Data from: Density-related reproductive costs and natal conditions predict male life history in a highly polygynous mammal

# Male southern elephant seals at Marion Island Elephant seals at subantarctic Marion Island in the south Indian Ocean (46°54'S 37°44'E) have been monitored at an individual (mark-recapture) and population (census counts) level since 1983 (Pistorius, de Bruyn, &amp; Bester, 2011). Almost all pups born at the island were tagged with two livestock tags on the hind flippers every breeding season (austral September-November), with tags containing information about cohort and individual identity. Beaches were surveyed regularly inside (7-day intervals) and outside (10-day intervals) breeding seasons, during which both tagged and untagged individuals were recorded according to age group and breeding state (or social status). For each breeding season, all individuals at the island were tallied on 15 October – the peak haul-out date of this colony (Condy, 1979). The life-history traits of males from the Marion Island population are age- and breeding state-structured; dispersion from the natal colony is relatively low for both pre-breeders (ψ_(a 1-5)^E = 0.05) and breeders (ψ_(a ≥6)^E = 0.14) with approximately half of pre-breeders returning; breeding season detection probabilities are high across years (p = 0.95 ± SD 0.05); and tag loss probabilities are constant for all adult ages (see Lloyd et al., 2020 for details). There is a low level of individual heterogeneity in survival probability between individuals of the same age and breeding state (σ = 0.000017), but larger inter-individual differences in breeding success (i.e., the probability of being dominant; σ = 0.23; Lloyd et al., 2020). Therefore, individual heterogeneity in breeding success is likely prevalent and must be considered when making predictions (Vaupel &amp; Yishiin, 1985; Cam et al., 2002). <br> # Data analysis Only males that had recruited to the breeding population were considered. This provided a dataset of 291 individuals with complete life histories (i.e., birth to ‘apparent’ death [see below]) and 35 individuals with incomplete life histories (i.e., still alive at time of study). Base models were initially established to determine if recruited male life-history traits were determined by intrinsic effects such as age, breeding state and individual heterogeneity amongst others (Table A2; Grueber et al., 2011; Lloyd et al., 2020). <br> Several density-dependent factors related to competition intensity during breeding and natal conditions were investigated as covariates of these demographic traits (Table 1). See Appendix: Relative beach cost for more about the substantiation and method of estimating relative beach cost. <br> Multi-collinearity was checked using variance inflation factors, with a threshold of 5 (O’Brien, 2007). Linear models representing biological hypotheses about the structure of male life-history traits (Table A3) were fitted and selected using an information-theoretic approach (Akaike’s Information Criterion, AICc) in R 3.5.2 (R Core Team, 2019). Where models were equivalent (ΔAIC ≤ 2; Burnham &amp; Anderson, 2004), the simpler model (fewer parameters) was favoured. Predicted estimates of the most parsimonious models are reported as the mean, and lower and upper 95% confidence intervals. <br> # a) Actuarial senescence Generalized linear models were fitted to data coded as 1 (alive) and 0 (dead) each “seal year” for males with complete life histories. A seal year began at the beginning of a breeding season and ended before the start of the following breeding season. Few males skipped breeding seasons (n = 43 of 726 cases) and adult males were equally detectable (see goodness-of-fit Test 2.CT in Lloyd et al., 2020). Thus, animals not seen for consecutive years were presumed dead and not temporarily emigrated. Given the findings of Lloyd et al. (2020), a base model was established by fitting survival data to models of age (linear), polynomials of age (quadratic), logarithm of age, breeding state (subordinate and dominate), and relative dominance (number of times previously and currently dominant relative to the population average of each age class; Table A2). Because few age classes were examined (from ages 5 to 14), age was scaled in the quadratic model to prevent correlation between age and 〖age〗^2. <br> # b) Breeding improvement Generalised linear mixed models (R package ‘lme4’; Bates et al., 2015) were fitted to data coded as 1 (dominant) and 0 (subordinate) each annual breeding season for males with complete life histories. Given that dominant males at the study colony have very high paternity rates (Wilkinson &amp; van Aarde, 1999), breeding success was approximated as the probability to have a dominant social status. Males seen as both dominant and subordinate during the same breeding season were assigned the breeding state that the individual most frequently occupied during that year, particularly that breeding state occupied during the middle and late breeding season when dominant males most likely impregnate oestrus females (Le Boeuf &amp; Laws, 1994). A base model was established by fitting breeding success data to models of age (linear), polynomials of age (quadratic), and logarithm of age. An individual random effect was included to account for any unobservable individual variation not explained by age alone (Caswell &amp; Vindenes, 2018; Lloyd et al., 2020). <br> # c) Recruitment age Linear models were used to fit covariates that may explain the age at which males recruited to the breeding population. Individuals with complete and incomplete life histories were included in this analysis. Recruitment age was defined as the age an individual was first seen participating in a breeding event, which ranged from 5 and 10 years of age. Pre-breeders generally do not haul out at Marion Island during the breeding season (Condy, 1979). Therefore, each individual had an assigned recruitment age with several associated covariates that may explain why the individual recruited at this time. A base model was established by comparing a recruitment age model that included no covariate effects (intercept only model) to models containing breeding state at recruitment, year of recruitment, and birth cohort. <br> # d) Pup weaning mass Given the lack of literature investigating how male elephant seal demographics are determined by pup weaning mass, but its apparent importance in female elephant seal (Oosthuizen et al., 2018) and other polygynous male life history (Rödel &amp; von Holst, 2009), a supplementary analysis was performed to determine which density-dependent factors influence pup weaning mass across cohorts (Appendix: Pup weaning mass). This was specifically done to aid result interpretation and is not a primary aim of the study. <br> ### Covariate explanation: # survival = 1 - seen alive, 0 - not seen subsequently and presumed dead # bs = breeding state, 0 - seen as subordinate breeder, 1 - seen as dominant breeder # bs.cum = cumulative breeding state (tally of how many times an individual was dominant including that year) # bs.rel = relative breeding state per age class (relative to rest of population) # cohort = cohort identity, numbered 1 to 25 for Breeding success.csv and Survival.csv, numbered 1 to 27 for Recruitment age.csv # birth.cohort = total number of pups produced per breeding season # cohort.sex.ratio = male:female pup ratio per breeding season # recruit = age of recruitment to breeding population # exp.b = experience as a subordinate breeder (tally of how many times an individual was subordinate excluding that year) # exp.bm = experience as a dominant breeder (tally of how many times an individual was dominant excluding that year) # rel.b = relative experience as a subordinate breeder per age class (relative to rest of population) # rel.bm = relative experience as a dominant breeder per age class (relative to rest of population) # am = total number of male breeders counted on 15 October per breeding season (peak haul-out date during breeding season) # af = total number of female breeders counted on 15 October per breeding season (peak haul-out date during breeding season) # sex.ratio = male:female breeder ratio per breeding season # beach = cost to be on a particular beach, scored as # 1 - subordinate breeder, # 2 - dominant breeder on beach with few females and subordinate breeders, # 3 - dominant breeder on beach with many females and subordinate breeders # beach.cum - cumulative beach cost (tally of beach scores including that year) # beach.rel - relative cumulative beach cost per age class (relative to rest of population)