We analyse the effects of various treatments on cotton aphids ("Aphis gossypii"). The standard analysis of count data on cotton aphids determines parameter values by assuming a deterministic growth model and combines these with the corresponding stochastic model to make predictions on population sizes, depending on treatment. Here, we use an integrated stochastic model to capture the intrinsic stochasticity, of both observed aphid counts and unobserved cumulative population size for all treatment combinations simultaneously. Unlike previous approaches, this allows us to explore explicitly and more accurately to assess treatment interactions. Markov chain Monte Carlo methods are used within a Bayesian framework to integrate over uncertainty that is associated with the unobserved cumulative population size and estimate parameters. We restrict attention to data on aphid counts in the Texas High Plains obtained for three different levels of irrigation water, nitrogen fertilizer and block, but we note that the methods that we develop can be applied to a wide range of problems in population ecology. Copyright (c) 2010 Royal Statistical Society.