Treatment of time in fish population dynamics is flexible. By convention, stock size in number or weight Nt or Bt refers to the start (however defined) of year t. Yield Yt and catch in numbers Ct are annual sums. Recruitment Rt is usually an annual number, though it may be an annual biomass, and is typically modeled as occurring at a discrete point during the year, rather than as a continuous process. This may reflect the origin of much fish population dynamics theory in higher latitudes, where seasonality is pronounced, as are the corresponding biological processes.
Models of individual growth (see section titled 'Growth of individuals') are usually continuous in time, but size at age is often simplified to an annual average, rather than a continuously varying measure. In modeling mortality, instantaneous - rather than simple - rates are used, with the notable exception of some salmon models, or in simplified models written in discrete time. Reflecting the conventions above, a detailed fish population model may combine continuous-time processes (fishing and natural deaths) with discrete-time processes (recruitment and growth). Considerable variation in approach is found among applications; here, equations typically will be given with implied 1-year time steps.
Was this article helpful?