Influence of migration timing and total length on relative reproductive success
We explored the relationship between arrival date at the weir (i.e., a proxy for arrival date at the spawning ground) and the number of offspring produced to understand if specific arrival times were associated with higher relative reproductive success and if this varied by sex. We first summed the number of offspring that were assigned to a parent by the week they were sampled at the weir and then used a chi-square test to see if the total number of offspring produced per week was independent of sex. We summarized relative offspring production by week for this analysis only to ensure that sufficient observations were present across temporal periods to apply a chi-square test which was performed using R (R Core Team 2020). We assessed statistical significance using an alpha level of 0.05.
Additionally, we were interested in understanding the relative predictive importance of arrival date and adult length on offspring production for Yellowstone Cutthroat Trout in Burns Creek. We modeled the effect of length (total length in mm), date (Julian date of arrival at an instream weir directly downstream from spawning habitats), and an interaction term (length * date) to explain relative offspring production for males and females individually. To model the effects of total length and arrival timing we used generalized linear models with a negative binomial distribution to account for overdispersion in offspring production (Figure 2 ). Models were analyzed using the MASS package (Venables and Ripley 2002) in R (R Core Team 2020). We developed a suite of four a priori models including: 1) length (total length), 2) date (fitted as the quadratic function: arrival time * arrival time2), 3) length + date, and 4) length * date. Each model was run separately for males and females. Models were compared using Akaike’s information criterion corrected for small sample size (AICc ), and the top model was the one with the lowest AICc value (Burnham and Anderson 2002). Models that had an AICc score within 2.0 units of the best model’s score were also considered as belonging to the set of top models.
Effective population size (N e) and number of breeders (N b)
Effective population size can be estimated on multiple different scales, including over a generation (N e) or single reproductive cycle (N b, effective number of breeders). Both metrics provide insights relevant to conservation and management. Namely, N e quantifies the extent of drift and inbreeding experienced in a given population (Charlesworth 2009) and N b estimates the number of effective breeders for a single reproductive season. A number of factors affect both N e and N b, including operational sex ratio, variation in family size, inbreeding, and changes in population size; however these factors operate at different time scales (Waples 2002). We estimated both N e andN b for Yellowstone Cutthroat Trout, using the full likelihood method implemented in COLONY assuming random mating. Effective population size was calculated using the pooled parental population, which represented multiple different age classes. In contrast, we estimated N b using only outmigrating juveniles, which would estimate the number of breeders contributing to the juvenile cohort.