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
Heterogeneity of mantle length-body mass relationship in different Ommastrephes bartramii populations based on linear mixed model
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摘要: 为研究不同群体柔鱼 (Ommastrephes bartramii) 生长的异质性，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 (W=aLb) 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性差异 (P<0.01)；各月份间也均存在极显著性差异 (P<0.01)。东部群体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。Abstract: We had collected neon flying squid (Ommastrephes bartramii) samples from 2016 to 2018 in North Pacific Ocean, and studied their gender and month differences of the 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 (W = aLb). 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 also 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 were growing at negative allometry, and the degree of fullness was negatively related to the 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 were 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.
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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 stocks O. bartramii in North Pacific Ocean
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
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
图 4 柔鱼不同月份胴长体质量分布图
Figure 4. Distribution of mantle length and body mass of O. bartramii in different months
图 5 不同群体柔鱼体质量-胴长关系
Figure 5. Mantle length-body mass relationship for different O. bartramii populations
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 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 of 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 populationLWR m = a×Lb ln(m)=ln(a)+b×ln(L) −466.402 0.183 265 RSS m=a×L(b+RSS) ln(m)=ln(a)+(b+RSS)×ln(L) −472.338 0.181 617 RSI m=a×exp(RSI)×Lb ln(m)=[ln(a)+RSI]+b×ln(L) −472.27 0.181 641 RSI&S m=a×exp(RSI)×L(b+RSS) ln(m)=[ln(a)+RSI]+(b+RSS)×ln(L) −469.057 0.181 428 RMS m=a×L(b+RMS) ln(m)=ln(a)+(b+RMS)×ln(L) −489.107 0.179 784 RMI m=a×exp(RMI)×Lb ln(m)=[ln(a)+RMI]+b×ln(L) −492.772 0.179367 RMI&S m=a×exp(RMI)×L(b+ RMS) ln(m)=[ln(a)+RMI]+(b+RMS)×ln(L) −595.137 0.166 468 RS&MS m=a×L(b+RSS+RMS) ln(m)=ln(a)+(b+RSS + RMS)×ln(L) −494.452 0.178 558 RS&MI m=a×exp(RSI)×exp(RMI)×Lb ln(m)=[ln(a)+RSI + RMI]+b×ln(L) −497.694 0.178 211 RS&MI&S m=a×exp(RSI)×exp(RMS)×L(b+RSI+ RMS) ln(m)=[ln(a) + RSI + RMS]+(b+RSI + RMI)×ln(L) −596.138 0.165 394 西部群体
Western populationLWR m = a×Lb ln(m)=ln(a)+b×ln(L) −1 795.63 0.099 003 RSS m=a×L(b+RSS) ln(m)=ln(a)+(b+RSS)×ln(L) −1 797.15 0.098 614 RSI m=a×exp(RSI)×Lb ln(m)=[ln(a)+RSI]+b×ln(L) −1 797.31 0.098 603 RSI&S m=a×exp(RSI)×L(b+RSS) ln(m)=[ln(a)+RSI]+(b+RSS)×ln(L) −1 796.72 0.098 512 RMS m=a×L(b+RMS) ln(m)=ln(a)+(b+RMS)×ln(L) −1 807.04 0.097 626 RMI m=a×exp(RMI)×Lb ln(m)=[ln(a)+RMI]+b×ln(L) −1 807.41 0.097 615 RMI&S m=a×exp(RMI)×L(b+ RMS) ln(m)=[ln(a)+RMI]+(b+RMS)×ln(L) −1 807.59 0.097 215 RS&MS m=a×L(b+RSS+RMS) ln(m)=ln(a)+(b+RSS + RMS)×ln(L) −1 808.14 0.097 347 RS&MI m=a×exp(RSI)×exp(RMI)×Lb ln(m)=[ln(a)+RSI + RMI]+b×ln(L) −1 808.56 0.097 333 RS&MI&S m=a×exp(RSI)×exp(RMS)×L(b+RSI+ RMS) ln(m)=[ln(a) + RSI + RMS]+(b+RSI + RMI)×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 4 不同月份东西部群体柔鱼胴长与体质量关系
Table 4. 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判定系数R2
Coefficient of determinationP 东部群体
Eastern population5 m =1.9×10−3L2.295 7 394 0.670 6 0.001 6 m =1×10−5L3.160 1 456 0.973 8 0.001 西部群体
Western population7 m = 9×10−6L3.205 3 124 0.889 5 0.001 8 m = 2×10−5L3.090 9 283 0.934 5 0.001 9 m = 2×10−5L3.059 7 331 0.952 0 0.001 10 m = 1×10−5L3.178 3 165 0.972 8 0.001 11 m = 5×10−5L2.902 8 105 0.947 7 0.001
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表 3 不同性别东西部群体柔鱼胴长与体质量关系
Table 3. 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判定系数R2
Coefficient of determinationP 东部群体
Eastern population雌性 m=3×10−5L2.981 8 744 0.892 9 0.001 雄性 m=2×10−4L2.621 0 106 0.794 3 0.001 西部群体
Western population雌性 m=1×10−5L3.159 9 512 0.968 1 0.001 雄性 m =2×10−5L3.103 5 496 0.941 5 0.001
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