A Statistical Model for Estimation of Fish Density Including Correlation in Size, Space, Time and between Species from Research Survey Data

Trawl survey data with high spatial and seasonal coverage were analysed using a variant of the Log Gaussian Cox Process (LGCP) statistical model to estimate unbiased relative fish densities. The model estimates correlations between observations according to time, space, and fish size and includes zero observations and over-dispersion. The model utilises the fact the correlation between numbers of fish caught increases when the distance in space and time between the fish decreases, and the correlation between size groups in a haul increases when the difference in size decreases. Here the model is extended in two ways. Instead of assuming a natural scale size correlation, the model is further developed to allow for a transformed length scale. Furthermore, in the present application, the spatial- and size-dependent correlation between species was included. For cod (Gadus morhua) and whiting (Merlangius merlangus), a common structured size correlation was fitted, and a separable structure between the time and space-size correlation was found for each species, whereas more complex structures were required to describe the correlation between species (and space-size). The within-species time correlation is strong, whereas the correlations between the species are weaker over time but strong within the year.

本研究针对具备高空间与季节覆盖度的拖网调查数据，采用对数高斯Cox过程（Log Gaussian Cox Process, LGCP）的变体统计模型开展分析，以估算无偏的鱼类相对密度。该模型可依据时间、空间与鱼类体型评估观测值间的相关性，同时纳入零观测值与过度离散现象。模型利用了如下规律：渔获鱼类的数量相关性会随个体间空间与时间距离的缩小而增强，且同次拖网中不同体型组间的相关性会随体型差异的减小而升高。本研究从两个维度对该模型进行拓展：其一，不再预设自然尺度的体型相关性，而是进一步优化模型以支持转换后的长度尺度；其二，在本次应用中加入了物种间的空间与体型依赖相关性。针对大西洋鳕（Gadus morhua）与黑线鳕（Merlangius merlangus），我们拟合了具有统一结构化的体型相关性；且针对每个物种，均发现了时间与空间-体型相关性之间的可分离结构，而描述物种（及空间-体型）间的相关性则需要更为复杂的结构。物种内部的时间相关性较强，而跨物种的时间相关性较弱，但在同一年度内的相关性较强。