Author: Michael Sears
Position: Assistant Professor
Institution: Southern Illinois University
E-mail: msears@zoology.siu.edu
Additional Authors: Jay Diffendorfer, Karen Lips, and Joe Mendelson III
Submitted Date: April 11, 2008
Published Date: April 14, 2008
This comment was originally posted as a “Reader Response” on the publication date indicated above. All Reader Responses are now available as comments.

Parmesan and Singer (PS) criticized our results that support an epidemic spread of Bd along three lines: modeling of error in LYO, the use of DOD, and the arbitrary selection of waves. We address each of these issues.

We disagree that our explorations of error in LYO were ‘statistically inappropriate’ because ‘increasing data noise will eventually cause loss of any statistical relationship…” This statement contradicts a large body of literature devoted to assessing analytical and statistical models based on data with inherent uncertainty(2, 3, 4), where Monte Carlo methods are used to explore the effects of error (1,2,5,6). In fact, in fields such as fisheries where inferences from models have both economical and biological impacts, examining the influence of error on prediction is common(6,7). Studies regarding amphibian declines should be held to a comparable standard.

Because no a priori model or sampling design was implemented before amphibian declines were noticed, LYO data include both measurement and process error. When dependent variables contain both types of error, and particularly if either creates bias, then error should be considered while analyzing and interpreting results(5). PS are correct that increasing error decreases the ability to detect signal, but fail to recognize the problems with inference when error is biased. For instance, LYO might underestimate extinctions or overestimate declines. After examining the Atelopus database, there was ample reason to assume LYO (and DOD) contained large amounts of error and that LYO was biased; nearly half of the available data for 54 species showed discrepancies with DOD for an average of 11.2 years. This examination casts doubt on conclusions from Pounds et al., which used data with a 1-year time lag to predict data with, conservatively, a resolution of 5 years. Thus, we felt obligated to simulate the effects of error and bias inherent to both LYO and DOD. Results suggested that models of epidemic spread were less sensitive to error than were models of temperature dependent outbreaks.

PS argue that DOD is inappropriate for analysis, citing two papers. However, the first, "Bd occurs in populations that are not declining," refers to an endemic, post-invasion, situation with no bearing on disease spread as we discussed. The second, "amphibians have disappeared in the absence of Bd [citation 4]," is flawed because that study did not demonstrate absence of Bd. In fact, the absence of Bd prior to that event was demonstrated in our paper, something PS failed to recognize. Finally, we cannot understand how PS feel DOD is an inappropriate surrogate for Bd presence yet support research using LYO. Given the 1 year time lag used in Pounds et al, LYO (though never stated) must have some biological meaning related to Bd becoming pathogenic and killing frogs. We expressly developed DOD to correct the temporal bias obvious in LYO. We admit DOD is not a high quality surrogate for the presence of Bd, but LYO likely contains even more error as an estimate of species disappearance. Thus, if PS think using DOD makes our results invalid, they should have less confidence in LYO, and also dismiss the conclusions of Pounds et al.

PS are mistaken in thinking we made arbitrary selection of starting locations – we used the two oldest records of Bd in the Andean region. Given the known temperature and moisture requirements of the fungus, we then assumed that it was most likely to spread along upland areas with appropriate climate conditions. Epidemiologists have used similar approaches to track a wide range of diseases. A better approach would have been to compare sets of candidate models that included varying numbers and locations of waves in an information theoretic approach(8), using model ranking procedures to select the best model. We know of one team currently working on this approach and look forward to their results.

In addition to these points, PS end with a poor attempt at comparing our work to Pounds et al. They mention the ‘moderately consistent’ relationship that Pounds reported between spatial patterns and climate change but failed to note that we resoundingly showed this analyses was flawed and is in disagreement with La Marca et al. (and our own work), mainly because Pounds et al. did not include the last six years of data in the Atelopus database. Furthermore, it is illogical for PS to assert that the reported relationships between LYO and climate change are ‘strongly consistent with climate change’ after arguing DOD are flawed.

1. Hilborn, R., Mangel, M., 1997. The ecological detective: confronting models with data. Princeton University Press, Princeton, NJ.
2. Jager, H. I. and King, A. W. 2004. Ecosystems 7: 841-847.

3. Lek, S. 2007. Ecological Modelling 207: 1-2.

4. Barry, s. and Elith, J. 2006. Journal of Applied Ecology 43:413-423.

5. Chen, Y. and Paloheimo, J. E. 1998. Fisheries Research 38:9-17.

6. Haddon, M. Modelling and quantitative methods in fisheries. Chapman and Hall/CRC Boca Raton Florida. 406pp.

7. Fisheries Stock Assessment Models. Edited by Funk, F. T. J., Quinn II, J. Heifetz, J.N. Ianelli, J.E., Powers, J.F. Powers, J.F. Schweigert, P.J. Sullivan, C.-I, Zhang, Alaska Sea Grant College Program Report No AK-SG-98-01, University of Alaska, Fairbanks, 1998.

8. Burnham, K.P., Anderson, D.R., 2002. Model selection and multimodel inference: A practical information-theoretic approach. Springer-Verlag, New York.