The Rabbit and Quail Production Modifier

This unit was first programmed in Basic in 1974 by R.H. Giles and recommended for inclusion in TVA's WRAP system. It or its derivative including edge volumes is appropriate for an intensive cottontail rabbit, quail, and small game management program.

Equal acreages do not have equal edges. The production of rabbits and quail per acre is a function of edges and corners of their faunal space. Production can be modified by changing the relative amount of edge in each tract. A means is needed, not for calculating the the likely change in animal populations from modifying the habitat, but for comparing tracts of different acreages since each has a unique edge and thus a likely unique effect on the animal abundance. The desired value was a production modifier, a value much like a site index, useful for identifying in a set, the proper production curve (or modifying such curves).

The following describes the coefficient called REF or relative edge factor. REF is the ratio of the hypothetical acreage within the zone of influence of an irregular tract to the same acreage of an hypothetical minimum edge (i.e., that of a circular area) for the same size tract. The concept is shown in Fig 1.

Fig. 1. Relations of tract, zone of influence, perimeters, and acreages of actual and hypothetically equivalent tracts (not to scale). A = actual tract; QC and QB are area of zone of influence of the edge; B = hypothetical tract of same acreage but minimum edge; C = hypothetical tract of same perimeter (circumference) but minimum acreage.

Calculations of irregular map areas are tedious and (without great care and expense) are only approximations. Thus, consistent with admonitions for rational robustness, the usual estimates of acreage, the estimates of the width of the zone of influence, the likely ambiguity of owners' goals for rabbits and quail, and the highly dynamic nature of most such habitat, the methods used were those for calculating the acreages of forest fires from their irregular perimeters (Forbes 1956:7:29).

The width of the zone of influence of the edge is designated Z. It is the distance from the edge within which 90% of observed rabbit activity occurs including foraging, nesting, and escape from large predators. Actual observations, reports, tracks, and photographs are used.

A circle is the two-dimensional form that has the minimum edge per unit area.

The acreage, Q in the zone of influence Z of any circle is

Q = R² - (R - Z)²)

where R is the radius. When an area is irregular as in Figure 1 (A), and the radius is not known, it is possible to convert this area to an hypothetical circular acreage, A, based on the perimeter or edge length.

The perimeter of a circular area of radius R is

P = 2 R

Therefore, when acreage is known,

A = R²

Then

R = (A /)^0.5

and thus

P = 2 (A/)²

or

A = (P / 2 )²

To calculate the acreage in the zone of influence of the larger C-type (Fig. 1) non-circular areas, the following is used:

Q_C = ( P_C / 2)² - ((( (A /)^0.5) - Z)²)

To calculate Q_B, the zone of influence in an hypothetical circular area of specified acreage, then

Q_B = A_B - ((((A /)^0.5)) - Z²)

Using appropriate conversions for acreage, where one acre = 43,560 square feet, and substituting, then REF, a measure of how much a field exceeds a minimum standard is

REF = Q_C / Q_B

Figure 2. Types of corners showing the edge zone of influence. For Type 2 corners three cover types converge and edge overlap at a small area (purple). Corners have to be of smaller angle that 120 degrees and larger than 30 degrees.

Corners

For every corner of Type 1 that occurs along the edge of the opening, some enhancement occurs. There appear to be "overlaps" of linear edge at such places (as at the green and purple in Figure 2.), but these have been accommodated in the above calculations.

Corners of Type 1 are believed to enhance small game production by T₁ (2.8) times that of an equivalent zone of influence area (shown as green in Figure 2.) The corners of Type 2 re believed to increase production by T₂ (e.g., 3.5) times that of equivalent edge zone area. These influences have not been extensively studied but can be estimated by field experts and used. N is the number of corners.

Thus, the additional influence of corner I is

I_C = ((T₁ x N₁ x Z² / 43560) + ((T₂ x N₂ x Z²) 43560

and I_B is developed similarly for the circular area.

Thus, REF with corner influence computer is: