• Allee effects;
  • behaviour-based models;
  • density dependence;
  • individual-based models;
  • matrix models


  • 1
    During the past 15 years, models have been used increasingly in predictive population ecology. Matrix models used for predicting the fates of populations are often extremely basic, ignoring density dependence, spatial scale and behaviour, and often based on one sex only. We tested the importance of some of these omissions for model realism, by comparing the performance of a variety of population models of varying levels of complexity.
  • 2
    Detailed data from more than 13 years of behavioural and demographic research on a population of alpine marmots Marmota marmota in Berchtesgaden National Park, southern Germany, were used to parameterize four different population models. The models ranged from a simple population-based matrix model, to a spatially explicit behaviour-based model.
  • 3
    The performance of the models was judged by their ability to predict basic population dynamics under equilibrium conditions. Only a spatially explicit individual-based model ignoring optimal behaviour predicted dynamics significantly different to those observed in the field, highlighting the importance of considering realistic patterns of behaviour in spatially explicit models.
  • 4
    Using realistic levels of environmental and demographic stochasticity, variance in population growth rates predicted by all models was high, even within the range of population densities experienced in the field. This emphasizes the difficulty of using population-level field data to determine overall patterns of density dependence for use in population models.
  • 5
    All models were also used to predict potential density-dependent effects on alpine marmot population growth. In this regard, the models differed greatly. It was concluded that the simplest matrix model was adequate for making predictions regarding population sizes or densities under equilibrium conditions, but that for predictions requiring an understanding of transient dynamics only the behavioural model would be adequate.
  • 6
    An emergent feature of this study of alpine marmot population dynamics was the prediction of a demographic Allee effect with a profound influence on population dynamics across a very broad range of population sizes. Three mechanisms were identified as underlying this Allee effect: stochastic skews in sex ratio and demographic composition at low population sizes; less efficient social thermoregulation during hibernation in small groups; and difficulties with mate finding during dispersal, even at relatively high population sizes.