Colleen K. Kelly and Michael G. Bowler. 2005. A new application of storage dynamics: differential sensitivity, diffuse competition, and temporal niches. Ecology 86:1012–1022.

The modifications necessary when the two species have different mean lifetimes are very simple. If the lifetimes are close or the fluctuations in  (as opposed to the fluctuations in recruitment) are small, then it remains true that

and the species with the smaller mean recruitment exhibits the larger fractional recruitment fluctuations.  Since

the species with the smaller product of death rate and abundance fluctuates more.  Equation (2) (which is the same as Eq. A.7) takes the more general form

(B.1)

It may be difficult to extract the value of  with any precision in the presence of recruitment fluctuations, but we can illustrate the potential effects of unequal lifetime by reference to Jatropha (Kelly et al. 2001).  In these data J. chamelensis is commoner than J. standleyi but the difference is not really significant.  The measured growth rate of J. standleyi is greater than that of J. chamelensis but again the errors are such that the difference is not very significant.  However, the mean age of the trees in the J. chamelensis sample is about half that of the J. standleyi sample growing under comparable conditions, and if this difference reflects the underlying exponentials (which is by no means certain) then .  Then  for approximately equal populations and the growth rate divided by the death rate is much larger for J. standleyi (the "rarer").  Such considerations should be borne in mind with real data.

LITERATURE CITED

Kelly, C. K., H. Banyard Smith, Y. M. Buckley, R. Carter, M. Franco, W. Johnson, T. Jones, B. May, R. Perez Ishiwara, A. Perez-Jimenez, A. Solis Magallanes, H. Steers, and C. Waterman. 2001. Investigations in commonness and rarity: a comparative analysis of co-occuring, congeneric Mexican trees. Ecology Letters 4:618–627.