基于线性混合效应模型的黄(鱼安)鱇体长体重关系的时空差异

为了研究黄（鱼安）鱇（Lophius litulon）生活史特征的异质性，根据秋（2016年10月）、冬（2017年1月）、春（2017年5月）和夏（2017年8月）4个季节在山东近海的底拖网调查数据，对该物种体长-体重关系的时空差异进行了研究。本文构建了广义线性模型和9个线性混合效应模型，用来研究黄（鱼安）鱇的体长-体重关系（W=aL^b）及其时空差异。b的固定值（2.77）小于3，表示黄（鱼安）鱇为负异速生长，肥满度与体长负相关，身体趋于细长。根据AIC值最小原则，最复杂的线性混合效应模型（即水域和季节对两个参数a和b均存在随机效应）拟合效果最佳；交叉验证的结果同样表明，该模型的预测效果最为可靠。根据最佳模型和广义线性模型的差异性分析结果，黄（鱼安）鱇体长-体重关系的时空差异是极显著的（P<0.01）。在最佳模型中，a值在春季最大，其次是秋季和冬季，而夏季最小；b值则与此相反。整体来看，纬度高的黄（鱼安）鱇个体a值较大，b值较小，而a、b值与水深没有表现出明显规律。本研究表明，季节和纬度对黄（鱼安）鱇的体长-体重关系具有显著的影响，混合效应模型能把水域和季节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，从而进一步证实了此模型在数据来源异质性研究中的优势。

Linear mixed-effects models for estimating spatiotemporal variations of length-weight relationships for Lophius litulon

In order to provide data support for stock assessment and fishery management of Lophius litulon, the spatiotemporal variations of the length-weight relationships for this species were studied, based on the survey data from the bottom-trawl surveys in Shandong coastal waters in the four seasons:autumn (October 2016), winter (January 2017), spring (May 2017) and summer (August 2017). One generalized linear model and 9 linear mixed effect models were constructed to study the length-weight relationships (W=aL^b) and their spatiotemporal variations. According to the principle of minimum AIC value, the most complex linear mixed effect model (i.e. regions and seasons have random effects on parameter a and b) was the best. Cross validation results showed that the prediction effect of this model is the most reliable one among the 10 candidate models. F-test between the best model and the generalized linear model revealed that the spatiotemporal variations of the length-weight relationships were significant (P<0.01). In the best model, the a value of the individuals in spring was the largest, followed by autumn and winter, and finally summer; the trend of the b value was opposite of the a estimates. The estimates for a increased with latitude, without an obvious trend for depth, which might be resulted from limited sample size. The fixed value of b (2.77) was less than 3, indicating the negative allometric growth pattern of L. litulon. The fatness was negatively related to length and tended towards a slender body. This study showed that season and latitude have significant influences on the length-weight relationships of L. litulon. The mixed effect model could reflect the heterogeneity of regions and seasons in a single model more accurately and conveniently, which could be applied to more heterogeneity studies of fish life history traits.