Cohort tracking using size‐frequency population survey data to estimate individual growth

Abstract The relationship between a species' growth rate and its size—its growth function—represents essential biological information for supporting sustainable fisheries and wildlife management. Yet, growth functions are known for only a fraction of species. Progress is especially limited in marine invertebrates, including shellfish, due to challenges rearing early life stages in the lab and identifying statolith ring patterns indicative of individual age. We overcome these challenges by deriving a species' growth function using multi‐year size‐frequency population survey data collected from 71 subtidal sites over 35 years. We fit Gaussian mixture models to the data at each survey site and year to identify cohorts, then tracked cohorts between survey years to estimate cohort growth over time. We then used the estimates of growth to parameterize growth functions containing initial and asymptotic size constraints based on the survey data. We demonstrated our method with the kelp forest gastropod and commercial fisheries species, Kellet's whelk ( Kelletia kelletii ). The assembled survey data included 28,816 whelks, 9–180 mm in shell length. Through cohort tracking, we generated 297 estimates of cohort growth. We fit seven growth functions to the growth estimates and used information criterion and least squares to select the best‐fit model; in this case the Richards, characterized by maximum initial growth at small size that initially declines exponentially and then linearly with size, reaching asymptotic growth by approximately 40 years of age. We also analyzed and compared select portions of the population survey data to test for biogeographic and fisheries management effects on growth. The method we developed can support research on species with size‐frequency population survey data, and the function we derived for Kellet's whelk can inform research on its population biology and sustainable fisheries management.