Trophic links’ length and slope in the Tuesday Lake food web with species’ body mass and numerical abundance

Abstract

Summary Previously unnoticed patterns emerged in the lengths and slopes of trophic links of the food web of Tuesday Lake, Michigan, USA, when species were plotted on axes of log body mass (vertical) vs. log numerical abundance (horizontal). Link length was defined as equal to the number of orders of magnitude difference in mean body size between predator and prey plus the number of orders of magnitude difference in numerical abundance between predator and prey. The average length over all trophic links was 6·2 [SD (standard deviation) = 2·8] orders of magnitude in 1984, and 5·8 (SD = 2·6) in 1986. Thus, for the average link, the ratio of the mean body mass of predator to prey, times the ratio of the numerical abundance of prey to predator, was about one million (106 ±). To a first approximation the typical predator was 10 times as long as its prey but 1000 times less numerically abundant. Link length distributions were approximately normal. Mean link lengths in 1984 and 1986 were not statistically different, but were more than an order of magnitude larger than the mean distance between all possible ordered pairs of species in each year. Ordered pairs of species that were between 9 and 11 orders of magnitude apart were the most likely to be links in both years. The angle of a (non‐cannibalistic) link was defined so that an angle of 135° indicates that the predator was larger than the prey by exactly as many orders of magnitude as the prey was numerically more abundant than the predator, and so that the biomass (mean body mass times numerical abundance) of predator and prey were equal. For all non‐cannibalistic links, the median angle was 132° in 1984 and 129° in 1986. Both of these angles were significantly less than 135°. Angle deviated much from its median value only for short links. When the link was short or had the median angle, the predator species’ biomass was probably greater than that of the prey species. Several models of food web structure failed to reproduce the observed normal distribution of link lengths. Observed predation matrices with species ordered by body mass had links arranged in blocks suggesting functional groups. Models that incorporated this block structure reproduced the normal link length distribution, but a model that forced a normal link length distribution did not produce blocks. The cascade model explained the median angle of trophic links.