Longitudinal sightings data were collected from two neighboring populations of fish-eating killer whales over the last 30 years, 1978–2007 [23
]: the Northern and Southern Resident killer whales which inhabit the inland and nearshore waters of Washington state (USA) and British Columbia (Canada). These populations are discrete; they do not interbreed, and neither immigration nor emigration have been observed [24
]. During annual photographic surveys, nearly every individual in the population has been recorded. Each individual has unique pigmentation, scars, and fin shapes, allowing us to track the survival and reproductive performance of each female over time. Although detailed age and birth data do exist for recent years, information on birth defects, still births, or mortality risk to pregnant females is not available. Due to low adult mortality [22
], the majority of females in our study are expected to live beyond the onset of menopause.
The age structure of females from the northern and southern populations was calculated to illustrate that over the last 30 years, each population has fluctuated in size, but more importantly, the age structure of both populations have changed (Fig. ). In the smaller Southern Resident population, recruitment of young females has generally declined, while the proportion of older animals has remained relatively constant. The larger Northern Resident population appears to have increased in most years since the 1970s, and has shown an increase in the youngest component of the population (Fig. ). The proportion of post-reproductive females has also fluctuated through time (Fig. ), and it is unclear what role these animals may have in maintaining population structure.
Figure 2 Changes in the age-structure of female killer whales, from two populations since 1976. Dashed lines are included for clarity to demarcate individuals aged 15, 30, and 40 years. After the 2007 survey, there are 49 females in the southern population (9 (more ...)
To evaluate support for the attentive mother hypothesis, we examined whether covariate attributes of mothers (age, dead/alive, birth order) had any impact on the survival of calves (ages 0 to 1) or on juvenile survival (< age 5) for individuals born since 1978. Binomial generalized linear models (GLMs) with a logit link were used to model survival (
) as a function of covariates, e.g.
. The Schwarz criterion or BIC [39
] was calculated for each competing model, and differences between BIC values were used as an approximation to the Bayes factor [40
]. If there are two competing models, the approximate Bayes factor supporting model 1 over model 2 is BF12
= exp [-(BIC1
)/2]. When two models are considered, this formula allows the posterior probability of each model given the data to be computed, Pr [M1
] = BF12
), because the Bayes factor can also be viewed as the ratio of the posterior model probabilities.
To examine support for the grandmother hypothesis, we first looked at impacts of grandmothers on their daughters, and second evaluated potential impacts of grandmothers on grandoffspring survival. The reproductive lifespan of mature females was modeled using GLMs to evaluate support for including mothers' survival status as a covariate. Because the precise onset of reproductive termination cannot be determined, we defined the response variable (reproductive lifespan) as the number of years between the last and first birth. Only females whose mothers' survival status did not change over their reproductive histories were included in this calculation. An alternative effect grandmothers may have is that by providing additional care, daughters may be more productive (shortening the time between births). To examine support for this hypothesis, we constructed a model of interbirth intervals (IBI) as the response variable. The survival status of each females' mother (alive/dead) was included as a covariate to evaluate whether females with alive mothers had a shorter IBI compared to females with dead mothers. As the second component of evaluating the grandmother hypothesis, we expanded GLMs of survival to include the grandmothers' survival status as a covariate – in these models, we compared the age-specific survival rates of juveniles with living grandmothers to those with dead grandmothers. Two analyses were performed; in the first case we examined the impact of grandmothers on survival of calves (aged 0 to 1), in the second we examined this factor across juveniles (aged < 5).
One hypothesis for why survival of primiparous calves may be relatively low is that older mothers may be more experienced than younger mothers [41
]. An alternative hypothesis is that there may be an evolutionary tradeoff between current survival and future reproduction – young females may prioritize their own survival above that of potential offspring, delaying reproduction [36
]. To evaluate evidence supporting this hypothesis, we first had to quantify lifetime reproductive success (LRS) for each female. Several different approaches have been used to measure LRS. Lahdenpera et al. (2004) used the number of births as a response variable, however using the raw number of births has been criticized because it doesn't account for survival to maturity [14
]. A second approach is to calculate the individual growth rate, λ
] – this method has only been applied to short-lived species and cannot be applied to right-censored data, such as that in our study. A third approach involves estimating total recruits to the population, R0
]. This latter method may be more robust than calculating the individual λ
because it is considered rate-insensitive [45
The total number of recruits could not be calculated for every animal in our study because many females either have partially observed reproductive histories or have not yet reached menopause. Instead, we developed a proxy for recruits, defining a recruit to be an offspring that lives to maturity (age 10) [22
]. For each post-reproductive female whose entire reproductive history is known, we calculated the number of recruits, which was treated as a fixed constant (Fig. ). For females whose reproductive histories were incomplete, we performed Monte Carlo simulations to generate hypothetical distributions of future recruitment until the onset menopause. The reproductive performance of these individuals in the beginning of their reproductive lives may help inform potential tradeoffs between age at maturity and reproductive success; specifically, mothers that delay reproduction may produce more recruits. Three types of uncertainty were included in these simulations of future recruitment for these individuals (aged greater than 25): uncertainty in the future survival of the mother, uncertainty in the future reproductive performance of the mother, and uncertainty in the future survival of newborns to reproductive maturity. Estimates of natality from previous work were used as age-specific probabilities of producing calves [26
]. Survival estimates of juveniles from the best model in our analysis (constant survival) were used with previously published estimates of adult survival for projecting individuals forward from birth [41
]. Given the recruits per female at each iteration of the simulation, we used the known age at maturity for each female (age at first birth) to estimate the potential effect on the number of recruits. Recruits were modeled using Poisson GLMs, with age at maturity as a covariate: R0
) = B0
Figure 3 Relationship between age at first parturition, offspring and 10-year old recruits (a), effect of senescent mothers on the reproductive lifespans and interbirth intervals of their daughters (b, c), and the simulated relationship between age at maturity (more ...)