COMMUNITY AREA AND FOOD-CHAIN LENGTH - THEORETICAL PREDICTIONS

In combination with the simplest forms of the species-area curve (a power function or a simple proportionality between species and area), the cascade model predicts that the maximal chain length of a community food web (the height) should increase more slowly than linearly as a function of the logarithm of area and asymptotically in islands with extremely large area and extremely large numbers of species. The average chain length, according to the cascade model, should exceed 3.5 as soon as islands are large enough to have thirty or more species and should approach a finite limit, approximately 4.0, in webs from arbitrarily large islands. Thus the ratio of the height to the average chain length in the cascade model asymptotically increases without limit in webs from very large islands with very large numbers of species. According to the superlinear homogeneous model, both the height and the average chain length increase as a power, less than one, of the number of species, and therefore as a power, less than one, of area. The ratio of maximal to average chain length in the superlinear homogeneous model asymptotically approaches the limit e in webs from very large islands with very large numbers of species. The quantitative predicted length-area curves derived here are best tested by average food-chain lengths computed from observed complete food webs on islands of widely varying sizes, from small to large, in which other environmental factors such as productivity, environmental variability, and distance from a source of colonization do not vary notably. If the predicted area-height curves are to be tested with data from islands of small to moderate sizes, tailored simulations are recommended for obtaining the predicted distribution of height.