Under the Beverton-Holt model, recruitment approaches an asymptote as spawning biomass increases:

0.2 0.4 0.6 0.8 Scaled spawning biomass

Figure 1 Examples of spawning success (V>), in terms of recruits per spawner, from three spawner-recruit models: linear (dashed), Beverton-Holt (solid), and Ricker (dash-dot).

Figure 1 Examples of spawning success (V>), in terms of recruits per spawner, from three spawner-recruit models: linear (dashed), Beverton-Holt (solid), and Ricker (dash-dot).

0.2 0.4 0.6 0.8 Scaled spawning biomass

0.2 0.4 0.6 0.8 Scaled spawning biomass

0.2 0.4 0.6 0.8 1.0 Scaled spawning biomass

Figure 2 Spawner-recruit curves for various levels of steepness, with x-axis scaled to virgin spawning biomass and y-axis scaled to virgin recruitment. (a) Beverton-Holt model with steepness h = 0.4 (solid), 0.6 (dashed), or 0.8 (dash-dot); (b) Ricker model with steepness h' = 0.98 (solid), 1.79 (dash), or 2.77 (dash-dot). These values satisfy h' = log (4h) - log (1 - h), the intrinsic population growth rate.

Figure 2 Spawner-recruit curves for various levels of steepness, with x-axis scaled to virgin spawning biomass and y-axis scaled to virgin recruitment. (a) Beverton-Holt model with steepness h = 0.4 (solid), 0.6 (dashed), or 0.8 (dash-dot); (b) Ricker model with steepness h' = 0.98 (solid), 1.79 (dash), or 2.77 (dash-dot). These values satisfy h' = log (4h) - log (1 - h), the intrinsic population growth rate.

a scaling parameter, it scales recruitment to a specific stock size, not to an asymptotic recruitment that may occur only at infinite population size.

A third apparent parameter in eqn [10] is This is the unfished spawning biomass per recruit (see section titled 'Per-recruit analyses') corresponding to R0, and it is completely determined by the stock's mortality, maturity, and growth schedules (when weight is used to quantify S). With recruitment at age a = 1, and given spawning contribution at the beginning of each year

where Wa is weight at age, pa is the proportion mature at age, M is the natural mortality rate, and A the oldest age considered.

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