1. 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., Chapter 10: Ecosystem Models. In: Handbook of fish biology
and fisheries. pp , Ed. by P. J. B. Hart and J. D. Reynolds, Blackwell Science, Oxford, Vol. 2.

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…

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

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

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

6. 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

7. 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

8. 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)

9. 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 )

10. 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)

11. 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

12. 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