Monte Carlo Analysis Of Refuge Site Selection: Statistical Properties And An Empirical Example

The Monte Carlo method can be a useful technique providing information on central tendencies and tolerance for selection data. There are many statistical hypothesis tests that are employed in selection studies, but most require the data are normally distributed to adhere to the null hypothesis based on a normal distribution. Monte Carlo methods build a null distribution to test hypotheses based on available conditions and therefore do not require distributions of data to be normal. A Monte Carlo is also an extremely flexible technique and can be designed to test hypotheses for any particular experimental design. I designed a Monte Carlo method that uses use/availability data to detect patterns of selection in a species population. The Monte Carlo randomly re-samples from an available distribution a sample size equal to the sample size of the data making the used distribution with 1,000 permutations. For each re-sample, two statistics (mean and standard deviation) are calculated and compared to the statistics of the used distribution. A tail probability is then calculated. Because this method is not common among selection studies and each Monte Carlo design potentially behaves with different dynamics when considering sample size and Type I and II error rates, I performed randomization tests on simulated datasets to evaluate Type I and II error rates for sample sizes from 2 to 50. Datasets were generated by drawing data points (samples) from a Gaussian distribution (i.e., hypothetical species response curve) of specified parameters and compared to conditions associated with an available distribution. The change in error rates as a function of species selection away from mean available distribution as well as differences in standard deviations were assessed using randomization procedures (number of significant results). Type I error was generally low at all samples and parameters of available distributions examined while power increased as a function of sample size and divergence away from the mean of the available conditions. Power in the standard deviation statistic of each hypothetical used distribution was more influenced by the standard deviations associated with the available distributions. Power in the mean statistic was unaffected by the standard deviation of the available distributions. Power in the mean statistic also produced lower Type II error rates at lower sample sizes than the standard deviation statistic and at smaller differences between each hypothetical used distribution and the simulated available distributions. In a case study using the Monte Carlo method designed to evaluate refuge site selection, I sampled abiotic variables including temperature, moisture, and rock size related to potential refuge rocks in the Smoky and Flint Hills of Kansas. I collected data associated with refuge sites for 9 species and large amounts of abiotic data from haphazardly chosen rocks adjacent to the observed or used sites. Only five species were abundant enough for analysis, Diadophis punctatus being the most abundant. I found that thermal properties, humidity, and rock size varied in their importance among species and between locations. I predict that along with thermal properties, a major factor in these squamates selecting a particular refuge habitat is the refuge site's humidity properties and the relative homogeneity of thermal and humidity properties under refuge rocks mediated by rock size.