Mathematical modeling of population dynamics with Allee effect

Allee effect that refers to a positive relationship between individual fitness and population density provides an important conceptual framework in conservation biology. While declining Allee effect causes reduction in extinction risk in low-density population, it provides a benefit in limiting establishment success or spread of invading species. Population models that incorporated Allee effect confer the fundamental role which plays for shaping the population dynamics. In particular, non-spatial predator-prey and invasion models have shown the influence of Allee effects on population dynamics, and spatial models have illustrated its critical roles for pattern formation and the manifestation of traveling wave fronts. We highlight all such no-spatial and spatial population models and their contributions in deeper understanding of population dynamics. In addition, we briefly outline the trends for future research on Allee effect which we think are interesting and widely open.