Population growth and competition models with decay and competition consistent delay

We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in the growth term is consistent with the rate of instantaneous decline in the population given by the model. Our formulation is a modification of Arino et al. (J Theor Biol 241(1):109-119, 2006) by taking the intraspecific competition between the adults and juveniles into account. We provide a complete global analysis showing that no sustained oscillations are possible. A threshold giving the interface between extinction and survival is determined in terms of the parameters in the model. The theory of chain transitive sets and the comparison theorem for cooperative delay differential equations are used to determine the global dynamics of the model. We extend our delayed logistic equation to a system modeling the competition between two species. For the competition model, we provide results on local stability, bifurcation diagrams, and adaptive dynamics. Assuming that the species with shorter delay produces fewer offspring at a time than the species with longer delay, we show that there is a critical value, [Formula: see text], such that the evolutionary trend is for the delay to approach [Formula: see text].

Synergistic effects of climate and landscape change on the conservation of Amazonian lizards

The leading causes of the worldwide decline in biodiversity are global warming, allied with natural habitat loss and fragmentation. Here, we propose an analysis of the synergistic effects of these two factors in 63 species of Amazonian lizards. We predicted that the high-climatic suitability areas of species would be significantly impacted by different deforestation scenarios and the resultant landscape structure and considered that forest-dwelling species would be especially susceptible to deforestation scenarios. We also pointed out species threatened by both drivers and suggested critical areas for their future conservation. According to our results, most species will face future reductions in suitable areas for their occurrence according to five different patterns, two of which represent significant risks for 15 species. Some of these species already deal with severe habitat loss and fragmentation of their current distribution ranges, whereas others will suffer a considerable area reduction related to future range shifts. We emphasize the importance of protected areas (PAs), especially indigenous lands, and the need to plan combined strategies involving PAs' maintenance and possible implementation of ecological corridors. Finally, we highlight eight species of thermoconformer lizards that constitute present and future conservation concerns related to the combined effects of climate change and habitat loss and that should be carefully evaluated in extinction risk assessments.

An alternative delayed population growth difference equation model

We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribution that takes into account that those individuals that die during the delay, do not contribute to growth. The model introduced differs from a delayed logistic difference equation, known as the delayed Pielou or delayed Beverton-Holt model, that was formulated as a discretization of the Hutchinson model. The analysis of our delayed difference equation model identifies a critical delay threshold. If the time delay exceeds this threshold, the model predicts that the population will go extinct for all non-negative initial conditions. If the delay is below this threshold, the population survives and its size converges to a positive globally asymptotically stable equilibrium that is decreasing in size as the delay increases. We show global asymptotic stability of the positive equilibrium using two different techniques. For one set of parameter values, a contraction mapping result is applied, while the proof for the remaining set of parameter values, relies on showing that the map is eventually componentwise monotone.

Preserving 40% forest cover is a valuable and well-supported conservation guideline: reply to Banks-Leite et al

Banks-Leite et al. (2021) claim that our suggestion of preserving ≥ 40% forest cover lacks evidence and can be problematic. We find these claims unfounded, and discuss why conservation planning urgently requires valuable, well-supported and feasible general guidelines like the 40% criterion. Using region-specific thresholds worldwide is unfeasible and potentially harmful.