# Chytrid fungus and logistic regression against temperature

Chytrid fungus refers to the fungus Batrachochytrium dendrobatidis (Bd). In amphibians, it causes a disease known as Chytridiomycosis. It is one of the worst diseases to strike out at multiple species of animals on the planet. This horrible disease degrades the skin, which in amphibians is a sensitive, permeable organ that is part of the respiratory system. Chytridiomycosis eventually leads to death and is a serious threat to many amphibian species in areas such as North America, Central America, Asia, Africa, and even in Australia.

While not necessarily threatened with extinction by Chytrid fungus, even Northern Leopard Frogs may be affected by the widespread organism. Photo by Jason Polak.

As humans, we have contributed to the spread of Chytrid. For example, the bullfrog Lithobates catesbeianus is an excellent reservoir of Bd and has been associated with increased presence of the bacteria in areas where it has become an invasive species due to imports for food. Chytrid fungus has also been responsible for huge losses and declines of frog species in Panama.

Bd grows between 4-25 C°. Therefore, we expect to see a decrease in prevalence in Bd infections in species in the wild as the temperature of the water rises. Matthew Forrest and Martin Schlaepfer tested this and modeled the presence or absence of a Bd infection against water temperature using binomial logistic regression. In their sample of 201 Lowland Leopard frogs, they grouped 10-12 individuals and plotted the proportion of individuals with Bd to illustrate their model:

Logistic equation model reproduced from Forrest and Schlaepfer.

The curve is their logistic regression equation, which is
$$p = \frac{1}{1+e^{4.56-0.226t}}$$ where $t$ is the temperature in Celsius, and $p$ is the proportion of individuals with Bd. This is just one example of the steps we need to take towards better understanding the ecology of the Bd organism so that we can better prevent it from eradicating beautiful species of amphibians that are integral parts of our biosphere.