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Unformatted text preview: EXST025  Biological Population Statistics Page 21 Another Recruitment Curve (Geaghan & Castilla, 1986)
Very little has been done with continuous recruitment, the type least well fitted by
the Ricker model and Beverton Holt model.
Suppose we have a fishery operation on a population which is truly continuous (though not
necessarily constant).
Recall
Nt = N! eqft +mt
this describes mortality only, lets add recruitment as a function of time
Nt+˜t = N> eqf˜t +m˜t r ˜ t
then r is the number of individuals entering the population on a daily basis.
since, eX ¸ 1 + X
Nt+˜t = N> (1 qf˜t m ˜ t) r ˜ t
Nt+˜t = N> qf˜t N> m ˜ tN> r˜t Ut+˜t = U> qf˜t U> m ˜ tU> rq ˜ t where t = t! , and t + ˜ t = any time t, and let U> (at time t) be determined by events at
time t1 on the right hand side of the equation,
Ut = U! qft U>" m(t1)U>"
>"
Ut = U! q D fi
3œ! >"
D Ci
3œ!
>"
D fi
3œ! rq(t1) >" m D Ui
3œ! rq(t1) >"
>"
Ut = U! q D Ci m D Ui rq(t1)
3œ!
3œ!
This model, if fitted on cumulative data, is highly colinear, and either requires much data to
overcome this, or something like Ridge regression.
Another good tactic is to reduce the model to a 3 parameter model instead of a 4
parameter model by entering a known or previously estimated constant (eg. m or
q).
A related model has been suggested by Chapman and Breiwick (in Serber), where
they start at the same place, but do not bring M down from the exponent. Their
model requires an estimate of M, and has been used on annual whale data. ...
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This note was uploaded on 12/29/2011 for the course EXST 7025 taught by Professor Geaghan,j during the Spring '08 term at LSU.
 Spring '08
 Geaghan,J

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