Critical patch sizes in spatial population dynamics with two habitat fragments

This work starts from the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation to model diffusive populations in fragmented regions characterized by patches with different environmental conditions. Using this model, we found an expression for the general case of critical patch size, i.e. sizes below which the population goes extinct in a system of two patches (life-beneficial regions) surrounded by sinks (life-detrimental regions). This expression alone is an interesting result because it allows for the study of phenomena and interpretations presented in this work, as well as other features not included in this study. From the analysis of this expression, we extracted the analytical prediction that in a system formed by a patch and two semi-infinite sinks, if we replace one semi-infinite sink with a patch plus another semi-infinite sink, more lethal than the original, the added patch will only be beneficial to the original system if it is large enough to compensate for the added sink. This interpretation arises from a case study done with a specific set of parameters, but will appear for other values that meet the presented condition.

Keywords:
Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation; Minimum size of fragmented regions; Relation between neighbor patches