Dominance/diversity models (continued)

Lecture graphics

If the relative abundances of spp. are governed by relatively independent factors, then we might expect the relative importances of spp. to be approx. normally-distributed

Note that old-field succession tends to: [Whittaker 1972, Taxon 21:213-251]

geometric -------> log-normal -------> increased dominance by

trees -------> steepening of log-normal distribution

According to May (1975 in Cody and Diamond, eds., Ecology and Evolution of Communities):

... the lognormal distribution is associated with [results] of random variables, and factors that influence large and heterogeneous assemblies of species indeed tend to do so in this fashion.

... if the environment is randomly fluctuating, or alternatively as soon as several factors become significant ..., we expect the statistical Law of Large Numbers to take over and produce the ubiquitous lognormal distribution.

Colinvaux (1986 Ecology text, p. 676):

Log-normal populations result when the abundance of each species pop'n is determined at random relatively independently of other species populations. The prevalence of log-normal distributions shows that the relative distributions of animals and plants very often is determined by random processes.

Thus, interactions appears to be less important in the lognormal model than in the niche pre-emption (geometric series) model

The log-normal model may be expected in relatively spp.-rich communities where many factors (which are largely independent) influence spp. performance

Broken-stick model

P_r = (N/s) [1/(s-i+1)], where

s = no. spp.,

N = no. individuals,

i = spp. sequence from least to most important, and

P_r = I.V. of sp. n in sequence from least important (i=1) thru sp. in question

e.g., given N=100 individuals of s=3 spp.,

Spp.	Pr
1	(100/3)[1/(3-1+1)] = 11.1
2	(100/3)[1/(3-1+1) + 1/(3-2+1) = 27.8
3	(100/3)[1/(3-1+1) + 1/(3-2+1) + 1/(3-3+1)] = 61.1
Note Pr =	100

Acc. to May (1975), this model is applicable to communities comprising a limited number of taxonomically similar spp. ... (Colinvaux 1986 refers to spp. of a guild)

... in competitive contact w/ each other in a relatively homogeneous habitat; in this situation, a more structured pattern of relative abundances of spp. (other than that resulting from conditions associated w/ log-normal distribution) may be expected. The basic picture is one of intrinsically even resource division of some major environmental resource. In this model, species are limited by competition at randomly located boundaries.