Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics

Population viability in a host-parasitoid system is mediated by interactions between population stage structure and life stage differential susceptibility to toxicants

“…These results contribute to the growing body of evidence suggesting that a population-level perspective is critical for understanding the nuances of how economically important species react to toxicant exposure 4,[25][26][27][28][29][30] . We suggest that this perspective, coupled with more detailed population-structured models of differential susceptibility that incorporate pesticide/toxicant resistance (e.g., 31,32 ) points the way forward in developing optimal resource management schemes and the development of ecological risk assessments. Toxicity of imidacloprid to adult D. rapae.…”

Technological Developments Since the Deepwater Horizon Oil Spill

“…The marine food web matrix was incorporated into the Atlantis model, after which Ainsworth et al (2018) simulated impacts from the DWH incident on fish guilds and their subsequent recovery, and Court et al (2020) estimated the direct and total economic impacts associated with changes in commercial and recreational fishing activity following the DWH incident. Ackleh et al (2019) developed a nonevolutionary model to describe predatorprey dynamics and then extended it to an evolutionary model under the influence of an environmental toxicant. The discrete-time predator-prey model simulates how prolonged exposure to a toxicant or environmental disturbance, such as an oil spill, may impact predator-prey dynamics when only the prey evolves resistance to the toxicant.…”

Corrigendum to “Persistence and Stability analysis of discrete-time predator-prey models: a study of population and evolutionary dynamics”, Journal of Difference Equations and Applications, 25(2019), 1568–1603

“…With the additional condition (1) on the second partial derivative of the fitness function, the inequality 0 <J 33 < 1 holds for sufficiently small ν, and the proof as given in [1] follows. We note that, for sufficiently small α, this condition is guaranteed to hold.…”

“…In addition, in the proofs of Lemmas 2.3 and 3.10, we incorrectly state that A and A are invariant instead of stating that they are positively invariant. Thus, to remedy the proofs of Lemmas 2.3 and 3.10, notice that one can show using Theorem 2.9 in [3] that for the 2D model given in (1) and for the 3D model given in (5) there exist bounded sets ⊂ A and ⊂ A that are invariant and hence are global attractors. We remark that A and A are globally attracting sets.…”