基于线性混合模型的不同群体柔鱼胴长体质量关系的异质性研究

韩霈武; 李楠; 方舟; 陈新军

doi:10.12131/20200117

基于线性混合模型的不同群体柔鱼胴长体质量关系的异质性研究

doi: 10.12131/20200117

韩霈武^1,,
李楠¹,
方舟^{1, 2, ,},
陈新军^{1, 2}

1.
上海海洋大学海洋科学学院，上海 201306
2.
大洋渔业资源可持续开发教育部重点实验室/国家远洋渔业工程技术研究中心/农业农村部大洋渔业开发重点实验室/农业农村部大洋渔业资源环境科学观测实验站，上海 201306

基金项目: 国家重点研发计划项目 (2019YFD0901404)；国家自然科学基金面上项目 (41876141)；农业部外海渔业开发重点实验室开放基金 (LOF 2018-02)

详细信息

作者简介:
韩霈武 (1996—)，男，硕士研究生，研究方向为大洋性头足类生物学。E-mail: 2718344838@qq.com

通讯作者:
方　舟 (1988—)，男，博士，讲师，从事头足类渔业生物学研究。E-mail: zfang@shou.edu.cn

中图分类号: S 931.1
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出版历程
- 收稿日期: 2020-05-29
- 修回日期: 2020-06-20
- 网络出版日期: 2020-11-19
- 刊出日期: 2020-12-04

Heterogeneity of mantle length-body mass relationship in different Ommastrephes bartramii populations based on linear mixed model

Peiwu HAN^1
,,
Nan LI¹,
Zhou FANG^{1, 2
, ,},
Xinjun CHEN^{1, 2}

1.
College of Marine Sciences of Shanghai Ocean University, Shanghai 201306, China
2.
Key Laboratory of Sustainable Exploitation of Oceanic Fisheries Resources, Ministry of Education/National Engineering Research Center for Oceanic Fisheries/Key Laboratory of Ocean Fisheries Exploitation, Ministry of Agriculture and Rural Affairs/Scientific Observing and Experimental Station of Oceanic Fishery Resources, Ministry of Agriculture and Rural Affairs, Shanghai 201306, China

摘要

摘要: 为研究不同群体柔鱼 (Ommastrephes bartramii) 生长的异质性，文章根据2016—2018年在北太平洋采集的柔鱼样本，对该物种胴长和体质量的性别和月间差异进行了分析。构建了广义线性模型 (Generalized linear model, GLM) 和9个线性混合模型 (Linear mixed model, LMM)，用于研究不同群体柔鱼的胴长和体质量关系 (m=aL^b) 在性别及时间上的差异。结果显示，东、西部群体不同性别柔鱼胴长、体质量均存在极显著差异 (P<0.01)；各月份间也均存在极显著差异 (P<0.01)。东部群体异速生长参数 (b) 的固定值 (2.763 4) 小于3，表示其为负异速增长，肥满度随胴长增加而减少，胴体趋于细长；西部群体b的固定值 (3.117 19) 大于3，表示其为正异速增长，肥满度随胴长增加而增大，胴体趋于宽厚。研究表明，性别和月份对不同群体柔鱼胴长和体质量关系均有显著影响，线性混合模型能将性别和月份的异质性通过随机效应在单个模型中更准确、方便地体现出来，进一步证实了此模型在个体生长异质性研究中的优势。
- 柔鱼 /
- 胴长-体质量关系 /
- 线性混合模型 /
- 性别差异 /
- 北太平洋
Abstract: We had collected neon flying squid (Ommastrephes bartramii) samples from 2016 to 2018 in North Pacific, and studied their gender and monthly differences of mantle length-body mass relationship, so as to understand the heterogeneity in the growth of different O. bartramii populations. One generalized linear (GLM) model and nine linear mixed models (LMM) were applied to study the difference in gender and time for mantle length-body mass relationship (m=aL^b). The results show that there was a significant difference in the mantle length and body mass between female and male O. bartramii of eastern and western populations (P<0.01). Moreover, there was a significant difference between different months (P<0.01). The fixed value of b (2.763 4) was less than 3 in the eastern population, which indicates that O. bartramii was growing at negative allometry, and the degree of fullness was negatively related to mantle length, and the body tended to be slender. The fixed value of b (3.117 19) was more than 3 in the western population, which indicates that O. bartramii was growing at positive allometry, and the degree of fullness was positively related to the mantle length, and the body tended to be thick. The study indicates that month and gender have a significant effect on the mantle length-body mass relationship for different O. bartramii populations. The LMM reflects the heterogeneity of gender and month more accurately and conveniently in a single model through random effects, thereby further confirming the advantage of this model in the study of heterogeneity in individual growth.
- Ommastrephes bartramii /
- Mantle length-body mass relationship /
- Linear mixed model /
- Sexual difference /
- North Pacific

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图 1 北太平洋柔鱼不同群体采样站点

Figure 1. Sampling station of different populations O. bartramii in North Pacific

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图 2 东部群体柔鱼不同性别胴长体质量频率分布图

Figure 2. Frequency distribution of mantle length and body mass of O. bartramii of different sex for eastern population

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图 3 西部群体柔鱼不同性别胴长体质量频率分布图

Figure 3. Frequency distribution of mantle length and body mass of O. bartramii of different sex for western population

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图 4 柔鱼不同月份胴长体质量分布图

a. 东部群体胴长分布图；b. 东部群体体质量分布图；c. 西部群体胴长分布图；d. 西部群体体质量分布图

Figure 4. Distribution of mantle length and body mass of O. bartramii in different months

a. Distribution of mantle length for eastern population; b. Distribution of body mass for eastern population; c. Distribution of mantle length for western population t; d. Distribution of body mass for western population

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图 5 不同群体柔鱼体质量-胴长关系

a. 东部群体雌性体质量-胴长关系；b. 东部群体雄性体质量-胴长关系；c. 西部群体雌性体质量-胴长关系；d. 西部群体雄性性体质量-胴长关系

Figure 5. Mantle length-body mass relationship for different O. bartramii populations

a. Relationship between BM and ML of female for eastern population; b. Relationship between BM and ML of male for eastern population; c. Relationship between BM and ML of female for western population; d. Relationship between BM and ML of male for western population

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表 1 不同月份柔鱼样本基本信息

Table 1. Basic information of O. bartramii samples in different months

群体 Population	年份 Year	月份 Month	样本数量 Number of sample	胴长范围 Range of mantle length/mm
东部群体 Eastern population	2016—2017	5	394	163~500
东部群体 Eastern population	2016—2017	6	456	212~516
西部群体 Western population	2016—2018	7	124	187~290
		8	283	195~357
		9	331	199~386
		10	165	190~377
		11	105	215~421

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表 2 不同群体柔鱼胴长-体质量关系模型的拟合效果指标

Table 2. Fitting effect index (AIC) of mantle length-body mass relationship models for different O. bartramii populations

种群 Population	模型缩写 Model abbreviation	模型 Model	对数转化 Log-transformed	赤池信息量准则 AIC	均方根误差 RMSE
东部群体 Eastern population	LMR	m = a×L^b	ln(m)=ln(a)+b×ln(L)	−466.402	0.183 265
	RSS	m=a×L⁽^b^+R_SS)	ln(m)=ln(a)+(b+R_SS)×ln(L)	−472.338	0.181 617
	RSI	m=a×exp(R_SI)×L^b	ln(m)=[ln(a)+R_SI]+b×ln(L)	−472.27	0.181 641
	RSI&S	m=a×exp(R_SI)×L⁽^b^+R_SS)	ln(m)=[ln(a)+R_SI]+(b+R_SS)×ln(L)	−469.057	0.181 428
	RMS	m=a×L⁽^b^+R_MS)	ln(m)=ln(a)+(b+R_MS)×ln(L)	−489.107	0.179 784
	RMI	m=a×exp(R_MI)×L^b	ln(m)=[ln(a)+R_MI]+b×ln(L)	−492.772	0.179367
	RMI&S	m=a×exp(R_MI)×L^(b+R_SI)	ln(m)=[ln(a)+R_MI]+(b+R_MS)×ln(L)	−595.137	0.166 468
	RS&MS	m=a×L⁽^b^+R_SS+R_MS)	ln(m)=ln(a)+(b+R_SS + R_MS)×ln(L)	−494.452	0.178 558
	RS&MI	m=a×exp(R_SI)×exp(R_MI)×L^b	ln(m)=[ln(a)+R_SI + R_MI]+b×ln(L)	−497.694	0.178 211
	RS&MI&S	m=a×exp(R_SI)×exp(R_MS)×L⁽^b^+R_SI+R_SI)	ln(m)=[ln(a) + R_SI + R_MS]+(b+R_SI + R_MI)×ln(L)	−596.138	0.165 394
西部群体 Western population	LWR	m = a×L^b	ln(m)=ln(a)+b×ln(L)	−1 795.63	0.099 003
	RSS	m=a×L⁽^b^+R_SS)	ln(m)=ln(a)+(b+R_SS)×ln(L)	−1 797.15	0.098 614
	RSI	m=a×exp(R_SI)×L^b	ln(m)=[ln(a)+R_SI]+b×ln(L)	−1 797.31	0.098 603
	RSI&S	m=a×exp(R_SI)×L⁽^b^+R_SS)	ln(m)=[ln(a)+R_SI]+(b+R_SS)×ln(L)	−1 796.72	0.098 512
	RMS	m=a×L⁽^b^+R_MS)	ln(m)=ln(a)+(b+R_MS)×ln(L)	−1 807.04	0.097 626
	RMI	m=a×exp(R_MI)×L^b	ln(m)=[ln(a)+R_MI]+b×ln(L)	−1 807.41	0.097 615
	RMI&S	m=a×exp(R_MI)×L^(b+R_SI)	ln(m)=[ln(a)+R_MI]+(b+R_MS)×ln(L)	−1 807.59	0.097 215
	RS&MS	m=a×L⁽^b^+R_SS+R_MS)	ln(m)=ln(a)+(b+R_SS + R_MS)×ln(L)	−1 808.14	0.097 347
	RS&MI	m=a×exp(R_SI)×exp(R_MI)×L^b	ln(m)=[ln(a)+R_SI + R_MI]+b×ln(L)	−1 808.56	0.097 333
	RS&MI&S	m=a×exp(R_SI)×exp(R_MS)×L⁽^b^+R_SI+R_SI)	ln(m)=[ln(a) + R_SI + R_MS]+(b+R_SI + R_MI)×ln(L)	−1 808.09	0.096 976
注：第一列为柔鱼的不同群体，第二列为第三、四列模型的缩写 RSS、RSI、RSI&S、RMS、RMI、RMI&S、RS&MS、RS&MI 和 RS&MI&S 分别为斜率 b 的性别随机效应、截距 ln(a) 的性别随机效应、截距 ln(a) 与斜率 b的性别随机效应、斜率 b 的月份随机效应、截距 ln(a) 的月份随机效应、截距 ln(a) 与斜率 b 的月份随机效应、斜率 b的性别与月份随机效应、截距 ln(a) 的性别与月份随机效应,以及截距 ln(a) 与斜率 b 的性别与月份随机效应Note: The first column shows different O. bartramii populations. The second column shows the abbreviations of models detailed in the third and fourth columns. RSS, RSI, RSI&S, RMS, RMI, RMI&S, RS&MS, RS&MI和RS&MI&S indicate random effects on slope (b) in sexual difference, random effects on intercept [ln (a)] in sexual difference, random effects on intercept [ln (a)] and slope (b) in sexual difference, random effects on slope (b) in months, random effects on intercept [ln (a)] in months, random effects on intercept [ln (a)] and slope (b) in months, random effects on slope (b) in sexual difference and months, random effects on intercept [ln (a)] fin sexual difference and months, and random effects on intercept [ln (a)] and slope (b) in sexual difference and months, respectively.

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表 3 不同月份东西部群体柔鱼胴长与体质量关系

Table 3. Mantle length-body mass relationship for different O. bartramii populations in different months

群体 Population	月份 Month	胴长与体质量关系 Mantle length-mass relationship	样本数量 Number of samples	判定系数R² Coefficient of determination	P
东部群体 Eastern population	5	m =1.9×10⁻³L^{2.295 7}	394	0.670 6	0.001
东部群体 Eastern population	6	m =1×10⁻⁵L^{3.160 1}	456	0.973 8	0.001
西部群体 Western population	7	m = 9×10⁻⁶L^{3.205 3}	124	0.889 5	0.001
	8	m = 2×10⁻⁵L^{3.090 9}	283	0.934 5	0.001
	9	m = 2×10⁻⁵L^{3.059 7}	331	0.952 0	0.001
	10	m = 1×10⁻⁵L^{3.178 3}	165	0.972 8	0.001
	11	m = 5×10⁻⁵L^{2.902 8}	105	0.947 7	0.001

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表 4 不同性别东西部群体柔鱼胴长与体质量关系

Table 4. Mantle length-body mass relationship of O. bartramii of different sex for different populations

群体 Population	性别 Sex	胴长与体质量关系 Mantle length-mass relationship	样本数量 Number of samples	判定系数R² Coefficient of determination	P
东部群体 Eastern population	雌性	m=3×10⁻⁵L^{2.981 8}	744	0.892 9	0.001
东部群体 Eastern population	雄性	m=2×10⁻⁴L^{2.621 0}	106	0.794 3	0.001
西部群体 Western population	雌性	m=1×10⁻⁵L^{3.159 9}	512	0.968 1	0.001
西部群体 Western population	雄性	m =2×10⁻⁵L^{3.103 5}	496	0.941 5	0.001

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