Ecological Applications, 22(5), 2012, pp. 1628–1639 Ó 2012 by the Ecological Society of America

Maternal allocation in bison: co-occurrence of senescence, cost of reproduction, and individual quality SANDRA HAMEL,1,3 JOSEPH M. CRAINE,2

AND

E. GENE TOWNE2

1

Department of Arctic and Marine Biology, Faculty of Biosciences, Fisheries and Economics, University of Tromsø, 9037 Tromsø, Norway 2 Division of Biology, Kansas State University, Manhattan, Kansas 66506 USA

Abstract. Parental allocation strategies are of profound interest in life history because they directly impact offspring fitness and therefore are highly valuable for understanding population dynamics and informing management decisions. Yet, numerous questions about reproductive allocation patterns for wild populations of large mammals remain unanswered because of the challenges for measuring allocation in the wild. Using a nine-year longitudinal data set on life-history traits of mother–calf bison pairs, we identified sources of variation in relative maternal allocation (calf mass ratio on mother mass) and assessed the occurrence of reproductive costs associated with differential maternal allocation. We found that heavy mothers provided a lower allocation but still produced heavier calves than light mothers. Older females produced lighter calves and tended to decrease allocation as they aged, supporting the occurrence of reproductive senescence. Mothers that had produced a calf the previous year produced lighter calves and allocated less than mothers that did not lactate the previous year, revealing reproductive costs. However, greater maternal allocation did not reduce the probability of breeding in successive years, and the amount of allocation provided by a mother was positively correlated among the offspring she produced, illustrating individual heterogeneity. Although life-history studies are usually classified as either supporting costs of reproduction or individual quality, our study demonstrates that these contrasting evolutionary forces can shape variation within a single trait. Our work illustrates that many processes can coevolve within a population, emphasizing the need to integrate multiple concepts to better understand the evolution of life-history traits. With regard to management of bison herds, if the goal of culling programs is to select for animals with the best performance, this research suggests that managers should account for the condition and previous reproductive status of mothers when taking culling decisions on juvenile bison. Key words: bison; costs of reproduction; individual heterogeneity; mass; relative maternal allocation; reproductive constraint hypothesis; senescence; terminal allocation/investment.

INTRODUCTION Parental allocation strategies are of considerable interest to life-history theory because they have a direct impact on offspring fitness, and concomitantly on parent fitness. The allocation provided to an offspring profoundly influences its development and body growth, which in turn often directly affects juvenile survival and adult fitness (Ylo¨nen et al. 2004, Skibiel et al. 2009). In species where juvenile mortality can be high and variable (Gaillard et al. 2000, Levitis 2011), knowledge of how parental allocation strategies affect offspring body condition and on how those strategies may vary within a population is a key to understanding population dynamics because offspring condition usually has a strong influence on survival and recruitment (Skibiel et al. 2009, Baron et al. 2010). Furthermore, juvenile Manuscript received 5 December 2011; revised 28 February 2012; accepted 13 March 2012. Corresponding Editor: N. T. Hobbs. 3 E-mail: [email protected]

development often has long-term consequences on fitness, especially when offspring condition is closely related to adult condition (Lindstro¨m 1999). For example, in polygynous mammalian species, male reproductive success is more variable and dependent on body size and condition than female reproductive success (Trivers and Willard 1973, Clutton-Brock 1988). Hence, parental allocation provided solely by the mother is often greater when raising a son than a daughter (Lee and Moss 1986, White et al. 2007) because larger body size increases the chances that the son may obtain high reproductive success, thereby increasing his mother’s fitness (Trivers 1972). Maternal allocation to offspring is likely to depend on the amount of resources available to the mother (King et al. 2011). Mothers are thus expected to adjust their allocation strategy to the environmental conditions they experience at each reproductive occasion, because these conditions will affect the availability of resources in the habitat (Ba˚rdsen et al. 2008, Schubert et al. 2009). In capital breeders, however, reproduction depends also on

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accumulated body reserves (Stearns 1992, Jo¨nsson 1997), as opposed to income breeders that rely almost entirely on energy gained from short-term resources acquisition. Allocation strategies of capital breeders are thus often highly dependent on body condition (FestaBianchet et al. 1998, Dobson et al. 1999), since individuals in better condition have more resources to allocate to their offspring than individuals in poorer condition. Therefore, relative maternal allocation, accounting for differences in mother condition, should better measure allocation strategies in capital breeders than absolute maternal allocation. Offspring mass, for instance, is often used as a measure of maternal allocation (Broussard et al. 2005, Ba˚rdsen et al. 2008, Hamel et al. 2011), but a ratio of offspring mass on mother mass should be more relevant to the fitness consequences of maternal allocation in these species. The latter has not commonly been used as a measure of maternal allocation because of the difficulty for gathering sufficient mass data on mother–offspring pairs (but see, e.g., Martin and Festa-Bianchet 2010). In addition to the influence of individual condition, several hypotheses pertain to maternal allocation strategies, and it is not always clear which underlining process operates. Allocation strategies are likely to vary according to other intrinsic characteristics of the mother, such as its age and previous reproductive experience (McNamara and Houston 1996). In agestructured populations, young individuals usually improve reproductive performance as they gain reproductive and foraging experience with age (reproductive constraint hypothesis; Curio 1983), whereas reproductive senescence leads to a decline in reproductive performance at older ages (McCleery et al. 2008, Rebke et al. 2010). Additionally, the terminal investment hypothesis predicts that individuals should invest more in reproduction as they age because their residual reproductive value decreases (Pianka and Parker 1975). A range of allocation patterns with age is therefore possible, depending on the relative importance of each process. Furthermore, life-history theory predicts trade-offs among life-history traits when resources are limited (Williams 1966). Allocation to one reproductive occasion should therefore reduce allocation to future reproductive attempts, leading to costs of reproduction (Stearns 1992). Allocation strategies should then vary between previously breeding and non-breeding individuals, but also among previous breeders depending on their relative allocation (Creighton et al. 2009, Hamel et al. 2011). Therefore, because offspring characteristics such as number, mass, and sex may reflect the amount of maternal allocation, current allocation might also be influenced by the characteristics of the previous offspring (Oksanen et al. 2002, Martin and Festa-Bianchet 2011). Many of the questions regarding reproduction and maternal traits come into focus for North American Plains bison (Bison bison). Bison are capital breeders

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because their reproduction depends on accumulated reserves. Females that have a higher body mass in the fall are more likely to give birth than lighter females, and parturient females lose body mass compared with barren females (Green and Rothstein 1991a). In addition, female mass and calf mass both show high variance and are influenced by climatic conditions (Craine et al. 2009). This suggests that reproductive potential and maternal allocation likely vary importantly among mothers, and that reproductive trade-offs should be more easily detected (Hamel et al. 2010). Furthermore, reproductive competition among males is intense and results in a high variance in male reproductive success (Roden et al. 2003), so there is a high potential for differential allocation between sons and daughters. In addition, most bison herds are actively managed based on culling decisions for juvenile that are usually depending on differences in mass among juvenile bison (Gates et al. 2010). Yet, there has been little accounting for co-variation in maternal condition and previous reproductive status that might affect juvenile mass when selecting animals to remain in herds or establishing new herds. Here, we use nine years of longitudinal data on marked bison to test a number of hypotheses (Appendix B: Table B1) regarding the factors affecting variation in maternal allocation among mothers and how current allocation influence future fitness. We assess not only which factors affected offspring mass at weaning, an absolute measure of allocation, but also the ratio of offspring mass on mother mass, which is a relative allocation measure that is better suited for measuring maternal allocation in this species. Specifically, we assessed (1) how maternal and offspring characteristics (mother mass, mother age, mother previous reproductive status, primiparity, calf sex, as well as previous calf sex and mass) influenced offspring mass and relative maternal allocation and (2) how previous allocation and maternal traits affected the probability of future reproduction and the allocation provided to the next offspring. In long-lived iteroparous species, mothers should adopt a conservative reproductive tactic adapted to their own condition (Festa-Bianchet and Jorgenson 1998, Martin and Festa-Bianchet 2010). Therefore, we expected to find a stronger influence of maternal traits on allocation strategies than offspring traits. Analyzing the patterns of reproductive performances in relation to maternal traits allowed us to test several evolutionary hypotheses. If offspring mass and relative maternal allocation decline with mother’s age, then reproductive senescence rather than terminal allocation takes place (Weladji et al. 2010). An increase in fitness costs of reproduction with mother’s age, such as a lower probability of future reproduction after allocating to current reproduction in old females will provide support to the terminal investment hypothesis (Weladji et al. 2010). The reproductive constraint hypothesis will be supported if maternal allocation and reproductive

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success are greater for multiparous than primiparous females, or if these reproductive performances increase with age in young females. The individual quality hypothesis will be supported if heavy females are found to reproduce successfully at each reproductive occasion, and to always produce heavier offspring by providing less relative maternal allocation than light females. In contrast, costs of reproduction will be supported if females that allocated more to reproduction show a reduced probability of reproducing at the next occasion and produce lighter future offspring than females that allocated less to reproduction. METHODS Study area and population Bison were weighed at the Konza Prairie (39805 0 N, 96835 0 W), a 34.9-km2 tallgrass prairie preserve in the northern Flint Hills ecoregion in Kansas, USA. Vegetation is dominated by perennial warm-season grasses, primarily Andropogon gerardii, Sorghastrum nutans, and Schizachyrium scoparium, but also cool-season grasses such as Bromus arvensis in infrequently burned areas. In 1987, 30 bison were introduced into a 4.5-km2 unit and in 1992, the area accessible to the animals expanded to 9.6 km2 spread across 10 watersheds (Towne 1999). Of these 10 watersheds, two have been burned in the spring since 1988 at each of three fire frequencies (1, 2, and 20 years), while four have been burned sequentially at 4year intervals. We considered the potential influence of using data from an introduced population to be negligible because data collection for this study started 15 years after the introduction, over a period when population size was maintain constant. Since 1994, bison are gathered into a corral trap each November, where each individual is weighed on an electronic chute scale. Bison calves are about seven months of age when weighed, about one month before physiological weaning (Green 1990). Although a calf is weaned at seven to eight months, it usually remains with the mother through the winter. Note that mass at weaning is a combination of mass at birth, resulting only from maternal allocation during gestation, and offspring growth until weaning, which results from both maternal allocation during lactation and offspring foraging. Nevertheless, the influence of foraging is usually assumed to be minimal in ungulates because maternal mass and milk production are the most important predictors of offspring growth rate in these species (Robbins and Robbins 1979). All calves are sexed and fitted with a numbered ear tag, providing age of every animal each year. Calf–mother pairs are identified by behavioral observations such as suckling and proximity soon after the annual roundup, ensuring that observations prior to roundup of mothers with calves match with those afterward. Supplemental feed was provided when the animals were held in the corral trap (i.e., approximately 3 days), but otherwise they were not nutritionally supplemented. Since 2000, female calves

received vaccinations for brucellosis and all animals received injections of ivermectin for internal parasite control. The desired stocking density of 30 bison/km2 was reached in 2002, and the overwintering population has since been maintained at about 300 animals by culling most 2-year-olds, males older than 7 years, and females that were either 15 years old and barren or had not calved in the previous two years. The sex ratio of mature females to males was maintained at approximately 5:1. Between 2002 and 2010, we performed censuses (near daily in spring to weekly in summer) to record presence/ absence of a calf for each mother, and hence determined the yearly reproductive status of each female. Calving typically begins in mid-April, with about 75% of all calves born by 1 June. We considered the date at which a calf was first observed as the approximate birth date, but parturition dates were likely underestimated for some calves born after peak calving. Reproductive rate of mature females included only calves that survived until the autumn roundup and averaged 65%, with a range of 44–83% among years. Calf mortality before roundup is difficult to determine, but it is likely between one and three calves per year at most if we exclude stillborn calf (E. G. Towne, personal observation). Primiparity for each mother was determined based on the visual surveys of calf pairings during the nine years, but also through surveys before 2002 that did not determine first occurrence dates of calves. Statistical analyses We first evaluated the influence of maternal characteristics and current and previous calf traits on variation in current calf mass using linear mixed models (LMMs). The first LMM included the following fixed effects: maternal mass, age, reproductive status the previous year (with vs. without a calf ), primiparity (primiparous vs. multiparous), current calf sex, as well as two-way interactions (Appendix A: Table A1). Because birth date of calves varied considerably in the spring and calves were all weighed at the same time in the autumn, we included calf birth date as a covariate in the model to account for calf age. The relationship between mother age and calf mass was not linear (Fig. 1), being low at age 2, increasing substantially at age 3 and remaining stable until age 8, after which it declined gradually until age 19. Although the data set included five 2-year-old mothers, calf birth date was only known for two of them, too few to compare this age class with other mothers. We therefore excluded these two 2-year-olds and analyzed mother age using an 8-year-old threshold model, so that age was coded under two continuous variables. The first variable described the relationship for mothers between age 3 and 8, and the second one the relationship between age 9 and 19. To account for repeated measures on mothers and possible cohort effects, we included ‘‘mother identity nested in mother cohort’’ and ‘‘mother cohort’’ as random intercepts. We

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FIG. 1. (A) Mother mass, (B) calf mass, (C) ratio of calf mass to mother mass, and (D) probability of future reproduction for females that had a calf in relation to mother age in bison (Konza Prairie, USA; 2002–2010). Values are means, and error bars are 95% CI. Numbers above the x-axis show the sample size of each age.

also included ‘‘year’’ as a random intercept to account for annual variation in resources and in environmental conditions that can influence calf mass. Note here that including ‘‘year’’ as a random effect does not explain how environmental variations might affect calf mass, but rather separates the variance associated with yearly variations in the environment from the influence of maternal traits on calf mass. This first LMM based on the complete data set included 640 calf mass measure-

ments recorded over nine years, including 190 mothers from 25 cohorts. We then performed a second LMM on a reduced data set that included only mothers that had a calf the previous year, to assess how traits of the previous calf affected the current calf mass. In addition to the variables already in the first LMM, we included previous calf sex, previous calf mass, and their interaction. This second LMM included 331 calf mass measurements over 9 years, including 130 mothers from

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FIG. 2. (A–C) Calf mass and (D–F) ratio of calf mass to mother mass in relation to (A, D) mother mass and sex of the calf, (C) mass of the calf produced by the mother the previous year, (B, E) mother mass and reproductive status of the mother the previous year, and (F) maternal allocation the previous year in bison (Konza Prairie, USA; 2002–2010). Dots represent actual values, solid and dashed lines represent models’ predictions, and dotted lines represent 95% CI.

22 cohorts. The range of calf mass measurements in the reduced data set was equivalent to that of the complete data set (Fig. 2A vs. 2C). Calf mass may not be representative of maternal allocation because heavier mothers may wean a calf of similar mass than lighter mothers, but this allocation would represent a lower relative allocation of resources compared with lighter mothers. Thus, we assessed in a second step whether relative maternal allocation (i.e., the ratio of calf mass on maternal mass, referred to as ‘‘maternal allocation’’ thereafter) varied according to the same variables tested in step one. We performed two new LMMs based on the complete and the reduced data sets used in step one. We included the same variables, but replaced (1) the response variable ‘‘calf mass’’ with ‘‘maternal allocation’’ and (2) the explanatory variable ‘‘calf mass the previous year’’ with ‘‘maternal allocation the previous year’’ (the ratio of calf on mother mass the previous year). In addition, we modeled mother age as one continuous variable because the relationship between maternal age and allocation showed a gradual decrease from age 3 to 19 (Fig. 1). Although 2-year-olds showed a much lower allocation than other young females, they were also excluded from these analyses

because calf birth date was only known for two 2-yearold mothers. As a final step, we assessed whether a mother allocation to her calf affected her probability of reproduction the following year, at time t þ 1. We performed a generalized linear mixed model (GLMM) using mother reproductive status at t þ 1 as the binary response variable, and including the same random effects as for the LMMs. As fixed effects, we included variables describing mother and calf traits at time t: maternal allocation, calf sex, mother mass, mother age, primiparity, and their interactions (listed in Appendix A: Table A3). Again, we included calf birth date as a covariate. The relationship between mother age and the probability of future reproduction was not linear (Fig. 1). The probability of future reproduction was slightly lower for primiparous females, aged 2 to 4, was then high and relatively stable in young and prime-aged multiparous females, aged 4 to 12, and finally dropped at age 13 to remain relatively stable until old ages (except for age 19, which included only three females). Because mother age and primiparity were highly correlated (all 2- and 3-year-olds were primiparous, most 4-year-olds were primiparous, and all mothers 5 years and older were multiparous; r ¼ 0.72), we could

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not include both variables in the same model. We therefore analyzed mother age in three categories: young and primiparous (2–4 years), young/prime-aged and multiparous (4–12 years), and old multiparous (13 years and older). We used ‘‘young/prime-aged multiparous’’ as the reference level, so that one estimate contrasted young primiparous vs. young/prime-aged multiparous, hence testing for the influence of primiparity (hereafter referred to as ‘‘primiparity’’), and the other estimate contrasted old multiparous vs. young/prime-aged multiparous, therefore testing for an age effect (hereafter referred to as ‘‘mother age’’). Similar results were obtained modeling age as a second-order polynomial, as a linear trend with a threshold at 12 years, or as a nonlinear relationship (using a generalized additive mixed model with the R package gamm4; available online).4 Because the model including age as a threecategory variable provided the lowest model deviance and controlled for the strong correlation between primiparity and mother age, we present results from this model only. For this analysis, although we only had two 2-year-olds for which calf birth date was available, we grouped these two females in the young primiparous age class. Results with and without these two mothers were similar. This GLMM included a total of 515 observations recorded over 8 years, including 165 mothers from 23 cohorts. All analyses were performed in R (R Development Core Team 2010) using the package lme4 (available online).5 For the LMMs, we used the function lmer, whereas for the GLMM we used glmer with a binomial family and a logit link. In mixed models, it is not obvious to determine the number of parameters included in the model, and therefore the degrees of freedom on which p values are computed are often approximated (Baayen et al. 2008). Some approximations can be overly conservative, while others can be anti-conservative. One way to avoid this issue is to perform Markov chain Monte Carlo (MCMC) bootstrapping based on the posterior distribution of the parameters, and estimate a 95% Bayesian highest posterior density confidence interval (also called 95% credible interval, hereafter referred to as CI, see Baayen et al. 2008 for details). Another advantage of using CI is that they present effect size and provide precision of estimates (Nakagawa and Cuthill 2007). We therefore considered that a variable had a significant influence if its CI excluded zero. For LMMs, CI were obtained using the R function pvals.fnc using 10 000 simulations (Baayen et al. 2008). This function, however, has not been implemented yet for GLMM. We therefore programmed a R script to obtain the CI for GLMM based on a similar method as for the function pvals.fnc (see Supplement). For the significant variables in the GLMM, we also presented odds ratios, a measure of 4 5

http://CRAN.R-project.org/package¼gamm4 http://CRAN.R-project.org/package¼lme4

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effect size in logistic regression (see footnote of Appendix A: Table A3 for details on interpretation of odds ratios). We centered all input variables and standardized all continuous variables. Centering input variables removes the collinearity between the main effects and the interaction predictors, therefore allowing the interpretation of main effects independently from interactions (Schielzeth 2010). Standardizing continuous variables allows comparing the importance of each predictor relative to one another (Schielzeth 2010). Because our models included binary predictors, we standardized continuous variables by dividing by two standard deviations to allow comparisons with binary variables (Gelman 2008). We present results following the order of relative importance of the predictors in the models. Because the interpretation of parameter estimates for variables standardized by dividing by two standard deviations can be more difficult than a normal standardization, we illustrated results based on the non-transformed variables. RESULTS Calf mass Across all calves, autumn mass varied from 61 to 219 kg (Fig. 2A, B). Approximate calf birth date had the strongest influence on calf mass; calves first observed in mid-April were 30 kg heavier at weaning than calves first observed in early June (Appendix A: Table A1). Once this variation was taken into account, calf mass increased with mother mass and decreased with age after mothers reached 8 years of age (Appendix A: Table A1). Mothers weighing 485 kg (first deciles) weaned calves 20 kg heavier than mothers weighing 375 kg (ninth deciles), independently of age. For mothers aged 3 to 8, calf mass averaged 145 kg, with no change in mean calf mass over this age range (Fig. 1B; Appendix A: Table A1). For mothers aged 9 to 19, calf mass at weaning decreased gradually from 145 to 125 kg (Fig. 1B; Appendix A: Table A1). This decline in calf mass with age was greater for heavy mothers than light mothers; the difference in calf mass at weaning between heavier and lighter mothers decreased as mothers aged (Fig. 3B). Calf mass was also impacted by whether mothers had a calf the year before. Mothers that had a calf the previous year weaned a calf 10 kg or 7% lighter than mothers that did not reproduce the previous year (Appendix A: Table A1). This difference also increased with mother mass, although there was a large variability (Fig. 2B; Appendix A: Table A1). Male calves weighed 12 kg or 8% more than female calves. In addition, the mass difference between sons and daughters increased with mother mass (Fig. 2A), and decreased with mother age from age 9 to 19 (Fig. 3A). Among females that had reproduced the previous year, calf masses in years t and t  1 were positively correlated (Fig. 2C; Appendix A: Table A1). Mothers that had a son the previous year produced calves that were 3 kg lighter than calves of

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FIG. 3. Calf mass in relation to mother age and (A) sex of the calf and (B) mother mass in bison (Konza Prairie, USA; 2002– 2010). Dots represent the mean (6SE) for each age based on real values, whereas the inserts illustrate the model’s predictions (dotted lines show 95% CI) for each group. For illustration purposes, female mass was divided in two quantiles, ‘‘heavier females’’ (294–433 kg) and ‘‘lighter females’’ (434–538 kg), representing mothers that weighed more and less than the median.

mothers that had a daughter the previous year (Appendix A: Table A1). Variation among years and mothers explained about 25% each of the residual variance in calf mass, whereas variation among mother cohorts explained little variation (Appendix A: Table A1) (Appendix C: Fig. C1). The average calf mass was 146 kg and varied by about 20 kg among both mothers and years (Appendix A: Table A1) (Appendix C: Fig. C1). Maternal allocation Analyses on maternal allocation mirrored those on calf mass, except that allocation did not appear to change with age (Fig. 1C; Appendix A: Table A2). Although

heavy mothers produced heavier calves (Fig. 2A), relative allocation decreased with increasing mother mass (Appendix A: Table A2). For example, relative maternal allocation was 5% lower for mothers weighing 485 kg than mothers weighing 375 kg. This difference in allocation with mother mass varied with primiparity (Appendix A: Table A2): mothers weighing 390 kg, the average mass of primiparous mothers (range ¼ 294–473 kg), allocated 3% more to their calf if they were primiparous than if they were multiparous. Similarly to calf mass, maternal allocation was higher if mothers did not have a calf the previous year (Fig. 2E). This effect, however, did not vary with mother mass (Fig. 2E; Appendix A: Table A2). Finally, mothers allocated about

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FIG. 4. Probability of future reproduction for bison mothers in relation to current mother mass (Konza Prairie, USA; 2002– 2010). The solid line represents the model’s predictions; dashed lines show 95% CI. Small vertical lines represent the distribution of the actual data.

2.5% more to a son than to a daughter (Appendix A: Table A2), a difference that increased with mother mass (Fig. 2D). Considering only mothers that had a calf the previous year (Appendix A: Table A2), results were similar to analyses on calf mass. Maternal allocation to the previous calf had the strongest influence on current allocation and was positively related to allocation to the current calf (Fig. 2F). Mothers that had a son the previous year allocated about 1.2% less to their current calf, independent of their sex, than mothers that had a daughter (Appendix A: Table A2). Overall, the order of importance for the predictors of variation in maternal allocation was the same as for variation in calf mass, except that maternal age was not important (Appendix A: Table A2). Much of the variability in maternal allocation resulted from variation among years and mothers, both explaining about 25% of the residual variance, whereas variation among mother cohorts was not important (Appendix A: Table A2) (Appendix C: Fig. C1). The average maternal allocation was 34% and varied by 65% among both mothers and years (Appendix A: Table A2) (Appendix C: Fig. C1).

Probability of future reproduction Mother mass and mother age were the strongest predictors of mothers’ probability of reproduction the following year (Appendix A: Table A3). The probability of weaning a calf again the next year was about 10 times more likely for each increase of 85 kg in mother mass (Fig. 4; odds ratio [CI] ¼ 10.6 [5.0–25.8] for one unit of the standardized variable ‘‘mother mass,’’ where one standardized unit equaled 85 kg, see footnote in Table A3 of Appendix A). Old multiparous mothers were 10 times less likely to wean a calf again the next year than young/ prime-aged multiparous mothers (Appendix A: Table A3; odds ratio ¼ 0.095 [0.015–0.399]). There was also an influence of approximate parturition date: the probability of successive reproduction was half as likely for mothers that had a parturition delay of 40 days (Appendix A: Table A3; odds ratio ¼ 0.45 [0.24–0.81] for one unit of the standardized variable ‘‘birthdate’’, where one standardized unit equaled 40 days). The importance of this covariate, however, was three times smaller than mother mass and age (Appendix A: Table A3). Much of the variability in the probability of future reproduction resulted from variation among mothers,

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explaining about 62% of the residual variance, whereas variation among years was lower and variation among mother cohorts was not important (Appendix A: Table A3) (Appendix C: Fig. C1). The average probability of future reproduction of mothers was 60% and varied by 613% among mothers and 68% among years (Appendix A: Table A3) (Appendix C: Fig. C1). In contrast to the analyses of calf mass and maternal allocation, variation in the probability of reproduction among mothers was greater than variation within mothers (Appendix C: Fig. C1). DISCUSSION Although variation in maternal allocation in bison was influenced by offspring traits, most variation resulted from differences in maternal characteristics. These results suggest that bison mothers adjust their allocation primarily to their own condition rather than to the offspring they produced, in agreement with the conservative reproductive strategy usually observed in long-lived iteroparous species (Clutton-Brock 1988). In opposition to predictions from life-history theory, previous maternal allocation did not influence the probability of breeding in successive years. Instead, future reproduction was principally affected by mothers’ mass and age. Overall, year and mother identity accounted for a large portion of the model’s residual variance for both maternal allocation and future reproduction. This finding suggests that in addition to annual variation in maternal characteristics, lifetime maternal traits, fixed at birth or during development (Tuljapurkar et al. 2009), and annual variation in environmental conditions also influence maternal allocation strategies. Since these annual variations accounted for 25 to 40% of the variance, future studies should aim at determining which environmental factors modulate these variations in allocation strategies in bison. In bison, mother mass, age, and reproductive experience had the greatest influence on absolute and relative maternal allocation strategies, as well as on the probability of breeding in consecutive years. The most influential maternal trait was mass. Maternal mass often has a pivotal influence in female reproductive strategies (Bercovitch et al. 1998, Broussard et al. 2005), particularly in capital breeders like bison because heavier individuals have more stored resources than lighter individuals (Festa-Bianchet et al. 1998). Interestingly, heavy bison mothers produced heavier offspring than light mothers, but they allocated relatively less resources to produce their calves than lighter mothers. This, along with the finding that heavier mothers also had a greater probability of reproducing again in the next reproductive attempt than lighter mothers, suggests that heavy mothers were less resource limited than light mothers. These results illustrate the critical value of having a high mass for reproduction in capital breeders. They also reinforce the profound importance of maternal mass as a decisive quality in female reproduc-

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tion (Jones et al. 2010), and confirm the positive covariation among traits previously found in other species that suggested that females with high-quality traits often perform better (Dobson et al. 1999, McCleery et al. 2008, Hamel et al. 2009). In age-structured populations, reproductive strategy is expected to vary with age. According to the reproductive constraint hypothesis, an improvement is first expected in young individuals as they gain reproductive experience before they reach the prime-aged plateau (Curio 1983). Although few 2-year-old females produced calves, both calf mass and maternal allocation were low in 2year-old mothers and then dramatically increased in the ensuing years. In addition, primiparous mothers produced offspring of similar mass to those of multiparous females, but had to allocate a greater percentage of their stored resources to do so. Our results thus suggest that inexperienced mothers might suffer from a lower physiological capacity or lower energy transfer efficiency than experienced mothers (Green 1990, Ku¨nkele and Kenagy 1997, Lang et al. 2011). After the prime-age stage, a decrease in reproductive performances is expected in older individuals due to senescence (Williams 1957). Nevertheless, the terminal investment hypothesis stipulates that investment in reproduction should increase as females age because their residual reproductive value declines (Pianka and Parker 1975). Few studies have been able to show actual terminal investment, but many have demonstrated the existence of terminal allocation (Weladji et al. 2010). In our study, very old mothers and females that had not reproduced in the past two years were removed from the population, and this selective culling likely underestimated the senescence patterns (Rebke et al. 2010) and overestimated terminal investment or allocation processes. Although research in natural or non-selectively culled populations will be required to clearly evaluate biological patterns in old bison, our findings point toward the occurrence of senescence rather than terminal investment/allocation because no trait showed improvement at older ages. Instead, the mass of the calf produced and the probability of future reproduction both declined after females reached asymptotic mass (as in other bison populations; Shaw and Carter 1989, Green 1990), and the relative maternal allocation showed a slight, although not significant, decline with age. Reproduction the previous year also influenced reproductive allocation patterns. Mothers that weaned a calf the previous year produced lighter offspring and allocated less to their new offspring than mothers that did not lactate the previous year. Among previous breeders, however, mothers that had allocated more to their offspring also allocated more to their new offspring than mothers that had allocated less. These results suggest two underlying processes. First, reproduction per se has a negative impact on subsequent offspring, supporting the occurrence of indirect costs of reproduction (sensu Hamel et al. 2010). Second, the level of

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allocation provided is positively correlated among the offspring a mother produces, supporting again the occurrence of individual quality effects. Many lifehistory studies are often classified as either supporting costs of reproduction or individual quality effects (e.g., Weladji et al. 2008, Fisher and Blomberg 2011). Our work, however, demonstrates that these two contrasting processes can co-occur within a population, reinforcing the importance of studying the covariation among as many traits as possible. Increased maternal allocation can result in fitness costs of reproduction, as shown in mountain goat (Oreamnos americanus) where mothers producing heavier offspring had a reduced probability of future reproduction (Hamel et al. 2011). In red deer (Cervus elaphus; Clutton-Brock et al. 1983) and in the bison population we studied, however, the amount of maternal allocation did not influence mothers’ future reproduction. Allocation can be measured as a binary outcome, contrasting breeders vs. non-breeders (i.e., females allocating vs. not, so maternal allocation per se), or as a continuous variable that compares the amount of allocation among breeders. In contrast with maternal allocation per se, the influence of variation in the amount of maternal allocation has rarely been studied in wild species, likely owing to the scarcity of longitudinal data on offspring mass in long-lived species. It is therefore difficult to determine the cause for the nondetection of costs of reproduction resulting from variation in the amount of maternal allocation among breeders. On one hand, this cost might be rarely detected because the amount of maternal allocation is less variable than other reproductive traits (Hamel et al. 2010). Variability in maternal allocation could be low because it is usually measured using female mass, as in our study, and mass consists of variation in both body reserves and size. Using a direct measure of body reserves is likely to better represent female variation in maternal allocation, but obtaining reliable body fat measures is challenging in live animals. On the other hand, reproduction (maternal allocation per se) might be limited in this population, but when a female does reproduce, the amount of allocation she is able to provide might not be limited. This seems to be supported by the findings that mothers that had allocated to reproduction the previous year, no matter how much, allocated less to their new offspring than mothers that did not allocate the previous year, but if a mother allocated more relative to other mothers, she also allocated more the following year. More studies are needed to evaluate whether among-mother variation in maternal allocation leads to important fitness costs of reproduction in long-lived species. Offspring sex affected allocation strategies, although it was less important than maternal characteristics. As expected for polygamous species, females produced heavier offspring and appeared to allocate more resource if they nursed a son than a daughter. Caution

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should be used in interpreting weaning masses as a direct index of allocation, since some of the mass gained by offspring comes from direct foraging, which does not impose energetic costs to mothers. Despite this caveat, additional evidence supports the occurrence of greater energetic costs of sons compared to daughters. Mothers that had a son the previous year produced lighter offspring and allocated less resource to their new offspring, irrespective of their sex, than if they had had a daughter the previous year. These results support previous findings in other polygamous species that sons require more allocation than daughters (Festa-Bianchet et al. 1994, Bercovitch et al. 2000). Greater allocation to sons can lead to sex-differential costs of reproduction, either as reproductive pauses (Gomendio et al. 1990) or lower probability of producing sons in consecutive years (Be´rube´ et al. 1996). Reproduction of bison mothers, however, was not influenced by the sex of the offspring they produced the previous year, as reported in another bison population (Green and Rothstein 1991b). This suggests that the greater allocation provided to a son is not an overriding cost for a bison mother. This, along with our finding that the amount of allocation did not affect future reproduction, supports again that maternal allocation was not limited among bison mothers. It further suggests that costs of reproduction are likely to be more detectable by contrasting females allocating vs. not allocating to reproduction rather than by contrasting mothers providing different amount of allocation. As in many other species, offspring mass in bison has a central influence on future body condition and reproductive success (Green and Rothstein 1991b). Understanding maternal allocation strategies is therefore essential, since they have fundamental consequences on long-term evolutionary pressures and population dynamics. Using a nine-year longitudinal data set on several life-history traits of mother–offspring pairs, we have shown that maternal characteristics had the strongest influence on maternal allocation strategies. Even though many hypotheses have been proposed to explain distinct evolutionary processes related to reproduction, our results suggest that several of these processes can co-occur within a population. Indeed, our study provides support to the individual quality, the costs of reproduction, the reproductive constraint, and the senescence hypotheses, demonstrating that many processes can coevolve within a population. Therefore, studies need to integrate these different concepts to fully understand the evolution of life-history traits. This research also has important implications for management decisions. Most bison herds are actively managed through culling decisions on juveniles (Gates et al. 2010). Along with questions of the age structure of animals selected for culling (Millspaugh et al. 2008, Buhnerkempe et al. 2011), individuals can also be selected based on their performance in a given environment, for example by selecting the heaviest calves or the mothers that produce the heaviest calves to remain in a herd.

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Although there has been little research into culling strategies for bison, if performance is to be incorporated to allow managers to make more informed decisions on which females and juveniles to cull, our research suggests that maternal condition, age, and previous reproductive status, as well as offspring birth date should be considered for selection criteria in herds not supplemented nutritionally. If culling aims at maximizing production, light and old females should be selected against because they produce lighter calves and have a lower probability of future reproduction. If the goal of culling is to select the most fit calves and fitness is related to mass, calves born early in the season from young/ prime-aged mothers that were barren the previous year should be selected since they are more likely to have higher mass. Also, comparing two calves of equal mass would suggest that calves born late from older mothers that had reproduced previously might actually perform better later in life having already overcome a number of disadvantages. Accounting for variation in maternal effects on calf mass can assist in decisions at an early age about the potential for lifetime fitness of animals. ACKNOWLEDGMENTS This research was supported by National Science Foundation grant DEB-0816629 to J. M. Craine and grants to the Konza Prairie LTER. Numerous volunteers, especially T. VanSlyke and J. Larkins, assisted in roundups. We are grateful to B. Bolker for help with the MCMC bootstrapping for the GLMM. We thank R. Rødven for fruitful discussions and S. D. Cˆote´ and M. Festa-Bianchet for constructive comments on a previous draft of the manuscript. LITERATURE CITED Baayen, R. H., D. J. Davidson, and D. M. Bates. 2008. Mixedeffects modeling with crossed random effects for subjects and items. Journal of Memory and Language 59:390–412. Ba˚rdsen, B.-J., P. Fauchald, T. Tveraa, K. Langeland, N. G. Yoccoz, and R. A. Ims. 2008. Experimental evidence of a risk-sensitive reproductive allocation in a long-lived mammal. Ecology 89:829–837. Baron, J.-P., J.-F. Le Galliard, T. Tully, and R. Ferrie`re. 2010. Cohort variation in offspring growth and survival: prenatal and postnatal factors in a late-maturing viviparous snake. Journal of Animal Ecology 79:640–649. Bercovitch, F. B., M. R. Lebron, H. S. Martinez, and M. J. Kessler. 1998. Primigravidity, body weight, and costs of rearing first offspring in rhesus macaques. American Journal of Primatology 46:135–144. Bercovitch, F. B., A. Widdig, and P. Nu¨rnberg. 2000. Maternal investment in rhesus macaques (Macaca mulatta): reproductive costs and consequences of raising sons. Behavioral Ecology and Sociobiology 48:1–11. Broussard, D. R., F. S. Dobson, and J. O. Murie. 2005. The effects of capital on an income breeder: evidence from female Columbian ground squirrels. Canadian Journal of Zoology 83:546–552. Be´rube´, C. H., M. Festa-Bianchet, and J. T. Jorgenson. 1996. Reproductive costs of sons and daughters in Rocky Mountain bighorn sheep. Behavioral Ecology 7:60–68. Buhnerkempe, M. G., N. Burch, S. Hamilton, K. M. Byrne, E. Childers, K. A. Holfelder, L. N. McManus, M. I. Pyne, G. Schroeder, and P. F. Doherty. 2011. The utility of transient sensitivity for wildlife management and conservation: Bison as a case study. Biological Conservation 144:1808–1815.

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Clutton-Brock, T. H. 1988. Reproductive success: studies of individual variation in contrasting breeding systems. University of Chicago Press, Chicago, Illinois, USA. Clutton-Brock, T. H., F. E. Guinness, and S. D. Albon. 1983. The costs of reproduction to red deer hinds. Journal of Animal Ecology 52:367–383. Craine, J. M., E. G. Towne, A. Joern, and R. G. Hamilton. 2009. Consequences of climate variability for the performance of bison in tallgrass prairie. Global Change Biology 15:772–779. Creighton, J. C., N. D. Heflin, and M. C. Belk. 2009. Cost of reproduction, resource quality, and terminal investment in a burying beetle. American Naturalist 174:673–684. Curio, E. 1983. Why do young birds reproduce less well? Ibis 125:400–404. Dobson, F. S., T. S. Risch, and J. O. Murie. 1999. Increasing returns in the life history of Columbian ground squirrels. Journal of Animal Ecology 68:73–86. Festa-Bianchet, M., J.-M. Gaillard, and J. T. Jorgenson. 1998. Mass- and density-dependent reproductive success and reproductive costs in a capital breeder. American Naturalist 152:367–379. Festa-Bianchet, M., and J. T. Jorgenson. 1998. Selfish mothers: reproductive expenditure and resource availability in bighorn ewes. Behavioral Ecology 9:144–150. Festa-Bianchet, M., J. T. Jorgenson, and W. D. Wishart. 1994. Early weaning in bighorn sheep, Ovis canadensis, affects growth of males but not of females. Behavioral Ecology 5:21– 27. Fisher, D. O., and S. P. Blomberg. 2011. Costs of reproduction and terminal investment by females in a semelparous marsupial. PLoS ONE 6:e15226. Gaillard, J.-M., M. Festa-Bianchet, N. G. Yoccoz, A. Loison, and C. Toı¨ go. 2000. Temporal variation in fitness components and population dynamics of large herbivores. Annual Review of Ecology, Evolution, and Systematics 31:367–393. Gates, C. C., C. H. Freese, P. J. P. Gogan, and M. Kotzman. 2010. American bison: status survey and conservation guidelines 2010. International Union for the Conservation of Nature, Gland, Switzerland. Gelman, A. 2008. Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine 27:2865–2873. Gomendio, M., T. H. Clutton-Brock, S. D. Albon, F. E. Guinness, and M. J. Simpson. 1990. Mammalian sex ratios and variation in costs of rearing sons and daughters. Nature 343:261–263. Green, W. C. H. 1990. Reproductive effort and associated costs in bison (Bison bison): do older mothers try harder? Behavioral Ecology 1:148–160. Green, W. C. H., and A. Rothstein. 1991a. Trade-offs between growth and reproduction in female bison. Oecologia 86:521– 527. Green, W. C. H., and A. Rothstein. 1991b. Sex bias or equal opportunity? Patterns of maternal investment in bison. Behavioral Ecology and Sociobiology 29:373–384. Hamel, S., S. D. Cˆote´, and M. Festa-Bianchet. 2011. Tradeoff between offspring mass and subsequent reproduction in a highly iteroparous mammal. Oikos 120:690–695. Hamel, S., S. D. Cˆote´, J.-M. Gaillard, and M. Festa-Bianchet. 2009. Individual variation in reproductive costs of reproduction: high-quality females always do better. Journal of Animal Ecology 78:143–151. Hamel, S., J.-M. Gaillard, N. G. Yoccoz, A. Loison, C. Bonenfant, and S. Descamps. 2010. Fitness costs of reproduction depend on life speed: empirical evidence from mammalian populations. Ecology Letters 13:915–935. Jones, J. H., M. L. Wilson, C. Murray, and A. Pusey. 2010. Phenotypic quality influences fertility in Gombe chimpanzees. Journal of Animal Ecology 79:1262–1269. Jo¨nsson, K. I. 1997. Capital and income breeding as alternative tactics of resource use in reproduction. Oikos 78:57–66.

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MATERNAL ALLOCATION IN BISON

King, E. G., D. A. Roff, and D. J. Fairbairn. 2011. Trade-off acquisition and allocation in Gryllus firmus: a test of the Y model. Journal of Evolutionary Biology 24:256–264. Ku¨nkele, J., and G. J. Kenagy. 1997. Inefficiency of lactation in primiparous rats: the costs of first reproduction. Physiological Zoology 70:571–577. Lang, S. L. C., S. J. Iverson, and W. D. Bowen. 2011. The influence of reproductive experience on milk energy output and lactation performance in the grey seal (Halichoerus grypus). PLoS ONE 6:e19487. Lee, P. H., and C. J. Moss. 1986. Early maternal investment in male and female African elephant calves. Behavioral Ecology and Sociobiology 18:353–361. Levitis, D. A. 2011. Before senescence: the evolutionary demography of ontogenesis. Proceedings of the Royal Society B 278:801–809. Lindstro¨m, J. 1999. Early development and fitness in birds and mammals. Trends in Ecology and Evolution 14:343–348. Martin, J. G. A., and M. Festa-Bianchet. 2010. Bighorn ewes transfer the costs of reproduction to their lambs. American Naturalist 176:414–423. Martin, J. G. A., and M. Festa-Bianchet. 2011. Sex ratio bias and reproductive strategies: what sex to produce when? Ecology 92:441–449. McCleery, R. H., C. M. Perrins, B. C. Sheldon, and A. Charmantier. 2008. Age-specific reproduction in a long-lived species: the combined effects of senescence and individual quality. Proceedings of the Royal Society B 275:963–970. McNamara, J. M., and A. I. Houston. 1996. State-dependent life histories. Nature 380:215–221. Millspaugh, J. J., R. A. Gitzen, D. S. Licht, S. Amelon, T. W. Bonnot, D. S. Jachowski, D. T. Jones-Farrand, B. J. Keller, C. P. McGowan, M. S. Pruett, C. D. Rittenhouse, and K. M. S. Wells. 2008. Effects of culling on bison demographics in Wind Cave National Park, South Dakota. Natural Areas Journal 28:240–250. Nakagawa, S., and I. C. Cuthill. 2007. Effect size, confidence interval and statistical significance: a practical guide for biologists. Biological Reviews 82:591–605. Oksanen, T. A., E. Koskela, and T. Mappes. 2002. Hormonal manipulation of offspring number: maternal effort and reproductive costs. Evolution 56:1530–1537. Pianka, E. R., and W. S. Parker. 1975. Age-specific reproductive tactics. American Naturalist 109:453–464. R Development Core Team. 2010. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Rebke, M., T. Coulson, P. H. Becker, and J. W. Vaupel. 2010. Reproductive improvement and senescence in a long-lived bird. Proceedings of the National Academy of Sciences USA 107:7841–7846. Robbins, C. T., and B. L. Robbins. 1979. Fetal and neonatal growth patterns and maternal reproductive effort in ungulates and subungulates. American Naturalist 114:101–116.

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Roden, C., V. Hilde, M. Guy, and V. E. Linda. 2003. Reproductive success of bison bulls (Bison bison bison) in semi-natural conditions. Animal Reproduction Science 79:33–43. Schielzeth, H. 2010. Simple means to improve the interpretability of regression coefficients. Methods in Ecology and Evolution 1:103–113. Schubert, K. A., G. de Vries, L. M. Vaanholt, H. A. J. Meijer, S. Daan, and S. Verhulst. 2009. Maternal energy allocation to offspring increases with environmental quality in house mice. American Naturalist 173:831–840. Shaw, J. H., and T. S. Carter. 1989. Calving patterns among American bison. Journal of Wildlife Management 53:896– 898. Skibiel, A. L., F. S. Dobson, and J. O. Murie. 2009. Maternal influences on reproduction in two populations of Columbian ground squirrels. Ecological Monographs 79:325–341. Stearns, S. C. 1992. The evolution of life histories. Oxford University Press, Oxford, UK. Towne, E. G. 1999. Bison performance and productivity on tallgrass prairie. Southwestern Naturalist 44:361–366. Trivers, R. L. 1972. Parental investment and sexual selection. Pages 138–179 in B. Campbell, editor. Sexual selection and the descent of man. Aldine Publishing, Chicago, Illinois, USA. Trivers, R. L., and D. E. Willard. 1973. Natural selection of parental ability to vary the sex ratio of offspring. Science 179:90–92. Tuljapurkar, S., U. K. Steiner, and S. H. Orzack. 2009. Dynamic heterogeneity in life histories. Ecology Letters 12:93–106. Weladji, R. B., Ø. Holand, J.-M. Gaillard, N. G. Yoccoz, A. Mysterud, M. Nieminen, and N. C. Stenseth. 2010. Agespecific changes in different components of reproductive output in female reindeer: terminal allocation or senescence? Oecologia 162:261–271. Weladji, R. B., A. Loison, J.-M. Gaillard, Ø. Holand, A. Mysterud, N. G. Yoccoz, M. Nieminen, and N. C. Stenseth. 2008. Heterogeneity in individual quality overrides costs of reproduction in female reindeer. Oecologia 156:237–247. White, A. M., R. R. Swaisgood, and N. Czekala. 2007. Differential investment in sons and daughters: do white rhinoceros mothers favor sons? Journal of Mammalogy 88:632–638. Williams, G. C. 1957. Pleiotropy, natural selection, and the evolution of senescence. Evolution 11:398–411. Williams, G. C. 1966. Natural selection, the costs of reproduction, and a refinement of Lack’s principle. American Naturalist 100:687–690. Ylo¨nen, H., T. J. Horne, and M. Luukkonen. 2004. Effect of birth and weaning mass on growth, survival and reproduction in the bank vole. Evolutionary Ecology Research 6:433– 442.

SUPPLEMENTAL MATERIAL Appendix A Summary of the LMM and GLMM models (Ecological Archives A022-086-A1). Appendix B Summary of the hypotheses evaluated and how they were supported by our study (Ecological Archives A022-086-A2). Appendix C Prediction intervals for the random effects (Ecological Archives A022-086-A3). Supplement R code for producing a function equivalent to pvals.fnc for GLMMs (Ecological Archives A022-086-S1).

Appendix A. Summary of the LMM and GLMM models. Table A1. Summary of the LMM models describing variation in bison calf mass at weaning in relation to maternal traits and current calf traits (A, complete data set: nTOTAL = 640, nMOTHER = 190, nCOHORT = 25, nYEAR = 9), as well as to the previous calf traits (B, reduced data set including only mothers that had a calf the previous year: nTOTAL = 331, nMOTHER = 130, nCOHORT = 22, nYEAR = 9). A: Complete model - all females (R2=0.67) Fixed variable: Intercept Calf sex (M) Mother mass Mother age.1 Mother age.2 Status t-1 (Calf) Primiparity (Yes) Birthdate Calf sex (M)*Mother mass Calf sex (M)*Mother age.1 Calf sex (M)*Mother age.2 Calf sex (M)*Status t-1 (Calf) Mother mass*Mother age.1 Mother mass*Mother age.2 Mother mass*Status t-1 (Calf) Calf sex (M)*Primiparity (Yes) Mother age.1*Primiparity (Yes) Mother mass*Primiparity (Yes) Random variable (intercept): Mother ID (nested in Mother cohort) Mother cohort Year Residual

Estimate (95% CI) 146.03 (130.91; 156.54) 5.78 (3.69; 7.95) 15.01 (10.25; 21.76) 10.77 (-7.92; 22.33) -11.93 (-15.94; -7.27) -4.40 (-6.33; -2.97) 5.66 (-8.07; 14.10) -26.48 (-29.56; -24.00) 4.91 (1.87; 8.12) 3.63 (-1.84; 7.67) -4.03 (-7.33; -0.97) -0.05 (-1.66; 1.37) 11.25 (2.28; 22.33) -10.46 (-18.48; -0.72) -4.03 (-6.91; -0.20) 2.69 (-0.20; 5.25) 6.30 (-11.64; 17.55) -0.56 (-6.88; 6.21) Variance SD 104.63 10.23 1.99 1.41 107.66 10.38 200.45 14.16

t-value 22.74 5.63 4.96 1.46 -5.49 -5.38 1.05 -19.60 3.23 1.60 -2.64 -0.07 2.28 -2.33 -2.51 2.04 0.89 -0.18 %V 25 0.5 26

B: Reduced model - females that had a calf the previous year (R2=0.60) Fixed variable: Calf sex t-1 (M) Calf mass t-1 Calf sex t-1 (M)*Calf mass t-1

Estimate (95% CI) -2.68 (-4.70; -0.75) 14.41 (9.50; 19.22) -1.26 (-5.31; 2.68)

t-value -2.07 3.98 -0.71

Notes: Significant effects are shown in bold. For the reduced data set, estimates are only presented for the variables that were not already included in the model based on the complete data set. All input variables were centred, and continuous variables were standardized by dividing by two standard deviations, so that all parameter estimates can be used as a measure of relative importance of each variable (see Methods). The reference level for the categorical

variables is shown in parentheses. R2: generalized R2 of Nagelkerke (1991), CI: Bayesian highest posterior density confidence intervals (see Methods); SD: standard deviation; %V: percentage of the total residual variance explained by each random effect. Calf sex: male (M) vs. female; Calf sex t-1: sex of the previous calf; Calf mass t-1: mass of the previous calf; Status t-1: reproductive status the previous year, had a calf (Calf) vs. did not have a calf; Primiparity: primiparous females (Yes) vs. multiparous females; Mother ID: mother identification. We used a threshold model to estimate the influence of mother age: Mother age.1 is a continuous variable from age 3 to 8, and Mother age.2 is a continuous variable from age 9 to 19 (see Methods).

Table A2. Summary of the LMM models describing variation in relative maternal allocation (ratio of calf mass on mother mass) in bison, in relation to maternal mother traits and current calf traits (A, complete data set: nTOTAL = 640, nMOTHER = 190, nCOHORT = 25, nYEAR = 9), as well as to the previous calf traits (B, reduced data set including only mothers that had a calf the previous year: nTOTAL = 331, nMOTHER = 130, nCOHORT = 22, nYEAR = 9). A: Complete model - all females (R2=0.49) Fixed variable: Intercept Calf sex (M) Mother mass Mother age Status t-1 (Calf) Primiparity (Yes) Birthdate Calf sex (M)*Mother mass Calf sex (M)*Mother age Calf sex (M)*Status t-1 (Calf) Mother mass*Mother age Mother mass*Status t-1 (Calf) Calf sex (M)*Primiparity (Yes) Mother age*Primiparity (Yes) Mother mass*Primiparity (Yes) Random variable (intercept): Mother ID (nested in Mother cohort) Mother cohort Year Residual

Estimate (95% CI) 0.339 (0.289; 0.372) 0.012 (0.007; 0.017) -0.037 (-0.050; -0.024) -0.006 (-0.076; 0.065) -0.009 (-0.014; -0.006) 0.012 (-0.036; 0.041) -0.060 (-0.068; -0.055) 0.011 (0.004; 0.019) -0.003 (-0.011; 0.004) 0.0001 (-0.004; 0.003) -0.009 (-0.023; 0.014) -0.005 (-0.012; 0.004) 0.004 (-0.002; 0.009) 0.030 (-0.051; 0.090) -0.016 (-0.029; -0.002) Variance 0.00055 0.00004 0.00059 0.00115

SD 0.023 0.006 0.024 0.034

t-value 16.87 5.02 -5.55 -0.17 -4.67 0.63 -18.69 3.22 -0.69 0.08 -1.00 -1.36 1.51 0.89 -2.56 %V 24 2 25

B: Reduced model - females that had a calf the previous year (R2=0.26) Fixed variable: Calf sex t-1 (M) Ratio calf mass t-1 Calf sex t-1 (M)*Ratio calf mass t-1

Estimate (95% CI) -0.006 (-0.011; -0.001) 0.028 (0.016; 0.039) -0.001 (-0.011; 0.008)

t-value -2.07 3.14 -0.38

Notes: Ratio calf mass t-1: maternal allocation the previous year, ratio of calf mass the previous year on mother mass the previous year; Mother age: mother age as a continuous variable from age 3 to 19. See footnotes of Table A1 for the other abbreviations’ definitions and for table specifications.

Table A3. Summary of the GLMM model describing the probability of reproduction the following year (t+1) for bison mothers in relation to current traits of both the mother and the calf (nTOTAL = 515, nMOTHER = 165, nCOHORT = 23, nYEAR = 8). Fixed variable: Estimate (95% CI) z-value Intercept 0.38 (-0.23; 0.95) 1.42 Calf sex (M) 0.01 (-0.24; 0.27) 0.01 Ratio calf mass 0.26 (-0.47; 0.99) 0.67 Mother mass 2.36 (1.60; 3.25) 6.26 Mother age (Old) -2.35 (-4.17; -0.92) -3.23 Primiparity (Yes) 0.64 (-0.31; 1.71) 1.22 Birthdate -0.80 (-1.43; -0.21) -2.73 Calf sex (M)*Ratio calf mass -0.50 (-1.05; 0.01) -1.97 Calf sex (M)*Mother mass 0.32 (-0.27; 0.94) 1.05 Calf sex (M)*Mother age (Old) 0.64 (-0.28; 1.72) 1.36 Calf sex (M)*Primiparity (Yes) 0.06 (-0.63; 0.73) 0.18 Ratio calf mass*Mother mass 0.41 (-0.92; 1.75) 0.61 Ratio calf mass*Mother age (Old) 1.51 (-0.57; 4.23) 1.19 Ratio calf mass*Primiparity (Yes) 0.30 (-1.29; 1.98) 0.33 Mother mass*Mother age (Old) 2.25 (-0.52; 6.17) 1.31 Mother mass*Primiparity (Yes) 1.01 (-0.75; 2.96) 1.03 Random variable (intercept): Mother ID (nested in Mother cohort) Mother cohort Year

Variance 0.63 0 0.39

SD 0.79 0 0.63

%V 62 0 38

Notes: Significant effects are shown in bold. All input variables were centred, and continuous variables were standardized by dividing by two standard deviations, so that all parameter estimates can be used as a measure of relative importance of each variable (see Methods). The reference level for the categorical variables is shown in parentheses. CI: Bayesian highest posterior density confidence intervals (see Methods); SD: standard deviation; %V: percentage of the total residual variance explained by each random effect. Calf sex: male (M) vs. female; Ratio calf mass: maternal allocation, ratio of calf mass on mother mass; Mother age: mother age in two categories, young/prime-aged multiparous females (4-12 years) vs. old multiparous females (13 years and older, “Old”); Primiparity: young primiparous females (2-4 years, “Yes”) vs. young/prime-aged multiparous females (4-12 years); Mother ID: mother identification. Model AUC = 0.75 (AUC=area under the receiver operating characteristic curve, which measures the overall predictive accuracy of a model independent of a specific threshold; Fielding & Bell, 1997). AUC values vary from 0.5 (very poor fit) to 1 (excellent fit), and represent the percentage of randomly drawn pairs (i.e. one of each group) that the model classifies correctly. In the Result section, we presented the GLMM estimates in the form of odds ratios, a measure of effect size in logistic regression. An odds ratio is the odds of an event occurring in one group to the odds of it occurring in another group, i.e. [p/(1−p)] / [q/(1−q)], where p and q represent the probabilities of each event. An odds ratio of 1 indicates that the event is equally probable in both groups. When the ratio moves towards 0, the event is less likely to occur in the first group, whereas when it moves towards infinity, the event is more likely to occur in the first group. For a continuous variable, an odds ratio is the odds of an event occurring with an increase of one unit of the variable. Because continuous variables were standardized (see below), one unit of a variable represented a wide range of the same variable non-standardized. For example, a difference of one unit for the standardized variable female mass represented an actual variation of 85 kg. Thus, an odd ratio of 5 would mean that the event is 5 times more likely to occur with each increase of 85 kg in female mass.

LITERATURE CITED Fielding, A.H. AND J.F. Bell. 1997. A review of methods for the assessment of prediction errors in conservation presence/absence models. Environmental Conservation 24:38-49. Nagelkerke, N.J.D. 1991. A note on a general definition of the coefficient of determination. Biometrika 78:691-692.

Appendix B. Summary of the hypotheses evaluated and how they were supported by our study. Table B1. Summary of hypotheses, predictions, and the evidences of support provided by our study. Hypotheses Conservative reproductive tactic

Predictions Stronger influence of maternal traits on allocation strategies than offspring traits

Reproductive senescence

Offspring mass, relative maternal allocation, and/or reproductive success decline with mother age

Terminal allocation

Offspring mass, relative maternal allocation, and/or reproductive success decline with mother age

Terminal investment

Fitness costs of reproduction, i.e. probability of future reproduction after allocating to current reproduction, increase with mother age Offspring mass, relative maternal allocation and reproductive success increase with age in young females, and/or are greater in multiparous than primiparous females

Reproductive constraint

Results Support Offspring traits had an influence but the greatest variation in Yes maternal allocation and in the probability of future reproduction was explained by mother mass, age, and previous reproductive status Mass of offspring produced progressively declined from age 8 (age Yes* at which asymptotic mass is reached) until death; probability of reproduction declined importantly from age 12 until death; maternal allocation showed a slight but non-significant decline from age 3 until death Mass of offspring produced progressively declined from age 8 (age No* at which asymptotic mass is reached) until death; probability of reproduction declined importantly from age 12 until death; maternal allocation showed a slight but non-significant decline from age 3 until death Costs of reproduction did not vary with age No*

Calf mass and maternal allocation were low in 2-year-old mothers and increased dramatically in the ensuing years; probability of reproducing in successive years increased with age in young females; primiparous mothers allocated more to their offspring but produced offspring of similar mass

Yes

Individual quality

Heavy females reproduce successfully at each reproductive occasion and produce heavier offspring by providing less relative maternal allocation than light females

Large residual variance in calf mass, maternal allocation, and probability of future reproduction explained by mother identity; heavy mothers produced heavier offspring by providing less relative allocation than light mothers; heavy mothers had a higher probability of reproducing successfully in successive years; the level of allocation provided was positively correlated among the offspring a mother produced

Yes

Costs of reproduction

Females allocating more to reproduction show a reduced probability of reproducing at the next occasion and/or produce lighter future offspring than females allocating less to reproduction

Previously reproductive females produced lighter future offspring and allocated less to their new offspring than previously barren females, but mothers allocating more to reproduction did not have a reduced probability of reproducing again compared with mothers allocating less

Yes†

* Very old and barren females were removed from the population. This selective culling very likely underestimated the senescence patterns and overestimated † terminal investment or allocation processes. Indirect costs of reproduction in terms of the quality of the future offspring produced as a result of reproduction per se, but no cost as a result of variation in the amount of allocation provided when reproduction occurs.

Appendix C. Prediction intervals for the random effects.

Figure C1: Ninety five percent prediction intervals showing the variability of the intercept according to the random effects “year” (top row) and “mother identification nested in mother cohort” (bottom row), for the three models evaluated: variation in calf mass (left column, see Table A1), variation in relative maternal allocation (middle column, see Table A2), and probability of future reproduction of mothers (right column, see Table A3). The zeros on the x-axes represent the intercept value for each model. The other values represent deviations from the intercept, which units are in “kg” for calf mass, in “percentage” for maternal allocation, and in “logit of a probability” for reproduction. Each horizontal line represents the deviation from the intercept for each year/mother, where the blue dot is the mean and the line is the variation within each year/mother. The range of blue dots represent the between year/mother variation. For example, the between-mother variance for calf mass was about 40 kg, meaning that calves produced by different mothers differed on average by 40 kg, whereas the within-mother variance was about 15 kg, meaning that calves produced by the same females differed on average by 15 kg.

Supplement: R code for producing a function equivalent to pvals.fnc for GLMMs #----------------------------------------------------------------------------------------------------------------# my.mer.sim function from Ben bolker to simulate data from a glmer # (http://glmm.wdfiles.com/local--files/examples/glmmfuns.R) #----------------------------------------------------------------------------------------------------------------my.mer.sim <- function (object, nsim = 1, seed = NULL, ...) { if (!is.null(seed)) set.seed(seed) if (!exists(".Random.seed", envir = .GlobalEnv)) runif(1) if (!is.null(object@call$offset)) warning("offset ignored -- not yet implemented") RNGstate <- .Random.seed dims <- object@dims sigma <- lme4:::sigma(object) etasim.fix <- as.vector(object@X %*% fixef(object)) etasim.reff <- (as(t(object@A) %*% matrix(rnorm(nsim * dims["q"]), nc = nsim), "matrix")) if (length(object@V) == 0 && length(object@muEta) == 0) { etasim.resid <- matrix(rnorm(nsim * dims["n"]), nc = nsim) etasim <- etasim.fix + sigma*(etasim.reff+etasim.resid) return(etasim) } if (length(object@muEta)>0) { etasim <- etasim.fix+etasim.reff family <- object@call$family if(is.symbol(family)) family <- as.character(family) if(is.character(family)) family <- get(family, mode = "function", envir = parent.frame(2)) if(is.function(family)) family <- family() if(is.null(family$family)) stop("'family' not recognized") musim <- family$linkinv(etasim) n <- length(musim) vsim <- switch(family$family, poisson=rpois(n,lambda=musim), quasipoisson=rqpois(n,musim,sigma), binomial={ resp <- model.response(object@frame); if (!is.matrix(resp)) { binom1 <- TRUE rbinom(n,prob=musim,size=1) } else { binom1 <- FALSE sizes <- rowSums(resp) Y <- rbinom(n, size = sizes, prob = musim) YY <- cbind(Y, sizes - Y) colnames(YY) <- colnames(resp) yy <- split(as.data.frame(YY), rep(1:nsim,each=length(sizes))) yy <- as.data.frame(yy) } }, stop("simulation not implemented for family", family$family))

if (!(family$family=="binomial" && !binom1)) { vsim <- matrix(vsim,nc=nsim) } return(drop(vsim)) } stop("simulate method for NLMMs not yet implemented") } #-----------------------------------------------------------------------------------------------------------------# MCMC Bootstrapping #-----------------------------------------------------------------------------------------------------------------glm.fitted.model=XX # where XX is name of the model fitted glm.dataset=YY # where YY is the name of the original dataset new.model=x2~ZZ #where ZZ is the model formula, i.e. the fixed and the random effects n=10000 ndigits=4 coefs = summary(glm.fitted.model)@coefs ncoef = length(coefs[, 1]) vals=data.frame(array(NA,dim=c(n,ncoef))) for (i in 1:n) { print(i) print(date()) # simulate 0-1 x2 = my.mer.sim(glm.fitted.model) # need to bond the new variable "x2" with the original dataset data.sim=cbind(glm.dataset, x2) # refit estimates glm.sim=glmer(new.model, data=data.sim, family="binomial") # save estimates vals[i,] = as.vector(glm.sim@fixef) } #-----------------------------------------------------------------------------------------------------------------# Calculate 95% highest posterior density confidence interval #-----------------------------------------------------------------------------------------------------------------nr = nrow(vals) prop = colSums(vals > 0)/nr ans = 2 * pmax(0.5/nr, pmin(prop, 1 - prop)) HPDlower=as.vector(array(NA,dim=ncoef)) HPDupper=as.vector(array(NA,dim=ncoef)) for (j in 1:ncoef){ HPDlower[j]=quantile(vals[,j],0.025) HPDupper[j]=quantile(vals[,j],0.975) } fixed = data.frame(Estimate = round(as.numeric(coefs[,1]), ndigits), MCMCmean = round(apply(vals, 2, mean), ndigits), HPD95lower = round(HPDlower, ndigits), HPD95upper = round(HPDupper, ndigits), pMCMC = round(ans, ndigits), pT = round(as.numeric(coefs[,4]), ndigits), row.names = names(coefs[,1])) colnames(fixed)[ncol(fixed)] = "Pr(>|t|)" print(fixed)