2. CRFM - Barbados Summary

Population dynamic models Multispecies Predation R G M F r Stock B Z Environment Fishing Climate Management 2 kind of models: Individually based models Population models

Population growth

Surplus production = population growth rate Max B∞ = K

Biological turnover rates are a function of Body size (Wmax)

r ≈ P/B ≈ Z The intrinsic rate of natural increase ≈ Production to biomass ratio ≈ total mortality rate Can get a pretty good idea from here how hard we can fish a stock Blueweiss et al. (1978)

Modified from Banse & Mosher (1980) r ≈ P/B ≈ Z Modified from Banse & Mosher (1980) Log P/B ratio is a linear function of log body size

Only 2 biological questions in fisheries management How much? = Fishing pressure (effort f) How? = Fishing pattern (catchability q) (selectivity s)

Fishing mortality = ‘How much’ * ’How’ Catch = Fishing mortality * Biomass Catch per unit effort = catchability * Biomass

Catch equation Number of deaths ti - ti+1 Number caught in interval i Mean number in interval i Thus or

All models use a variant of the catch equation Cohort models (Y/R) Population models

Simple estimators Catch Production The exploitation rate (E) is if F = M Gulland’s estimator for unfished stocks: Cadima’s estimator for fished stocks: Multispecies: Jeppe’s estimator for fished stocks:

We do not always need a model If information is available on biomass and catch in a corresponding area then Estimate Z from catch-curve or from r as and

Options of management B B Y F Y F BMSY, Minimum SSB, MBAL, Bpa Stocking, Bio-manipulation, Enhancement B B Size of capture: tc Mortality index: Z=F+M Exploitation rate: E = F/Z Effort control: f = F/q F control: F0.1, Fmed etc. Closed area Closed season Y Y F F MSY, TAC, ITQ, Bag limit That is all. Any available or conceivable regulation can be reduced to one of the three terms.