Table 3.

Equations for simulating grain yields at different planting densities.

Model	Parameter				SD	R 2
	a	b	c	d
y = a + bx + cx2 + dx3	0.0866	0.3795	−0.0366	0.0011	0.1617	0.7094**
y = (a + bx)/(1 + cx + dx2)	−0.0750	0.4998	0.1251	0.0155	0.1625	0.7059**
y = abxxc	0.5139	0.9142	0.8004		0.1642	0.6978**
y = ab(1/x)x	4.4996	0.0375	−0.4096		0.1653	0.6921**
y = e(a + b/x + cln(x))	1.5039	−3.2825	−0.4096		0.1653	0.6921**
$y=a-{\mathrm{be}}^{(-{\mathrm{cx}}^{\mathrm{d}})}$	1.2547	0.8139	0.0876	2.1365	0.1690	0.6766**
y = a/(1 + e(b−cx)^(1/d))	1.2801	5.2384	1.3602	4.3607	0.1744	0.6485**
y = a/(1 + be−cx)	1.2842	5.6329	0.9126		0.1748	0.6396**
y = (ab + cxd)/(b + xd)	0.6216	290.2861	1.2823	4.9440	0.1754	0.6389**
$\mathrm{y}=\mathrm{a}{\mathrm{e}}^{-{\mathrm{e}}^{\mathrm{b}-\mathrm{c}\mathrm{x}}}$	1.2858	1.1270	0.7789		0.1754	0.6338**
y = a(b − e−cx)	2.0265	0.6320	0.6188		0.1711	0.6299**
y = a + bx + cx2	0.5760	0.1534	−0.0073		0.1728	0.6266**
y = a + bcos(cx + d)	−7.4411	8.8201	0.0401		0.1732	0.6245**
y = a(1−e−bx)	1.2943	0.4721			0.1737	0.6231**
y = a${\mathrm{e}}^{(-(\mathrm{x}-\mathrm{b}{)}^2/2{\mathrm{c}}^2)}$	1.3785	10.4161	9.0758		0.1760	0.6224**
y = 1/(a + bx + cx2)	1.2646	−0.1042	0.0050		0.1787	0.6066**
y = a + b/x	1.4096	−1.2566			0.1794	0.6017**
y = aeb/x	1.4296	−1.0818			0.1824	0.5835**
y = ab1/x	1.4296	0.3390			0.1824	0.5835**
y = ax/(b + x)	1.4417	1.2856			0.1856	0.5632**

x and y in the model denote density and relative grain yield, respectively. **Significant at the 0.01 probability level.