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Deterministic population models for adaptive dynamics are derived mathematically from individual-centred stochastic models in the limit of large populations. However, it is common that numerical simulations of both models fit poorly and give rather different behaviours in terms of evolution speeds and branching patterns. Stochastic simulations involve extinction phenomenon operating through demographic stochasticity, when the number of individual ‘units’ is small. Focusing on the class of integro-differential adaptive models, we include a similar notion in the deterministic formulations, a survival threshold, which allows phenotypical traits in the population to vanish when represented by few ‘individuals’. Based on numerical simulations, we show that the survival threshold changes drastically the solution; (i) the evolution speed is much slower, (ii) the branching patterns are reduced continuously and (iii) these patterns are comparable to those obtained with stochastic simulations. The rescaled models can also be analysed theoretically. One can recover the concentration phenomena on well-separated Dirac masses through the constrained Hamilton–Jacobi equation in the limit of small mutations and large observation times. [ABSTRACT FROM PUBLISHER]

Mutualisms are ubiquitous in nature, as is their exploitation by both conspecific and heterospecific cheaters. Yet, evolutionary theory predicts that cheating should be favoured by natural selection. Here, we show theoretically that asymmetrical competition for partners generally determines the evolutionary fate of obligate mutualisms facing exploitation by third-species invaders. When asymmetry in partner competition is relatively weak, mutualists may either exclude exploiters or coexist with them, in which case their co-evolutionary response to exploitation is usually benign. When asymmetry is strong, the mutualists evolve towards evolutionary attractors where they become extremely vulnerable to exploiter invasion. However, exploiter invasion at an early stage of the mutualism's history can deflect mutualists’ co-evolutionary trajectories towards slightly different attractors that confer long-term stability against further exploitation. Thus, coexistence of mutualists and exploiters may often involve an historical effect whereby exploiters are co-opted early in mutualism history and provide lasting ‘evolutionary immunization’ against further invasion. [ABSTRACT FROM AUTHOR]

Enhancing the predictive power of models in biology is a challenging issue. Among the major difficulties impeding model development and implementation are the sensitivity of outcomes to variations in model parameters, the problem of choosing of particular expressions for the parametrization of functional relations, and difficulties in validating models using laboratory data and/or field observations. In this paper, we revisit the phenomenon which is referred to as structural sensitivity of a model. Structural sensitivity arises as a result of the interplay between sensitivity of model outcomes to variations in parameters and sensitivity to the choice of model functions, and this can be somewhat of a bottleneck in improving the models predictive power. We provide a rigorous definition of structural sensitivity and we show how we can quantify the degree of sensitivity of a model based on the Hausdorff distance concept. We propose a simple semi-analytical test of structural sensitivity in an ODE modeling framework. Furthermore, we emphasize the importance of directly linking the variability of field/experimental data and model predictions, and we demonstrate a way of assessing the robustness of modeling predictions with respect to data sampling variability. As an insightful illustrative example, we test our sensitivity analysis methods on a chemostat predator-prey model, where we use laboratory data on the feeding of protozoa to parameterize the predator functional response., (Copyright © 2011 Elsevier Ltd. All rights reserved.)