A stock–recruitment model for highly fecund species based on temporal and spatial extent of spawning

• A stock–recruitment model is described based on contraction of spawning extent.
• R = αK(1 − exp[−S/(mK)]).
• S = spawners, K = carrying capacity, α = recruits per habitat, m = spawner group size.
• Approximated as R = R0(1 − exp(5ln(1−h)S/S0)).
• R0 = virgin recruitment, h = steepness; S0 = virgin spawning biomass.

A stock–recruitment model is described for highly fecund species based on the contraction of the spatial and temporal extent of spawning when a population is reduced in size: R = αK(1 − exp[−S/(mK)]), where S is the number of spawners, K is the carrying capacity in units of the number of habitat patches that can produce recruits, α is the average number of recruits per unit of habitat, and m is the number of spawners that group together to spawn. The model is based on three simplifying assumptions: (1) the environment is divided into K units; (2) the presence of one spawner provides sufficient eggs to fill the capacity of that unit, any additional spawners in that unit will not increase recruitment; and (3) groups of fish are randomly distributed over the environment. The model allows for a flat top curve, which is consistent with highly fecund species that are continuous spawners and do not aggregate to spawn. It also allows for a strong relationship between spawners and recruits, which is more consistent with species that aggregate in time and space to spawn. This stock–recruitment model can be approximated in terms of parameters commonly used in contemporary stock assessment models (virgin recruitment, R0, and steepness of the stock–recruitment relationship, h, virgin spawning biomass, S0): R = R0(1 − exp(5ln(1 − h)S/S0)). The functional form is compared with the Beverton–Holt stock–recruitment model.