Richard hypothesis 

d/w = resource separation ratio.

d/w < 1, species cannot coexist;

1 < d/w < 3, there will be some competition between species

d/w > 3, species coexist harmoniously

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Population sizes at various times

N_t = N₀e^rt

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Per capita rate of increase, r, related to the net reproductive rate, R₀

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r, is affected by organismal size and generation time.

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When conditions are optimal for the population, r is at its maximum rate and is called the intrinsic rate of increase (_rmax).

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r<0, the population decreases

r=0, the population remains constant

r>0, the population increases