Liz Hofer and David Hik contributed various insights. Frank Doyle suggested that wind might affect vigilance. Paul Alaback lent a notebook computer and advice for vegetation data that I never analyzed. The computer wizardry of Steve Wilson and Gillies Galzy saved me from many epic situations. David Ward, John Boulanger, Ray Peterson and his graduate students helped with preliminary analysis. Staff at the Animal Science office were always helpful and tolerant of my photocopying catastrophes. Kluane National Park Reserve provided a cabin and other essential logistical support. Funding was provided by two scholarships from the Northern Scientific Training Program.  1 INTRODUCTION Vigilance is not mutually exclusive with processing food, but is largely mutually exclusive with food searching and handling. When plant density and biomass are high and intake rate is constrained mainly by processing rates, vigilance by herbivores can be "cost-free" (lllius and FitzGibbon 1994). When food plants are scarcer, however, encounter and handling rates limit food intake thereby creating a trade-off between vigilance and the foraging needs of herbivores (lllius and FitzGibbon 1994; also see review in Lima and Dill 1990). Wild herbivores and other prey could experience the latter scenario for much, perhaps most, of their lives. Thus, the trade-off between food intake and vigilance has been a major evolutionary force in shaping their behaviour (Lima and Dill 1990). Although food density, intra-group competition and other factors not directly related to predation may also affect vigilance (review in Elgar 1989, but see Saino 1994), the assumption that vigilance is largely concerned with looking for predators is strongly supported by observations of Thomson's gazelles {Gazella thomsoni). FitzGibbon (1989) found that when having a choice of two gazelles of the same sex feeding within 5 m of each other and on the edge of the same group, cheetahs {Acinonyxjubatus) chased the less vigilant gazelle in 14 out of 16 chases. Furthermore, less vigilant gazelles delayed longer before fleeing and thus were more likely to be killed during an attack (FitzGibbon 1989).  2 While a more vigilant individual may be safer, excessive vigilance may also bring an unnecessary loss of feeding opportunities. Thus, the optimal level of vigilance during feeding should be sensitive to predation risk factors (reviews in Elgar 1989 and Lima and Dill 1990). This hypothesis is based on strong theoretical grounds (e.g. Lima 1987) and is supported by empirical studies of various taxa in which vigilance decreased as group size increased (reviews in Elgar 1989 and Lima and Dill 1990; Saino 1994); as distance to visually obstructive cover increased (review in Elgar 1989; Lazarus and Symonds 1992); and as distances to a safe refuge decreased (Risenhoover and Bailey 1985; review in Elgar 1989). Also, studies of ungulates have concluded that mothers become less vigilant as their offspring become older and thus less vulnerable (Risenhoover and Bailey 1985; FitzGibbon and Lazarus 1994). Responses of vigilance to the independent effects of the above factors are relatively well known, but there has been little effort to understand interactions among these factors. An exception is Risenhoover and Bailey's (1985) study of bighorn sheep (Ovis canadensis) which implicitly assessed interactions and which concluded that foraging efficiency (as affected by vigilance costs) was more sensitive to the effects of distance to refuge (cliffs) and density of visually obstructive cover in groups of 1-5 than in groups of 6-10 and 11-36 sheep. Their conclusion, however, was based on a non-significant regression.  3 In this paper I propose the Interactive Risk Factors Hypothesis (IRFH), and explicitly test whether predation risk factors have an interactive (multiplicative) rather than an independent (additive) effect on vigilance. In the IRFH I propose that the magnitude of the vigilance response to factor "A" may be large when risk from factors "B" and "C" is high, but decreases as the latter becomes smaller. This implies that when risk from factors "B" and "C" is low, individuals can afford - without significantly jeopardizing safety - to increase vigilance very little or not at all as risk due solely to factor "A" increases. The alternative hypothesis is that predation risk factors have an independent rather than interactive effect on vigilance. This alternative implies that vigilance always increases at a constant magnitude as risk due solely to factor "A" increases, regardless of whether risk from factors "B" and "C" is high or low. Thus, a response to factor "A" predicted by an independent model overemphasizes safety at the expense of foraging when risk from factors "B" and "C" is low, and overemphasizes foraging at the expense of safety when risk from factors "B" and "C" is high. In contrast, safety and foraging are always balanced in the interactive model (Fig. 1). Dall's sheep (0. dalli dalll) are well suited for testing the IRFH. Like other mountain Caprinae (Geist 1987), they can find almost complete security from predators on cliffs (Murie 1944; Sumanik 1987) - where food is usually scarce but also feed in food-rich areas away from cliffs. They have a wide range of group sizes, and live in places where large carnivores are still abundant.  4  max.  mid  mm. low  high  Risk from Other Factors ("B" & "C")  FIGURE 1. Interactive versus independent risk factors models. In the independent model (broken lines), the vigilance response to factor "A" is constant, regardless of risk from factors "B" and "C". In the interactive model (solid line), the vigilance response to factor "A" is sensitive to risk from factors "B" and "C". Thus, a response to factor "A" predicted by an independent model overemphasizes safety at the expense of foraging when above the diagonal line of the interactive model, and overemphasizes foraging at the expense of safety when below the same line. In contrast, safety and foraging are always balanced in the interactive model.  5 Furthermore, in other taxa it may not be obvious whether vegetation cover is visually obstructive or protective, leading to confounding interpretations of the utility of vigilance (Lima 1987; Lazarus and Symonds 1992). Mountain sheep (Ovis spp.), however, appear not to use visually obstructive vegetation cover (hereon referred to as "cover") for protection (Geist 1971), and thus allow for a more straightforward interpretation of this factor. For adult female sheep engaged in a foraging bout, I tested the following IRFH predictions: 1) Vigilance increases with decreasing group size, but the magnitude of this response becomes smaller as (a) distance to cliffs decreases, and/or (b) distance to cover increases. 2) Vigilance increases with increasing distance to cliffs, but the magnitude of this response becomes smaller as (a) group size increases, and/or (b) distance to cover increases. 3) Vigilance increases with decreasing distance to cover, but the magnitude of this response becomes smaller as (a) group size increases, and/or (b) distance to cliffs decreases. 4) The magnitude of any of the above responses will be greater for mothers with neonates (young <3 weeks old) than for adult females within 2 months prior to the lambing season.  6 METHODS Study Site Characteristics Study site and season Fieldwork took place on Sheep Mountain (SrOO'-enO'N, 138°30'138°150'W), Kluane National Park Reserve, Yukon Territory, Canada, between 13 March and 31 May of 1993. Sheep Mountain has a semi-arid, continental climate, and its phytogeography has been described in detail by et al. (1975). Its southerly slopes, along with adjacent Williscroft Creek, are the traditional winter and lambing range of a population which during the spring of 1993 was estimated by Hoefs (1993) at 300 sheep. This estimate included about 100 males (3 years and older), 150 adult females and two year-olds of both sexes (pooled), 10 yearlings, and 40 to 50 young of the year (Hoefs 1993). Most lambs are born during May and early June (Hoefs and Cowan 1979; Bunnell 1980). Except for the occasional harvest by native people, which was legalized in the 1970's, this population has not been legally hunted since 1942.  Risk-related habitat attributes Sheep Mountain is a mosaic of open areas with unobstructed visibility, and areas of visually obstructive cover made up of Salix spp., Picea glauca and Populus spp. Cliffs of different sizes are present throughout the study area, but some of the lower slopes used by sheep may be >500 m from them (see map by Hoefs et al. 1975). Given that predators such as wolves (Canis lupus) can  7 maneuver on extremely rugged terrain (Hoefs etal. 1986; Sumanik 1987), small isolated outcrops are unlikely to provide sufficient safety for sheep. Thus, I defined cliffs as continuous areas of exposed bedrock with a minimum incline of 45°, reaching a minimum height of 20 m and minimum width of 100 m. Most cliffs in the study area were much larger and steeper.  Predators At Sheep Mountain, coyotes (Canis latrans) are the main predators of adult sheep. Other potential predators include wolves, wolverines {Gulo gulo), grizzly bears (Ursus arctos) and lynx (Felis lynx). In addition to being at risk from these predators, very young lambs can also be taken by golden {Aquila chrysaetos) and bald (Haliaeetus leucocephalus) eagles, and red foxes (Vulpes vulpes) (Hoefs and Cowan 1979; Buries and Hoefs 1984; Nette etal. 1984; Hoefs et al. 1986). During the study, however, predation pressure was particularly low. I recorded my data during a low in the 10-year population cycle of snowshoe hares {Lepus amehcanus: e.g. Krebs et al. 1986), which are the winter staple of coyotes and lynx (Keith et. al 1977). In a study area with its western boundary only 5 km away from Sheep Mountain, the populations of these predators plunged in response to hare declines. At the onset of the 1992-93 winter, lynx and coyote populations were estimated to be, respectively, one fourth and one fifth of what they had been during the previous peak of the hare cycle (Kluane  8 Boreal Forest Ecosystem Project, Boutin ef a/., pers. comm.). By the time my study began in late winter, lynx and coyotes were probably even scarcer. The extreme coyote decline coincided with a sheep population size that was slightly larger than the average recorded since 1969 (Hoefs 1975, 1993), suggesting a particularly low ratio of this main predator to sheep. To document the relatively low predation risk experienced by sheep during my study, I recorded all coyote vocalizations, predator sightings, and sheep-predator interactions that I was aware of. When predators interacted with sheep or coyotes vocalized either during the focal animal sample or within 2.0 h prior to it (N=15), I considered "predator presence" to be a factor potentially affecting vigilance. Sample sizes were inadequate for analysis of direct predator effects on vigilance (only in four out of 124 occasions did sheeppredator interactions occur during my sample). Thus, I excluded all samples with "predator presence" from analyses.  Reproductive Class and Group Size Criteria Reproductive classes analyzed The only reproductive classes I analyzed were adult females (>2.75 years old, sensu Hoefs and Cowan 1979) within 6 weeks prior to the 1993 lambing season, and mothers with lambs that were <3 weeks old. For brevity, I will refer to the former as "pre-lambing females" and to the latter as "mothers". I do not know what proportion of pre-lambing females were pregnant. I determined  9 whether a sheep was a mother by her close and constant proximity to a neonate or, when this was not obvious, whether I saw her nurse. Prior to data recording, I spent up to 30 min of preliminary observation to confirm the reproductive and/or age class of focal animals. If I was unsure of a sheep's class, I did not collect data.  Defining a group Deciding which individuals belong to a group and which do not is one of the most overlooked issues in the methodology of behavioural studies. Ambiguities arise when animals are not tightly clumped, particularly if individuals enter and leave clusters of conspecifics during short periods of time (Martin and Bateson 1986). Some ungulate studies have offered either no definition (e.g. Berger 1978, 1991; Berger et al. 1983; Risenhoover and Bailey 1985; Prins and lason 1989) or an ambiguous one (e.g. Berger and Cunningham 1988). Still others have defined groups on the basis of some arbitrary inter-individual distance (e.g. Alados 1985; FitzGibbon 1990; Scheel 1993; Frid 1994). While the latter may be convenient, it is also tautological. Small shifts of interindividual distances are not necessarily biologically meaningful, and a definition of group should be robust to them. I defined a group as a set of individuals which, in terms of the structural attributes of the environment, were under similar predation risk. In other words, I considered sheep to be in the same group if they shared an open space  10 contained by the same cover and/or cliffs, or if they were on the same aspect of the same cliff. This rationale is based on the fact that cover may hide predators (e.g. Prins and lason 1988) and cliffs may be refuges for sheep (Murie 1944; Sumanik 1987). Perhaps most importantly, these 3-dimensional structures may visually separate sheep from each other, affecting their ability to stay together in large groups (Jarman 1974), which ultimately affects predation risk (review in Elgar 1989). The following observation of a coyote chase supports this rationale. Fifteen sheep (adult females and juveniles) were about 350 m from the nearest cliff when a single coyote ran towards them. The sheep reacted with a short run, stopped, clustered tightly, and turned staring at the coyote. Shortly after, the coyote left without attempting any further attack. Only 75-100 m from the attacked group, but visually separated by a strip of forest, 11 sheep not only showed no reaction to the coyote, but continued to feed during the attack. A shortcoming of my group definition is that it does not address social bonds. While social bonds might not affect how group size dilutes the probability of an individual being preyed on (Hamilton 1971), they might affect vigilance by determining whether a group has sentinels (review in Lima and Dill 1990). Given the short term nature of my study and the fact that animals were unmarked, it was impossible to consider social bonds in the definition. On the other hand, my group definition has biological validity because it addresses factors that affect both group cohesiveness and the boundaries of safe and dangerous zones. Furthermore, as long as animals are in a 3-dimensional  11 habitat — with cliffs and/or cover to define spaces - the definition is replicable for other ungulate studies.  Determining size of groups with neonates According to FitzGibbon and Lazarus (1994), vigilance by neonates has low utility because neonates may not yet recognize that predators are dangerous. This implies that when neonates are part of a group, total group size is a misleading indicator of group vigilance. Thus, the total number of individuals minus the number of neonates may be a more adequate measure of group size for comparing the vigilance of mothers and pre-lambing females. Using the latter measure of group size was easy to justify for my study. My observations of mothers took place early in the lambing season, when mother-young pairs associated with other such pairs, but before they coalesced into larger groups that include non-reproductive individuals. Thus, for most of my observations the mother-neonate ratio was 1:1 and both measures of group size were strongly correlated (ISM 9, r=0.97, P<0.01).  Recording Behaviour Behaviour definitions I considered sheep to be handling food if they did not walk and kept their mouths on or within one jaw-length of the vegetation that I assumed they were clipping. I considered sheep to be searching for food if they took one or more  12 steps away from either the vegetation patch where they had been handling food or from where they had stood in vigilant posture. I considered sheep to be vigilant if they interrupted food searching or handling to stand with the head raised above shoulder height.  Focal animal sampling Collection of data used for analyses began after 12 days of preliminary behavioural observations. This practice period allowed observers to fine tune recording skills. To minimize disturbance to the focal animal and potential predators, observers used spotting scopes and were >200 m from focal animals. I used continuous recording of focal individuals (Martin and Bateson 1986) to measure the time sheep spent vigilant, food searching and food handling during feeding bouts. From these records, which were timed to the nearest second, I calculated the proportions of observation time that sheep spent vigilant. A notebook computer programmed as an event recorder was the recording medium. Simultaneously with the continuous recording, a second observer recorded the focal animal's group size and distances to the nearest cliffs and nearest cover with an instantaneous scan (Martin and Bateson 1986) at the start of the sample and every subsequent 3 min. These measurements were averaged to describe the "mean" conditions which may have been affecting focal animals' vigilance (group size rarely changed during a recording session). To  13 estimate the distances recorded during scans, observers used the 1:6200 phytogeographic map of Hoefs et al. (1975), as well as known reference points on the landscape (sheep torso lengths, flagging, the length of cliff bands, etc). One oversight is that observers measured distance to the nearest cover only, and I did not account for the potential effect of having cover in more than one direction (as in a clearing surrounded by forest). During scans, observers also recorded whether an animal's position in the group was central or peripheral. I considered position in the group to be undefined if group geometry was linear or if there were <5 animals in the group. Recording sessions began when sheep were either handling or searching for food. This recording rule might underestimate vigilance in relation to the other two activities (Altmann 1974), but the bias should be constant and have little bearing on analyses of vigilance responses to risk. Recording sessions ended either after 15 min (79% of all samples) or if the animal stopped handling food plants for 1 min. If the latter occurred, I eliminated the last minute from the sample to exclude the transition to non-feeding activities. I assumed that these criteria (Underwood 1982,1983) limited my sampling to animals that were feeding intensively, and thus that individual differences in short term hunger caused little variability of vigilance (review in Krebs and Kacelnik 1991) between my samples.  14 Selecting a focal animal When selecting a focal animal for observation, I attempted to evenly distribute sampling throughout the entire range of conditions used by each reproductive class. In other words, I tried to avoid skewing the distribution of independent variables towards the sheeps' preferred habitats and social situations. Thus, when available for our observation, I chose focal animals in undersampled combinations of independent variables (e.g. sheep in small groups, far from cliffs, and near cover) over other potential focal animals. If all groups available for our observation were under the same potential risk, my choice of group and focal animal was random.  Independence of sheep observations Focal animals were not marked, which potentially creates a pseudoreplication problem (Hurlbert 1984). To minimize this problem, I considered my observations of groups or individuals to be biologically independent only if (1) they occurred on different days or (2) they involved individuals that I could temporarily distinguish by their position in the landscape. For the same reason, I did not treat adult females before and after lambing as paired samples.  Statistical Analyses I analyzed the effects of predation risk factors on the proportion of time spent vigilant by feeding sheep with two multiple regressions. The first  15 regression tested predictions 1, 2 and 3 (see Introduction) using 105 focal animal samples of pre-lambing females. Independent variables in the starting equation were group size, distance to cliffs, distance to cover, and their second and third order interactions. Group sizes ranged from 1-100 individuals, distances to cliffs from 5-850 m and distances to cover from 3-400 m. The second regression tested prediction 4 (see Introduction) by comparing vigilance responses to predation risk factors between pre-lambing females and mothers. Variables in the starting equation were reproductive status, group size, distance to cliffs, distance to cover, and their second, third and fourth order interactions. To avoid biasing results towards either reproductive class, I chose data subsets in which the range of group sizes (1-5), distances to cliffs (5-55 m) and distance to cover (10-150 m) completely overlapped between reproductive classes (N=19 focal animal samples of mothers, N=13 samples of pre-lambing females). To meet the assumptions of normality and homoscedasticity for the dependent variable, I arcsin transformed the proportion of time spent vigilant, and log transformed continuous independent variables, which had skewed distributions (Zar 1984; Kleinbaum and Kupper 1978; McCullagh and Nelder 1983). I confirmed the success of these transformations by plotting studentized residuals against predicted values; the plot resembled the prototypical horizontal band. I confirmed the assumption that errors were normally distributed by doing a probability plot of residuals (Wilkinson 1990). The lack of curvilinear trends in  16 the transformed data was confirmed by plotting residuals against each continuous independent variable (Kleinbaum and Kupper 1978). I used backward stepwise procedures to reduce both models to their most significant form (Kleinbaum and Kupper 1978; McCullagh and Nelder 1983; Wilkinson 1990). Stepping was non-automated and the criteria for removing or re-entering variables into the model were based both on significance values of 0.05 and on tolerance values (Wilkinson 1990). Because statisticians warn sternly against the use of correlated independent variables in general linear models (Kleinbaum and Kupper 1978; McCullagh and Nelder 1983), variables could not become part of the significant model unless their tolerance was >0.1. In both analyses the average leverage equaled p/N. Only a single sample — representing a unique combination of independent variables — had leverage >2p/N (Wilkinson 1990).  17 RESULTS Effects of Group Size and Distance to Cliffs The significant model resulting from backward stepwise regression for pre-lambing females showed that vigilance decreased with increasing group size, but the magnitude of this response became progressively smaller (i.e., the slope of the regression line became progressively shallower) as distance to cliffs decreased (Table 1; Fig. 2a). Also, vigilance increased with distance to cliffs, but the magnitude of this response became progressively smaller as group size increased (Fig. 2b). Figure 2a shows that group size may have very little effect on vigilance when sheep are at the base of a cliff, and Figure 2b shows that distance to cliffs has almost no effect on vigilance when sheep are in groups with 80 or more members. These results, which included sheep feeding in a very large range of group sizes and distances to cliffs, strongly support predictions 1a and 2a of the IRFH (see Introduction). The IRFH prediction that the magnitude of the group size effect depends on distance to cliffs (prediction 1a) has further support in the comparison of vigilance of pre-lambing females and mothers (Table 2). In this analysis — for which sheep were within only 10 to 55 m from cliffs - group size had no significant effect on the vigilance of either reproductive class probably because the animals were very close to the safety of cliffs.  18 TABLE 1. Reduced regression model estimating vigilance responses (arcsin of % time vigilant) of pre-lambing females (N = 105 focal animal samples). Prior to reduction with backward stepwise procedures, independent variables in the model were distance to cliffs, distance to cover, group size, and the second and third order interactions of these variables. Group sizes ranged from 1-100, distances to cliffs from 5-850 m, and distances to cover from 3-400 m.  Variable (log transformed)  Coefficient  Tolerance  P  Constant  0.12  Distance to Cliffs  0.12  0.59  O.001  (Group Size) X (Dist. to cliffs)  -0.056  0.592  <0.001  0.008  ANOVA SUMMARY  DF  F  Regression  2  16.21  Residual  102  P  <0.001  R2  Standard error of estimate  0.24  0.11  19 FIGURE 2. Estimated response of vigilance (V) to the interaction of group size (G) and distance to cliffs (C) for pre-lambing females (N=105 focal animal samples). The families of lines are generated from the model V=0.118+0.124C0.056CG. (R2=0.24; PO.001; Table 1). Figure 2a shows the response to group size for sheep feeding, in decreasing order of Y-intercept, at 800, 400, 200, 100, 50, 25, 10 and 5 m from cliffs. Figure 2b shows the response to distance to cliffs for sheep feeding in groups with, in decreasing order of Y-intercept, 1, 2, 5, 10, 20, 40, 80 and 100 members.  20 0.6  0.5 Distance to Cliffs (m) ,800  0.4  /,400 / / ,200 /''/' J 00  0.3  // / ,  '//\,2b  0.2 =  'in  n,,S HI,,  y _'  0.1 -  0,0 0.5  0.0  1.0  1.5  2.0  LOG OF GROUP SIZE 0.6  1  1  1  1  Group Size 1  0.5  2 0.4 5 10 0.3  20 40  0.2  80 ~~———100  0.1  0.0 0.70  1.14  1.58  2.02  2.46  LOG OF DISTANCE TO CLIFFS (M)  2.90  21 TABLE 2. Reduced regression model comparing vigilance responses (arcsin of % time vigilant) between pre-lambing females and mothers (respectively: N = 13 and 19 focal animal samples). Prior to reduction with backward stepwise procedures, independent variables in the model were distance to cliffs, distance to cover, group size, reproductive status, and the second, third and fourth order interactions of these variables. Group sizes ranged from 1-5, distances to cliffs from 5-55 m, and distances to cover from 10-150 m.  Variable  Coefficient  P  (log transformed) Constant  0.23  <0.001  (Dist. to Cliffs)X (Reproductive Status)  0.10  0.001  ANOVA SUMMARY  Regression Residual  DF  F  1  12.54  30  P O.001  R  Standard error of estimate  2  0.30  0.10  Effects of Distance to Cover In both the analysis of pre-lambing females and the comparison between reproductive classes, distance to cover had no significant effect on vigilance, and was excluded from the reduced models of Tables land 2 These results do not support predictions 1 b, 2b and 3 (see Introduction), but neither reject nor support the IRFH (the IRFH would have been rejected if distance to cover would have had an additive effect). Cover had no significant effect possibly because I measured distance to only the nearest cover, and having cover nearby in more than one direction (as in a clearing surrounded by forest) may have affected my results. The possibility that distance to cover does affect vigilance as an interactive factor is supported by a posteriori analysis. For pre-lambing females, I tested the significant model estimating the interaction of distance to cliffs and group size (Table 1) in three subsets of distances to cover: <20 m, 21-50 m, and >50 m. For sheep within 20 m of cover, the effect of the group size-distance to cliffs interaction was much stronger (R2=0.42, SEE=0.11, P<0.001, N=32) than for sheep at distances to cover of 21-50 m (R2=0.14, SEE=0.12, P>0.05, N=30) and >50 m (R2=0.16, SEE=0.16, P=0.04, N=43), and than for the entire data set (R2=0.24, Table 1, PO.001, N=105). These results suggest that sheep close to cover are more sensitive to the effects of group size and distance to cliffs than sheep farther from cover. They also suggest that, had I controlled for distance to  23 cover in more than one direction, predictions 1b, 2b and 3b might have been supported.  Effects of Reproductive Class In the reproductive class comparison, which included only groups of 1-5 sheep within distances to cliffs of 5-55 m, mothers became more vigilant as distance to cliffs increased, but pre-lambing females did not (Table 2, Fig. 3). This result supports prediction 4 of the IRFH.  Position in Group: a Non-Effect? Whether an animal had a central or peripheral position in the group affected vigilance in studies of various taxa (review in Elgar 1989), including bighorn sheep (Berger and Cunningham 1988). Thus, although position in group was not a focus of my predictions, it potentially was an important factor to control. Of the 80 samples of pre-lambing females in which I recorded this variable, the focal animals' position was undefined in 29 (36.3%) (group geometry was linear or there were <5 animals in the group), and in 31 (38.8%) sheep switched between being central and peripheral. Only in one instance did they remain in a central position throughout the sample. Thus, it is unlikely that position in group significantly affected my results.  0.6  0.5 < g  0,4  UJ  0.3 IX  O  0.2 -  CO  O <  0.1 0,0 0.69  0.90  1.11  1.32  1.53  1.74  LOG OF DISTANCE TO CLIFFS (M)  FIGURE 3. Response of vigilance (V) to the interaction of reproductive status (R) and distance to cliffs (C) for adult females (N = 19 focal animal samples of mothers; 13 of pre-lambing females). Estimates are based on the model V = 0.233 + 0.100CR (R 2 = 0.30; P<0.001; Table 2).  25 Predator Records To put my vigilance observations in the context of the relatively low predation risk experienced by sheep during the study, I provide a summary of predator records. Coyotes, the primary sheep predator at Sheep Mountain (Hoefs and Cowan 1979; Buries and Hoefs 1984), were known to be present on 22 days (31.9% of field days, including 14 days in which they were heard but not seen). Also, bears or wolves were recorded on three days. Thus, terrestrial predators were known to be in the study area for a total of 25 days (36.2% of field days). I am aware of only two chases of sheep by terrestrial predators, and neither resulted in predation (Appendix A). Eagles, which prey on lambs (Nette et al. 1984), were seen at the study site on eight days (11.6% of field days), but only three times flying in the vicinity of mothers. The eagles did not attack neonates and the mothers showed no visible reaction to them. Only four sheep mortalities were recorded for the winter-spring of 1992-93. Of these mortalities, three were of unknown cause (Hoefs pers. comm.) and one involved a wolf and six coyotes (both species were present at the carcass, but the actual killing was not observed: Kluane National Park Staff pers. comm.).  26 DISCUSSION In previous studies, vigilance has decreased with increasing group size (reviews in Elgar 1989 and Lima and Dill 1990; Saino 1994), increasing distance to visually obstructive cover (review in Elgar 1989; Lazarus and Symonds 1992); and decreasing distance to refuges (Risenhoover and Bailey 1985; review in Elgar 1989). The Interactive Risk Factors Hypothesis predicts that the magnitude of any of these responses will decrease as risk due to the other two factors decreases. Also, on the basis that ungulate mothers become less vigilant as their offspring mature and thus become less vulnerable to predators (Risenhoover and Bailey 1985; FitzGibbon and Lazarus 1994), the IRFH predicts that the magnitude of any vigilance response will be smaller for prelambing females than for mothers with neonates. My results support the IRFH and do not support the alternative hypothesis in which risk factors have an independent effect on vigilance. Pre-lambing females became less vigilant as group size increased, but the magnitude of this relationship decreased as sheep got closer to cliffs. Furthermore, group size may affect vigilance very little when sheep are at the base of a cliff probably because group size decreases predation risk insignificantly when animals are so close to a refuge. Similar to Risenhoover and Bailey's (1985) conclusion, prelambing females became more vigilant as distance to cliffs increased, but the magnitude of this relationship decreased with group size. My results further suggest that distance to cliffs may have no effect on vigilance when sheep are in  groups of more than 80 members. Also, when sheep were 5-55 m from cliffs, mothers with neonates became more vigilant as distance to cliffs increased, but pre-lambing females did not. The IRFH predicts all of these observations. The vigilance responses of both pre-lambing females and mothers highlight the interaction between distance to cliffs and group size. When I compared these reproductive classes at 5-55 m from cliffs, the vigilance of neither class responded to group size. This was in spite of sheep being in groups of 1-5 members - the range in which the greatest shifts in vigilance occurred in other ungulate studies without effects of distance to refuge (e.g. Berger 1978; Alados 1985; Berger and Cunningham 1988). This result strongly suggests that the effect of group size on vigilance, which has previously been considered to be "ubiquitous" (Lazarus and Symonds 1992:520; see also review in Elgar 1989), can be completely overridden by close proximity to an effective refuge. It is noteworthy that, even as close as 5-55 m from cliffs, mothers did increase vigilance with increasing distance to cliffs. This response emphasizes the importance of cliffs as a refuge for sheep from predators. The lack of a similar response by pre-lambing females supports other ungulate studies concluding that mothers with neonates trade-off safety for food more than females without neonates. Mothers with neonates incur this greater cost -- in spite of the physiological demands of lactation - presumably because their fitness is largely dependent on the security of their neonates which are very  vulnerable to predators (Festa-Bianchet 1988; Berger 1991, FitzGibbon and Lazarus 1994). Although the effects of distance to cover were not statistically significant, a posteriori analyses suggested that this factor is part of a three-way interaction with group size and distance to cliffs. When sheep were <20 m from cover, the interaction between group size and distance to cliffs affected vigilance much more strongly than when farther from cover. I expect distance to cover to affect vigilance because coyotes and other predators are likely to hide behind cover while stalking sheep. Had I analyzed the effect of having cover nearby in more than one direction, rather than analyzing distance to nearest cover only, a priori analysis may have found cover to be significant as an interactive effect. Future studies should consider measuring distance to cover in four standard directions around a 360° radius, and whether these distances should be combined in an additive, multiplicative, or some other function. As attested by the R2 values of regressions, most of the variation in vigilance is not explained by my models. This result, however, is not unique to my study. For example, a recent study of carrion crows (Corvus corone corone) was able to predict only 4.3% and 7.0%, of the variation in time spent vigilant and in vigilance rate, respectively, by using the inverse of flock size as a predictor, and by controlling for food density, time of day, and presence of predators (Saino 1994). While I have evidence that position in group (review in Elgar 1989) was unlikely to affect my results (sheep remained in a central  29 position in only one out of 80 records), the unexplained variation of my data is probably due to other factors known to affect vigilance that I did not account for. These factors include condition of individuals (Bachman 1993), nearest neighbour distance (Underwood 1982), light intensity (Scheel 1993), dominance rank (Lovari and Rosto 1985; review in Elgar 1989), social bonds (review in Lima and Dill 1990), intra-group competition, ambient temperature, time of day, food density and quality, and individual foraging skills (reviews in Elgar 1989, but see Saino 1994 for a non-effect of food density and time of day). Also, it is likely that strong winds drowning sounds and blowing away scents force sheep to rely more on sight and increase vigilance. This possibility may be particularly relevant for my study area, where periods of calm are interspersed with highspeed katabatic winds draining from the Saint Elias Ice-cap. It is noteworthy that — in spite of all these potential sources of variation and with distance to cover excluded from significant models - the interaction of group size and distance to cliffs explained 24% of the variation in pre-lambing females' vigilance, and the interaction of reproductive status and distance to cliffs explained 30% of the difference between the vigilance of pre-lambing females and mothers. It is important to keep in mind that I made my observations when the population of coyotes - the main sheep predator at my study site - had plunged in response to a low in the snowshoe hare cycle (Kluane Boreal Forest Ecosystem Project; Boutin et al. pers. comm.). This decline suggests a particularly low rate of encounter between sheep and coyotes. During my study,  other predators appeared also to be relatively scarce. The rate of encounter between prey and their predators, which is at least partially a function of predator density, is itself a predation risk factor. Perhaps animals respond to temporal shifts in their rate of encounter with predators by accordingly relaxing or intensifying their vigilance response to other predation risk factors (see FitzGibbon and Lazarus 1994). This prediction is consistent with the IRFH and may be testable by comparing vigilance responses between periods in which predator densities differ. The IRFH is a general hypothesis. Encounter rate with predators is only one more factor that can be used to generate new predictions. The IRFH should be able to handle any other factors that affect risk, and is potentially applicable to any terrestrial prey. To maximize fitness, animals must balance safety with other requirements, including efficient foraging (reviews in Lima and Dill 1990; Krebs and Kacelnik 1991). Thus, for a given level of risk there is a theoretically optimal level of vigilance (e.g. Lima 1987). Assuming that predation risk factors influence fitness independently implies that animals should always become more vigilant as risk due to any one factor becomes greater, even though other conditions may have reduced risk to a very low, even negligible level. Under this assumption, safety can be overemphasized at the expense of foraging, and viceversa. In contrast, the IRFH model allows for the possibility that — when risk is low due to other conditions --  31 animals can increase vigilance very little or not at all in response to a particular factor that would otherwise strongly affect vigilance. In other words, in the IRFH model safety and feeding are always balanced (Fig. 1), which is more consistent with optimality theory. My results support the IRFH model, which may provide a more realistic approach to understanding vigilance than merely assuming that predation risk factors have independent effects.  REFERENCES Alados, C.L. 1985. An analysis of vigilance in the Spanish Ibex (Capra pyrenaica). Z. Tierpsychol. 68:58-64. Altmann, J. 1974. Observational study of behaviour: sampling methods. Behaviour 49:227-267. Bachman, G.C. 1993. The effect of body condition on the trade-off between vigilance and foraging in Belding's ground squirrels. Anim. Behav. 46:223-244. Berger, J. 1978. Group size, foraging, and antipredator ploys: an analysis of bighorn sheep decisions. Behav.Ecol. Socibiol. 4:91-99. Berger, J. 1991. Pregnancy incentives, predation constraints and habitat shifts: experimental and field evidence for wild bighorn sheep. Anim. Behav. 41:61-77. Berger, J. and C. Cunningham. 1988. Size-related effects on search times in North American grassland female ungulates. Ecology 69:177-183. Bunnell, F.L. 1980. The lambing period of mountain sheep: synthesis, hypotheses, and tests. Can. J. Zool. 60:1-14. Buries, D.W. and M. Hoefs. 1984. Winter mortality of Dall Sheep (Ovis dallidalli) in Kluane National Park, Yukon. Can. Field Nat. 98:479-484. Elgar, M.A. 1989. Predator vigilance and group size in mammals and birds: a critical review of the empirical evidence. Biol. Rev. 64,13-33.  Festa-Bianchet, M. 1988. Seasonal range selection in bighorn sheep: conflicts between forage quality, forage quantity, and predator avoidance. Oecologia 75:580-586. FitzGibbon, CD. 1989. A cost to individuals with reduced vigilance in groups of Thomson's gazelles hunted by cheetahs. Anim. Behav. 37:508-510. FitzGibbon, CD. 1990. Why do hunting cheetahs prefer male gazelles? Anim.Behav. 40:837-845. FitzGibbon, CD. and J. Lazarus. 1994. Anti-predator behaviour of Serengeti ungulates: individual differences and population consequences. In: Serengeti II: Research, Management and Conservation of an Ecosystem. (Ed. by A.R.E. Sinclair and P. Arcese). University of Chicago Press. Chicago. Frid, A. 1994. Observations on habitat use and social organization of a huemul (Hippocamelus bisulcus) coastal population in Chile. Biological Conservation 67:13-19. Geist, V. 1971. Mountain Sheep: A study in Behavior and Evolution. Univ. of Chicago Press. Chicago. Geist, V. 1987. On the evolution of Caprinae. Pages 3-40. In: The biology and management of Capricornis and related mountain antelopes (Ed. by H. Soma). Croom Helm. London. Hamilton, W. D. 1971. Geometry for the selfish herd. J. Theor. Biol. 31:295-311.  Hoefs, M., I. McT. Cowan, and V.J. Krajina. 1975. Phytosociological analysis and synthesis of Sheep Mountain, southwest Yukon Territory, Canada. Syesis8: 125-228. Hoefs, M., and I. McT. Cowan. 1979. Ecological investigation of a population of Dall sheep (Ovis dalli dalli Nelson).Syesis 12: 1-81. Hoefs.M., H. Hoefs and D.Buries. 1986. Observations on Dall Sheep {Ovis dalli dalli)-Grey Wolf (Canis lupus pambasileus) interactions in the Kluane Lake Area, Yukon. Can. Field Nat. 100:78-84. Hoefs, M. 1993. Annual helicopter survey of the Sheep Mountain population of Dall sheep. Unpublished report to Kluane National Park. 6 pp. Hurlbert, S.H. 1984. Psudoreplication and the design of ecological field experiments. Ecol. Monogr. 54:187-211. Illius, A.W. and C. D. FitzGibbon. 1994. Costs of vigilance in foraging ungulates. Anim. Behav. 47:481-484. Jarman, P.J. 1974. The social organization of antelope in relation to their ecology. Behaviour 48:215-267. Keith, LB, A.W. Todd, C.J. Brand, R.S. Adamcik, and C.H. Rusch. 1977. An analysis of predation during a cyclic fluctuation of snowshoe hares. Proceedings of the International Congress of Game Biologists. 13:151175. Kleinbum, D.G. and L.L. Kupper.1978. Applied Regression Analysis and other Multivariate Methods. Boston: Duxbury Press. 556 pp.  35 Krebs, C.J., B.S . Gilbert, S. Boutin, A.R.E. Sinclair, and J.N.M. Smith. 1986. Population biologogy of snowshoe hares. I. Demography of foodsupplemented populations in the southern Yukon, 1976-1984. J. Anim. Ecol. 55:963-982. Krebs, J.R. and A. Kacelnik. 1992. Decision making. Pages 105-137 In: Behavioural Ecology. (Ed by J.R. Krebs and N.B. Davies). Blackwell Scientific Publications. Oxford. Lazarus, J. and M. Symonds. 1992. Contrasting effects of protective and obstructive cover on avian vigilance. Anim. Behav. 43:519-521. Lima, S.L. 1987. Vigilance while feeding and its relation to the risk of predation. J.Theor.Biol. 124:303-316. Lima, S.L. and L.M. Dill. 1990. Behavioural decisions made under the risk of predation: a review and prospectus. Can. J. Zool. 68:619-640. Lovari, S. and G. Rosto. 1985. Feeding rate and social stress of female chamois foraging in groups. In: The Biology and Management of Mountain Ungulates (Ed. by S. Lovari),pp. 102-105. London: Croom Helm. Martin, P. and P. Bateson. 1986. Measuring Behaviour. Cambridge. Cambridge University Press. McCullagh, P. and J.A. Nelder. 1983. Generalized Linear Models. London: Chapman and Hall. Murie, A. 1944. The Wolves of Mount McKinlev. U.S. Dep. Int., Nat. Parks Serv. Fauna Ser. 5.  Nette, T., D. Buries and M. Hoefs. 1984. Observations of Golden Eagle (Aquila chrysaetos) predation on Dall Sheep (Ovis dalli dalli) lambs. Can. Field Nat. 98:252-254. Prins, H.H. and G.R. lason. 1989. Dangerous lions and nonchalant buffalo. Behaviour 108:262-296. Risenhoover, K.L. and J.A. Bailey. 1985a. Foraging ecology of bighorn sheep: implications for habitat management. J.Wildl.Manage. 49:797-804. Saino, N. corone 1994. Time budget variation in relation to flock size in carrion crows (Corvus corone corone). Anim. Behav. 47:1189-1196. Scheel, D. 1993. Watching for lion in the grass: the usefulness of scanning and its effects during hunts. Anim. Behav. 46:695-704. Sumanik, R.S. 1987. Wolf ecology in the Kluane Region, Yukon Territory. M.S. Thesis (Forestry).Michigan Technological University. Underwood, R. 1982. Vigilance behaviour in grazing african antelopes. Behaviour.79:82-107. Underwood, R. 1983. The feeding behaviour of grazing African ungulates. Behaviour 84:195-242. Wilkinson, L 1990. SYSTAT: The System for Statistics. Evanston, IL.USA: Systat, Inc. Zar, J.H. 1984. Biostatistical Analysis. 2nd edtion. New York: Prentice Hall.  37 APPENDIX A. Summary of terrestrial predators recorded. (Does not include 14 days in which coyotes were heard but not seen).  Predator  Mo./Day  Habitat  Interaction with Sheep  1 coyote  3/13  GFM1 500 m from cliffs.  None  1 coyote  3/13  GFM 200 m from cliffs.  None  1 coyote  3/14  GFM 600 m from cliffs.  None  1 coyote  3/22  Frozen lake 500 m from cliffs.  None  1 coyote  3/26  GFM 350 m from cliffs.  Unsuccessfully chased 15 sheep. See text.  2 coyotes  3/27  GFM 200 m from cliffs.  4 sheep (no adult males), 200 m from coyotes & at base of a cliff, stopped feeding & moved closer cliff. Coyotes did not approach sheep.  1 coyote  4/3  Open slope 300 m from cliffs.  25 sheep (no adult males) were 300 m from the coyote & 50 m from cliffs . Neither species showed an obvious reaction towards the other.  1 coyote coyote  5/6  GFM 400 m from cliffs  3 females 200 m from both & cliffs surrounded by trees, stopped feeding when coyote began to howl. After 3 min coyote left & 2 sheep resumed feeding.  1 wolf2  3/21  GFM >300 m from cliffs.  None  to  38 1 grizzly bear  4/21  Delta >1 km from cliffs.  None  1 grizzly 5/26 bear (tracks)  Ridgetop 50 m above cliffs.  None  1 grizzly bear2  Open slope  Unsuccessfully chased single adult female far from cliffs.  5/30  GFM = Grassland-Forest Mosaic Observed by Kluane National Park Staff  

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