Mathematics and selective fishing

We have been frequently disputing here the rationality of mathematical models widely applied in fisheries management as producing inadequate science and, hence, flawed recommendations. For example, the well-known fact that Atlantic cod has evolved to reproduce at a younger age and smaller size, recently documented by Ulf Dieckmann, an Austrian biologist of the International Institute for Applied Systems Analysis, near Vienna, was one of the causes of the 'heretic' claims that selective fishing to save younger and smaller fish is wrong. Until some decades ago, most codfish reached sexual maturity at the age of 10, and only when they measured at least one metre long. Now, codfish reach sexual maturity at the age of six, when they measure only 65 centimetres.

In April 2005, I reported here how the counter-productive selectivity rules have been disputed from biological, genetic, and ecological aspects by two scientists from Iceland, Jonas Bjarnasson and Jon Kristjansson, and Niels Daan of Holland, while Dr Mikko Heino of the Bergen Institute of Marine Research, had already asked in 2003: “Does fishing cause genetic evolution in fish stocks?”. See also my July 2008 column 'Do we change our fish in water'.

In a more recent studies of 29 species, mostly fish, Canadian and American scientists found that in selectively fished species rates of evolutionary change were three times higher than in other species, (see: www.pnas.org/content/early/2009/01/12/0809235106). According to Dr Chris Darimont of the University of California, Santa Cruz, such fish were reaching reproductive age about 25 per cent faster; they may not reproduce as well, and on average have far fewer eggs than one year older ones.

From the point of view of ecology, the human predation, which targets larger individuals, is the opposite of what occurs in nature, for predators typically take juveniles or the nearly dead, rather than healthy adults. Taking so many large, reproducing adults from a population is recipe for rapid downward trend in the size/age ratio. Such changes have been observed in several exploited fish populations as well as in prolonged laboratory experimental work on small, short-living species, such as silversides and guppies.

The number of fisheries scientists and managers is growing, who understand that whatever the presently applied mathematical models and their operators are telling, the traditional selectivity regulations should be reassessed with the view of saving larger fish at the expense of the smaller ones, part of which could be fished out. Recently, Dr William Silvert wrote on the FISHFOLK internet discussion list: “Scientists rely so heavily on mathematics in their search for knowledge that they may be unable to deal with data that do not fit standard mathematical frameworks. This is a serious limitation in the environmental sciences”.

Recently the model-run science was also criticised by a mathematician. He is Professor George Sugihara, a theoretical ecologist of the Scripps Institution of Oceanography in LaJolla, California. Professor Sugihara, together with C N K.Anderson and seven others, used complexity theory to show that protecting smaller fish by setting minimum size is wrong, for the larger, older fish stabilise the population and provide better offspring. These practices, based on a make-believe stability of the rather chaotic fishery systems, produce fluctuating populations that can boom or bust even when food is abundant.

Their study analysed the collapse of the sardine fishery in California in the middle of the last century, concluding that the cause was selective harvesting of big fish that left behind mainly juveniles. It showed mathematically that size-selectively populations are unstable. A slight nudge can create a boom - or a catastrophic collapse.

Accordingly, food shortages among a population made up of juveniles with less stored body fat could result in massive deaths and a stock collapse even in a short famine. Food abundance does not necessarily mean all the fish get bigger, either; it could en¬courage reproduction and a population boom - which might in turn overwhelm the food supply and lead to another famine and bust. It is an unstable system. The recent boom of the sardine fishery with a million tons of sardines annually from Canada to Mexico illustrates this reality.

But this instability is not understood by people who run fisheries, Professor Sugihara insists. By law they manage fisheries for 'maximum sustainable yield'. The notion that such a yield exists implies that fish grow at an equilibrium rate and that the harvest can be adjusted in accordance with that growth to keep yields stable. In contrast, Professor Sugihara sees fisheries as a complex, chaotic system, akin to financial networks in which only short-term forecasts may work.

While some people involved with fishery management are already suggesting that conservation regulations should be changed to safeguard larger fish in protected species, sceptics are saying that Professor Sugihara’s analysis needs a real-world test to see how the fishing industry responds to such changes. Reportedly, Professor Sugihara is now negotiating with fishing industry groups to try to put this theory into practice. But hasn’t non-selective fishing passed real-world tests in the Mediterranean?

According to John F. Caddy, the former Chief of FAO’s Marine Resources Service, Mediterranean fisheries have long targeted juvenile bottom fish, of which some have survived to mature. This strategy has worked for decades, although apparently it is no longer so, probably due to the combined influence of relentless fishing, land runoff and habitat destruction.

In view of the increasing criticism so far hardly heeded to, I wonder if there is a need for a serious review of the prevailing fisheries management methodology by an international and respected institution such as the FAO, which over a generation ago was among its major promoters.