Towards a mathematical model of limestone pavement vegetation. III. Estimation of the determinants of species frequencies

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Abstract
Models of the determination of the frequencies of 31 species of bryophytes, lichens, and algae in limestone pavement grikes were calculated by multiple regression. Independent variables were parameters of microclimate and surface pH. Percentages of variance accounted for varied from 14 to 72. In most cases the balance is attributable to replicate errors in the estimates of species frequencies and the abundance of zeros in the data. The models were used to predict species frequencies in other grikes, and in most species the mean difference between predicted and observed frequencies was less than 10%. Determinants of species frequency were found to be similar for species growing near the bottoms of the grikes but differed for those occurring near the tops.It is suggested that a two-phase analysis would be more informative than straightforward regression. In phase (a) the conditions under which the expected frequency is nonzero would be delimited; in phase (b) multiple regression would be performed on the observations falling within this region. This proposal is shown to be related to Hutchinson's concepts of fundamental and realized niches. It would also eliminate the problem of the multiple zero.

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