Developing height growth model of Larix kaempferi based on genetic and climate effects

doi:10.12302/j.issn.1000-2006.202112005

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2023, Vol. 47 ›› Issue (4): 51-60.doi: 10.12302/j.issn.1000-2006.202112005

Special Issue: 第三届中国林草计算机应用大会论文精选（Ⅱ）

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Developing height growth model of Larix kaempferi based on genetic and climate effects

GAI Junpeng¹^,²(), CHEN Dongsheng³^,^*(), JIA Weiwei¹, WANG Zheng¹^,²

1. College of Forestry, Northeast Forestry University, Harbin 150040, China
2. The Second Forestry and Grassland Monitoring and Planning Institute of Inner Mongolia Autonomous Region, Xing'an 137400, China
3. Research Institute of Forestry, National Forestry and Grassland Administration Key Lab for Forest Tree Breeding, Chinese Academy of Forestry,Beijing 100091, China

Received:2021-12-03 Revised:2022-03-21 Online:2023-07-30 Published:2023-07-20

Abstract

Abstract:

【Objective】 This study provides supports for accurate site quality evaluation and reasonable management plans for Larix kaempferi by studying the effects of genetic and climate changes on plant height. 【Method】 Using height growth data from L. kaempferi trees aged from 5 to 18 years in the Changlinggang Forest Farm in Jianshi County, Hubei Province and the Logistic equation as the basic theoretical growth model, we introduced provenances and climate variables reflecting genetic effects and used repetition as random parameters to construct a tree height growth model. Using this model, we were then able to analyze the effects of genetic and climate changes on tree height growth. 【Result】 Temperature and precipitation were the main climatic factors affecting L. kaempferi tree height growth in this area. Furthermore, the fitting accuracy of the model with temperature and precipitation inputs was higher than that of the basic model. Additionally, nonlinear mixed model based on repetition as a random effect (R_adj²=0.820 3) fit better than did the growth model considering genetic and climatic factors (R_adj²=0.806 2) and the basic logistic model (R_adj²= 0.798 9). The height growth of different provenances was in accordance with the law of ‘slow-fast-slow’ growth; however, the time to reach the fast-growing point varied, and there were significant discrepancies in height growth among different provenances at different time nodes. 【Conclusion】 Genetic and climatic factors affected the height of L. kaempferi. Furthermore, the construction of a mixed model based on genetic and climatic effects can effectively improve the fitting accuracy of a model.

Key words: provenance, climate change, tree height growth, nonlinear mixed effect model, dumb variable

CLC Number:

S757

GAI Junpeng, CHEN Dongsheng, JIA Weiwei, WANG Zheng. Developing height growth model of Larix kaempferi based on genetic and climate effects[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2023, 47(4): 51-60.

Figures/Tables 11

Table 1

Table 2

Table 3

Table 4

Basic model fitting statistics containing provenance dumb variables"

模型 model	参数个数 number of parameter	$R a d j 2$	RMSE	AIC	BIC	Log Likelihood
(1)	4	0.798 9	1.525	65 218	65 249	-32 605
(7)	15	0.806 2	1.496	64 569	64 670	-32 271

Table 4

Table 5

Fitting results of mixed models based on different combinations of random effect parameters"

模型 model	随机效应参数 random effect parameter	参数个数 number of parameter	$R a d j 2$	AIC	BIC	Log Likelihood	LRT	P
(7)	—	13	0.806 2	64 569	64 670	-32 271
(7-1)	a₁	14	0.819 5	63 446	63 555	-31 709
(7-2)	a₃	14	0.820 0	63 397	63 506	-31 685
(7-3)	a₄	14	0.818 3	63 566	63 675	-31 769
(7-4)	a₅	14	0.819 4	63 451	63 559	-31 711
(7-5)	a₁,a₂	16	0.820 2	63 384	63 508	-31 676	70.792	<0.000 1
(7-6)	a₁,a₃	16	0.820 2	63 387	63 512	-31 678
(7-7)	a₂,a₃	16	0.820 1	63 390	63 514	-31 679
(7-8)	a₂,a₄	16	0.819 8	63 413	63 537	-31 690
(7-9)	a₂,a₅	16	0.820 0	63 390	63 515	-31 679
(7-10)	a₁,a₂,a₃	19	0.820 3	63 379	63 526	-31 670	17.840	0.000 5
(7-11)	a₁,a₂,a₄	19	0.820 0	63 408	63 556	-31 685
(7-12)	a₁,a₂,a₅	19	0.820 3	63 384	63 531	-31 673
(7-13)	a₁,a₃,a₅	19	0.820 2	63 390	63 538	-31 676

Table 5

Table 6

Variance compositions, parameters and fitting statistics of the model"

项目 item	参数 parameter	模型(1) model(1)	模型(7) model(7)	模型(7-10) model(7-10)	项目 item	参数 parameter	模型(1) model(1)	模型(7) model(7)	模型(7-10) model(7-10)
固定参数 fixed parameter	a₁	15.235	13.710	13.751	固定参数 fixed parameter	a₃₁		-0.044	-0.029
	a₂	12.894	15.140	15.051		a₃₃		-0.022	-0.033
	a₃	0.238	0.273	0.271	随机参数 random parameter	a₁			0.431
	a₄		-3.77×10^-4	-4.32×10^-4		a₂			0.675
	a₅		-2.25×10^-5	-2.50×10^-5		a₃			0.007
	a₁₁		2.147	1.574		a₁、a₂			-0.393
	a₁₃		2.148	2.748		a₁、a₃			-0.557
	a₂₁		-2.206	-1.318		a₂、a₃			0.669
	a₂₂		-1.302	-1.141	拟合统计量 fitting statistics	$R a d j 2$	0.798 9	0.806 2	0.820 3
	a₂₃		-0.970	-1.477		RMSE	1.525	1.496	1.440

Table 6

Fig.1

Fig. 2

Table 7

Table 8

Fig. 3

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种源编号 No.	种子来源 provenance	纬度 latitude (N)	经度 longitude (E)	采种地概况 general situation
种源编号 No.	种子来源 provenance	纬度 latitude (N)	经度 longitude (E)	海拔/m altitude	年平均气温/℃ average annual temperature	年降水量/mm annual precipitation
1	草津国有林	36°35'	138°30'	1 374	6.9	1 747
2	浅间国有林	36°20'	138°30'	927	9.3	1 360
3	富士山梨县有林	35°30'	138°45'	844	10.5	1 595
4	日光国有林	35°45'	138°10'	1 726	5.9	1 795
5	伊那国有林	36°45'	139°25'	1 444	5.9	2 003
6	松本国有林	36°20'	139°45'	1 620	14.0	1 266

树龄/a tree age	种源1 provenance 1		种源2 provenance 2		种源3 provenance 3		种源4 provenance 4		种源5 provenance 5		种源6 provenance 6
树龄/a tree age	株数 trees	树高/m tree height	株数 trees	树高/m tree height	株数 trees	树高/m tree height	株数 trees	树高/m tree height	株数 trees	树高/m tree height	株数 trees	树高/m tree height
5	400	2.98	150	2.93	467	3.10	392	3.28	614	3.12	249	3.01
6	401	3.65	148	3.58	469	3.68	390	3.94	612	3.73	251	3.63
7	401	4.40	150	4.31	468	4.32	391	4.68	614	4.41	248	4.33
8	397	5.24	150	5.10	465	5.02	383	5.53	614	5.17	249	5.11
9	399	6.13	149	5.93	458	5.77	376	6.45	597	6.01	245	5.97
10	396	7.05	150	6.78	459	6.54	378	7.37	597	6.86	244	6.85
11	294	8.09	113	7.68	326	7.58	267	8.40	394	7.85	170	7.81
12	293	9.00	110	8.54	324	8.39	264	9.32	397	8.72	169	8.73
13	295	9.87	108	9.34	325	9.17	266	10.21	394	9.56	169	9.60
14	296	10.67	107	10.08	327	9.91	265	11.04	394	10.35	168	10.42
15	296	11.39	107	10.74	325	10.60	264	11.81	396	11.09	169	11.18
16	287	12.06	106	11.38	325	11.24	262	12.50	393	11.75	168	11.86
17	286	12.61	106	11.91	325	11.81	264	13.10	393	12.36	167	12.48
18	288	13.08	105	12.37	324	12.33	264	13.64	393	12.89	167	13.02

因子 factor	树高连年生长量 annual growht amount of tree height	平均最冷月气温 the coldest month temperature	秋季降水 autumn precipitation	年平均气温差 average annual temperature difference	1月最高温 the highest temperature in January	1月最低温 the lowest temperature in January	1月均温 average temperature in January	上年秋季降水量 last autmn precipitation
树高连年生长量 annual growth amount of tree height	1
平均最冷月气温 the coldest month temperature	-0.561^*	1
秋季降水 autumn precipitation	-0.583^*	0.008	1
年平均气温差 average annual temperature difference	0.578^*	-0.888^**	-0.126	1
1月最高温 the highest temperature in January	-0.628^*	0.897^**	0.171	-0.782^**	1
1月最低温 the lowest temperature in January	-0.554^*	0.903^**	0.253	-0.884^**	0.790^**	1
1月均温 average temperature in January	-0.635^*	0.944^**	0.223	-0.862^**	0.968^**	0.918^**	1
上年秋季降水量 last autumn precipitation	-0.672^*	0.247	-0.349	0.474	0.22	0.31	0.273	1

种源 provenance	a₁	a₂	a₃	t₀/a	t₁/a	t₂/a	18 a树高/m 18-years- tree height	速生期树高增长量/m tree height growth in fast-growing
1	14.94	14.37	0.26	10.4	5.3	15.6	13.08	9.08
2	14.22	12.98	0.25	10.4	5.0	15.7	12.37	8.45
3	14.66	12.12	0.23	10.8	5.1	16.5	12.33	8.14
4	15.83	13.04	0.24	10.6	5.1	16.0	13.64	9.22
5	15.23	12.79	0.24	10.8	5.2	16.4	12.89	8.63
6	15.33	13.72	0.24	10.9	5.4	16.3	13.02	8.85
均值 mean				10.6	5.2	16.1	12.89	8.73

树龄/a tree age	均方 mean square			机误 error	F
树龄/a tree age	种源 provenance	重复 repetition	种源×重复 provenance× repetition	机误 error	F
5	3.031	12.028	0.686	0.313	4.611^**
11	15.315	60.731	5.257	2.141	2.982^*
16	42.036	63.608	7.769	3.238	5.544^**

Developing height growth model of Larix kaempferi based on genetic and climate effects

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