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.