Data and scripts used in "Age-dependent patterns of spatial autocorrelation in fish populations"

The population spatial autocorrelations were estimated using data from scientific bottom trawl surveys performed annually by the Norwegian Institute for Marine Research and the Polar Research Institute of Marine Fisheries and Oceanography from January to March, from 1985 to 2016 (Jakobsen et al. 1997; Aanes &amp; Vølstad 2015). The trawl survey was spatially stratified and sampled locations were approximately uniformly distributed in space. The survey has been mostly standardized with respect to sampling gear and performance, except for a reduction in the mesh size of the codend from 35-40 mm to 22 mm in 1994 to prevent potential sampling size bias among 1-year-old cod and haddock. For more details on sampling protocols see Jakobsen et al. (1997), Johannesen et al. (2009), Fall et al. (2020). The fish were sampled onboard, following the instructions given in Mjanger et al. (2020) and otoliths were collected to determine the age of the individuals (Johannesen et al. 2009, Mehl et al. 2016). When the catch so big that length-measuring the entire catch was unfeasible, a representative random subsample was measured. From this subsample, otoliths to age the fish were collected for an extra subsample of the fish, following a length stratified sampling design. Before 1993, 5 individuals per 5 cm length group were aged for a spatially stratified subset of trawls, from 1993 to 1995 only 2 individuals per 5 cm length group were aged, but for a larger subset of trawls. Since 1996, 1 individual per 5 cm length group has been aged in all trawls. Lastly, the collected data were then used to make age-length keys to raise or extrapolate the age distribution of each catch. In total 8288 trawls were performed, where 7037 contained haddock, 8145 contained cod and 5153 contained beaked redfish.<br>The study region was subdivided using a grid with hexagonal cells because this shape homogenises the distances between centroids of neighbouring cells. The data presented here correspond to a grid cell size resolution of 6400 km2. In addition, the analysis was repeated after shifting the hexagonal grid along the latitudinal and longitudinal gradients 15 times. This resulted in slight differences in how samples were grouped to average cell densities, preventing grid cells with fewer samples from generating outliers that could cause biases in the results.<br><br>Files:Data:<br>ylu_6400_list.rdayu_6400_list.rdazlu_6400_list.rdazu_6400_list.rda<br>Scripts:SI_Functions.RSI_Hexagon.RSI_DensityMaps.v1.RSI_Synchrony.v1.RSI_Synchrony_Ages.v1.R<br>Description<br>Data:ylu_6400_list.rda – List containing arrays with average density estimates by grid cell for each species and age class. Each array is named as: “species name” (i.e. Cod, Haddock or B_redfish), “_spatial offset of the grid in degrees” (e.g. -1). The dimensions of the arrays correspond to [Years, Grid id, Age class]yu_6400_list.rda - List containing matrix with total average density estimates by grid cell for each species. Each matrix is named as: “species name” (i.e. Cod, Haddock or B_redfish), “_spatial offset of the grid in degrees” (e.g. -1). The dimensions of the matrix correspond to [Years, Grid id]zlu_6400_list.rda - List containing arrays with the distances in km between the grids corresponding to the data in “ylu_6400_list.rda”. Each array is named as: “species name” (i.e. Cod, Haddock or B_redfish), “_spatial offset of the grid in degrees” (e.g. -1). The dimensions of the arrays correspond to [Grid id, Grid id, Age class]zu_6400_list.rda - List containing matrix with the distances in km between the grids corresponding to the data in “yu_6400_list.rda”. Each array is named as: “species name” (i.e. Cod, Haddock or B_redfish), “_spatial offset of the grid in degrees” (e.g. -1). The dimensions of the matrix correspond to [Grid id, Grid id]Scripts: SI_Functions.R – Compilation of functions used in the other of the scripts. SI_Hexagon.R – R script to create the hexagonal grid overlaid across the Barents Sea (i.e. hex_grid_LL_M). Specify the resolution of the grids. The default in the uploaded data and scripts is aSI_DensityMaps.v1.R – R script to map the density by grid cells of each study species. Corresponds to Figure 1.SI_Synchrony.v1.R – R scripts to estimate and plot the spatial autocorrelation of the population and the two life stages (i.e. juveniles or immature, and adults or mature). The spatial autocorrelation estimates (i.e. SynchResults) are represented by three parameters: logitrhoinf = degree of autocorrelation at infinitylogitrhoinf = degree of autocorrelation as distance approaches 0logl = spatial scaling (i.e. standard deviation of the gaussian function optimized over the spatial autocorrelation data<br> The output data is then plotted to: Synchronies.6400.tiff - Spatial autocorrelation plot with each species at the population level and life stage level (juveniles and adults). Corresponds to Figure 2.<br>SI_Synchrony_Ages.v1.R – R scripts to estimate and plot the spatial autocorrelation of each age class. The spatial autocorrelation estimates (i.e. SynchResults) are structured in the same way as in “SI_Synchrony.v1.R”. The spatial autocorrelation estimates are then plotted in the following ways: 1. SynchronyDifferences_6400.tiff = Plots the change in the spatial autocorrelation parameters after accounting for the effect of local cohort dynamics. i.e. Figure 4. 2. RidgesSynch_6400.tiff = Ridges plots showing the density distribution of the bootstrapped spatial autocorrelation parameters of density and cohort-independent density for cod and haddock, and ages 1 to 8. i.e. Figure 3.3. SynchAgesRibbons_Den6400.tiff = Spatial autocorrelation plots corresponding to age classes 1 to 8 of cod and haddock. i.e. Figure S2 in Appendix.<br>

本研究采用挪威海洋研究所（Norwegian Institute for Marine Research）与极地海洋渔业与海洋学研究所（Polar Research Institute of Marine Fisheries and Oceanography）于1985-2016年1-3月开展的年度科学底拖网调查（bottom trawl surveys）数据，估算种群空间自相关性（spatial autocorrelation）（Jakobsen等，1997；Aanes & Vølstad，2015）。该拖网调查采用空间分层设计，采样点位在空间上近似均匀分布。除1994年为避免1龄鳕鱼（cod）和黑线鳕（haddock）的采样尺寸偏差，将网囊网目尺寸从35-40mm调整为22mm外，调查在采样装备与作业流程上基本标准化。关于采样方案的更多细节可参考Jakobsen等（1997）、Johannesen等（2009）与Fall等（2020）。
鱼类样本采集于船上，遵循Mjanger等（2020）的操作指南，并采集耳石（otoliths）以确定个体年龄（Johannesen等，2009；Mehl等，2016）。当渔获量过大，无法对全部个体测量体长时，会抽取具有代表性的随机子样本（subsample）进行体长测量。针对该子样本，采用长度分层采样设计，额外抽取子样本采集耳石用于年龄鉴定。1993年前，针对空间分层的拖网子集，每5cm体长组取5个个体进行年龄鉴定；1993-1995年，仅每5cm体长组取2个个体，但覆盖了更多的拖网子集；1996年起，所有拖网均按每5cm体长组取1个个体进行年龄鉴定。最终，采集的数据用于构建年龄-长度关键表（age-length keys），以推算或外推各渔获的年龄分布。本次调查共完成8288次拖网作业，其中7037次捕获黑线鳕，8145次捕获鳕鱼，5153次捕获棘红鲉（beaked redfish）。
本研究采用六边形网格（hexagonal grid）对研究区域进行划分，因该形状可使相邻网格质心间的距离趋于均一。本次呈现的数据对应6400 km²的网格分辨率。此外，研究还将六边形网格沿纬向与经向分别偏移15次后重复分析，以此使样本分组以平均网格密度的方式略有差异，避免样本量较少的网格生成异常值，进而导致分析结果出现偏差。

### 数据文件
`ylu_6400_list.rda`：包含数组的列表，存储各物种、各年龄组按网格单元计算的平均密度估计值。每个数组命名格式为："species name"（即Cod、Haddock或B_redfish）+"_spatial offset of the grid in degrees"（例如-1）。数组维度为[年份，网格ID，年龄组]。
`yu_6400_list.rda`：包含矩阵的列表，存储各物种按网格单元计算的总平均密度估计值。每个矩阵命名格式为："species name"+"_spatial offset of the grid in degrees"。矩阵维度为[年份，网格ID]。
`zlu_6400_list.rda`：包含数组的列表，存储与`ylu_6400_list.rda`数据对应网格间的千米距离。每个数组命名格式为："species name"+"_spatial offset of the grid in degrees"。数组维度为[网格ID，网格ID，年龄组]。
`zu_6400_list.rda`：包含矩阵的列表，存储与`yu_6400_list.rda`数据对应网格间的千米距离。每个数组命名格式为："species name"+"_spatial offset of the grid in degrees"。矩阵维度为[网格ID，网格ID]。

### 脚本文件
`SI_Functions.R`：整合了其他脚本所使用的函数集。
`SI_Hexagon.R`：用于在巴伦支海生成叠加六边形网格的R脚本（即`hex_grid_LL_M`），可指定网格分辨率，本次上传数据与脚本的默认分辨率为6400 km²。
`SI_DensityMaps.v1.R`：用于绘制各研究物种按网格单元的密度分布的R脚本，对应图1。
`SI_Synchrony.v1.R`：用于估算并绘制种群及两个生活史阶段（即幼鱼/未成熟个体、成鱼/成熟个体）的空间自相关性的R脚本。空间自相关性估计值（即`SynchResults`）由三个参数表征：`logitrhoinf`：无穷远处的自相关程度；`logitrho0`：距离趋近于0时的自相关程度；`logl`：空间尺度参数（即基于空间自相关数据优化得到的高斯函数（Gaussian function）标准差）。输出结果将绘制成：`Synchronies.6400.tiff`——展示各物种种群水平及生活史阶段（幼鱼、成鱼）空间自相关性的绘图，对应图2。
`SI_Synchrony_Ages.v1.R`：用于估算并绘制各年龄组空间自相关性的R脚本。空间自相关性估计值（即`SynchResults`）的结构与`SI_Synchrony.v1.R`中的一致。空间自相关性估计值将通过以下方式可视化：
1. `SynchronyDifferences_6400.tiff`：绘制在考虑局域同龄群动态效应后的空间自相关参数变化，对应图4。
2. `RidgesSynch_6400.tiff`：山脊图（ridges plot），展示鳕鱼、黑线鳕及1-8龄个体的密度与独立于同龄群的密度的自举（bootstrapped）空间自相关参数的密度分布，对应图3。
3. `SynchAgesRibbons_Den6400.tiff`：对应鳕鱼、黑线鳕1-8龄个体的空间自相关绘图，即附录中的图S2。