A model for the interaction between gadoid larvae and their nauplii prey

A continuous model for the growth and death of gadoid larvae, including ecological interactions with their nauplii prey, is examined. The present model has a simpler structure than the model due to Cushing and Horwood [D.H. Cushing, J.W. Horwood, The growth and death of fish larvae. J. Plankt. Res. 16 (3) (1994) 291-300] as it does not explicitly incorporate larval metabolism, although indirectly metabolism is included by means of equations for larval growth. Despite this, the model yields related, although not entirely equivalent, results to those obtained by Cushing and Horwood. In the present model, overcompensation (cf. [W.E. Ricker, Stock and Recruitment, J. Fish. Res. Board. Can. 11 (1954) 559-623]) occurs at limited initial food levels, while at infinite food levels, the recruitment curve becomes monotonically increasing towards an upper limit (cf. [R.J.H. Beverton, S.J. Holt, On the dynamics of exploited fish populations. Fish. Invest. Lond. I 19 (1957)]). Moreover, the present study suggests that the duration of the larval stage, the metamorphosis time tau is highly important to the recruitment process, in accordance with Cushing and Horwood. When food is limited the metamorphosis is delayed, causing the larval population to experience (density dependent) mortality for a sufficient long time to make the recruitment curve overcompensatory. It is not necessarily the desire to derive a particular formula for the recruitment curve, as this is probably impossible anyway, except for particular examples. However, reduced versions of the model that in some sense are close to the original model, are examined, and it is argued that many general features of the general model are retained in such examples.