Predator–prey systems depend on a prey refuge

Dynamic analysis of a phytoplankton-fish model with the impulsive feedback control depending on the fish density and its changing rate

This paper proposes and studies a comprehensive control model that considers fish population density and its current growth rate, providing new ideas for fishing strategies. First, we established a phytoplankton-fish model with state-impulse feedback control based on fish density and rate of change. Secondly, the complex phase sets and impulse sets of the model are divided into three cases, then the Poincaré map of the model is defined and its complex dynamic properties are deeply studied. Furthermore, some necessary and sufficient conditions for the global stability of the fixed point (order-1 limit cycle) have been provided even for the Poincaré map. The existence conditions for periodic solutions of order-k(k≥2) are discussed, and the influence of dynamic thresholds on system dynamics is shown. Dynamic thresholds depend on fish density and rate of change, i.e., the form of control employed is more in line with the evolution of biological populations than in earlier studies. The analytical method presented in this paper also plays an important role in analyzing impulse models with complex phase sets or impulse sets.

From theory to practice in pattern-oriented modelling: identifying and using empirical patterns in predictive models

To robustly predict the effects of disturbance and ecosystem changes on species, it is necessary to produce structurally realistic models with high predictive power and flexibility. To ensure that these models reflect the natural conditions necessary for reliable prediction, models must be informed and tested using relevant empirical observations. Pattern-oriented modelling (POM) offers a systematic framework for employing empirical patterns throughout the modelling process and has been coupled with complex systems modelling, such as in agent-based models (ABMs). However, while the production of ABMs has been rising rapidly, the explicit use of POM has not increased. Challenges with identifying patterns and an absence of specific guidelines on how to implement empirical observations may limit the accessibility of POM and lead to the production of models which lack a systematic consideration of reality. This review serves to provide guidance on how to identify and apply patterns following a POM approach in ABMs (POM-ABMs), specifically addressing: where in the ecological hierarchy can we find patterns; what kinds of patterns are useful; how should simulations and observations be compared; and when in the modelling cycle are patterns used? The guidance and examples provided herein are intended to encourage the application of POM and inspire efficient identification and implementation of patterns for both new and experienced modellers alike. Additionally, by generalising patterns found especially useful for POM-ABM development, these guidelines provide practical help for the identification of data gaps and guide the collection of observations useful for the development and verification of predictive models. Improving the accessibility and explicitness of POM could facilitate the production of robust and structurally realistic models in the ecological community, contributing to the advancement of predictive ecology at large.

Matching consumer feeding behaviours and resource traits: a fourth-corner problem in food-web theory

For decades, food web theory has proposed phenomenological models for the underlying structure of ecological networks. Generally, these models rely on latent niche variables that match the feeding behaviour of consumers with their resource traits. In this paper, we used a comprehensive database to evaluate different hypotheses on the best dependency structure of trait-matching patterns between consumers and resource traits. We found that consumer feeding behaviours had complex interactions with resource traits; however, few dimensions (i.e. latent variables) could reproduce the trait-matching patterns. We discuss our findings in the light of three food web models designed to reproduce the multidimensionality of food web data; additionally, we discuss how using species traits clarify food webs beyond species pairwise interactions and enable studies to infer ecological generality at larger scales, despite potential taxonomic differences, variations in ecological conditions and differences in species abundance between communities.

Spatio-temporal variation in European starling reproductive success at multiple small spatial scales

Understanding population dynamics requires spatio-temporal variation in demography to be measured across appropriate spatial and temporal scales. However, the most appropriate spatial scale(s) may not be obvious, few datasets cover sufficient time periods, and key demographic rates are often incompletely measured. Consequently, it is often assumed that demography will be spatially homogeneous within populations that lack obvious subdivision. Here, we quantify small-scale spatial and temporal variation in a key demographic rate, reproductive success (RS), within an apparently contiguous population of European starlings. We used hierarchical cluster analysis to define spatial clusters of nest sites at multiple small spatial scales and long-term data to test the hypothesis that small-scale spatio-temporal variation in RS occurred. RS was measured as the number of chicks alive ca. 12 days posthatch either per first brood or per nest site per breeding season (thereby incorporating multiple breeding attempts). First brood RS varied substantially among spatial clusters and years. Furthermore, the pattern of spatial variation was stable across years; some nest clusters consistently produced more chicks than others. Total seasonal RS also varied substantially among spatial clusters and years. However, the magnitude of variation was much larger and the pattern of spatial variation was no longer temporally consistent. Furthermore, the estimated magnitude of spatial variation in RS was greater at smaller spatial scales. We thereby demonstrate substantial spatial, temporal, and spatio-temporal variation in RS occurring at very small spatial scales. We show that the estimated magnitude of this variation depended on spatial scale and that spatio-temporal variation would not have been detected if season-long RS had not been measured. Such small-scale spatio-temporal variation should be incorporated into empirical and theoretical treatments of population dynamics.