Replies

A more biologically ignorant statement it is hard to conceive. Reduce the population of cod by half without changing any of its capacity determining variables, and you double the external resources per remaining cod. Their growth rate will therefore increase, compared to what it would have been. There are automatic restoring forces in biological niches. Equilibrium populations are set by balancing rates and approach from either direction on "S" curves. The forces acting temporarily on the population number and those acting on its equilibrium level are distinct. You might as readily say that power terms don't set equilibrium temperatures.

The survival of the collective is still a sum of the survival of the individual cod. It is the survival probability of the individual cod that has changed.

OK, now I start assigning homework.

A population P of 1000 individuals I1, I2, ... is subjected to a stress that has a 10% chance of killing any given member of the population. The chances are effectively independent.

(1) what is the probability that the pair of individuals {I9, I43}, both elements of P both die?

(2) what is the probability that the entire population dies?

(3) what is the probability that the population falls below 100 (due to the immediate action of the stresser alone)?

(4) A hypothetical person gives as his answer to (2) the answer "10%", reasoning that the property of the ensemble must be the same as that property in each of its members, since the ensemble is nothing but the members taken together. What is ratio between the correct answer and his answer i.e. the extent of his mathematical error?

(5) Same as the previous, different question asked of the same hypothetical. What error in reasoning does the hypothetical person of (4) commit?