Effect of scale on food web structure.

Karl Havens (1) infers that 50 highly and evenly resolved food webs confirm the convention (2) that seven food web properties are "scale-invariant" or roughly constant among food webs with widely varying numbers of species. Also in line with the convention, an eighth food web property, connectance, is inferred to be scale-dependent and to decrease as the number of species increases (2). I have reanalyzed the 50 food webs and found that the conventional patterns should be rejected in favor of the competing hypotheses (3-5) that six of the seven properties are scaledependent and that the eighth, connectance, is scale-invariant (4). Havens (1) analyzes 50 lake food webs with from 10 to 74 (mean = 38) species. The fractions of top (T), intermediate (I), and basal (B) species as well as the fractions of all trophic links (L) between top and intermediate species (TI), top and basal species (TB), intermediate and intermediate species (II), and intermediate and basal species (IB) are analyzed as a function of the total number of species (S) in the webs. [Top species have prey but no predators; intermediate species have both prey and predators; and basal species have predators but no prey (6).] Havens asserts that none of these fractions varies in a statistically significant manner with S and that the variation ofL with S matches the previously suggested (2) function L = S1-4. This forces directed connectance [L/S2, (4)] to decrease with S. Alternative hypotheses assert that fractions of species and links are scale-dependent (3, 5). Significant fractions of T, TI, and TB may occur only in webs with small S, in which predators of top species are often missed or excluded. Food webs with large S contain mostly I and II and relatively small B. The theoretical and empirical support (3, 5) for these alternative hypotheses suggests that T, B, TI, and TB decrease with S while I and II increase. The scale-dependence hypotheses and the scale-invariance convention lead to different predictions that can be tested with one-tailed P tests, using the data in the report by Havens. If one assumes that simple linear regressions are valid, significant decreases in T and B, and the significant increase in I with S (P < 0.05), corroborate the scale-dependence hypothesis (Fig. 1). (We assume that the simple linear regressions in the report by Havens are valid.) The results of decreases in TI and TB and an increase in II corrobate the scale-dependence hypothesis (7). At P = 0.064, the decrease in TB is only slightly above the conventionally accepted level of statistical significance of P = 0.05. Because no specific alternatives to the scale-invariance