TABLE OF CONTENTS
Chapter 1. Why Care about Small Animals Moving Randomly
This chapter documents the acute need for quick and inexpensive estimation of absolute density of small animals. It explains what alternative tools are available for this purpose and why they are impractical for everyday pest management decisions.
Chapter 2. Trap Function and Overview of the Trapping Process
This section defines a trap and articulates the various roles traps play, including increasing the efficiency whereby animals are detected, harvested, and thwarted from being pests (mass trapping).
This section explains that trapping is a process of intersection of moving targets with the trap or with an attractant plume emanating from the trap. Diagrams are offered for typical spatial contexts of trapping. Six steps of trapping are articulated that fall into three main categories: finding the trap (findability), engaging the trapping mechanism (efficiency), and keeping the catch contained in the trap (retention). The concept of random walks is introduced and explanation is provided for why the composite probability for findability, efficiency, and retention is typically very low for random movers. Definitions and examples are offered for the core elements of trapping: plume reach, maximum mover dispersion, and trapping radius and area. A foundational trapping equation is offered that postulates catch is the sum across a trapping area of probability of catch when movers originate at a particular distance from a trap multiplied by the number of movers originating at that given distance. The key parameters of trapping are identified as a setup for detailed analysis in the following three chapters.
Chapter 3. Random Displacement in the Absence of Cues
This section summarizes key features of random walks and details the computer software that author Paul Weston wrote for simulating random walks with manipulable step lengths, meander (amount of turning), and run time. Diagrams are presented for classical random walks of which diffusing molecules and Brownian motion are exemplars.
This section contrasts tracks of molecules (very high local meander) with those for displacing organisms (low local meander) and explains how the distribution of turn angles comprising a stretch of track can be plotted so as to reveal the spread (circular standard deviation, or c.s.d.) of the normal distribution that results when new headings are selected randomly.
Chapter 4. The Geometry of Trap Interceptions
This section demonstrates that the proportion of straight-line movers that will be intercepted by a trap upon departing on random headings from a common origin is trap length divided by the circumference of a circle whose radius is the distance from mover origin to the trap. Thus, the relationship between proportion of interceptions and distance from a trap is an inverse function, not a log function as other trapping researchers have just assumed. We then document that the graphical technique of plotting distance of origin from a trap on the x-axis against 1/catch on the y-axis generates a straight line whose slope can be used to calculate trap length or plume reach.
This section establishes that the relationships developed above for trap interceptions of ballistic movers hold also for random walkers. However, when the slope of an inverse plot of release distance vs. 1/proportion caught is used to mathematically extract plume reach, an additional length is registered that we call "gain." Gain results from functional track broadening due to meander. Gain is a positive attribute of foraging animals because it increases the efficiency of resource finding during local search.
Chapter 5. Interpreting Catch in the Single Trap
Here we establish that catch in a trap is equal to the
About the Author: Dr. James R. Miller serves as Distinguished Professor of Entomology at Michigan State University. Dr. Miller's research centers on insect reproductive physiology, behavior, and chemical ecology. Current basic research projects address mechanisms of moth pheromone disruption, sensory physiology of pheromone reception and host-plant acceptance by herbivorous Diptera.
