Areographic fragmentation analysis of Texas mammal distributions: a fractal analysis

Habitat fragmentation, the leading cause in the decline of biodiversity, affects the geographic range distribution of Texas mammals through the loss of habitat and the disjunction of populations. The fragmentation of a distribution has been referred to as areographic fragmentation and the effects of fragmenting a distribution can be quantified by measurements of area and perimeter that are not affected by scale. Fractal theory provides an appropriate method of determining areographic fragmentation through the quantification of distribution shape, perimeter length, and patchiness via the fractal dimension.

The sensitivity of the fractal dimension to changes in distribution morphology requires measurements of area and perimeter be determined from detailed maps. Through the use of geographic information systems, maps depicting distributions at greater spatial resolution than currently available were produced with reasonable accuracy.

Fractal dimensions were used as a scale-invariant statistic to quantify shape (areato-perimeter), perimeter length (length-of-trail), and patchiness (Korcak's empirical law). Like other biological objects, the distributions of Texas mammals may be scale invariant at several separate scales; however, this phenomenon may actually represent a lack of fit by the areographic models with the data.

Fractal dimensions of mammal distributions were examined for patterns in taxonomy, feeding preference, and spatial structure. No significant difference was found between taxonomic and feeding structure categories. However, differences between eastern and western distributions did exist. These differences were primarily based upon the perimeter length of distributions with western species exhibiting more complex boundaries.

Maps have long been used as resources of data when collecting data in the field is too labor intensive or when the biological question being addressed is extremely complex. Yet, all maps are made with limitations that affect the data extracted from them. The effects of cartographic design, model impro\ement, and spatial resolution were examined. Fractal dimensions calculated from predicted distribution maps representing increased model complexit}- did not differ significantly from those dimensions calculated using simple mapping models for the length-of-rail and Korcak areographic methods. Significant differences were only found to exist for dimensions calculated from the areato-perimeter method. Further examination of the fractal dimensions calculated using increased model resolution revealed no differences exist between taxonomic, feeding preferences, and spatial categories. The results of this study indicate that Texas mammal distributions are the function of individualistic responses to environmental variables and evolutionary history.