东海北部小黄鱼异方差生长模型

为揭示同方差和异方差结构对鱼类生长模型估计精度的影响,本研究以东海小黄鱼(Larimichthys polyactis)为案例,选用2007 2009年东海北部近海常规监测的小黄鱼基础生物学测定资料,采用对数正态函数型、幂函数型和指数函数型方差结构,分别对Schnute生长模型3种基本形式的von Bertalanffy(LVB)、Gompertz和Schnute模型进行了拟合分析,并采用似然比检验和AIC准则,选择确定最优拟合模型。结果表明,在渔获群体低龄化的条件下,其生长模型的参数估计值对方差结构较为敏感;对数正态函数型、幂函数型和指数函数型方差结构函数对3种生长模型的参数估计值较为接近,参数标准误和变异系数相对较小,小黄鱼生长模型以异方差结构函数拟合的效果较同方差结构更为精确和稳健;采用幂函数型和指数函数型方差结构拟合生长模型,其AIC值较同方差条件大幅降低,生长模型拟合的各月龄组置信区间范围差距缩小,明显提高了生长模型拟合度。

Modeling variance heterogeneity in growth: An example for small yellow croaker, Larimichthys polyactis in the northern East China Sea

Growth models are important components of population biology study and are generally essential to adequately assess the impact of fishery.Given a specific functional form,the appropriate estimation of growth parameters depends on the error structure assumed for the data.For example,if variability in size is constant as a function of age,an additive error structure is suitable.However,if the variability in size increases with age,a multiplicative error or variance modeling is appropriate.Variance heterogeneity will typically not in?uence the parameter estimates significantly,but if ignored it may result in severely misleading the standard error and predic-tion intervals.The four parameters model formulated by Schnute contains a number of specific growth models that can be used to explain the pattern of growth in small yellow croaker(Larimichthys polyactis).We used data trans-formation and variance modeling to investigate the effect of assuming a different error structure in the model.We used data from stow net surveys conducted between May–September in 2007–2008 and from bottom trawls con-ducted in the northern region of the East China Sea between October–April in 2007–2009.We used the likelihood ratio test(c2 distribution) and Akaike’s Information Criterion to quantitatively compare the fit of nested submodels.Error structure had a significant effect on the fitted models.The estimated parameter values for the lognormal er-ror,power variance,and exponential variance structure models were similar.Furthermore,relatively small standard errors and narrow confidence intervals suggest that the integration of variance structure in the growth models is more accurate and robust than in the additive models.The log-transformation models and variance structure mod-els fit the data better than the additive models.The funneling observed in the plots of deviance residuals against age for the additive models was reduced in the corresponding plots for the lognormal error and variance structure models.The power variance and exponential variance models yielded significantly different estimates than the additive models(c2 test,P<0.001) and had lower AIC values.Together,our results suggest the integration of variance structure to estimate growth improves goodness of fit and predictive power.