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What Is the Species Richness Distribution?

Authors:
Pablo A Marquet at Pontifical Catholic University of Chile
Pablo A Marquet
Mauricio Tejo
Mauricio Tejo
Mauricio Tejo
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Rolando Rebolledo at University of Valparaíso
Rolando Rebolledo
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Marquet* PA, M Tejo & R. Rebolledo (2020) What is the distribution of
species richness? In: Unsolved Problems in Ecology. Dobson A., R.D.,
Holt & D. Tilman (eds). Princeton University Press. Pp. 177-188.
... Thus, the number of coexisting species S * is a stochastic variable as well and may be smaller than the overall number species S in the immigration flux from the larger basin, with S * ≤ S . The number of coexisting species has a corresponding probability distribution whose evolution is governed by a master equation derived from Eq. 2 (SI Appendix, section 2) (89). The richness, denoted as S * , is defined as the average number of the (co)existing species and is related to the SAD via ...
... The exact solution for the distribution of the number of coexisting species, S * , can be obtained for ρ = 0 (a binomial distribution) and ρ = 1 (a sum of hypergeometric functions) (SI Appendix, section 3) (74). For intermediate competition strengths, 0 < ρ < 1, a mean-field approximation results in a binomial distribution for the species richness distribution as in ref. 89; however, we discuss how this mean-field solution differs from the richness distribution from simulations in SI Appendix, section 3. ...
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... We note that ϕ(0|p) estimates the likelihood of the absence of a species in the local sample. Therefore, the probability of observing S p species in V p when the metacommunity richness is S follows a binomial distribution with an average given by and variance S[1 − ϕ(0|p)]ϕ(0|p) (see Materials and Methods), aligning with several theoretical models in ecology [see, e.g., (39,40)]. ...
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