Table 4. General forms of anamorphic and polymorphic projection equations.

Model types	Model names	Equation forms
Anamorphic	Schumacher	Y 2 = Y 1 exp   ( − β ( 1 / T 2 γ − 1 / T 2 γ ) )
	Hossfeld	Y 2 =   1 / ( ( 1 / Y 1 ) − β ( 1 / T 2 γ − 1 / T 1 γ ) )
	Chapman-Richards	Y2 = Y1((1 − exp(−βT1))/(1−exp(−βT2)))γ
	Gompertz	Y2 = Y1exp(−β (exp(γT2)−exp(γT1)))
Polymorphic	Schumacher	Y2 = exp(ln(Y1)(T1/T2)β + α(1 − (T1/T2)β))
	Hossfeld	Y2 = 1/((1 − Y1)(T1 − T2)γ + (1/α)(1 − (T1/T2)γ))
	Chapman-Richards	Y 2   =   ( α / γ ) [ 1 / 1 − β ) ( 1 − ( 1 − ( γ − α ) Y 1 ( 1 − β ) ) ) ( T 2 − T 1 ) [ − γ ( 1 − β ) ] ) ( 1 / ( 1 − β )
	Gompertz	Y 2 = exp ( ln ( Y 1 ) exp ( − β ( T 2 − T 1 ) + γ ( T 2 2 − T 1 2 ) ) + α ( 1 − exp ( − β ( T 2 − T 1 ) + γ ( T 2 2 − T 1 2 ) ) ) )

Y₁ = dimeter and height of trees at age T₁
Y₂ = dimeter and height of trees at age T₂
exp = exponential function
ln = natural logarithm, and
α,β,γ are coefficients to be estimated.