Tropical Forest Community Ecology

Tropical Forest Ecology: Sterile or Virgin for Theoreticians? 123

or those of its neighbors. Hubbell’s focus was
the distribution of tree species abundances in
plots≤50 ha and biogeographic patterns of
species distributions. Westet al. (1997) and
Enquist (2002) framed a theory of forest struc-
ture, production, and dynamics. They assumed
that (1) only terminal twigs carry leaves; (2) each
terminal twig has the same diameter and leaf
area, regardless of its tree’s species; (3) trunks
and non-leafy branches all fork intonsuccessors,
each shorter by a factorn−^1 /^3 and narrower by
a factorn−^1 /^2 than its predecessor; (4) a tree’s
heightHis proportional to th etotal path l ength
from its root collar to th etip of any l eafy twig;
(5) a tree’s massMis proportional to its total
above-ground wood volume, which is proportional
toD^2 H, whereDis its trunk diameter; and (6)
a tree’s dry matter production is proportional to
its leaf areaLA. Thus a tree’s height is propor-
tional toD^2 /^3 , its mass is proportional toD^2 H,
and therefore toD^8 /^3 , and its leaf areaLAand dry
matter production are proportional toD^2 , which
is proportional toM^3 /^4. Many other “laws” of for-
est structure and production have been derived
from these relations (Enquistet al. 1998, 1999,
Enquist and Niklas 2001, Niklas and Enquist
2001).
Both theories appear to fit masses of data. Their
explanatory power, however, is limited. The neu-
tral theory ignores differences between species
that are crucial to understanding tree diversity
(Leighet al. 2004, Willset al. 2006). More-
over, like Volterra, most neutral theorists track
numbers of individuals in different species rather
than tackling spatial arrangements, as Bramson
et al. (1996, 1998) and Chav eand L eigh (2002)
began to do. Enquist’s (2002) theory assumes
that a given leaf area is equally productive in
th ecanopy or at th efor est floor, which is non-
sense (Muller-Landauet al. 2006a). Moreover, it
assumes that a tree’s heightHis related to its
diameterDasH = cD^2 /^3 , when in fact this
relation varies according to the heights of its
neighbors (King 1986, 1996). Indeed, the rela-
tion 1/H = 1 /Hmax+ 1 /aDb, whereaandb
ar efitt ed positiv econstants, match es data for
the trees of a mature forest species much bet-
ter (Katoet al. 1978, Thomas 1996a). Enquist’s
theory fails to predict the productivity/biomass

allometry in seedlings and saplings (Reichet al.

2006), or the relation between the diameter,

height, total photosynthesis and diameter growth

rate among a forest’s trees (Muller-Landauet al.

2006a).

WHAT MATHEMATICAL THEORY

HAS DONE

Despite the obstacles, mathematical theory has

contributed substantially to forest ecology. I now

review some of these accomplishments, showing

what theory has illumined, how it can mislead,

and what still needs doing.

Limits on gross production

Gross production is governed by the area of

leaves a forest deploys per unit area of ground

(its leaf area index, orLAI), the light these leaves

receive, and the photosynthesis this light sup-

ports. W enow consid er th efirst two of th es e

items. Most tropical forests have a leaf area index

between 6 and 8 (Leigh 1999). At Pasoh Reserve,

Malaysia, whereLAI=8(Katoet al. 1978), 0.3%

of th elight abov eth ecanopy r each es th eground.

The relation of the vertical distributions of leaf

ar ea and light abundanc efrom th ecanopy down-

ward suggests that each unit ofLAIhalves the

light passing through it (Yoda 1974, 1978). In

forests where this is so, ifLAI=7, only 1/2^7

(1/128) of the above-canopy light reaches the

forest floor. Most tropical forests let about 1%

of th elight abov eth ecanopy r each th eground

(Leigh 1999). In the shaded understory, cover-

age by seedlings and ground-herbs is low enough

to suggest that they receive barely enough light

to surviv e(L eigh 1975, Givnish 1988). In tropi-

cal forest, the few data available suggest thatLAI

rarely exceeds 8, presumably because extra leaves

ar ea losing proposition, andLAIis seldom less

than 6, for each unit decrease inLAIdoubles the

light reaching the forest floor. Accurate informa-

tion onLAIis rare, but forests on soils of very

different quality apparently support a similar dry

weight of leaves (Malhiet al. 2004, p. 575), about

8 tons ha−^1 (Leigh 1999).