Diseases such as malaria and dengue fever are spread by intermediaries, in this case, mosquitoes. The health and economic burdens of such mosquito-borne diseases are enormous. We know that mosquitoes are expanding their ranges and invading new habitats in response to warmer temperatures. Accurately predicting changes in both the size and spread of mosquito populations is essential for anticipating changes in disease dynamics.

To model how changing environments will affect mosquito populations, we need to know how quickly a population can grow under different scenarios. To estimate changes in population growth rate scientists input measures of development time, survival, body size and reproductive output into their models. Body size and reproductive output are particularly difficult to measure directly in mosquito populations so researchers traditionally rely on the relationship between wing length, which is easier to measure, body size and reproductive output.

These are the relationships that the Centre for Geometric Biology are challenging. Underlying most models of mosquito distributions is the assumption that there is a directly proportional relationship between wing length, body size and reproductive output, or in other words, wing length and reproductive output increase at the same rate.

Scientists from the Centre analysed a range of existing data and found that this wasn’t true for most mosquito species.

In fact, explains Dr Louise Nørgaard, lead author on the study, larger females contribute disproportionately more to the replenishment of the population so it is not a straight-line relationship. And surprisingly, when we factor in this non-linear relationship smaller females are also contributing more to population replenishment than is assumed in current models.

This is important because increasing temperatures result in smaller females. So, temperatures where populations have been considered unviable, will, in fact, persist.

There is an additional complication when dealing with underlying assumptions of linearity; Jensen’s Inequality. This relates to a counter-intuitive mathematical rule that in non-linear relationships, such as this one, you can’t predict the mean reproductive output from the mean wing length in the same way you can for linear relationships. In fact, reproductive output in warmer climates will be even greater than predicted without accounting for Jensen’s Inequality.

There is another application of population models that will also be affected by these underlying assumptions. In the fight against Dengue fever, mosquitos that carry a bacteria called Wolbachia are bred in the lab and released into the wild to reduce the transmission of the dengue virus. Females released from the lab are bigger than their wild counterparts and so will contribute disproportionately more to the population when they breed. We are likely underestimating the impact of releasing Wolbachia-infected mosquitos in tackling this disease.

The authors conclude that to predict the response of disease vectors like mosquitos to global change we need to better represent the relationship between size and reproductive output.

This research was published in the journal Global Change Biology.