The collective organization of living organisms in heterogeneous environments is a central issue in population dynamics. In particular, it is relevant to know how fragmented structures arise and, mainly, if in the long term the population will survive or become extinct. We address these problems from the perspective of single species populations. The FKPP equation provides a fundamental mathematical description of the spatial distribution at the mesoscopic level, governed by elementary processes (growth, competition for limited resources and random dispersion), and can be generalized in several realistic directions by including for instance: density-dependencies in growth and diffusion rates, selective spatial spreading, nonlocality, and fluctuations, under appropriate boundary conditions. We will discuss mainly the role of noise and boundary conditions on the survival of the population, as well as on the emergence of spatial structures (Fig. 1).
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Figure 1: Examples of patterns emerging from the interplay between spatial dynamics and environment heterogeneity [2]
Acknowledgements
We acknowledge partial support from CAPES, CNPq and FAPERJ.
References
[1] MAF dos Santos, et al., arXiv preprint arXiv:2008.02907
[2] V Dornelas, et al., arXiv preprint arXiv:2003.00100
[3] V Dornelas, EH Colombo, C Anteneodo, Physical Review E 99, (2019) 062225
[4] EH Colombo, C Anteneodo, Journal of Theoretical Biology 446, (2018) 11-18