Antlion Foraging: Tracking Prey Across Space And Time
Ecology, Oct, 1999 by Philip H. Crowley, Mary C. Linton
where P is the number of ants or of caterpillars trapped per day, [Epsilon] is the extractable biomass in milligrams per ant or per caterpillar (0.057 and 39.6 mg/prey, respectively; Linton 1995), and t is the handling time per ant or per caterpillar (0.028 and 0.125 d/prey, respectively; Linton 1995).
On rainy days, neither antlion larvae nor their prey were active; by the next rain-free day, prey and antlion activity levels generally returned to normal (Linton 1995). Rain days were therefore simply removed from the data and ignored, under the assumption that any costs of metabolic maintenance and pit rebuilding would be independent of the foraging strategy being used, and therefore could not shift the ranking of gains among strategies.
STRATEGIES
For this analysis, we characterized antlion foraging strategies as consisting of four components, each quantified by a set of discrete, representative values.
1. Interval, the minimum number of days over which an antlion remains in place at a site. - We assumed that each day an antlion would gain the energy available at its present time and pit location and then would assess its weighted-average foraging gain over some number of immediately preceding days plus the present day (i.e., the interval). Thus, the antlion remained at the same location to complete its assessment for the duration of the interval, and stayed on thereafter until the gain rate was too low over the most current interval. We investigated intervals of duration 1, 3, 6, 10, 16, 25, 35, 45, and 55 days.
2. Weighting, the relative contribution of each day's foraging gain to the overall site assessment. - We assumed that the current day's foraging return provided the most important information for evaluating the present pit location, and geometrically discounted the contribution of preceding days to the weighted-average gain. Each day's gain is weighted by the weighting raised to the power n, where n is the number of days that have elapsed within the interval since the gain was obtained. For example, with an interval of 6 d and a weighting of 0.9, the present day's gain is multiplied by [0.9.sup.0] = 1, the previous day's gain is weighted by [0.9.sup.1] = 0.9, the gain achieved the day before that is weighted by [0.9.sup.2] = 0.81, and so on, until the gain from five days previously is weighted by [0.9.sup.5]. The weighted-average gain is then simply the sum of these weighted values divided by the sum of the weights. The weightings we analyzed were 1, 0.95, 0.9, 0.8, 0.7, 0.5, and 0.3.
The temporal window t over which the forager is assumed to assess its gain rate is defined by the interval i and the weighting w, taken together. In effect, the weighting determines a different type of interval having a duration that can be expressed as 1/(1 - w), the sum of the geometric series of weights. Because the shorter of these two interval durations determines the effective evaluation period, we express the overall window size as
t = min{i, 1/(1 - w)}. (2)