Electronic supplementary material to
Persistence of the emerging pathogen Batrachochytrium dendrobatidis outside the amphibian host greatly increases the probability of host extinction.
Kate M. Mitchell1,3, Thomas S. Churcher1, Trenton W.J. Garner2, Matthew C. Fisher1*
1Department of Infectious Disease Epidemiology, Imperial College, St Mary’s Campus, Norfolk Place, London, W2 1PG, United Kingdom
2The Institute of Zoology, Zoological Society of London, Regent’s Park, London, NW1 4RY, United Kingdom
3Current address: Centre for Infectious Diseases, University of Edinburgh, Ashworth Laboratories, The King's Buildings, West Mains Road, Edinburgh, EH9 3JT, United Kingdom
*Corresponding author: [email protected]
- 1 - A: Experimental procedures
Infection Experiment
B. bufo tadpoles were kept singly in 140mL of water (pH 8.0), which was replaced every 4 days, in an 18 oC controlled-temperature room. Control animals (N=39) received uninfected water, while for exposed animals (N=24) each new volume of water contained around 50-100 mobile zoospores of the Pyrenean isolate of B. dendrobatidis Ibon Acherito 042. Infections continued until metamorphosis, and then ceased. Tadpoles surviving until metamorphosis received 13 doses over a period of 48 days. Following metamorphosis, juveniles were transferred to individual 1 litre plastic boxes and the experiment was ended at day 81. The zoospore load of each animal was assessed using the quantitative PCR (qPCR) protocol of Boyle et al. (2004).
Transmission Experiment
A set of B. bufo tadpoles at Gosner stage 24-25 were infected using five doses of cultured
B. dendrobatidis administered over 2 weeks, each dose composed of approximately 5000 visibly mobile zoospores. These ‘seed’ tadpoles were housed in groups in 8 litre tanks along with previously uninfected tadpoles with the following numbers of infected:total tadpoles: 1:20, 2:10,
4:20, 6:30 and 7:20, each of these being replicated four times to give a total of 20 tanks. This experiment was ended after 22 days. Transmission dynamics were inferred from the results of qPCR screens of tadpole mouthparts sampled at the end of the experiment.
- 2 - B: Parameter Estimation
Infection-specific death rates
Death rates were calculated separately for each experimental group (control or infected) for the tadpole stage and juvenile stage, by dividing the number of deaths occurring for each stage by the cumulative time for which animals were observed in each category. Infection-specific death rates were taken as the excess death rate of animals exposed to infection over that seen in controls, with confidence intervals on the infection-specific death rates calculated using the standard error of a rate difference. These data are shown in Table S1.
Transmission parameter
The transmission parameter, , was estimated by fitting a simple mathematical model (outlined below) to data from the infection experiment (Table S1). It is assumed that the rate at which tadpoles become infected is dependent on zoospore density, so values of are specific for a particular volume of infected water - in the case of the infection experiment, 140ml. The model assumes that at time 0, and at the start of every 4th day, the number of zoospores, Z, is set to the
dose level (denoted by D), from which it decays at a constant per capita rate Z . The change in
zoospore population size is described by the equation Z= D exp( -mZ z ) , where z indicates the time
(in years) since the last water replacement. The number of tadpoles remaining uninfected at time t,
dQ (t) Q( t ) , is given by the differential equation X Z(t)Q (t) . This model was fitted to the X dt X
observed data of the infection experiment ensuring that QX ( t ) gave the required number of infected
-1 tadpoles after 13 infections, using D = 75 and z = 13 year .
- 3 - In the transmission experiment, 11 out of 24 tadpoles became infected (95% C.I. 6.2-15.8) (Table
S1). Since the tadpoles were housed separately, this can be treated as a binomially distributed outcome, and hence a 95% confidence interval for the number of tadpoles infected has been calculated, from using the normal approximation to the binomial distribution to calculate the 95% confidence interval on the infection probability. This uncertainty in the experimental outcome has
been used to calculate a confidence interval for , for the initial estimate using D = 75 and z = 13 year-1. The model was fitted to the data by least squares regression using Markov chain Monte Carlo
(MCMC) sampling of the likelihood implemented with a Metropolis algorithm (Gilks et al. 1996).
The proposal distribution of the algorithm is normally distributed with a variance automatically calculated to give an acceptance rate of between 20 and 40% (Gelman et al. 2004). To estimate two chains were started at different values and their convergence assessed (Gelman et al. 2004).
Convergence was found to be rapid, and mixing of the chains was good. A burn-in period of 50,000 samples was taken and 10,000 samples were used from a further 50,000 samples. The parameter estimate for is reported as the mode and the 95% highest density region of the distribution of the samples (Table S2).
Given the huge uncertainty in Z , and additional uncertainty in D, a larger range of exploration for
was required. It was not feasible to calculate this using the MCMC sampling method, since is
correlated with Z, so instead point estimates were obtained for the maximum and minimum
-1 possible values for , using extreme values of D (50 or 100 zoospores) and Z (0 or 365 year ), and the 95% confidence limits on the number of tadpoles infected (all combinations shown in Table S2).
Point estimates were obtained using least squares regression in Berkeley Madonna. In the full transmission model, is adjusted for the assumed volume of the lake periphery inhabited by the tadpoles, of 1.7 ×106 litres (Tables 1 and S2).
Rate of zoospore release
- 4 - The mean numbers of tadpoles infected at the end of the transmission experiment are shown for each of the different scenarios investigated (Figure S1). The number of tadpoles infected at the start and end of each experiment were used to fit a simple mathematical model to estimate , the average per capita rate of zoospore release per year by infected tadpoles. The model consisted of the
dP (t) dP (t) following set of differential equations, X Z(t)P (t) , Y Z(t)P (t) and dt X dt X dZ( t ) =rP( t ) - m Z ( t ) with parameter definitions and estimates given in Table 1 (note that the dt Y Z value of was corrected for the volume of 8 litres used in the experiment – see Table S2). The rate of zoospore release was estimated by fitting the model simultaneously to the mean number of infected tadpoles for each scenario (Figure S1), to get a single value for . This was calculated by least squares regression using Markov chain Monte Carlo (MCMC) sampling of the likelihood, as
-3 detailed for the calculation of . Fixing the parameters = 1.23 × 10 and Z = 13, the estimated value obtained for was 9.5 × 104 (95% CI: 8.7 × 104 - 1.03 × 105) (calculated as the mode and the
95% highest density region of the distribution of the samples). To allow for the uncertainty in Z and , point estimates for the maximum and minimum possible values for were obtained in a
-1 similar way as for , using the extreme values of Z of 1 and 365 year , and extreme values for calculated in Table S2 (row 4, transmission experiment limits). From these calculations the limits for are 1 × 104 and 2 × 106, but a range of up to 6.6 × 106 is explored.
- 5 - Treatment No. of tadpoles Life- No. of deaths Cumulative Group Infection group introduced (of stage within life- time spent death rate -specific death (zoospores which became stage (of in life- (year-1) rate (year-1) per 140ml) infected over the which were stage (95% C.I.) experiment [95% infected) (years) C.I.]) Control 39 (0) Tadpole 4 (0) 6.79 0.59 - (0) Juvenile 5 (0) 1.53 3.28 -
Exposed 24 (11 [6.2-15.8]) Tadpole 8 (1) 3.63 2.21 1.62 (50-100) (-0.02 – 3.25)
Juvenile 9 (5) 0.51 17.47 14.19 (2.43-25.97)
Table S1. Results of the infection experiment, giving the number of infections and deaths occurring within each life stage for the different dose groups, and the calculated death rates. The cumulative observation time for each life stage (summed over all individuals) is shown and is used to calculate the death rate for each group ( = no. of deaths/cumulative time for each life-stage). Infection- specific death rate = exposed – control death rate. 95% C.I. = 95% confidence interval. For the number of tadpoles infected the confidence interval is calculated from the proportion infected, using the normal approximation to the binomial distribution; for the infection induced death rates the confidence interval is calculated using the standard error of a rate difference. The methods of parameter estimation are outlined in the section B (electronic supplementary material) and values for P and are reported in Table 1.
- 6 - Number of D, no. of Z, water volume , transmission (Notes) infected zoospores zoospore (litres) parameter tadpoles at added death rate (zoospore-1, year-1) end (year-1) 11 75 13 0.14 0.070 (0.059- Infection experiment 0.085) estimate (95% C.I.)a 15.8 (upper 100 0 0.14 0.022 Infection experiment, 95% (maximum) (minimum) lower limitb interval) 6.2 (lower 50 365 0.14 0.623 Infection experiment, 95% (minimum) (maximum) upper limitb interval) 8 1.23 × 10-3 (3.85 Transmission ×10-4, 1.09 × 10-2) experiment, estimate (lower, upper limits)c 1.7 × 106 5.76 × 10-9 (1.79 Full transmission ×10-9, 5.07 × 10-8) model, estimate (lower, upper limits)d
Table S2. Calculating the value and range for , the transmission parameter. For the infection experiment, the estimated value of and its lower and upper limits were calculated by fitting the simple model described in section B (electronic supplementary material) to the number of infected tadpoles shown in Table S1, with the given values for D and Z, using least squares regression. aMode and the 95% highest density region of the distribution of the samples obtained using MCMC sampling – see section B for details. bPoint estimate obtained using least squares regression in Berkeley Madonna, using extreme parameter estimates shown cFor subsequent fitting of the data from the transmission experiment, the estimate and extreme values shown in the table (rows 1-3) were used but corrected for the volume of 8 litres used. dFor the full transmission model, the estimate for was corrected for the estimated volume of 1.7 × 106 litres of the lake periphery which the tadpoles and zoopsores inhabit, and this is the range given in Table 1.
- 7 - 30 no. infected at start 25 no. infected at end s e
l total no. tadpoles in tank o
p 20 d a t
f o
15 r e b m
u 10 N
5
0 1/20 4/20 7/20 2/10 6/30 starting ratio of infected:total tadpoles
Figure S1. Results of the transmission experiment, showing the total number of tadpoles in each treatment and numbers infected at the start and end of the experiment (for the final number of infecteds, the mean + standard deviation from 4 replicates is shown).The rate of B. dendrobatidis release from infected tadpoles was calculated from this data; the method of parameter estimation is outlined in section B (electronic supplementary material) and values for are reported in Table 1.
- 8 - 5 .
3 (a) (b)
0 x10^10 . ) 8 3 - 3 12000 0 1 ( 5 . n N 2
2.5 10000 o _ r . _ e
t o _
e 0 f . s
e 2 8000 a 2 m r
Neither toads nor Bd d a o u r p l a t s 5
p .
o 1.5 6000 t
o 1 o n a z
d o f i
Both toads s s o 1 4000
_ s 0 . i . _
and Bd o 1 _ m N s 0.5 2000 n b a 5 . r 0 T 0 0 0
. Toads only 0 20 40 60 80 0 Time since Bd introduction (years) 1e+04 1e+05 1e+06 1e+07 Rate of zoospore release r
Figure S2. Stability and dynamics of the B. bufo and B. dendrobatidis populations, with an average
-1 zoospore lifespan of 1 year (Z = 1 year ) and no saprobic reproduction ( = 0). (a) Status of each population 35 years after introduction of B. dendrobatidis, across the full ranges of the transmission parameter,and the rate of zoospore release, Note that is on a log scale. (b) Population dynamics of adult toads and free-living zoospore population at the point ‘b’ indicated in (a). 1×105 7.5×10-9. All other parameters are as in Table 1. Bd = B. dendrobatidis.
- 9 -
5 5 . .
3 (a) 3 ) ) 0 0 8 8 . . - - 3 3 0 0 Neither
1 1 Bd ( toads ( n n 5 5
. . only
2 2 nor Bd
r r e e t t e e 0 0 . Both toads and Bd . Both toads and Bd m m 2 2 a a r r a a 5 5 p p . .
1 1 n n o o i i s s s s 0 0 i i . . 1 1 m m s s n n a a 5 5 . . r Toads r 0 0 T only T 0 0 . . 0 0 1e+04 1e+05 1e+06 1e+07 1e+04 1e+05 1e+06 1e+07 Rate of zoospore release r Rate of zoospore release r
Figure S3. Effect of saprobic growth. Stability of the B. bufo and B. dendrobatidis populations,
-1 with an average zoospore lifespan of 4 weeks ( Z = 13 year ) and additional saprobic reproduction, with (a) 0 < < Z and (b) > Z .Status of each population is shown 35 years after introduction of B. dendrobatidis, across the full ranges of the transmission parameter, and the rate
-1 -1 -6 of zoospore release, Note that is on a log scale. (a) Z = 13 year ,10 year , = 1 × 10 (b)
-1 -1 -6 Z = 13 year , 200 year , = 1 × 10 All other parameters as in Table 1. Bd = B. dendrobatidis.
Figure S3 shows the additional impact of permitting saprobic reproduction by B. dendrobatidis. Both panels in Figure S3 can be directly compared with Figure 2a (main text), where = 0. Note that zoospore saprobic reproduction increases the region of host extinction slightly, but greatly increases the region of parameter space over which co-existence of the two species is seen.
References
Boyle, D. G., Boyle, D. B., Olsen, V., Morgan, J. A. T. & Hyatt, A. D. 2004 Rapid quantitative detection of chytridiomycosis (Batrachochytrium dendrobatidis) in amphibian samples using real-time Taqman PCR assay. Diseases of Aquatic Organisms 60, 141-148
Gelman, A., Carlin, J. B., Stern, H. S. & Rubin, D.B. 2004 Bayesian data analysis, 2nd edn. London: Chapman & Hall.
Gilks, W. R., Richardson, S. & Spiegelhalter, D. J. 1996 Markov chain Monte Carlo in practice, London: Chapman & Hall.
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