Tropical Forest Community Ecology

Tropical Forest Ecology: Sterile or Virgin for Theoreticians? 127

During th etim eint erval dt,letmN(D)dtof these
trees die, letG(D− 1 )N(D− 1 )dttrees grow in from
the next lower diameter class, and letG(D)N(D)dt
trees grow out to the next diameter class. Finally,
let the tree death ratembe independent ofD(Leigh
1999). Sinc eingrowth must balanc eoutgrowth
and mortality,

G(D− 1 )N(D− 1 )=G(D)N(D)+mN(D).

Set

G(D)N(D)−G(D− 1 )N(D− 1 )

≈d[G(D)N(D)]/dD=−mN(D),

{ 1 /[G(D)N(D)]}d[G(D)N(D)]/dD

=d{ln[G(D)N(D)]}/dD=−m/G(D)

N(D)=[R/G(D)]exp−m

∫D

10 cm

dx/G(x)

whereR = N(9 cm dbh)G(9 cm dbh) is the
recruitment rate into the 10 cm diameter class.
If w eknow th ed eath rat em, th eav erag eh eight
H(D), and average rate of diameter increaseG(D),
of trees of all diametersD, w ecan calculat efor est
structur e(Kohyamaet al. 2003, Muller-Landau
etal. 2006b).
This, however, is just book-keeping, which does
not predict the death rate, diameter growth, or
average height of trees with diameterD. In fact, a
tropical forest has many tree species, which have
adapted to different levels of the forest by dealing
with the trade-off between survival, growth, and
reproduction in different ways. So far, few have
tried to predict the vertical distribution of a for-
est’s leaves, its “foliage height profile.” Although
Iwasaetal. (1984) mad ea start, th eorists hav enot
adequately related a forest’s foliage height profile
to the heights of its tallest trees, the light leaves
at different heights need to pay for their construc-
tion, support, and supply (Givnish 1988) and the
amount of light leaves at each height must let
pass below.

Soil quality and forest structure

Soil and above- versus below-ground
allocation

A forest’s leaf biomass, and its gross production,
depends little on soil fertility, although leaf fall

(and therefore leaf production) is lower on poorer

soil. Trees derive all their energy from leaves, yet

the returns from each successive unit increase

ofLAIare half those from its predecessor, while

the costs of making these leaves decline far more

slowly.

Th er eturns from additional fin eroots d eclin e

even more slowly. Let a forest take upUkg nitro-

gen (N) ha−^1 year−^1 .Uis roughlyU 0 /( 1 +Rv/R)

(King 1993), whereU 0 is th eav erag erat eof sup-

ply of “available” nutrients to the soil from litterfall

and external sources such as rainfall and weather-

ing bedrock,Rvis the dry mass of fine roots needed

to tak eup nutri ents at half th erat eU 0 of supply

• in good soil,Rv≈100 kg ha−^1 (King 1993) –
  andRkg ha−^1 is th efor est’s actual dry mass of
  fin eroots. To tak eup 99% of th esupply,Rmust
  b e99Rv, whereas taking up 99% of the incom-
  ing light requires only seven times the leaf area
  needed to take up half of it.
  A further problem is that, just as competi-
  tion to avoid being shaded by neighbors reduces
  a forest’s total photosynthesis, competing with
  neighbors for nutrients represents a tragedy of
  the commons that reduces a forest’s wood produc-
  tion, not to mention its reproductive investment
  (King 1993, Gersanet al. 2001). Consider a for-
  est of otherwise identical trees, each with a root
  biomass that yields optimum wood production
  per tree. A “selfish” tree can increase its nutrient
  uptake by increasing its root biomass and extend-
  ing its roots under neighbors. These neighbors
  must do likewise, to compensate their losses to
  the original selfish tree. In the end, trees wind
  up extending their roots under an average of six
  neighbors (King 1993). The inability of trees to
  exclude neighbors’ roots from under their own
  crowns, or mutually enforce a cooperative opti-
  mum in root production, sharply limits their wood
  production.
  King (1993) derived equations showing how
  soil nitrogen supply governs allocation to leaves,
  wood, and roots, assuming that nitrogen, N, is
  th elimiting nutri ent.To summariz ehis argum ent,
  let there bexgNg−^1 dry weight of leaf, and let
  a forest’s dry matter productionDPb e2(x/y−
  x^2 / 2 y^2 )DPmaxwhenxis less than the maximum
  useful foliar nitrogen concentrationy, andDPmax
  whenx≥y.Letpfandprb eth eproportions of