VARIATION IN LITTER SIZE: A TEST OF HYPOTHESES IN RICHARDSON S GROUND SQUIRRELS

Ecology, 88(2), 2007, pp. 306 314 Ó 2007 by the Ecological Society of America VARIATION IN LITTER SIZE: A TEST OF HYPOTHESES IN RICHARDSON S GROUND SQUIRRELS THOMAS S. RISCH, 1,4 GAIL R. MICHENER, 2 AND F. STEPHEN DOBSON 3 1 Department of Biological Sciences, P.O. Box 599, Arkansas State University, State University, Arkansas 72467-0599 USA 2 Department of Biological Sciences, University of Lethbridge, Lethbridge, Alberta T1K 3M4 Canada 3 Department of Biological Sciences, Auburn University, Auburn, Alabama 36849-5414 USA Abstract. We studied litter size variation in a population of Richardson s ground squirrels (Spermophilus richardsonii) in Alberta, Canada, from 1987 to 2004. Litter size at first emergence of juveniles from the natal burrow ranged from 1 to 14; the most common litter sizes, collectively accounting for 41.0% of 999 litters, were 6 and 7. The number of offspring surviving to adulthood (attained on emergence from hibernation as yearlings) increased with increasing litter size, a result that was not predicted by Lack s optimal litter size hypothesis, Mountford s cliff-edge effect, or the bad-years effect. Contrary to the negative effects predicted by the cost of reproduction hypothesis, litter size had no significant influence on survival of mothers to the subsequent year or on the size of the subsequent litter. Rather, our results best fit the predictions of the individual optimization hypothesis, which suggests that litter size is determined by the body condition and environmental circumstances of each mother. Supporting this hypothesis, survival of individual offspring was not significantly associated with litter size. Additionally, year-to-year changes in maternal body mass at mating were positively associated with concurrent changes in litter size (r ¼ 0.56), suggesting that litter size depends on the body condition of the mother. Because the mean number of recruits to adulthood increased as litter size increased (r 2 ¼ 0.96) and litter size increased with maternal condition, offspring productivity was greater for mothers in better body condition. Key words: Alberta, Canada; bad-years effect; cliff-edge effect; cost of reproduction; individual optimization; Lack s hypothesis; life history; litter size; optimal clutch size; Spermophilus richardsonii. INTRODUCTION Lack s (1947, 1948a, 1954, 1966) classic research on avian clutch sizes was seminal to investigations of reproductive life histories. Lack reasoned that brood size should be shaped by stabilizing selection, and he predicted that the optimal clutch size, defined as the size that leaves the most recruits, should be the average or most frequent clutch size in a population. Hence, evolutionary studies of life histories have examined survival of offspring in relation to their mother s clutch size (reviewed by Klomp 1970, Winkler and Walters 1983, Murphy and Haukioja 1986, Ydenberg and Bertram 1989, Godfray et al. 1991, Vander- Werf 1992, Monaghan and Nager 1997). Experimental tests typically demonstrated that the mean or modal clutch size was not the most productive (reviewed by Lessells 1986, Ydenberg and Bertram 1989, VanderWerf 1992), so several modifications of Lack s hypothesis have been proposed. The individual optimization hypothesis (Perrins and Moss 1975, Ho gstedt 1980, Pettifor et al. 1988, 2001) explains variation in clutch size as dependent on body condition and Manuscript received 15 February 2006; revised 10 August 2006; accepted 14 August 2006. Corresponding Editor: R. S. Ostfeld. 4 E-mail: trisch@astate.edu 306 environmental circumstances of nurturing parents, usually mothers. The clutch size laid by each female and the energy invested in each individual offspring should be, on average, those that will produce the greatest number of individuals that eventually recruit into the population. Thus, the distribution of clutch sizes is a function of the variance in the distribution of quality resources. If some females acquire or store more resources than others, a consequence may be a mean clutch size that is smaller than the most productive clutch size (Pettifor et al. 1988, Price and Liou 1989). Mountford s (1968) cliff-edge hypothesis states that a genotype for a particular clutch size should have a range of actual phenotypic values. Such variation is evidenced by females producing different clutch sizes in different years and could be due to environmental variation or even reflect random chance. The fitness of a genotype is the sum of success for all the phenotypes that a particular genotype produces. Thus, the most productive genotype is that for the clutch size that produces the largest sum (Mountford 1968, Morris 1996). The bad-years effect (Boyce and Perrins 1987), a bet-hedging model, assumes that there is variation in how the environment influences success at producing surviving offspring in good and bad years. For small clutch sizes, success at producing surviving offspring is assumed to be similar whether the year is good or bad

February 2007 VARIATION IN LITTER SIZE 307 for reproduction, whereas for large clutches offspring survival might be high in a good year but is predicted to be poor, perhaps falling to zero, in a bad year. To best capture the effect of good and bad years on fitness, bethedging models measure fitness using the geometric mean number of surviving offspring (e.g., Philippi and Seger 1989). An important necessary condition of the bad-years effect is that variance in offspring survival increases with increasing clutch size. A trade-off between present reproductive effort and future reproduction and/or survival might influence clutch size, an idea that is a variant of the cost of reproduction hypothesis (e.g., Reznick 1985, as modified by Risch et al. 1995). This hypothesis predicts that increased reproductive effort results in parental costs, such as diminished life span or decreased reproductive success later in life (Lack 1966, Williams 1966, Stearns 1976, Bell 1980, Partridge and Harvey 1985). Brood manipulation experiments have demonstrated that costs of enlarged broods include reduced survival of young and reduced parental survival (e.g., Dijkstra et al. 1990). Although Lack was best known for ideas about clutch size and offspring survival in birds, he also hypothesized that mammalian populations have an optimal litter size that, on average, produces the most young that survive to reproduce (Lack 1948b). However, few studies have investigated the number of surviving offspring produced in relation to litter size in mammals. Studies addressing these hypotheses in mammals have found either that mean litter size is smaller than the most productive litter size (Morris 1992, 1996, Risch et al. 1995) or that all litter sizes produce the same number of surviving offspring (Boutin et al. 1988). Some results are consistent with individual optimization of litter size in mammals (e.g., Risch et al. 1995), some with the cliffedge hypothesis (Morris 1996), and some with the costs of reproduction (Mappes et al. 1995, Huber at al. 1999, Neuhaus 2000, Koivula et al. 2003; but see Murie and Dobson 1987, Hare and Murie 1992). Richardson s ground squirrels (Spermophilus richardsonii) provide an excellent model for examining hypotheses concerning litter size, for several reasons. Litter size at weaning varies substantially among mothers, ranging from 1 to 14 individuals (Michener 1989a). Each mother produces a single litter annually, and individuals of both sexes attain sexual maturity on emergence from their first hibernation as yearlings (Michener 1985). Many aspects of the reproductive ecology and life history of Richardson s ground squirrels are known (Michener 1984, 1989a, b, 1998, Michener and Locklear 1990, Dobson and Michener 1995, Broussard et al. 2005, 2006). We used data from a long-term study with large samples of known-sized litters to assess the adequacy of the optimal litter size, individual optimization, cliffedge, bad-years, and cost of reproduction hypotheses for explaining the relationship between litter size and offspring survival to adult age in Richardson s ground squirrels. METHODS Richardson s ground squirrels were studied for 18 consecutive reproductive seasons from 1987 to 2004 at a site 5 km east and 1 km south of Picture Butte, Alberta, Canada (49852 0 N, 112843 0 W, elevation 870 m). The study area was centered on a 1.4-ha grassland dominated by introduced grasses and bordered by a farmyard and cultivated fields into which ground squirrels encroached. When the site was initially inspected in 1978, it supported a population of Richardson s ground squirrels, but grazing had ceased in 1977 and, in conjunction with growth of tall vegetation, the population was extinct by 1980 (Michener 1996). Beginning in 1985, selective burning, mowing, and grazing returned the site to suitable habitat for Richardson s ground squirrels. In 1985 and 1986, 14 adult females and 2 adult males were released on the site (Michener 1996). Adult females to be transplanted were captured after the spring mating period from a large population located ;3.25 km from the study site, then held captive for 18 53 days before release. Eight females that gave birth in captivity to litters of 4 8 young were released with their entire litter (a total of 47 juveniles), two females that gave birth to litters of 10 and 11 were each released with five juveniles, one female was released without her litter, and the remaining three released females had not given birth. Subsequently, population density in spring varied substantially, from ;14 adult females/ha (in 1987, 1995, 1996) to.90/ha (in 1990, 2001; Michener 2004). Litter size at weaning was monitored for all females in the population from 1987 to 2000 and for those females resident on approximately half of the site from 2001 to 2004. Survival to adulthood of offspring from those litters was recorded for each subsequent year from 1988 through 2005. Ground squirrels were selectively captured by trapping of target animals in unbaited live traps. At each capture, animals were weighed with a spring scale either to the nearest 2.5 g (juveniles,50 days old) or nearest 5 g (all other animals), examined, and released within a few minutes of capture. On first capture, usually as a newly emerged juvenile, each ground squirrel was uniquely identified with a numbered metal tag in each ear. To permit individuals to be identified from a distance, all adults received a unique mark on the pelage with hair dye. Juveniles initially received a dye mark that identified them to litter and subsequently were given an individually distinctive mark if they survived beyond 3 months of age. Each spring, the study site was surveyed daily from early February onwards to detect the emergence of adults from hibernation. Each ground squirrel was captured shortly after it emerged from hibernation, and adult females were recaptured several days later, near to the anticipated time of estrus and mating. Date of mating was determined from a combination of the appearance of the external genitalia, assessment of vaginal cytology from cells obtained in vaginal lavages,

308 THOMAS S. RISCH ET AL. Ecology, Vol. 88, No. 2 and behavioral observation (Michener and McLean 1996, Michener 1998). Body mass near the time of mating was available for those females weighed 2 days before or after the date of mating. The majority of females became pregnant (95 100% in all years except 1995, when only 69% became pregnant), and litters were born underground after 23 days of gestation (Michener 1989a). Most females were captured both 2 days before and after the expected parturition date; parturition was confirmed by a drop in body mass and condition of the external genitalia (stretched and bloodied vulva) or nipples (swollen, pink-tipped nipples surrounded by flattened fur). Juvenile Richardson s ground squirrels usually first emerge above ground when 28 30 days old (Michener 1985), immediately begin eating vegetation on emergence, and are weaned over the next several days. Thus, litter size at first emergence from the natal burrow coincides closely with termination of nutritional care by mothers and is a good estimator of maternal reproductive investment through gestation and lactation (Michener 1989a). First emergence of litters from the natal nest was detected by daily inspection of the burrow system occupied by each female from 26 days postpartum onwards. Once a litter was detected, the emergence location was flagged and trapping of juveniles began either immediately or, for litters that emerged in late afternoon, the next morning. Litter size at emergence from the natal nest was determined by trapping for one to several days until the entire litter was captured and all juveniles were ear-tagged and dyemarked. Each litter was then observed at morning emergence for an additional 1 2 days to confirm that all individuals had been captured and that members of adjacent litters had not intermixed. Of 1313 lactating Richardson s ground squirrels still alive at the expected time of litter emergence, 1190 weaned 1 14 juveniles. Predation of offspring, predominantly by North American badgers (Taxidea taxus) (Michener 2004), accounted for at least half (63 of 123) of litter failures. In 17 of 18 years, litter size was known unambiguously for 83% of litters (mean ¼ 94%). In 1990, high population density combined with synchronous emergence of litters resulted in rapid intermixing of juveniles from adjacent litters such that litter size was known unambiguously for only 55% of litters. After exclusion of any litters with uncertain maternity or with uncertain membership, litter size at first emergence from the natal burrow was known unambiguously for 1013 litters over the 18 years. Of these, nine litters of one offspring, two litters of two offspring, and three litters of three offspring that were known to have been partially reduced by predators, either badgers (Michener 2004) or unidentified predators, were eliminated from analysis. Although the smallest litter size recorded at birth for captive Richardson s ground squirrels, both from the study population (n ¼ 18 litters) and from the source population (Michener 1989a), is 4 and mean attrition in litter size between birth and first emergence is,1 young (Michener 1989a), we retained all other litters of 3 for which we had no confirmed evidence of predation. Thus, our analyses include 999 litters of 1 14 offspring. Emergence from hibernation in the spring following the year of birth was used as an estimate of offspring survival to adulthood. This estimate includes only offspring that neither died nor dispersed from the study site. Natal dispersal is sex-biased in most grounddwelling sciurids (Holekamp 1984, 1986, Byrom and Krebs 1999), with males dispersing more often and to greater distances than females. Undoubtedly some Richardson s ground squirrels, particularly males, dispersed and survived to adulthood elsewhere. Although we were unable to assess the extent of such off-site survival, we do know that over the 15-year period from 1987 to 2001 (when the entire population was monitored until the end of the mating season), none of 965 adult females and 9 of 337 adult males were confirmed or suspected immigrants, arriving on the study site either as juveniles or adults. To adjust for the likely underrepresentation in survival to adulthood by males as a consequence of successful dispersal, we assumed that if successful emigration was as likely as successful immigration, then actual survival of males could have been ;2.6% (9/337) higher than the number of known survivors on site. Because application of this adjustment factor did not affect any of the statistical inferences, we present the unadjusted data here. RESULTS The two most common sizes for newly emerged litters of Richardson s ground squirrels were 6 and 7 individuals; collectively, such litters accounted for 41.0% of 999 litters weaned over the 18-year period (Table 1). We initially examined the possible effects of maternal age (yearling through 5 yr of age) and calendar year of birth (1987 through 2004) on the association between juvenile survival to 1 yr of age and litter size. Litter size varied among years (Table 2, ANOVA; F 17, 981 ¼ 9.06, P, 0.0001), but not with age of mothers (F 4, 994 ¼ 0.84, P. 0.50). Consequently, an analysis of covariance was conducted to consider the effects of years on the relationship between litter size and juvenile survival using litter size as the covariate and year as a class variable. The overall model was significant (F 35, 963 ¼ 10.32, P, 0.0001), but the effect of year was not (F 17, 963 ¼ 0.95, P. 0.51). Although there was a significant litter size by year interaction on the number of juveniles that survived to 1 yr of age (F 17, 963 ¼ 1.94, P, 0.012), this interaction had a relatively small influence on the model as compared to the effect of litter size on survival (F 1, 963 ¼ 42.82, P, 0.0001). Thus, subsequent analyses contain no correction for either maternal age or calendar year, but year effects are explored as an influence on juvenile survival under the bad-years hypothesis. Because a mother s litter size in one year was not strongly associated with her litter size in the following year (see

February 2007 VARIATION IN LITTER SIZE 309 Distribution of litter sizes at first emergence from the natal burrow for 999 litters of Richardson s ground squirrels in Alberta, Canada, over the 18-year period 1987 2004 and measures of reproductive success for each litter size. TABLE 1. Litter size No. surviving offspring Frequency Arithmetic Litter success Geometric No. Percentage Mean Variance mean No. observed No. predicted Mountford s fitness prediction 1 5 0.5% 0.20 a 0.20 0.15 1 3.2 0.36 2 8 0.8% 0.38 a 0.27 0.30 3 5.2 0.54 3 35 3.5% 0.71 a,b 0.74 0.53 17 22.6 0.75 4 92 9.2% 0.88 a,b,c 0.81 0.67 52 59.5 0.96 5 158 15.8% 1.09 a,b,c,d 1.37 0.79 91 102.2 1.17 6 215 21.5% 1.32 a,b,c,d 1.62 0.99 145 139.0 1.39 7 195 19.5% 1.36 a,b,c,d 1.96 0.99 125 126.1 1.59 8 156 15.6% 1.90 b,c,d,e 2.91 1.42 116 100.9 1.82 9 80 8.0% 1.98 c,d,e 4.33 1.31 52 51.7 2.01 10 42 4.2% 1.79 b,c,d,e 2.12 1.40 32 27.2 2.21 11 10 1.0% 2.10 d,e 1.66 1.83 9 6.5 2.25.11 3 0.3% 2.67 e 1.33 2.56 3 1.9 Notes: Offspring survival is the number of juveniles that survived to adulthood (1 yr of age). Duncan s range test identified five groups of litter sizes (indicated by superscript letters) based on the mean number of surviving offspring. Litter success is the observed number of litters from which at least one offspring survived to adulthood, with predicted number of successful litters calculated on the assumption of an equal probability of producing at least one surviving offspring among all litters. Mountford s fitness predictions are estimated from the product of the litter size frequencies and offspring survival at each litter size. One litter each of 12, 13, and 14. Due to pooling of litter sizes, Mountford s fitness prediction could not be calculated for litters of.11. Results: Costs of reproduction, below), mothers that weaned a litter in more than one year were retained in our analyses. Mating date varied among years (Table 2; ANOVA, F 17, 978 ¼ 111.29, P, 0.0001). Because timing of reproduction may have a confounding effect on the relationship between litter size and number of juveniles that survived to adult age, we included mating date as a covariate and litter size as a class variable in an analysis of covariance. Mating date had no significant interaction with litter size (ANCOVA, F 10, 971 ¼ 0.41, P. 0.94) and no significant effect on the number of juveniles surviving to adult age from each litter size (F 10, 971 ¼ 0.44, P. 0.51). Thus, we did not adjust offspring survival for variation in mating date among years. Optimum litter size hypothesis Litter size at first emergence from the natal burrow in this population of Richardson s ground squirrels was 6.48 6 0.06 individuals (mean 6 SE; n ¼ 999). The modal litter size was 6, though litters of 7 were almost as abundant (Table 1). Based on number of offspring Annual date of mating, litter size at first emergence from the natal burrow, offspring survival to adulthood (1 yr of age), and maternal survival to the subsequent year over an 18-year period for Richardson s ground squirrels (mean 6 SE). TABLE 2. No. Offspring survival to adulthood Year females Date of matingà Litter size No. surviving Proportion surviving Maternal survival 1987 27 10 March 6 0.9 7.70 6 0.522 1.85 6 0.332 0.237 6 0.0451 70.4% 1988 38 8 March 6 0.4 7.11 6 0.232 2.21 6 0.267 0.315 6 0.0387 78.9% 1989 80 25 March 6 0.7 6.99 6 0.206 1.89 6 0.158 0.281 6 0.0241 83.8% 1990 72 9 March 6 0.4 6.14 6 0.235 0.56 6 0.097 0.119 6 0.0239 23.6% 1991 44 14 March 6 0.9 5.59 6 0.237 1.48 6 0.226 0.258 6 0.0368 56.8% 1992 66 3 March 6 0.4 6.09 6 0.237 1.67 6 0.152 0.283 6 0.0247 45.5% 1993 60 13 March 6 0.7 7.35 6 0.283 0.98 6 0.153 0.141 6 0.0211 38.3% 1994 55 15 March 6 0.7 6.76 6 0.223 0.31 6 0.082 0.048 6 0.0136 29.1% 1995 13 21 March 6 1.8 5.92 6 0.473 1.00 6 0.320 0.172 6 0.0566 61.5% 1996 21 16 March 6 0.9 7.76 6 0.292 1.95 6 0.312 0.241 6 0.0358 42.9% 1997 33 18 March 6 0.8 7.61 6 0.268 2.67 6 0.361 0.351 6 0.0442 78.8% 1998 77 17 March 6 0.8 6.57 6 0.193 1.08 6 0.119 0.159 6 0.0169 29.9% 1999 41 14 March 6 1.0 6.49 6 0.224 2.61 6 0.283 0.395 6 0.0381 82.9% 2000 121 10 March 6 0.6 6.69 6 0.167 1.96 6 0.127 0.300 6 0.0186 77.7% 2001 79 12 March 6 0.3 5.70 6 0.160 0.77 6 0.122 0.131 6 0.0197 64.6% 2002 66 2 April 6 0.6 5.11 6 0.142 0.56 6 0.102 0.113 6 0.0208 48.5% 2003 63 23 March 6 0.4 6.83 6 0.236 1.78 6 0.189 0.279 6 0.0311 88.9% 2004 43 10 March 6 0.8 5.72 6 0.219 0.77 6 0.152 0.130 6 0.0234 34.9% Sample size is identical for all five variables within a year, except that the date of mating was not known for one female in each of 1991, 1992, and 2000. à The date is reported 6SE, with SE given in days.

310 THOMAS S. RISCH ET AL. Ecology, Vol. 88, No. 2 old for whom mass at mating and litter size at emergence from the natal burrow were known in consecutive years; for those females with data available for.2 consecutive years, we randomly selected one pair of years for analysis. We found a significant positive correlation (Fig. 2; r ¼ 0.56, n ¼ 59, P, 0.0001) between yearly changes in maternal mass (from mating in one spring to the next) and concurrent yearly changes in litter size at emergence from the natal burrow for females 2 yr old. FIG. 1. Effect of litter size on proportion of mothers surviving to the next year and on the proportion of juveniles (mean 6 SE) within each litter surviving to adult (yearling) age in Richardson s ground squirrels in Alberta, Canada. Sample sizes are the same as for the number of litters of different sizes in Table 1. surviving to adulthood, litters of 12 14 were the most productive, but such large litters were extremely rare (Table 1). Of litter sizes that formed at least 0.5% of the sample of 999 litters, the most productive was 11, though this productivity differed little from litter sizes of 8, 9, and 10. Mean litter size differed significantly from the most productive litter size of 11 (one-sample t test; t 998 ¼ 76.6, P, 0.0001). The number of juveniles that survived to reproductive maturity increased significantly with litter size (r 2 ¼ 0.066, F 1, 997 ¼ 70.76, P, 0.0001). Duncan s range test indicated that the largest litters (9) exhibited higher success than smallest litters (3; Table 1). When examined in terms of mean offspring survival per litter size (Table 1), survival to reproductive maturity exhibited a strong linear increase with litter size (Table 1; r 2 ¼ 0.96, F 1,10 ¼ 245.9, P, 0.0001). Individual optimization We investigated whether the probability of reproductive success (having at least one offspring survive to adulthood) was related to litter size by generating a null expectation that assumed equal likelihood of offspring survival, regardless of litter size (Table 1). The observed number of litters that produced at least one yearling recruit did not differ significantly from the predicted values (v 2 ¼ 5.99, df ¼ 11, P. 0.85). To further examine whether survival of juveniles was independent of litter size, we regressed the proportion of recruits from litters (Fig. 1; using the transformation arcsine square-root [proportion]) on litter size. The regression was not significant (F 1, 997 ¼ 1.06, P. 0.30). Structural growth in Richardson s ground squirrels is determinate and plateaus before the age of 2 yr (Dobson and Michener 1995). Therefore, changes in mass of mothers when 2 yr old should mirror changes in physiological resources that are available for reproduction. We investigated this relationship for females 2 yr Cliff-edge effect We applied Mountford s (1968) procedure to identify the genotype that should be favored by natural selection. This procedure involves evaluating the reproductive success of a range of phenotypes that would be produced by a genotype that centered litter size on a mode larger or smaller than the actual mode, under the assumption that juvenile survival remains the actual value for each litter size. While this exercise assumes that the range of phenotypic litter sizes would remain constant as the modal litter size changes, it is nonetheless the most direct way to test the hypothesis. Using Mountford s (1968) procedure with litters of 1 11, larger litters exhibited greater predicted fitness (r ¼ 1.00, n ¼ 11, P, 0.0001; Table 1). Bad-years effect On a per litter basis, the number of juvenile ground squirrels that survived to adult age varied among years (ANOVA; F 17, 981 ¼ 15.90, P, 0.0001), as did litter size. The mean number of surviving offspring per year was significantly correlated with mean litter size for different years (Table 2; r ¼ 0.56, n ¼ 18, P, 0.02). By selecting the most extreme years for mean number of recruits produced per litter, we investigated the relationship between yearly mean productivity and yearly mean litter FIG. 2. Association between change in mother s mass measured from mating in one year to mating in the next year and concurrent yearly change in litter size at first emergence from the natal burrow between consecutive years. Sample size ¼ 59 female Richardson s ground squirrels aged 2 yr in year x. Duplicate data points are not indicated.

February 2007 VARIATION IN LITTER SIZE 311 FIG. 3. Effect of litter size on number of juvenile Richardson s ground squirrels surviving to adulthood (mean 6 SE) in two good years and three bad years for reproduction by Richardson s ground squirrels (see Results: Bad-years effect for identification of good and bad years). Sample sizes (number of litters) are given above error bars. size. We identified three bad years (1990, 1994, and 2002 in which,12% of offspring survived per litter; 193 litters) and two good years (1997 and 1999 in which.35% offspring survived per litter; 74 litters), and then used analyses of covariance to investigate the relationship between litter size and offspring survival using type of year (bad or good) as a class variable. The model was significant (r 2 ¼ 0.44, F 3, 263 ¼ 69.10, P, 0.0001), and there was a significant interaction between litter size and type of year (F 1, 263 ¼ 22.12, P, 0.0001; Fig. 3). Variance in number of juveniles surviving to adulthood increased up to litters of nine, then declined (Table 1), but exhibited an overall significant increase with increasing litter size (litter sizes 1 11, r 2 ¼ 0.57, F 1,9 ¼ 11.74, P, 0.008). Using all years of data, geometric mean numbers of juveniles surviving to adult age were calculated for different litter sizes. Because many litters failed to produce any recruits, we first added one to the number of recruits in each litter to avoid the technical problem of the log of zero being negative infinity (Sokal and Rohlf 1985), then subtracted one from the geometric mean of each litter size for comparison to the arithmetic mean. As expected, the geometric mean numbers of juveniles surviving to adult age from litters of different sizes were lower than the arithmetic means, and the most productive litter sizes as identified by the geometric mean number of surviving offspring were litters of 11 or more (Table 1). The magnitude of the difference between arithmetic and geometric means could not account for the difference between the mean or modal litter size (at 6.5 and 6, respectively) and the size of the most productive litters. The geometric mean number of survivors was positively correlated with litter size (Table 1; r ¼ 0.96, n ¼ 12, P, 0.0001). Costs of reproduction We explored whether litter size influenced either maternal survival or subsequent litter size. Survival rates of female Richardson s ground squirrels that produced different litter sizes did not differ significantly (Fig. 1; logistic regression, v 2 ¼ 0.07, P. 0.80). In addition, when we compared mean litter size for mothers that did and did not survive to the next year (6.47 6 0.07, n ¼ 575, and 6.50 6 0.10, n ¼ 424, respectively), the difference was not significant (Satterthwaite t 861 ¼ 0.25, P. 0.80). Because yearling Richardson s ground squirrels produce litters similar in size to older females (Michener 1989a, Broussard et al. 2005), we included females of all ages in the analysis of year-to-year changes in litter size; for those females with data available for more than two consecutive years, we randomly selected one pair of years for analysis. Mother s litter size in one year was weakly and positively associated with her litter size in the following year (Fig. 4, Kendall correlation; r ¼ 0.10; n ¼ 230; P, 0.05), and the mean year-to-year change in litter size per female was insignificant (0.09 6 0.16 offspring, paired t 229 ¼ 0.74, P. 0.46). DISCUSSION Of the five hypotheses that we tested to explain the distribution of litter sizes in Richardson s ground squirrels, only the individual optimization hypothesis was well-supported. We first discuss the four less wellsupported hypotheses. In contrast to the prediction of Lack s optimum clutch size hypothesis, the most productive litter size for Richardson s ground squirrels

312 THOMAS S. RISCH ET AL. Ecology, Vol. 88, No. 2 FIG. 4. Association of litter size in one year (year x) and litter size in the next year (year x þ 1) for adult female Richardson s ground squirrels. Dot size indicates the number of overlapping values (range 1 14); n ¼ 230. was larger than both the mean litter size and the most common litter size. Yearling Richardson s ground squirrels produce litters similar in size to older females (Michener 1989a, Broussard et al. 2005), so the divergence of the most productive litter from mean litter size was not attributable to lower fecundity in the first year of reproduction, as has been suggested in birds (e.g., Klomp 1970). For the cliff-edge effect, a fitness calculation is made under the assumption that litter size is significantly heritable (Mountford 1968). If one assumes that the phenotypic distribution of litter sizes would be similar for different genotypes, the product of frequencies of litter sizes and offspring survival values can be used to predict the fitness of genotypes for different litter sizes. Whereas the modal value of litter size should have the greatest estimated fitness under Mountford s (1968) procedure, we found that estimated fitness increased with increasing litter size. Thus, our results did not support a strong influence of the cliff-edge effect on litter size in Richardson s ground squirrels, perhaps because juvenile survival did not fall off the cliff at larger litter sizes (Table 1). Our detailed 18-year data set on the reproductive ecology of Richardson s ground squirrels included years that could be designated as good or bad in terms of producing recruits. The bad-years effect requires that variance in offspring survival increases with clutch size (Liou et al. 1993), and our sample of 999 litters of Richardson s ground squirrel was sufficient to analyze and confirm this necessary condition of the bad-years hypothesis. The geometric mean number of juveniles surviving to adult age among different litter sizes reflected increased fitness from large litters. Furthermore, in contrast to the predictions of the bad-years hypothesis (Boyce and Perrins 1987), the highest geometric mean number of recruits produced did not correspond to the most frequent litter size, but rather the largest litter sizes. The cost of reproduction hypothesis was originally conceived as a modification to Lack s original optimum clutch size hypothesis (Williams 1966) and can potentially explain the deviation of the most productive clutch from mean clutch size. Our analyses, however, did not demonstrate substantial short-term phenotypic costs of reproduction for Richardson s ground squirrels. We found no significant relationship between litter size and survival of mothers, in agreement with a previously reported lack of relationship for another population of Richardson s ground squirrels (Michener 1989a). Furthermore, litter size in one year was not correlated with litter size the following year. Failure to illustrate shortterm costs of reproduction in an unmanipulated freeliving population is consistent with individual optimization (Morris 1992), as females may be optimizing their reproductive effort to maximize the number of recruits produced at a level at which phenotypic costs are minimized. Many of our results supported the individual optimization hypothesis for Richardson s ground squirrels. Although the regression of number of juveniles surviving to adult age on litter size accounted for only 6.6% of the variation in numbers of surviving offspring, it was statistically significant. Also, individual variation and year-to-year variation masked a significant association that was more clearly evident when comparing the mean number of surviving offspring for each litter size: litter size then accounted for ;96% of the variation. The largest litters not only tended to produce more surviving offspring, but they also were more likely to produce at

February 2007 VARIATION IN LITTER SIZE 313 least one surviving offspring, patterns that are strongly suggestive of individual optimization. Finally, and perhaps most importantly, fully grown mothers that improved in body condition (viz., mass) from one year to the next produced larger litters, as expected if mothers were optimizing litter size to their improved body reserves. Although the hypotheses addressed in our study are not mutually exclusive, unique predictions of each hypothesis allow the alternatives to be evaluated. Few studies have addressed more that one or two of these alternatives concurrently (but see Boyce and Perrins 1987, Morris 1992, Risch et al. 1995, Murphy 2000), but our sample of 999 litters permitted evaluation of five hypotheses that could account for the distribution of litter sizes in a population of Richardson s ground squirrels. Our results support the individual optimization hypothesis, in which optimal litter size depends on local conditions and on a mother s state, an example of a state-dependent life history (McNamara and Houston 1996, Morris 1996, 1998). Graphically, such phenotypic plasticity can be represented by a norm of reaction (Risch et al. 1995, Clutton-Brock et al. 1996). The individual optimization hypothesis holds that females optimize the number of offspring depending on their ability to raise those offspring, which is contingent upon variables such as territory quality (Perrins and Moss 1975, Ho gstedt 1980) and parental quality, where the latter can be measured by body condition, age, or experience (Perrins and Moss 1975, Coulson and Porter 1985). Risch et al. (1995) predicted a significant association between yearly changes in mass of mothers with concurrent changes in litter size and reported a significant correlation in four of five populations of Columbian ground squirrels (S. columbianus). Richardson s ground squirrels also exhibit this pattern of litter size optimization based on changes in individual body condition. In bad years, however, female Columbian ground squirrels (Risch et al. 1995) and Richardson s ground squirrels that produce large litters do not recruit more offspring than females that wean small litters. Future studies would do well to address how unpredictable environmental conditions between mating and recruitment of offspring into the adult population, such as intensity of predation by badgers (Michener 2004), affect the evolution of state-dependent life histories. ACKNOWLEDGMENTS We thank the many field assistants who helped G. R. Michener with trapping and monitoring of Richardson s ground squirrels. D. 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