The Lotka�Volterra differential equations describe how things go between predators and their preys: owls may feast on mice, but when they get many fat healthy chicks the territory may run out of mice to eat. Hunger time for the owls! But when many of them died, mice get a new chance. In a lot of cases this results in the owl population going up and down with the mice, but with some delay. As in the graph below.
In Lake Victoria you have perch, preying on tilapia and furu (cichlids). And only a few years ago there still were so many that swimmers would feel fish mouths exploring the surface of their skins. But the complication is that all fish are preyed on by fishermen.
The shallow water hunt for breeding females. Every catch kills means death for hundreds of fish egg orphans. A round net is thrown, then mothers are scared out of their nest by a heavy explosive sound
By hunting down tilapia, fishermen destroy the prey of another of their favourite fish, the Nile perch. Nowadays, scaring a tilapia mother out of her nest is not an easy thing. For years, along all beaches of Uganda the water carries the dense bomb-like sounds of these thumping sticks. The remaining tilapia mothers - familiar with the sound from their egg-stage - have learnt to breed under rocks and to come out under no condition. Fishermen now started to kill the last ones by putting long nets around rocky areas and then, as a cordon, with 5 or more men, plunging in the water and wade around with sticks to poke under the rocks.
Kampala Reuters, Thu Jul 2, 2009 2:32pm GMT
Receipts for fish and fish products have declined steadily by 13% (from $142 million in 2005 to $124 million in 2008), and volumes fallen by 36% from 39,201 tonnes to 24,966 tonnes in the same period.
Fish are preyed on by fishermen. Fish are down. You now can see hungry fishermen leaving the islands to do Gods knows what. But there is a complication. we are still far from the top of the food chain. Not only fishermen and factories see income shrinking, but also those who prey on Ugandan fishermen: officials levying taxes and maintaining rules and regulations earn through bribes from fishermen (granting tax exemption, allowing illegal fishing methods), and exactly that main part of their income is rapidly declining due to impoverishment of their human prey. Less bribes for officers, who is going to pay the school fees of their children? Kenyan fishermen fishing from a Kenyan island Migingo, just over the mid lake border with Uganda, too far from the mainland to be harassed by Kenyan lake officers, were started to get targeted for bribes by Ugandan uniforms desperately trying to compensate their domestic income loss. They claimed the Kenyans had to pay for fishing in Ugandan waters. To avoid harassment, the Kenyan fishermen started paying. But this ended by Ugandan officers residing on Migingo. The Kenyans were smart enough to use this development: they now officially refused to pay, claiming rightly, that Migingo is Kenyan. The Ugandan army was of course unaware of that and got lured into occupying the island attracted by the booty extracted by the Ugandan lake officers. Now the Ugandan army is caught on a Kenyan island, everybody knows it, and everybody talks about it. Of course Kenya is just waiting: sooner or later they will go. Though we should assume the Ugandan government has fired some fools, they can not just make a retreat, because an African electorate want to see power and power only. The jungle law: show any weakness and you are finished, holds for everybody in Africa.
Fish down, then, with some delay, fishermen down, then with again some delay, lake officers down, but we have not yet reached the top of the food chain. Lake officers can't just prey on fishermen and take their bribes without giving a share to the headquarters who prey on their officers. Bosses know what their officers are receiving on "duty" and can safely pocket some wage funds without getting short of personnel. So there is good money there. The predator prey delay system is just about to reach these headquarters, but not yet really yet. .
Jinja, Uganda, brand new: "Proposed Lake Victoria Fisheries Organisation Headquarters Secretariat".
As you see, Lake Victoria's biomass has gone on land! But by the time all ten flags will fly from all ten poles, and all Toyota Landcruisers have been delivered, fish catches will be far under 50% and the lake will have ceased to sustain the repair and maintenance of this fish palace.
And, sooner or later, fish will get abundant in a lake deserted by people, and everything will start all over. Isn't Nature a wonderful dynamic evolutionary equilibrium?
Below are the equations for 1 predator and 1 prey, I leave it to the reader to extend it to the above system where 5 species are involved in a food chain sequence (but beware! choose your parameter values (α,β,γ,δ) prudently, for in some combinations of them everybody dies):
