Table 1 Frequency distribution functions and variation degrees of Malus floral traits

Numbering traits

Petal number

y = 102154000 ⋅ x^(−7.243)(R² = 0.9972)

y = 11002600 ⋅ x^(−6.124)(R² = 0.9931)

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III

Pistil number

\( \mathrm{y}=0.571+84.548\cdot {e}^{-1.411{\left(x-4.328\right)}^2} \)(R² = 0.9967)

\( \mathrm{y}=0.963+65.342\cdot {e}^{-0.825{\left(x-4.052\right)}^2} \)(R² = 0.9965)

0.0277

15

Stamen number

\( \mathrm{y}=2.667+81.333\cdot {e}^{-0.064{\left(x-21.700\right)}^2} \)(R² = 0.9951)

\( \mathrm{y}=1.541+73.573\cdot {e}^{-0.033{\left(x-20.273\right)}^2} \)(R² = 0.9973)

0.0439

13

Pistil and stamen number

\( \mathrm{y}=2.667+80.144\cdot {e}^{-0.042{\left(x-24.427\right)}^2} \)(R² = 0.9945)

\( \mathrm{y}=1.541+75.431\cdot {e}^{-0.028{\left(x-23.737\right)}^2} \)(R² = 0.9987)

0.0389

14

Petal, pistil and stamen number

\( \mathrm{y}=2.667+80.144\cdot {e}^{-0.037{\left(x-30.228\right)}^2} \)(R² = 0.9781)

\( \mathrm{y}=2.776+71.000\cdot {e}^{-0.027{\left(x-29.825\right)}^2} \)(R² = 0.9989)

0.0261

16

Sizing traits

Flower diameter

\( \mathrm{y}=-134.198+162.225\cdot {e}^{-0.004{\left(x-43.110\right)}^2} \)(R² = 0.9664)

\( \mathrm{y}=1.154+43.064\cdot {e}^{-0.011{\left(x-39.146\right)}^2} \)(R² = 0.9982)

−2.7975

2

I

Pedicel length

\( \mathrm{y}=1.897+36.917\cdot {e}^{-0.011{\left(x-29.016\right)}^2} \)(R² = 0.9277)

\( \mathrm{y}=1.998+42.694\cdot {e}^{-0.015{\left(x-26.524\right)}^2} \)(R² = 0.9924)

−0.2041

10

Pistil length

\( \mathrm{y}=-65.441+93.426\cdot {e}^{-0.012{\left(x-9.265\right)}^2} \)(R² = 0.8625)

\( \mathrm{y}=-0.335+44.185\cdot {e}^{-0.147{\left(x-8.309\right)}^2} \)(R² = 0.9802)

−1.9783

4

Stamen length

\( \mathrm{y}=3.251+44.014\cdot {e}^{-0.256{\left(x-9.065\right)}^2} \)(R² = 0.9695)

\( \mathrm{y}=0.405+58.096\cdot {e}^{-0.303{\left(x-7.956\right)}^2} \)(R² = 0.9988)

−0.3078

9

Sepal length

\( \mathrm{y}=-17.100+49.152\cdot {e}^{-0.049{\left(x-7.007\right)}^2} \)(R² = 0.9935)

\( \mathrm{y}=1.279+50.647\cdot {e}^{-0.309{\left(x-5.765\right)}^2} \)(R² = 0.9961)

−1.1178

5

Petal length

\( \mathrm{y}=-1.393+33.994\cdot {e}^{-0.023{\left(x-17.938\right)}^2} \)(R² = 0.9911)

\( \mathrm{y}=0.222+46.496\cdot {e}^{-0.056{\left(x-16.959\right)}^2} \)(R² = 0.9980)

−0.4758

7

Petal width

\( \mathrm{y}=-134.198+162.225\cdot {e}^{-0.004{\left(x-13.734\right)}^2} \)(R² = 0.9664)

\( \mathrm{y}=-1.350+40.760\cdot {e}^{-0.062{\left(x-11.650\right)}^2} \)(R² = 0.9944)

−2.5597

3

Claw length

\( \mathrm{y}=6.466+37.808\cdot {e}^{-1.875{\left(x-2.139\right)}^2} \)(R² = 0.9749)

\( \mathrm{y}=-0.414+45.463\cdot {e}^{-0.958{\left(x-2.018\right)}^2} \)(R² = 0.9211)

0.1417

12

Pedicel thickness

\( \mathrm{y}=-963.219+992.038\cdot {e}^{-0.046{\left(x-1.139\right)}^2} \)(R² = 0.8755)

\( \mathrm{y}=0.311+81.904\cdot {e}^{-22.977{\left(x-0.786\right)}^2} \)(R² = 0.9987)

−13.2426

1

Sepal width

\( \mathrm{y}=-3.203+36.806\cdot {e}^{-0.519{\left(x-3.118\right)}^2} \)(R² = 0.9661)

\( \mathrm{y}=-0.736+50.877\cdot {e}^{-1.385{\left(x-2.340\right)}^2} \)(R² = 0.9980)

−0.9277

6

Shaping traits

Petal length / petal width

\( \mathrm{y}=-0.287+39.567\cdot {e}^{-7.874{\left(x-1.299\right)}^2} \)(R² = 0.9738)

\( \mathrm{y}=1.356+46.233\cdot {e}^{-14.595{\left(x-1.457\right)}^2} \)(R² = 0.9991)

0.4330

8

II

Sepal length /sepal width

\( \mathrm{y}=-0.689+46.502\cdot {e}^{-0.658{\left(x-2.405\right)}^2} \)(R² = 0.9900)

\( \mathrm{y}=0.958+51.566\cdot {e}^{-1.032{\left(x-2.475\right)}^2} \)(R² = 0.9966)

0.1557

11