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Specific Model

Specific Model. Write on board Flow: James dispersal kernel plus common larval pool Fish: Discrete-time Logistic Growth, r & K shared by all Multiplicative Kelp Fishing: Linear Economic Payoffs Marginal profit depending on distance from port. Flow: e.g. kernel patch 17 (sum<1).

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Specific Model

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  1. Specific Model • Write on board • Flow: • James dispersal kernel plus common larval pool • Fish: • Discrete-time Logistic Growth, r & K shared by all • Multiplicative Kelp • Fishing: • Linear Economic Payoffs • Marginal profit depending on distance from port

  2. Flow: e.g. kernel patch 17 (sum<1)

  3. Flow: whole kernel + CLP(.005)

  4. Fish: Growth with Kelp Highest Kelp Steady State Line Lowest Kelp

  5. Issues to discuss • Interior vs. corner • Variability • GIS display

  6. Code • clear all • close all • load Kij; D=K_matrix; D=D+.005 % IxI matrix D from row to column though • %need not sum to 1 • load kelp_percent; kvec1=kelp_percent; % Ix1 vector kvec (kelp by patch) • f=find(isnan(kvec1)); kvec1(f)=1; • a=1; kvec = a+((2-a)/18)*kvec1; • bvec=[3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;3;2;2;2;2;2;2;2;2;2;2;2;2;1;1;1;1;1;1;1;1;1;1;1;1;1;1];%gives Ix1 vector bvec (marginal profit by patch), , • I=length(bvec); • dr = .05; • delta = 1/(1+dr); • r=.5; • K=1000; • bar(D(17,:)) • xlabel('Destination') • ylabel('% Landing') • title('Larvae Leaving Patch 17') • figure • imagesc(D),colorbar • title('Dispersal + Larval Pool') • xlabel('Destination Patch') • ylabel('Source Patch') • figure • ev=[0:round(1.5*K)]; • xv1=min(kvec)*(ev+r*ev.*(1-ev/K)); • xv2=max(kvec)*(ev+r*ev.*(1-ev/K)); • plot(ev,xv1,'k-',ev,xv2,'k-',ev,ev,'k-') • xlabel('x_t') • ylabel('x_{t+1}') • figure • s1 = D*bvec; • C=bvec./(delta.*kvec.*s1); %this is the constant that f' must equal, it is a vector by patch • estar = (K*(1+r-C))./(2*r); estar=max(0,estar); • s2=kvec.*(r*estar.*(1-estar/K))+estar; • xstar = (s2'*D)'; • hstar=xstar-estar; • f=find(hstar<0); • if isempty(f),disp('Harvests Positive'),else,disp('Negative Harvest'),estar(f)=xstar(f),hstar=xstar-estar;end • profstar = bvec.*hstar; • PVprofit = sum(profstar)*delta/(1-delta); • [estar xstar profstar] • PVprofit • E=reshape(estar,7,7); • X=reshape(xstar,7,7); • P=reshape(profstar,7,7); • B=reshape(bvec,7,7); • DD=reshape((sum(D'))',7,7); • KK=reshape(kvec,7,7); • subplot(3,2,1) • imagesc(E) • title('escapement') • colorbar • subplot(3,2,2) • imagesc(X) • title('adults') • colorbar • subplot(3,2,3) • imagesc(P) • title('profit') • colorbar • subplot(3,2,4) • imagesc(B) • title('marginal profit') • colorbar • subplot(3,2,5) • imagesc(DD) • title('good larvae') • colorbar • subplot(3,2,6) • imagesc(KK) • title('kelp') • colorbar

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