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Waterboatmen, and Testing for Lotka-Volterra-Type Interactions

Istock (1977) claims to have successfully applied the Lotka-Volterra model to his observations on corixid population dynamics. This assertion is based on five-fold evidence. (i) When the final population sizes in the enclosure experiments are fed into the Lotka-Volterra equations, the resulting configuration predicts coexistence. (ii) The two-species path of the natural populations "seems to respect" the zero isoclines calculated from the enclosure data. (iii) The point defined by the competitors' in situ late summer densities lies close to the intersection of the zero isoclines. (iv) The bivariate confidence ellipses for these natural population sizes enclose the greater part of the isoclines and (v) they "nicely surround" the in situ two-species path. Istock does not state what kind of evidence he would have searched for to indicate that the Lotka-Volterra model does not fit the data; to me the arguments cited to show that it does fit are inconclusive, if not questionable. While (i) is doubtless correct, the same qualitative prediction would obviously have been made in a number of alternative models. As far as (ii) is concerned, the zero isoclines for both competitors divide the plane into four regions, each of which is of necessity characterized by a different combination of tendencies (increase or decrease) in the competitor populations. However, except for one instance, the observed two-species paths at stations I + II are wholly contained within the sector where both populations should increase, although they include long segments where one or both species decrease. Therefore the two-species paths do not "respect" the isoclines, contrary to Istock's claim. (There is, of course, no reason why the positions of the isoclines should remain constant throughout he year, but the extent and direction of any shifts must remain speculative in the absence of data.) (iii) The point of intersection of the competitor zero isoclines has the coordinates