skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Revisiting Fishery Sustainability Targets
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.  more » « less
Award ID(s):
1942280
PAR ID:
10587155
Author(s) / Creator(s):
; ; ; ; ;
Publisher / Repository:
Society for Mathematical Biology
Date Published:
Journal Name:
Bulletin of Mathematical Biology
Volume:
86
Issue:
11
ISSN:
0092-8240
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ; ; ; ; ; ; et al (, Ecosphere)
    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. 
    more » « less
  2. ; ; ; ; (, Canadian Journal of Fisheries and Aquatic Sciences)
    Freshwater recreational fisheries regulations are a vital tool for achieving social and ecological fisheries objectives. However, angler behavior and fish biology may interact to influence regulation efficacy in unexpected ways. We combined models of fish growth and angler behavior to explore how angler behavior interacts with fish life history to shape the probability of fish harvest given capture across ages, life-stages, and sexes of walleye (Sander vitreus). Compared to females, males grew more quickly as juveniles, matured earlier, and reached smaller maximum sizes. Male walleye were therefore vulnerable to harvest for more of their reproductive lives than females because males spent more time at sizes where anglers were very likely to harvest them. We suggest that restricting harvest of large individuals in sexually-dimorphic species may favor the survival of large, reproductive-aged females. Moreover, we show that combining models of fish growth and harvester behavior can provide insights into how harvest affects fish with complex life histories over the course of their lives. 
    more » « less
  3. (, Journal of statistical physics)
    Stochastic models that incorporate birth, death and immigration (also called birth–death and innovation models) are ubiquitous and applicable to many problems such as quantifying species sizes in ecological populations, describing gene family sizes, modeling lymphocyte evolution in the body. Many of these applications involve the immigration of new species into the system. We consider the full high-dimensional stochastic process associated with multispecies birth–death–immigration and present a number of exact and asymptotic results at steady state.We further include random mutations or interactions through a carrying capacity and find the statistics of the total number of individuals, the total number of species, the species size distribution, and various diversity indices. Our results include a rigorous analysis of the behavior of these systems in the fast immigration limit which shows that of the different diversity indices, the species richness is best able to distinguish different types of birth–death–immigration models. We also find that detailed balance is preserved in the simple noninteracting birth–death–immigration model and the birth–death–immigration model with carrying capacity implemented through death. Surprisingly, when carrying capacity is implemented through the birth rate, detailed balance is violated. 
    more » « less
  4. (, Journal of statistical physics)
    Stochastic models that incorporate birth, death and immigration (also called birth–death and innovation models) are ubiquitous and applicable to many problems such as quantifying species sizes in ecological populations, describing gene family sizes, modeling lymphocyte evolution in the body. Many of these applications involve the immigration of new species into the system. We consider the full high-dimensional stochastic process associated with multispecies birth–death–immigration and present a number of exact and asymptotic results at steady state.We further include random mutations or interactions through a carrying capacity and find the statistics of the total number of individuals, the total number of species, the species size distribution, and various diversity indices. Our results include a rigorous analysis of the behavior of these systems in the fast immigration limit which shows that of the different diversity indices, the species richness is best able to distinguish different types of birth–death–immigration models. We also find that detailed balance is preserved in the simple noninteracting birth–death–immigration model and the birth–death–immigration model with carrying capacity implemented through death. Surprisingly, when carrying capacity is implemented through the birth rate, detailed balance is violated. 
    more » « less
  5. ; ; ; (, Fish and Fisheries)
    Abstract Size‐based harvest limits or gear regulations are often used to manage fishing mortality and ensure the spawning biomass of females is sufficiently protected. Yet, management interactions with species’ mating systems that affect fishery sustainability and yield are rarely considered. For species with obligate male care, it is possible that size‐specific harvest of males will decrease larval production. In order to examine how size‐based management practices interact with mating systems, we modelled fisheries of two species with obligate care of nests, corkwing wrasse (Symphodus melops, Labridae) and lingcod (Ophiodon elongatus,Hexigrammidae) under two management scenarios, a minimum size limit and a harvest slot limit. We simulated the population dynamics, larval production and yield to the fishery under a range of fishing mortalities. We also modelled size‐dependent male care to determine its interaction with management. In both species, the slot limit decreased yield by <12% (relative to minimum size limits) at low fishing mortalities; at higher mortalities, individuals rarely survived to outgrow the slot and spawning potential decreased substantially relative to unfished levels, similar to minimum size limits. Spawning potential decreased less when managed with a slot limit if we included a positive feedback between male size, care and hatching success, but the benefit of implementing the slot depended both on the relative proportions of each sex selected by the fishery and on our assumptions regarding male size and care. This work highlights that the effects of size‐ and sex‐selective fisheries management can be nuanced and produce counter‐intuitive results. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email