for all five classes were significantly correlated with tortoise counts, while scat counts and TCS
were inconsistent and unreliable. TCS were only correlated with tortoises at the two lowest TCS
classes, undoubtedly reflecting the large sample sizes in these classes, and the positive influence
of burrows being included with TCS. Scat counts were very unreliable, and even demonstrated
NEGATIVE significant correlations with tortoises with TCS classes of 2-3 and 7-9. These
results are very critical and interesting, because the majority of transects in any tortoise survey
data set contain low sign counts, and high sample sizes may mask interesting details among
gradients of sign densities. As demonstrated in the ANOVA analyses, scat counts being more
abundant than burrows dominate TCS, and parallel results are achieved with these two variables.
However, in the correlation analysis inconsistent scat correlations across the TCS gradient,
resulted in inconsistent TCS correlations. These data provide compelling evidence that burrows
are a more consistent and reliable surrogate for tortoise counts than scats or the combination of
burrows + scats (TCS). The current analysis extends and reinforces the similar conclusions
reached in the last report (Krzysik 2002). Additional transect data, as well as, additional
analyses are required and will be conducted for the next report to further elucidate this
Carcass counts were not correlated with transect live tortoise counts. A priori, everything else
being equal, one would expect that DWMAs with higher tortoises densities would also possess
higher carcass densities (a significant positive correlation), assuming mortality rates are similar.
DWMAs that suffered higher tortoise mortality should show a negative correlation between live
tortoises and carcasses. The carcass data suggest that BOTH tortoise densities and tortoise
mortality rates are similar at the DWMAs.
Motivated by the significant correlation of tortoises with their sign, an exploratory Stepwise
Linear Regression Model was developed to assess and statistically verify the relative importance
of the three sign counts to predict tortoise occurrence. This technique selects the best predictor
variable that explains most of the scatter around the regression line. Inherently, it eliminates
redundant variables that possess high multicollinearity. For example, TCS is a composite of the
other two sign counts. Traditionally, the validity and interpretation of stepwise techniques have
been questioned (Green 1979). However, there has recently been a revival in their applications.
The result of this analysis clearly demonstrated that burrow counts were the only predictor
variable necessary to explain the variability of tortoises on transects. Statistically, scats and
TCS did not contribute significant information to the regression. As in the correlation analysis,
Stepwise Linear Regression reinforces the validity in using burrow counts as a surrogate for
The data presented here and other evidence suggest that tortoise burrows appear to be a better
surrogate for comparisons of tortoise distribution and relative abundance patterns than either
scats or TCS. TCS was strongly correlated with scat counts, and essentially did not provide
additional statistical information. The data also show that scat counts are much more variable
than burrow counts, both within and between specific statistical comparisons. Importantly,
burrow counts along the standard triangular tortoise survey transects (10 yards wide) accurately
represent actual burrow density estimates, because the effective survey width using Distance
Sampling surveys is equal to 4.5 m on a side (Krzysik, in review). Effective survey width for
scats is approximately 1 m on a side. Therefore, burrow counts on 10 yard wide transects
directly represent burrow density, while scat counts are relative numbers at best, and cannot be
used as density estimates. Effective survey width is equal to half the width of survey transects
when all survey objects are detected (Buckland et al. 1993).
Analysis of Variance
Burrow counts (densities) were similar at all DWMAs and for both 1999 and 2001.
Interestingly, when only high (>6) TCS transects were analyzed, Superior – Cronese had higher
burrow counts than Fremont – Kramer. Pinto Mtn. did not have any high TCS transects.
Scat and TCS counts produced similar results in ANOVA, because TCS is usually dominated by
scat counts. Therefore, scat counts were used for all analyses, with the exception of the complete
Factorial ANOVA where TCS was also used. Pinto Mtn. had lower scat counts than the other
DWMAs in 1999, and when considering only Low TCS transects. Pinto Mtn. was not
represented in 2001 nor in high TCS transects. In 2001, Superior – Cronese had higher scat
counts than Fremont – Kramer. However, when high TCS transects were analyzed all DWMAs
had similar scat counts.
Live tortoise counts were similar at all DWMAs, for both 1999 and 2001, and for both low and
high TCS transects. However, statistical interpretation can be quite tenuous, because of the high
variability and low sample sizes associated with finding tortoises on survey transects.
Carcass counts were highest at Fremont – Cramer and Superior – Cronese. Depending on the
specific comparisons, these two DWMAs were either similar or the former had higher carcass
counts than the latter. Ord – Rodman and Pinto Mtn. had lower carcass counts than the two
above DWMAs, and they were similar to each other.
Based on the available data and sample sizes, the four DWMAs appear to be similar to one
another in their tortoise and sign counts, and therefore, of similar value as desert tortoise
conservation areas. Although there were some statistical differences with specific comparisons
of scat and carcass counts, these parameters may not be important in elucidating actual tortoise
densities. Although the analyses could not demonstrate statistical differences among DWMAs
with respect to live tortoise counts, the high variability and small sample sizes makes
interpretation tenuous. An interesting outcome of the ANOVA analyses was that burrow counts
(i.e., densities) were higher at Superior – Cronese than at Fremont – Kramer for the high TCS
transects. This suggests that either Superior – Cronese tortoises possess a higher burrow/tortoise
ratio, or tortoises are more abundant at this DWMA. Further analyses are being planned and will
be conducted to explore and further elucidate the patterns identified in this report.
OCR Images in Web Image Viewer | Online Tutorials
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Statistical Analysis of BLM Desert Tortoise Surveys
In Support of the West Mojave Management Plan
Desert Tortoises at DWMAs and
Association of Tortoise Encounters
and Sign Counts On Transects
5 September 2002
Anthony J. Krzysik, Ph.D.
11 Highland Terrace
Prescott, AZ 86305
This report compares four Desert Wildlife Management Areas (DWMAs) with respect to tortoise
survey transects, and also provides detailed statistical analyses and graphical presentations for
exploring and assessing the association of live tortoise encounters with tortoise sign counts on
surveyed 1.5 mile triangular transects. Three different databases were used in the analyses: 1370
(13 had missing data cells) transects surveyed in 1999 and 2001 at the four DWMAs, 624
transects surveyed in 1998, 1999, and 2001 at 7 “Calibration Plots”, and 876 transects surveyed
in 1998 at localities undisclosed in the database. Statistical procedures used in the analyses
were: Analysis of Variance (ANOVA), Parametric and Nonparametric Bivariate Correlation
Analyses, and Graphical Associations of Transect Means for the Association Analysis.
These data and analysis results support the U.S. Department of Interior, Bureau of Land
Management, West Mojave Management Plan. Ed LaRue of BLM is the primary monitor of this
analysis effort and the Principal Investigator for the incorporation of desert tortoise conservation
and management in the development of this plan. Kathy Buescher, Senior Wildlife Biologist at
Chambers Group, Inc., is the subcontract manager.
The databases used for these specific analyses were developed and sent to me by Emily Cohen,
Ric Williams, and Hubert Switalski. I edited and modified the databases for statistical analysis
Data analyses were conducted with the SPSS statistical package (SPSS 1999a). Four tortoise
sign counts were used in the analysis: burrows, scats, TCS, and carcasses. The variable burrow
is the actual observed tortoise burrow count on individual surveyed transects and was available
from the data matrix. The variable scat is the corrected tortoise scat count on individual
surveyed transects, and was calculated from the data matrix as (TCS – burrow). Raw scat counts
require to be “corrected” because some scats are found in clumps, which are treated as a “single
count”. The variable TCS (Total Corrected Sign) is the total burrow + corrected scat count on
individual surveyed transects and was available from the data matrix. The variable carcass is the
observation of tortoise shells (carapace/plastron) or skeletal remains on the transect. Survey
transects were further classified into three different subclasses based on their TCS and burrow
counts (Table 1).
Classification of tortoise survey transects based on TCS and burrow counts.
Tortoise sign require square root data transformation, because the data represent counts with
many data cells being “0”. Counts, particularly of rare events, follow a Poisson distribution
where the mean equals the variance, and therefore the mean and variance cannot be independent,
but vary identically. All the sign data was transformed as x = (x+0.5)
, where x represents a
tortoise sign variable (Sokal and Rohlf 1995).
Analysis of Variance (ANOVA) was used to statistically assess differences among DWMAs with
respect to burrows, scats, TCS, live tortoises, and carcasses. Years (1999, 2001) were analyzed
separately, and also combined to increase sample size for analyses. TCS classes Low and High
(Table 2) were analyzed separately and also combined for analyses.
Sample sizes at the four DWMAs in 1999 and 2001 for Low TCS and High TCS
The 5 percent significance level (P<0.05) was used based on experience and general acceptance
in ecological research and field biology. Burrows, scats, TCS, tortoises, and carcasses were each
used in separate analyses as dependent variables with DWMAs as “the factor”, the independent
variable. ANOVAs used Type III calculation of Sums of Squares, because this algorithm is
generally recommended, it is invariant with respect to cell frequencies, and when there are no
missing cells it is equivalent to Yates’ weighted-squares-of-means method (Milliken and
Johnson 1984, Shaw and Mitchell-Olds 1993).
Levene’s Test for equality of error variances was used for all analyses, and does not depend on
the assumption of normality (Levene 1960). Bartlett’s test is often used to assess homogeneity,
but its practical value has been questioned (Harris 1975), and this test is not very efficient and
strongly affected by non-normality (Zar 1999). Levene’s Test uses the average of absolute
deviations instead of the mean square of deviations, making it less sensitive to skewed
distributions (Snedecor and Cochran 1989). Levene’s Test checks to see if error variances are
homogeneous among the factors being compared in an ANOVA. Homogeneous variances are a
parametric assumption in ANOVA. ANOVA is a parametric statistical procedure that
technically requires parametric assumptions to be met: homogeneous error variances, normally
distributed data, adequate sample sizes, and independence of sampling or experimental errors
(random sampling, independence of observations). Nevertheless and importantly, ANOVA is
considered robust to departures from the first two of these assumptions, particularly when proper
transformations are employed (Sokal and Rohlf 1995, Underwood 1997, Zar 1999).
Additionally, SPSS algorithms are very robust to nonnormality (Morgan and Griego 1998).
Many researchers believe that the routine use of nonparametric statistics avoids many issues of
parametric assumptions, but these methods are equally affected by the last two critical
assumptions – independence of sampling errors and the loss of statistical power with inadequate
sample sizes (Krzysik 1998). The routine use of nonparametric analysis in ecological research is
not recommended (Johnson 1995, Smith 1995, Stewart-Oaton 1995), but see Potvin and Roff
(1993). Table 3 provides the results of Levene’s Test for the ANOVA analyses of DWMAs.
Burrows Scats TCS Tortoises Carcasses
Statistical significance of Levene’s Test for homogeneity of variances for ANOVA of
DWMAs in 1999 and 2001. Analyses were not conducted on TCS classes for 2001 because of
small sample size and the lack of surveys at Pinto Mountain. Note the high degree of
heterogeneity in the DWMA data set. Values of P <0.001 are highly significant.
ANOVA designs require the use of Post Hoc Multiple Comparison Tests to assess statistical
significance when there are more than two levels for any factor. Five Post Hoc multiple
comparison tests were used in the ANOVA analyses. The Bonferroni test, based on the
Student’s t statistic, adjusts the significance level for multiple comparisons. This test has the
widest range of applications, is conservative, and when there are few comparisons has high
power (Zolman 1993, SPSS 1999b). Conservative tests were desirable in these analyses, because
they minimize Type I error, the probability of rejecting a true null hypothesis (null hypothesis =
no significance difference) (Krzysik 1998). In other words, erroneously reporting significance
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