Integrated population models (IPMs) represent the single, unified analysis of population count data and demographic data. This modelling framework is quite novel and can be implemented within the classical or the Bayesian mode of statistical inference. Here, we briefly show the basic steps that need to be taken when an integrated population model is adopted, and review existing integrated population models for birds and mammals. There are important advantages of integrated compared to conventional analyses that analyse each dataset separately and then try to make an inference about population dynamics. First, integrated population models allow the estimating of more demographic quantities, because there is information about all demographic processes operating in a population, and this information is exploited. Second, parameter estimates become more precise, and this enhances statistical power. Finally, all sources of uncertainty due to process variability and the sampling process(es) are adequately included. Core of the integrated models is the link of changes in the population size and the demographic rates via a demographic model (usually a Leslie matrix model) and the likelihoods of all existing datasets. We discuss some critical assumptions that are typically made in integrated population models and highlight fruitful areas of future research. Currently, we have found 25 studies that used integrated population models. Central to most studies was statistical development rather than their application to address an ecological question, which is not surprising given that integrated population models are still a new development. We predict that integrated population models will become a common and important tool in studies of population dynamics, both in ecology and its applications, such as conservation biology or wildlife management. Keywords

Summary1. The dynamics of many populations is strongly affected by immigrants. However, estimating and modelling immigration is a real challenge. In the past, several methods have been developed to estimate immigration rate but they either require strong assumptions or combine in a piecewise manner the results from separate analyses. In most methods the effects of covariates cannot be modelled formally. 2. We developed a Bayesian integrated population model which combines capture-recapture data, population counts and information on reproductive success into a single model that estimates and models immigration rate, while directly assessing the impact of environmental covariates. 3. We assessed parameter identifiability by comparing posterior distributions of immigration rates under varying priors, and illustrated the application of the model with long term demographic data of a little owl Athene noctua population from Southern Germany. We further assessed the impact of environmental covariates on immigration. 4. The resulting posterior distributions were insensitive to different prior distributions and dominated by the observed data, indicating that the immigration rate was identifiable. Average yearly immigration into the little owl population was 0AE293 (95% credible interval 0AE183-0AE418), which means that ca 0AE3 female per resident female entered the population every year. Immigration rate tended to increase with increasing abundance of voles, the main prey of little owls. 5. Synthesis and applications. The means to estimate and model immigration is an important step towards a better understanding of the dynamics of geographically open populations. The demographic estimates obtained from the developed integrated population model facilitate population diagnoses and can be used to assess population viability. The structural flexibility of the model should constitute a useful tool for wildlife managers and conservation ecologists.

Abstract. Understanding population dynamics requires accurate estimates of demographic rates. Integrated population models combine demographic and survey data into a single, comprehensive analysis and provide more coherent estimates of vital rates. Integrated population models rely on the assumption that different data sets are independent, which is frequently violated in practice. Moreover, the precision that can be gained using integrated modeling compared to conventional modeling is only known from empirical studies. The present study used simulation methods to assess how the violation of the assumption of independence affects the statistical properties of the parameter estimators. Further, the gains in precision and accuracy from the model were explored under varying sample sizes. For capture-recapture, population survey, and reproductive success, we generated independent and dependent data that were analyzed with integrated and conventional models. We found only a minimal impact of the violation of the assumption of independence on the parameter estimates. Furthermore, we observed an overall gain in precision and accuracy when all three data sets were analyzed simultaneously. This was particularly pronounced when the sample size was small. These findings contribute to clearing the way for the application of integrated population models in practice.