Systematic review of modelling assumptions and empirical evidence: Does parasite transmission increase nonlinearly with host density?

Host-parasite dynamics are impacted by the relationship between host density and parasite transmission, and thus, all epidemiological models contain a central transmission-density function. Recent theoretical work demonstrates that this central parasite transmission function might be best represented by a nonlinear continuum from one linear extreme to another: density-dependent transmission at low host densities to density-independent transmission at high host densities. But how often are nonlinear transmission functions used, and when are they better at describing transmission in real host-parasite systems? To quantify existing modelling practices, we systematically reviewed seven representative ecology journals, finding 262 studies containing host-parasite models that contained linear and/or nonlinear transmission functions. We also reviewed the literature to find 28 experimental and observational studies that compared multiple transmission functions in real host-parasite systems, and tallied which functions were best supported in those systems. Finally, we created a flexible model simulation tool to explore and quantify the bias in model parameter estimates that is created when using an inaccurate transmission function. We found that most experimental and observational studies reported that nonlinear transmission-density functions outperformed simple linear transmission-density functions, supporting recent theoretical work. In contrast, most studies containing host-parasite models assumed that host density was constant and/or used a single, linear transmission function to explain how transmission rates changed with density. Using the wrong linear function and/or using a linear function when the underlying transmission-density relationship is even slightly nonlinear can substantially bias model parameter estimates, as demonstrated by our simulations over a broad parameter space. Some modelling studies may be using linear functions in host-parasite systems where nonlinear functions are more appropriate. If true, these models would yield substantially biased parameter estimates. To avoid such biases that compromise ecological understanding and prediction, we recommend that future studies compare multiple transmission functions, including nonlinear options, whenever possible.