The simplest spawner-recruit model assumes a linear (density-independent) relationship between spawning biomass and recruits:
Under this model, recruitment has no upper limit, which could allow population growth to infinity. For that reason, the linear model is seldom applied to real populations, but its simplicity retains value in theoretical studies.
The versions are equivalent, given a = 1/[ and [ = a/[. Here a is the asymptotic level of recruitment; [, the level of S at which recruitment is half its asymptotic level.
Unfortunately, spawner-recruitment data rarely fit models well, leading to considerable uncertainty. An alternative form of the Beverton-Holt model uses external data to constrain or fix recruitment parameters. In this form (Figure 2a), the two parameters are the recruitment R0 from the stock when unfished and steepness h, defined as the proportion of R0 produced by 20% of S0, the spawning biomass of the unfished stock. (The value of 20% is arbitrary but conventional.) In this parametriza-tion, the model becomes
with 0.2 < h <1.0. Steepness quantifies resilience to exploitation, and its values have been estimated by several authors through meta-analysis. Although R0, like a, is
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