Chytridiomycosis infection

  • Fungal disease caused by Batrachochytrium dendrobatidis (Bd)
  • Bd is a fungus that lives in the gut of animals
  • Infects frogs, and has caused decline in over 500 amphibian species
  • Causes skin disease in the frogs, which is often fatal

Image: New Scientist

Natural history

  • Bd fungus does not survive in warm climates (> 30 degrees)
  • Warm host climate also reduces lethality

Idea

If we can heat frogs, maybe we can reduce the impact of this infection

Experiment setup

  • Frogs separated into two classes: shaded and unshaded (heated)
  • Artifical refugia placed into each mesocosm (replicate)
  • Measure infection load and mortality

Image: Waddle et. al, Nature 2024

Hypothesis

  1. Do frogs in heated refugia experience a reduction in force of infection compared to non-heated refugia?
  2. Does prior infection confer an immune response that reduces future susceptibility?

Test using a stochastic compartmental model, with approximate Bayesian computation

Model setup

\lambda_h(t) = \beta_h \sum_{k=\{U,V\}}\sum_{j=1}^3 m_{k,j}I_{k,j},

  • m_{k,j} = Relative infectiousness of frog to I_{U,3}
  • I_{k,j} = Infection stage of frog

Parameters to estimate

Parameter Value
\beta_{\text{sh}}, \beta_{\text{un}}, \alpha, \omega fitted
\mu 0.021
\gamma_1 1/2.5 per week
\gamma_2 1/4.5 per week
Parameter Value
m_{U,1} 10
m_{U,2} 100
m_{V,1} 1
m_{V,2} 10
m_{V,3} 0.1

Data

  • 8 mesocosms, 4 shaded 4 unshaded
  • 20 frogs per mesocosm, 10 vaccinated, 10 unvaccinated, half infected at t_0
  • Half frogs experienced prior infection
  • Frogs observed at t=1, 2, 4, 6, 8, 10, 15 weeks only
  • Frogs that couldn’t be found presumed dead
  • Individual infection load data for each frog at each time point

Caution

For more data information, ask Claire Miller and/or read Waddle et. al Hotspot shelters stimulate frog resistance to chytridiomycosis.

Model identifiability

ABC summary statistic:

\Delta(\theta) = \sum_{x \in \Omega} \sum_{j=1}^7\left(x^\mathrm{sim}(t_j|\theta)-x^\mathrm{obs}(t_j)\right)^2,

where \Omega = \{S_k, \; I_{k,i} \; | \; k=\{U,V\}, \; i = 1, \dots, 3\}

Given infinite data, the model is fully identifiable

Our data is not infinite, so it is not be possible to recover all model parameters

Simulation-estimation experiment

  • Simulate the model using known parameters
  • Attempt to recover known parameters

Parameters obtained from a least-squares fit to the mean-field approximation

Tip

Estimates are valid up to the data-generating process (i.e. the model, including priors and summary statistics)

Model identifiability

Model identifiability

Model identifiability

Results

Simulation-estimation revealed that \omega, and the product of \alpha\beta were identifiable only

Parameter Prior Posterior (Mean, 95% CI)
\beta_\text{sh} \sim U(0,2) 0.675 (0.025, 1.876)
\beta_\text{un} \sim U(0,2) 0.401 (0.008, 1.767)
\alpha \sim U(0,0.5) 0.072 (0.003, 0.373)
\alpha\beta_\text{sh} 0.018 (0.001, 0.061)
\alpha\beta_\text{un} 0.009 (0.000, 0.031)
\omega \sim U(0,2) 0.569 (0.122, 1.688)

Posterior distributions

Predicted trajectories

Summary

  • Heating of artifical refugia can reduce infection by almost 50%

  • Prior infection highly protective (approx 97%)

  • Small numbers of frogs

  • Limited observation frequency

  • ABC-rejection not the most refined algorithm

These refugia are cheap, easy to deploy, used by the frogs.

Chytrid has become a global issue, maybe this can help to at least slow the issue.

Team

Claire Miller

Patricia Campbell

Jennifer Flegg

Experimental paper

Waddle et. al, Hotspot shelters stimulate frog resistance to chytridiomycosis Nature 2024

Code availability