Model projections of the fishery implications of the Allee effect in broadcast spawners

Authored by CJ Lundquist, LW Botsford

Date Published: 2004

DOI: 10.1890/02-5325

Sponsors: United States National Oceanic and Atmospheric Administration (NOAA) National Sea Grant College Program United States Department of Commerce (DOC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

There has been widespread concern that reduction in density of broadcast spawners by a fishery can have severe effects on reproduction. As fishing decreases density, fertilization efficiency declines, so that reproduction declines more rapidly than indicated by density, producing an Allee effect. However, this potentially precipitous decline in reproduction with declining density or stock size is not well understood at the population level. We used a simple deterministic model of the reproductive dynamics of a broadcast spawning invertebrate to show that the abrupt threshold often proposed as the form of this Allee effect is possible only when individuals are evenly spaced, and when sperm dispersal distribution is a constant out to a specified distance. When the spatial distribution is random and the sperm dispersal distribution is either Gaussian or exponential, fertilization success is linear up to 100\%; thus, zygote production is quadratic up to this density. As the width of the dispersal function decreases, fertilization reaches 100\% at higher densities, so that it may be beyond the highest density experienced by the population. In that case, zygote production is functionally linear. We then used a simulation model to assess the effects of aggregative behavior and stochastic variability in spatial patterns. We compared narrow and broad sperm dispersal distributions that were based on empirically determined fertilization of the green sea urchin, Strongylocentrotus droebachiensis, under two flow regimes. Zygote production exhibited a gradual nonlinear Allee effect as density decreased for the broader gamete dispersal distribution, but a functionally linear relationship with a much lower slope for the narrower sperm dispersal distributions. Increasing aggregation increased the slope of both fertilization and zygote production vs. density at the origin, but they remained linear for the narrower distribution. High interannual variability in zygote production due to different spatial configurations suggested that the geometric mean of recruitment is a better indicator of population consequences than the arithmetic mean, and it displays a sharper threshold than the arithmetic mean. Our results imply that potential Allee effects at low density in broadcast spawning populations rarely exhibit threshold behavior, and that these Allee effects may be too weak to be detected in stock-recruitment relationships.

Tags

Density Stock Population-dynamics Consequences Urchin strongylocentrotus-franciscanus Red-sea urchin Fertilization success External fertilization Marine invertebrate Genus haliotis