Calculating Relative Reproductive Success in Fish

The most precise measure of the reproductive success of individuals involves the genotyping of offspring and potential parents. In our study, this was not possible because the capture of small group members requires destruction of the shelters, which dissolves groups (14 , 22 (link), 97 ) and hence would have obstructed the collection of long-term life history data. Fortunately, several field studies of fish from the same population provided good estimates of the reproductive share within N. pulcher groups (14 , 96 (link), 97 ), revealing that reproductive success is greatly biased toward the dominants (15 , 36 ). Because of differences in the reproductive potential of the two sexes [the polygynous mating pattern renders a much higher maximum reproductive success for males than for females (67 )] and annual variation in colony-wide reproductive success, we standardized the reproductive success estimates of all marked individuals by transforming our counts of juveniles below helper size in each group into sex- and year-specific Z scores. Note that this estimates only the direct reproductive success of individuals, omitting any potential indirect fitness gains by helper effects on relatives. First, we calculated each individual’s expected share in its group’s reproduction based on the most recent parentage study in the same population (14 ): We assumed that dominant males sired 76% of offspring and that dominant females were the mothers of 82% of offspring. We further assumed that large (i.e., mature; >3.5-cm SL) subordinates in a group equally shared either 11% (males) or 5% (females) of their group’s reproductive success (assigning the remaining reproductive success to “unknown” individuals) (14 ). While it is possible that dispersal affects reproductive sharing in groups (54 (link)), these effects are unlikely to explain the patterns of reproductive success and dispersal behavior we report here (fig. S14B). Hence, we had information about an individual’s sex, social status, and reproductive success in a given year in 355 cases. On the basis of these, we calculated sex- and status-specific average annual reproductive success, i.e., average reproductive success in a given year of dominant females, dominant males, subordinate females, and subordinate males, respectively. For each individual, we then calculated its relative reproductive success throughout the observation period: sex- and status-specific Z scores were calculated for each individual and each year in which it was observed and then summed over the number of observation years [i.e., $Z=\frac{x_{ijk}-{\overline{x}}_{jk}}{S_{jk}}$ , where x_ijk is the reproductive success of individual i of sex j and status k, ${\overline{x}}_{jk}$ is the average annual reproductive success of individuals of sex j and status k, and S_jk is the standard deviation of annual reproductive success of individuals of sex j and status k (98 (link))]. We calculated Z scores for each individual throughout the observation period as a measure of its relative reproductive success compared to other individuals of the same sex and status (dominant or subordinate) observed at the same time.