Table 1. Description of parameters and variables.

Model	Equation	Parameter/variable	Description
Height allometry (H)	Appendix S1, eq. S1	η	Slope of the relationship between stem diameter and tree height
		ϕ	Asymptote of the relationship between stem diameter and tree height
Crown depth (V)	Appendix S1, eq. S2	ϖ	Ratio of crown depth to tree height
Crown radius (Rh)	Appendix S1, eq. S4	β	Crown shape (1 = cone, 0 = cylinder)
		r0	Maximum crown radius at a stem diameter of 0 cm
		r40	Maximum crown radius at a stem diameter of 40 cm
Crown area	Appendix S1, eq. S7	CAi,h	Projected area of crown i at height h (the midpoint of the crown)
Crown area index	Equation 1	CAIh	Crown area index at height h: includes crown area of trees taller than h
Growth (G)	Equation 2	δ	Baseline growth rate
	Figure 1, panel A	γ	Location parameter of the log-normal multiplier (size effect)
		ν	Scale parameter of the log-normal multiplier (size effect)
	Figure 1, panel B	ζ	Minimum value of the negative exponential multiplier (competition effect)
		κ	Decay rate of the negative exponential multiplier (competition effect)
Mortality (M)	Equation 3	ψ	Baseline longevity
	Figure 1, panel C	φ	Exponent of the increasing power function (size effect)
		θ	Inflection point of the logistic function (size effect), expressed as a proportion of D0.01
		D0.01	The diameter at which logistic function takes a value of 0.01 (size effect)
	Figure 1, panel D	ω	Minimum value of the negative exponential multiplier (competition effect)
		o	Decay rate of the negative exponential multiplier (competition effect)
Ingrowth (I)	Equation 5	τ	Baseline ingrowth rate, if species is present
	Figure 1, panel E	χ	Minimum value of the negative exponential multiplier (competition effect)
		υ	Decay rate of the negative exponential multiplier (competition effect)
		CAI0.05	Lower 5th percentile of CAI0 values at which ingrowth is capped (competition effect)
	Equation 5	ξ	Baseline ingrowth rate, if species is absent
Error distributions	Appendix S3, eq. S13	σH	Residual standard deviation of height
		σV	Residual standard deviation of crown depth
		σW	Residual standard deviation of crowth width
		ρHV	Correlation between tree height and crown depth
		ρHW	Correlation between tree height and crown width
		ρVW	Correlation between crown depth and crown width
		σG	Residual standard deviation of growth
	Appendix S3, eq. S16	ΩP	Overdispersion parameter when species is present
		ΩA	Overdispersion parameter when species is absent
Stand effects (E)	Equation 4	α	Scales stand effects for longevity
		π	Scales stand effects for ingrowth
Stand error structure	Appendix S3, eq. S17	σE	Standard deviation of stand effects