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Abstract Density-dependent population dynamic models strongly influence many of the world’s most important harvest policies. Nearly all classic models (e.g. Beverton-Holt and Ricker) recommend that managers maintain a population size of roughly 40–50 percent of carrying capacity to maximize sustainable harvest, no matter the species’ population growth rate. Such insights are the foundational logic behind most sustainability targets and biomass reference points for fisheries. However, a simple, less-commonly used model, called the Hockey-Stick model, yields very different recommendations. We show that the optimal population size to maintain in this model, as a proportion of carrying capacity, is one over the population growth rate. This leads to more conservative optimal harvest policies for slow-growing species, compared to other models, if all models use the same growth rate and carrying capacity values. However, parameters typically are not fixed; they are estimated after model-fitting. If the Hockey-Stick model leads to lower estimates of carrying capacity than other models, then the Hockey-Stick policy could yield lower absolute population size targets in practice. Therefore, to better understand the population size targets that may be recommended across real fisheries, we fit the Hockey-Stick, Ricker and Beverton-Holt models to population time series data across 284 fished species from the RAM Stock Assessment database. We found that the Hockey-Stick model usually recommended fisheries maintain population sizes higher than all other models (in 69–81% of the data sets). Furthermore, in 77% of the datasets, the Hockey-Stick model recommended an optimal population target even higher than 60% of carrying capacity (a widely used target, thought to be conservative). However, there was considerable uncertainty in the model fitting. While Beverton-Holt fit several of the data sets best, Hockey-Stick also frequently fit similarly well. In general, the best-fitting model rarely had overwhelming support (a model probability of greater than 95% was achieved in less than five percent of the datasets). A computational experiment, where time series data were simulated from all three models, revealed that Beverton-Holt often fit best even when it was not the true model, suggesting that fisheries data are likely too small and too noisy to resolve uncertainties in the functional forms of density-dependent growth. Therefore, sustainability targets may warrant revisiting, especially for slow-growing species.
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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.
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- Award ID(s):
- 1924537
- PAR ID:
- 10644880
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Ecosphere
- Volume:
- 16
- Issue:
- 10
- ISSN:
- 2150-8925
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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