All variables at equilibrium (including Biomass, Yields and Fi) Ecopath, All variables at equilibrium (including Biomass, Yields and Fi) Fishery is represented by Yields Yi Bi . (P/B)i . EEi = Yi + Σ Bj . (Q/B)j . Dcij Yi = Fi.Bi Ecosim Fishery is represented by Fi values that may vary, leading to a dynamics of biomass and Yields Conditional to the Fi process dBi/dt = gi .Σ Qij - Σ Qji + Ii – (M0i +Fi +Ei) Bi (with adapted formula for Qji) Formulas from Pauly, D., and Christensen, V., 2002. Chapter 10: Ecosystem Models. In: Handbook of fish biology and fisheries. pp. 211-227, Ed. by P. J. B. Hart and J. D. Reynolds, Blackwell Science, Oxford, Vol. 2.

fjt = Ss psjt Nst Fi =Sj [ fjt qijt)] We can consider the « exploitation dynamics » with a model representing also fishing activity as fishing actions decided by fishing units (fishers) resulting in fishing mortality rates for each resource component (Fi) Note that Fi refer to the resource components but they result from fishing actions of several kinds (fj) Fi =Sj [ fjt qijt)] Which result from fishermen decisions with several possible strategies (s) fjt = Ss psjt Nst Articulations between these three « aspects » of fishing activity…

The numbers of tactics (métiers), of strategies (fleets) and sampling strata are equal and determined from the number of stocks (resource definition)

The number of fleets (strategies) and the number of tactics (métiers) are not necessary equal...

Basic equations… dBit /dt = ri Bit (1-Bit /Ki) – Sj [ fjt qijt (Bit-aijKi) ] fjt = ?

dBit /dt = ri Bit (1-Bit /Ki) – Sj [ fjt qijt (Bit-aijKi) ] General question What may be considered is the replacement of this set of equations dBit /dt = ri Bit (1-Bit /Ki) – Sj [ fjt qijt (Bit-aijKi) ] by an ecosim set of equation ? dBi/dt = gi .Σ Qij - Σ Qji + Ii – (M0i +Fi +Ei) Bi

fjt = SsNst*decision to fish with métier j at time t Ecosystem model Description of Bi conditional to Fi dBi/dt = gi .Σ Qij - Σ Qji + Ii – (M0i +Fi +Ei) Bi (with adapted formula for Qji) socio eco model Description of fishing activity in terms of fishing units deciding to go fishing (or not) Fi=g(Ns, decisions) Fi= Sj [ fjt qijt ] fjt numbers of fishing days with métier j fjt = SsNst*decision to fish with métier j at time t

Fi= Sj [ fjt qijt ] fjt numbers of fishing days with métier j Fi=g(Ns, decisions) Fi= Sj [ fjt qijt ] fjt numbers of fishing days with métier j qijt catchability of métier j on « species » i at time t fjt = SsNst*psjt psjt Probability to decide to fish with métier j at time t) Nst is the number of fishing units having the same decision rule for fishing trip selection (fleet)

psjt Probability to decision to fish with métier j at time t) fjt = SsNst*psjt psjt Probability to decision to fish with métier j at time t) Nst is the number of fishing units having the same decision rule for fishing trip selection (fleet) psjt =(R js,t+1/sum(R J(s)t ) Rjs,t = exp [r sRjt ] Rjt is an expected utility for the choice of métier j Rjt = Si [ Pricei cpueijt] – Cjt ( linear combination of parameters) (conditional logit model, Mac Fadden) psjt+1=ms psjt + (1-ms ) (R js,t+1/sum(R J(s),s,t+1 )

fjt = SsNst*psjt ie two types of time process psjt Probability to decision to fish with métier j at time t) Nst is the number of fishing units having the same decision rule for fishing trip selection (fleet)

Nst process general idea economic models eg Smith C. Clark, Charles Psjt process psjt =(R js,t+1/sum(R J(s)t ) Rjs,t = exp [r sRjt ] Rjt is an expected utility for the choice of métier j Rjt = Si [ Pi * cpueijt] – Cjt ( linear combination of parameters) (conditional logit model, Mac Fadden, 1973) Further aspects e.g. psjt+1=ms psjt + (1-ms ) (R js,t+1/sum(R J(s),s,t+1 ) Nst process general idea economic models eg Smith C. Clark, Charles If units of fleet S make profit, their number increases If not their number decreases

Psjt process (model, high frequency) psjt =(R js,t+1/sum(R J(s)t ) Rjs,t = exp [r sRjt ] Rjt is an expected utility for the choice of métier j Rjt = Si [ Pi * cpueijt] – Cjt ( linear combination of parameters) (conditional logit model, Mac Fadden, 1973) Further aspects e.g. psjt+1=ms psjt + (1-ms ) (R js,t+1/sum(R J(s),s,t+1 ) Nst process (model, low frequency) general idea economic models eg Smith C. Clark, Charles If units of fleet S make profit, their number increases If not their number decreases