Mesocosm experiments enable researchers to study animal dynamics, but determining accurate estimates of survival and development rates of different life stages can be difficult, especially as the subjects may be hard to sample and mortality rates can be high. We propose a new methodology for estimating such parameters.We used an experimental set-up with 48 aquatic mesocosms, each with 20 first instar mosquito larvae and under 1 of 12 treatments with varying temperatures and nutrient concentrations. We took daily subsamples of the aquatic life stages as well as counting the emerging adults. We developed a method to estimate the survival and development probabilities at each life stage, based on optimising a matrix population model. We used two different approaches, one assuming the difference between predictions and observations was normally distributed, and the other using a combination of a normal and a multinomial distribution. For each approach, the resulting optimisation problem had around 100 parameters, making conventional gradient descent ineffective with our limited number of data points. We solved this by computing the formal derivatives of our matrix model.Both approaches proved effective in predicting mosquito populations over time, also when compared against a separate validation dataset, and the two approaches produced similar results. They also both predicted similar trends in the survival and development probabilities for each life stage, although there were some differences in the actual values. The approach which only used the normal distribution was considerably more computationally efficient than the mixed distribution approach.This is an effective approach for determining the survival and development rates of small animals in mesocosm experiments. We have not found any other reliable methodology for estimating these parameters, especially not from incomplete data or when there are many different experimental treatments. This methodology enables researchers to gain a much more detailed understanding of the life cycles of small animals, potentially leading to advances in a wide range of areas, for example in mosquito-borne disease risk or in considering the effects of biodiversity loss or climate change on different species.NWONWA.1160.1S.210Number theory, Algebra and Geometr
