Dynamics of a modified Leslie-Gower predator-prey model with Holling-type II schemes and a prey refuge

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

Predators consume prey for energy. Predators that acquire prey and prey that avoid predation both increase their chances of survival and reproduction (i.e., fitness). Routine predator-prey interactions elicit mutual adaptations that improve predator offenses, such as claws, teeth, and speed, as well as prey defenses, including crypsis, aposematism, and mimicry. Thus, predator-prey interactions resemble an evolutionary arms race.

How animals obtain and eat their food is called foraging behavior. Foraging can include searching for plants and hunting for prey and depends on the species and environment.

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Microbial predation refers to the process by which one microorganism kills and consumes another to obtain nutrients and energy. It encompasses both bacterial and protozoan predators. This interaction plays a crucial role in shaping microbial communities and regulating nutrient cycling.Bacterial Predators: Epibiotic vs. EndobioticBacterial predators are classified based on their mode of attack as either epibiotic or endobiotic. Epibiotic predators, such as Vampirococcus, attach to the surface of...

Small population sizes put a species at extreme risk of extinction due to a lack of variation, and a consequent decrease in adaptability. This weakens the chances of survival under pressures such as climate change, competition from other species, or new diseases. Large populations are more likely to survive pressures such as these, as such populations are more likely to harbor individuals that have genetic variants that are adaptive under new stresses. Small populations are much less...