To calculate PrR two data series were obtained, the l_xand m_x series. The first series, l_x, is the probability of survival to a given age x, obtained from the survival model output (Fig. 2). The second, m_x, is calculated as the proportion of offspring born to females of age x out of all females that were alive at that age. To get m_x we used the age of females, where known or estimated year of birth was available, and the age at which females gave birth. If a female was not observed in a given year it was recorded as “no birth”.

Mathematically, PrR is based on l_X and e_x, where e_x is the life expectancy at age x. A multiplication of these terms gives T_X (the total individual years lived after age x). PrR is then calculated from T_x at age B and M, which are the ages, where 5% and 95% of female fecundity has been realised (inferred from m_x). Thus, the formula for calculating PrR is:

The input was a lifetable consisting of l_x (from the basta model output) and m_x (calculated from the observational data). To test the statistical significance of the PrR value it was tested against the null hypothesis that survivorship and fecundity declines with the same rate, which would lead to PrR = 0. We simulated 9999 populations of 1000 individuals, where this null hypothesis was true and compared each of these null populations to each permutation of the observed population. The simulated null populations were generated based on the demographic parameters of the given killer whale population. The p-value was obtained by evaluating how many of these simulated populations had a PrR greater than or equal to the PrR values obtained form the observed populations, with the number of samples included in both the numerator and denominator^1,63.