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RESPONSE to Randolph et al.

Posted by PLOSBiology on 07 May 2009 at 22:14 GMT

Author: Richard S. Ostfeld
Position: Dr
Institution: Institute of Ecosystem Studies, Millbrook, New York, United States of America
Additional Authors: Charles D. Canham, Kelly Oggenfuss, Raymond J. Winchcombe, and Felicia Keesing
Submitted Date: September 08, 2006
Published Date: September 8, 2006
This comment was originally posted as a “Reader Response” on the publication date indicated above. All Reader Responses are now available as comments.

Our study concluded that deer abundance had no effect on temporal variation in Lyme-disease risk (DON, NIP, or DIN), that climatic variables had only weak and nonlinear effects, and that rodents and acorns had strong effects. These conclusions were based on a 13-year dataset to which we applied a likelihood framework for parameter estimation and a model comparison approach for evaluating the strength of evidence for models with different independent variables. Randolph et al imply that our conclusions might result solely from statistical flaws. They claim that our failure to find support for climate and deer arises because these data were "attributes of the entire study site," whereas rodent and acorn data were collected at multiple plots within the study site. Consequently, the primary criticism of Randolph et al is that we are guilty of pseudo-replication. This assertion is incorrect for the following reasons. First, the most general concern about pseudo-replication is that it inflates the numbers of degrees of freedom used in the assessment of critical values of a frequentist test statistic. In the traditional linear models framework that they advocate, standard practice would take into account the hierarchical nature of our variables (with climate or year as a "main plot" effect), to avoid inflating the degrees of freedom for a frequentist test of a main plot effect. However, our likelihood framework and model comparison approach do not rely on traditional test statistics, so the most important concern about pseudo-replication does not apply to our analyses. Second, had we been guilty of inflating the degrees of freedom for statistical tests of climate and deer abundance on Lyme disease risk (as Randolph et al. claim), we would have increased our likelihood of falsely finding significant effects. But in fact we found weak or no effects of climate and deer. Third, our conclusion that deer abundance had no predictive power was based on two measures of deer abundance, one of which was measured at individual plots. Fourth, Randolph et al. confuse the real issue of the independence of the dependent variables with the scale of measurement of the independent variables. Our study plots are widely enough spaced that we are confident that the dependent variables are statistically independent. The fact that in a given year they are all exposed to the same local climate does not constitute a lack of statistical independence. In fact, our study was specifically designed to evaluate prevailing hypotheses about impacts of macro-climatic variables on Lyme disease risk. Fifth, prior analyses of the first six years of data from this study were conducted using a single, area-wide, annual datapoint for each independent (climate, rodents, acorns) and dependent (DON, NIP, DIN) variable. These analyses also found no support for climate and strong support for rodents and acorns as determinants of Lyme-disease risk (Ostfeld et al. 2001).

Randolph et al. also appear to advocate reanalysis of the data after removing an "extreme outlier" in Fig. 4; however, we are philosophically opposed to the arbitrary removal of datapoints, and no non-arbitrary reasons for removing data would seem to exist. High values of both the independent variable (the product of acorn density and rodent density) and the dependent variable (DIN) are to be expected in a mast-driven system characterized by extreme variability in acorn production and rodent density.

The charge that our models "confound[ed] variation in space and time" is perplexing. Our models specifically addressed the degree to which Lyme disease risk in any given plot is explained by climate, deer, mice, chipmunks, and acorns, with both the spatial extent and time lag for each independent variable made explicit. The likelihood framework we used allowed us to incorporate variation both among plots within a year and between years. This approach allows a much more direct analysis than would "standard" approaches, such as the generalized linear models Randolph et al. apparently advocate. For example, the curvilinear responses to climate that were apparent in our data would require an elaborate linearization before analysis in a GLM approach. Likelihood methods have been widespread in many branches of science for years, but are still new in some fields, including ecology. One of the reasons for the rapid increase in the use of likelihood methods is that the methods provide a framework that encourages researchers to translate their hypotheses into formal and powerful statistical models, but without the artificial constraints and restrictive assumptions that accompany many of the traditional frequentist statistics.

(1) Ostfeld RS, Schauber EM, Canham CD, Keesing F, Jones CG, Wolff JO (2001) Effects of acorn production and mouse abundance on abundance and Borrelia burgdorferi infection prevalence of nymphal Ixodes scapularis ticks. Vector Borne Zoonotic Dis 1: 55-63.

Competing interests declared: We declare that we have no competing interests.