The Beverton and Holt yield per recruitment model is utilizing the individual growth model of von Bertalanffy and the Baranov mortality model. Baranov describes mortality as a continuous process in time where the number of individuals is monotonously reduced from the initial number

(number of recruits) and a fixed mortality rate (

). The number of individuals at time

then is

.

The marginal mortality rate (

) may be decomposed into a natural component (

) and mortality caused by fishing (

),

.

is a control variable in fisheries; when not fishing,

, while

increases as the fishing effort is increased.

Another control variable in fisheries is related to how large the targeted fish is, namely the age of the fish when caught, labeled

(age of first catch). Usually (as in this Demonstration) this is the age of a sudden shift in marginal mortality rate from

to

*, *often referred to as knife-sharp selection.

Individual fish growth is in the Demonstration modeled by the simple version of von Bertalanffy’s growth equation expressed in terms of weight, where the individual weight at time

is

,

being the length/weight relationship parameter (usually close to 3).

R. J. H. Beverton and S. J. Holt,

*On the Dynamics of Exploited Fish Populations*, Caldwell, NJ: Blackburn Press, 1957 (reprint).