| Abstract: |
| In 2006, Lou proved that, once the intrinsic growth rate $r$ in the logistic model is proportional to the spatially heterogeneous carrying capacity $K$ ($r=K^1$), the total population under the regular diffusion exceeds the total of the carrying capacity. DeAngelis et al (2016) argued that the prevalence of the population over the carrying capacity is only observed when the growth rate and the carrying capacity are positively correlated, at least for slow dispersal. Guo et al (2020) justified that, once $r$ is constant ($r=K^0$), the total population is less than the cumulative carrying capacity. Together with filling up the gap for when $r=K^{\lambda}$ for any real $\lambda$, we define a diffusion strategy as the tendency to have a distribution proportional to a certain positive prescribed function, once a diffusion coefficient grows infinitely, and explore the interplay of harvesting and dispersal strategies and their influence on the outcome of the competition for two resource-sharing species. While achieving extinction by excessive culling of the undesired species is simple and efficient, keeping biodiversity is a more complicated task. Proposing such heterogeneous harvesting that the two populations become an ideal free pair allows to guarantee coexistence. |
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