Whether the Weather Drives Patterns of Endemic Amphibian Chytridiomycosis: A Pathogen Proliferation Approach

The pandemic amphibian disease chytridiomycosis often exhibits strong seasonality in both prevalence and disease-associated mortality once it becomes endemic. One hypothesis that could explain this temporal pattern is that simple weather-driven pathogen proliferation (population growth) is a major driver of chytridiomycosis disease dynamics. Despite various elaborations of this hypothesis in the literature for explaining amphibian declines (e.g., the chytrid thermal-optimum hypothesis) it has not been formally tested on infection patterns in the wild. In this study we developed a simple process-based model to simulate the growth of the pathogen Batrachochytrium dendrobatidis (Bd) under varying weather conditions to provide an a priori test of a weather-linked pathogen proliferation hypothesis for endemic chytridiomycosis. We found strong support for several predictions of the proliferation hypothesis when applied to our model species, Litoria pearsoniana, sampled across multiple sites and years: the weather-driven simulations of pathogen growth potential (represented as a growth index in the 30 days prior to sampling; GI30) were positively related to both the prevalence and intensity of Bd infections, which were themselves strongly and positively correlated. In addition, a machine-learning classifier achieved ∼72% success in classifying positive qPCR results when utilising just three informative predictors 1) GI30, 2) frog body size and 3) rain on the day of sampling. Hence, while intrinsic traits of the individuals sampled (species, size, sex) and nuisance sampling variables (rainfall when sampling) influenced infection patterns obtained when sampling via qPCR, our results also strongly suggest that weather-linked pathogen proliferation plays a key role in the infection dynamics of endemic chytridiomycosis in our study system. Predictive applications of the model include surveillance design, outbreak preparedness and response, climate change scenario modelling and the interpretation of historical patterns of amphibian decline.

APPENDIX 1 -Details of the 'weather-linked Bd proliferation model' Figure A1. a) Bd growth in culture from the data of Piotrowski et al. (2004). The data are fitted with a quartic polynomial (black line). CLIMEX standard procedure is to use a plateau-shaped thermal function to approximate the typical quadratic response function such as that observed here.
We instead estimated T 0 and T 3 (growth limits) from where the fitted polynomial function intersected the x axis to the nearest half degree (3°C and 29°C, respectively). The lower and upper optimal performance temperatures T 1 and T 2 (between which growth is optimal) were estimated by combining observations from Piotrowski et al. (2004) and Woodhams et al. (2008). Lower optimal temperature (T 1 ) was adjusted to 10°C to accord with Woodhams et al. (2008) who demonstrate that Bd maintains relatively high population growth at low temperatures via life-history trade-offs, which see increased zoospore production as sporangium maturation rate decreases. The upper optimal temperature (T 2 ) was set to 25°C to accord with Piotrowski et al. (2004). The dotted line depicts these critical threshold temperatures as they relate to the data of Piotrowski et al (2004) (note that in CLIMEX growth potential at T 0 = T 3 = 0 and T 1 = T 2 = 1); b) Distribution of the 821 sites (n = 10183 specimen records) represented in the dataset of Murray et al. (2010) used to estimate the moisture response parameters for the CLIMEX mechanistic model; c) the predicted environmental suitability (as represented by the CLIMEX Ecoclimatic Index) for the persistence of Bd given the temperature and moisture parameters used in generating the growth index (GI). The fit of the model predictions with the observed global distribution of Bd (courtesy of Matt Fisher and Dede Olson http://www.spatialepidemiology.net/bd/), indicates that a reasonable moisture response curve was found (via iterative fitting) for the derivation of the growth index, GI (see main text and Zalucki and van Klinken 2006 for further details). a) c)

APPENDIX 2 -Multi-host infection patterns at Peter's Creek
Single-site, multi-host infection patterns Nine species were encountered at the main Peter's Creek study site over the duration of the study. We made 1431 captures and swabbed 1072 animals to investigate infection dynamics at this site, the difference representing recaptured animals within field trips that were not reswabbed. Overall apparent disease prevalence in the frog community was 37.5% (95%CI = 34.6 -40.5%), but this varied among species (Table A2). Of the nine species encountered, five were detected with Bd infections. Four of the five Bd-positive species were relatively well sampled, comprising 98% of captures (Adelotus brevis, Litoria pearsoniana, Litoria chloris and Litoria wilcoxii) so further analyses were restricted to these species. wilcoxii. In a logistic model, there was support for an interaction effect on infection between year and season (∆dev = 7.732, df = 2, p = 0.021) but no evidence for an effect of sex. This interaction appeared due to an unusual spike in prevalence in Summer in the second year of the study, at which time L. chloris not only had higher prevalence than in the preceding Spring (a trend reversal compared to the other two years in this species and compared to the consistent seasonal trend in both L. pearsoniana and L. wilcoxii) but also the highest prevalence of any species during this sampling period. Like in L. pearsoniana, infection in L.
chloris was much more likely in the second field season compared to the first or third ( Fig   A2b).  (Fig A2c).

Multi-site, multi-species survey
Before focussing on the model species at multiple sites, the RF modelling approach was tested for consistency with the above results on the 'maximal' dataset, comprising captures of the four main species from all sampled sites across the full course of the study (total of 2097 swabs analysed). The relationships between the predictor variables and the infection response, as indicated by partial dependence plots, strongly mirrored the patterns observed in the previous species by species parametric analyses with respect to the effects of species, year, sex and season (Fig A3). In a starting model that included each of the main variables  Figure A3. Results from preliminary Random Forests models indicating the effect of four variables (species, year, sex and season) on the probability of an individual returning a positive qPCR result. It can be seen that these results strongly mirrored those described in Appendix 2, in which a clear species, year and season effect was observed.

Methods
To investigate extent of infection in the model species, an intensive sampling effort across 20 additional populations spanning the geographic range of L. pearsoniana was undertaken.
Sampling occurred in October of the third year of the study (2008). Study sites were selected based on the data of Parris (2001). Selected study streams were searched until a predetermined number of frogs (n=15) had been captured and swabbed. We anticipated from our surveys at the main sites that prevalence in this species at this time of year would be peaking and therefore high if the site was infected, so our sample size reflected this expectation; our target of 15 animals ensured that we should detect at least 1 positive animal with 99% confidence if prevalence in the population was >25% and sampling approximated random (Digiacomo and Koepsell 1986). Murray et al. (2009) show that detection probability of L. pearsoniana is not a function of infection (i.e., infection does not influence likelihood of capture), indicating that these prevalence surveys likely represent a relatively unbiased picture of prevalence among these populations.

Results
In the extent of infection survey (n=201 frogs tested), Bd was detected at all of the 19 sites where >1 animal was tested. Mean prevalence was 71.1% (95%CI = 64.4-77.3%). Of 9 sites at which the target sample size was achieved, mean prevalence was 75.7% (95%CI = 67.8-82.6%), with one site having 100% of frogs in the sample infected (n=15).

APPENDIX 6 -Generalised linear model corroboration
Once the filtering process was complete and an adequate set of predictors was identified with RF (see Methods -Overview of statistical methods), logistic regression was used to confirm the importance of variables remaining in the pruned RF models. Although the machine learning method RF does an excellent job in navigating complex higher dimensional data structures, particularly where a large number of potentially cross-correlated and interactive predictor variables are of a priori interest, we included supplementary analyses with more conventional GLMs for the benefit of readers unfamiliar with machine learning methods in ecology. See also Appendix 3.

Methods
The large number of interactions possible in the maximal models could not be fitted, so only the main effects were tested. Curvature in the continuous response variables was considered using quadratic terms.