A few months ago, I blogged about the difference between density-dependent (DD) and frequency-dependent (FD) transmission. To recap, the difference is all about the shape of the contact rate function with regards to host density: in FD transmission, contact rate is assumed to be independent of host density. In DD transmission, contact rate is assumed to linearly increase with host density.

So, do we really only get two options? A linear increase or no relationship? As it turns out, there are a whole bunch of proposed transmission equations in the literature where contact rates are not linear or constant (e.g., McCallum et al. 2001). In fact, many authors have suggested that neither DD nor FD transmission are appropriate models; instead, the contact rate function (as measured by the transmission rate function) falls somewhere between the two, increasing non-linearly with host density (e.g., Fenton et al. 2002). The theoretical argument for a non-linear contact rate function is similar to the argument for using a Holling Type II functional response instead of a Holling Type I functional response for predator-prey interactions: a linear contact rate function might make sense at some host densities, but could contact rate really just keep increasing infinitely with host population density? Or should we expect saturation of contact rates at high host densities, where eventually adding another 100 or 1,000 hosts doesn’t appreciably change the per capita contact rate?

Most of the work in this area is from mathematical models/simulations, because it can be hard to measure animal contact rates (even when scientists get creative and use mouse raves and painted lice). We need more empirical data!!! This recent Ecology paper by Cross et al. (2013) is a good start. They quantified contact rates among female elk around Yellowstone using proximity logger collars, and found that contact rates increased non-linearly with group size, which they were kind of using as a proxy for density.

Given that the shape of the contact rate function is a fundamental assumption of every epidemiological model, I think there is shockingly little evidence to support the use of DD, FD, or non-linear transmission. MORE DATA, PLEASE.

**References:**

Cross, P., T. Creech, M. Ebinger, and K. Manlove. 2013. Female elk contacts are neither frequency nor density dependent. Ecology 94:2076–2086.

Fenton, A., J. Fairbairn, R. Norman, and P. J. Hudson. 2002. Parasite transmission: reconciling theory and reality. Journal of Animal Ecology 71: 893–905. (PDF link)

McCallum, H., N. Barlow, and J. Hone. 2001. How should pathogen transmission be modelled? Trends in Ecology & Evolution 16: 295–300. (PDF link)

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