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A Poisson process follows these postulates: $\lim\limits_{h\to0+}\frac{P(N_h=1)}h=\lambda$ i.e. the probability of occurrence one event in a very small interval of time is equal to the macroscopic rate or intensity ($\lambda\,$). $P(N_h\geqslant2)=o(h)$ i.e. the probability of occurrence of more than one events in an infinitesimal interval is essentially ...


I don't think your core question can be answered exactly, namely "...the theoretical maximum population to which the Tiger species could be restored", since there are too many variables to consider. However, the comment from @Remi.b is apt, in the sense that it shows that population growth rate per se (or reproductive rate) should not be the limiting factor. ...

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