Assessing maturity status of fish and invertebrate species is important for understanding population dynamics with results (e.g., estimates of reproductive potential) often used to inform fisheries management strategies (e.g., the setting of minimum legal size requirements for fishing). Maturity rates may vary substantially across a population's range, as well as between years. In addition, maturity data are typically obtained from fisheries-independent surveys that may be incomplete (or missing) from year to year. Here we propose a spatial generalized linear mixed model (GLMM) framework for maturity data that includes spatially correlated random effects to address variations in space, and a sliding window approach to deal with unbalanced maturity data in both space and time. We demonstrate, with both real data and a simulation study, that this combined approach results in unbiased estimates of important growth parameters. Results of using our spatial GLMM framework with Greenland halibut (Rheinhardtius hippoglossoides) mature-at-length data from surveys of the eastern Canadian Arctic show that females mature at a much larger size than do males. The length at which 50% of the stock is mature ($L_{50}$) is found to be higher in Baffin Bay compared to Davis Strait, and a declining trend in the $L_{50}$ in recent years is revealed for both sexes. Our proposed methodology extends far beyond our current application in being useful for analyzing unbalanced spatiotemporal data from an array of diverse scientific fields.

中文翻译：

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使用滑动窗口方法对成熟长度数据进行时空建模

评估鱼类和无脊椎动物物种的成熟状态对于了解种群动态非常重要，其结果（例如，繁殖潜力的估计）通常用于为渔业管理战略（例如，设定捕鱼的最低法定规模要求）提供信息。成熟率可能在人口范围内以及不同年份之间有很大差异。此外，成熟度数据通常是从独立于渔业的调查中获得的，这些调查可能每年都不完整（或缺失）。在这里，我们提出了成熟度数据的空间广义线性混合模型 (GLMM) 框架，其中包括空间相关的随机效应以解决空间变化，以及滑动窗口方法来处理空间和时间上的不平衡成熟度数据。我们通过真实数据和模拟研究证明，这种组合方法导致对重要增长参数的无偏估计。将我们的空间 GLMM 框架用于格陵兰大比目鱼的结果（Rheinhardtius hippoglossoides ) 来自加拿大北极东部调查的成熟长度数据表明，雌性的成熟体型比雄性大得多。50%的股票成熟时的长度（${\mathrm{大号}}_{50}$) 在巴芬湾被发现比戴维斯海峡更高，并且在下降趋势中${\mathrm{大号}}_{50}$近年来，男女双方都被揭露了。我们提出的方法远远超出了我们当前的应用范围，可用于分析来自一系列不同科学领域的不平衡时空数据。