### Dynamic modelling: open access fishery

**Overview:** The chart shows a dynamic model of an open access fishery, that is, a fishery where boats have unregulated access to a stock. Fish stocks are plotted on the *x* axis and a measure of the resources used to catch the fish (effort) on the *y* axis.

*This diagram uses the D3 data visualisation library*

### Oops! Your browser is unable to render this diagram.

Use a modern version of Firefox, Chrome, Safari, Opera or Internet Explorer (9 or upwards) to see it.

**Why?**The diagram uses Scalable Vector Graphics.The initial blue spiral shows the *theoretical* finding that under certain conditions an unregulated fleet may self-correct so that the stock is not exhausted. Next, the jagged blue line shows the crash of North Sea herring stocks prior to the Common Fisheries Policy described by a classic study; the orange line shows a likely continuation had the fishery not been closed. Finally, the green line shows that the crash could have been avoided if harvest had been reduced by 22% throughout the period.

**Interpretation:** The blue spiral describes a case where, contrary to expectations, under certain conditions an open access regime may not lead to a total collapse of the stock. Instead, the size of the fleet adjusts when stocks are low, as some vessels find fishing no longer profitable and exit the industry. It picks up again when stocks are higher and fishing is more profitable. Following this pattern, it eventually converges on an equilibrium (dynamical systems theory terms this an asymptotically stable spiral point).

But is this a realistic scenario? The second chart uses figures presented in [1]. The blue line shows the results of a very similar model simulating the behaviour of North Sea herring stocks over the period 1963-1977 using real data. Clearly in this fishery, the conditions were not right to reach an equilibrium, and lack of regulation lead to a collapse of the fish stock over a period of just 14 years. Continuation of fishing would likely have lead to the total disappearance of the fleet (orange line).

The green line shows that, according to my adaptation of the Bjorndal and Conrad model, reducing the amount harvested each year by 22% would have prevented the collapse of the stock and fleet. Under this scenario, a stable limit cycle (loop) rather than convergence on an equilibrium is predicted. The limit cycle is highly sensitive to the parameters used, and from this we can assume that a stable situation, without constant regulatory readjustment, would be difficult to achieve.

Since the consolidation of the Common Fisheries Policy in 1983, European marine fisheries are, of course, no longer open access, and quota restrictions apply.

**Technical details:**

*Model specification:*

Stock *X* at time *t*+1 is given by: *X*_{t+1} = [1 + *r*(1 − *X _{t}/K*) −

*αX*

_{t}

^{β−1}

*E*]

_{t}^{γ}*X*

_{t}Fishing effort

*E*at time

*t*+1 is given by:

*E*

_{t+1}=

*E*+

_{t}*η*[

*αX*

_{t}^{β}E_{t}^{γ−1}−

*(c/p)*]

_{t}where

*r*is the intrinsic growth rate,

*K*is the environmental carrying capacity,

*c*is cost per unit of effort,

*p*is price per unit of harvest, and

*α*,

*β*and

*γ*are constants determined by regression.

The initial squiggle exhibited by the limit cycle is due to the model using real fluctuating economic data, while it is later smooth due to the use of constant prices in the absence of further data.

*About the data:* The actual data has not been shown for comparison with the model because fleet data was available only for Norwegian vessels, rather than all the nationalities fishing the stock.

**References:**

[1] Bjorndal, T. and Conrad, J.M. (1987), *The dynamics of an open access fishery*, Canadian Journal of Economics, 20 (1), 74-85

[2]Conrad, J.M. (1995), *Bioeconomic models of the fishery*, chapter in "The Handbook of Environmental Economics", ed. Bromley, D.W., Blackwell