122 Egbert G. Leigh, Jra tree’s allocation between long life and early
reproduction, and how do trees’ life-history allo-
cation and anti-herbivore defenses influence their
soil?
2 What governs forest structure?First, what lim-
its tree height? Why are tropical trees far shorter,
and far shorter-lived, than redwoods (the world’s
tallest trees)? Second, what limits tree density and
basal area? Why do most tropical forests have a
basal area of 30±10 m−^2 ha−^1 , regardless of
soil quality (Lewisetal. 2004, pp. 429–430; Losos
et al. 2004, p. 71)? Third, th eratio of tr e eto
liana biomass and production is similar in trop-
ical forests the world around (Schnitzer 2005):
why? Fourth, what principles govern tree shape?
Why are there so many different tree architectures
(Hallé and Old eman 1970)? What ar eth er elativ e
costs and benefits of leaves at different heights
(Givnish 1984, 1987)? Finally, how does forest
structur e(canopy roughn ess, tr e ecrown siz eand
shape, tree density, liana abundance) vary with
climat eand soil quality?
3 Howdoherbivoresshapethecharacteristicsof trop-
ical forests?Herbivores and pathogens help drive
the trade-off between growing fast in high light
versus surviving in shade (King 1994, Kitajima
1994) and the trade-off between growing fast
on good soil versus surviving on poor soil (Fine
et al. 2004). How do tropical plants allocate
resources between enabling young to escape their
parents’ pests and pathogens (Janzen 1970) ver-
sus investing in defense (Regal 1977)? How does
this allocation affect soil fertility, forest productiv-
ity, and th eabundanc eand div ersity of animal
consumers (Corner 1964)? Finally, how does a
forest’s productivity affect the role of animals in
controlling its herbivores (Oksanenetal. 1981)?
4 Whyaretheresomanykindsof tropicaltree?How
do different allocations between early reproduc-
tion versus long life, growing in bright light versus
surviving in shade, and tolerating versus evading
drought contribute to tree diversity (Tyree 2003,
Tyreeet al. 2003, Wrightet al. 2003)? Do spe-
cialized pests play an essential role in maintaining
tree diversity? How are different strategies of anti-
herbivore defense related to the great differences
among tree species in the lifetime, toughness, and
photosynthetic capacity of their leaves (Wright
etal. 2004)?
FRAMING A MATHEMATICAL
THEORY OF FOREST ECOLOGY
This chapter considers how theoretical con-
cepts and their mathematical formulation can
help answer the questions of forest ecology.
Forest ecology lacks a coherent frame of deduc-
tive mathematical theory analogous to those
of the genetical theory of natural selection
(Fisher 1930), population genetics (Crow and
Kimura 1970), or animal ecology (MacArthur
1972). B ecaus eanimals mov eabout, “av erag-
ing” their environments, theorists like Volterra
(1931) could derive useful predictions by assum-
ing that population densities are uniform in space.
In contrast, the number of trees in each species
does not suffice to predict a forest’s dynamics
because:
1 A tree competes for resources with a few
near neighbors (Schaffer and Leigh 1976), while
its successful young usually compete with the
young of trees far beyond the competitive reach
of its seed-parent’s neighbors, a circumstance
that favors less destructive or spiteful forms of
competition (Wilson 1980, Leigh 1994). There-
fore theorists must consider the dynamics of
the spatial arrangements of trees of different
species (Schaffer and Leigh 1976). This is a
difficult proposition, even in the neutral case
(Bramsonet al. 1996, 1998, Chav eand L eigh
2002).
2 A tree’s competitive impact on its neighbors
depends on its crown’s height, size, shape and
total leaf area, the density and distribution of
its roots, and so forth. The theory of tree shape
must account for the costs and benefits of leaves
at different heights (Givnish 1987). No current
mathematical theory is adequate to resolve these
questions. It appears that only computer models
lik eSORTIE (Pacalaet al. 1996) can b emodifi ed
to handl eboth th edynamics of tr e earrang em ent
and the changes in sizes and shapes of the trees
involv ed, but simulations ar ea poor substitut efor
analytic theory.
Two general theories have recently been pro-
posed for forest ecology. Hubbell’s (2001) neutral
theory of forest dynamics and tree diversity
assumes that each tree has identical prospects of
death and reproduction, regardless of its species