Appendix D. Greater detail on recruitment fluctuations. A pdf file of this appendix is also available.
Equation 1 can be formally integrated to yield
|
|
where g is time before present
(t) – the age of those trees which matured g ago and for which
the recruitment variable was 
.
The asymptotic solution, relevant to mature forests other than plantations,
is
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(D.1)
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The function
|
(D.2)
|
is the age profile of species 
in
a mature forest.
If species is
stable in the long term, then both Eqs. 1 and D.1 yield
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(D.3)
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and from (D.2)
 
|
is an exponential and
|
The age profile 
fluctuates
about the exponential .
A measure of the recruitment fluctuation is thus provided by the fractional form
|
(D.4)
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Equation D.4 is the same as Eq. 4 in the main text. The fluctuations in recruitment are thus imprinted on the age profile of a population and can be read out for periods of up to a few mean lifetimes.
The stipulation that mortality is constant or regular across age/size classes for canopy level individuals is borne out both by data and logic. For canopy level trees, probability of mortality at any one point has been shown to be equivalent or to vary only gradually in a regular manner across age/size classes (e.g., Platt et al. 1988; Johnson and Frier 1989). Although relatively regular adult mortality has been demonstrated in only a subset of tree species, to infer otherwise would require assuming that at any one time, mortality of mature trees is low in one size class, high in the next largest size class, low again in the following size class, etc.
Johnson, E. A., and G. I. Frier. 1989. Population dynamics in lodgepole pine-Engleman spruce forests. Ecology 70:1335–1345.
Platt, W. J., G. W. Evans, and S. L. Rathbun. 1988. The population dynamics of a long-lived conifer (Pinus palustris). American Naturalist 131:491–525.