Spatiotemporal modeling of mature‐at‐length data using a sliding window approach

Abstract

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.

Environmental data science: Part 2

“…As noted in our editorial for Part 1 of the special issue (Zammit‐Mangion et al 2023), environmental data analyses are often concerned with processes evolving in space and/or time, and therefore make extensive use of spatial or spatio‐temporal models. Most of the contributions to Part 2 of the special issue develop and apply such models: Yan, Cantoni, Field, Treble, and Mills Flemming (2023) consider a spatio‐temporal application in fisheries science that involves estimating the maturity of fish stock; Nie, Wang, and Cao (2023) apply functional data analysis to the problem of sub‐region estimation for daily bike‐share rentals; Laroche, Olteanu, and Rossi (2023) examine irregularly sampled left‐censored pesticide concentration data from France, developing new methodology for modeling spatio‐temporal heterogeneity; while Mukherjee, Bagozzi, and Chatterjee (2023) use spatio‐temporal fields to model climate and social instability interactions, as a framework for studying conflict. Several contributions also consider the problem of spatial/spatio‐temporal interpolation or emulation: Granville, Woolford, Dean, Boychuk, and McFayden (2023) tackle the problem of interpolating spatial data for generating a fire index for wildfires in Ontario, Canada, while Cartwright, Zammit‐Mangion, and Deutscher (2023) develop a spatio‐temporal emulator based on convolutional variational autoencoders.…”

“…Spatio‐temporal analyses often involve dealing with data which are recorded on differing time scales, spatial scales, or both. Jahid et al (2023) examine this problem in the context of animal tagging and abundance estimation for grizzly bears in Alberta, Canada; Yan et al (2023) consider aggregation for fisheries stocks in Atlantic Canada; and Laroche et al (2023) deal with aggregation when examining censored pesticide data. The more methodological side of this problem is considered by Roth et al (2023) for calibration methods of flood hazard projections, when integrating model outputs with differing resolutions.…”

Using multivariate autoregressive state‐space models to examine stock structure of Greenland halibut in the North Atlantic

“…Greenland halibut ( Reinhardtius hippoglossoides , Walhaum, 1792; also known as Greenland turbot or black halibut) is a large flatfish distributed primarily in arcto‐boreal cold and deep waters, with continuous populations along continental slopes of the North Pacific, Atlantic, and Arctic Oceans (Hedges et al, 2017; Vihtakari et al, 2021). The species exhibits strong sexual dimorphism with females growing larger (~120 cm vs. 70 cm), older (>30 years vs. >20 years; Treble et al, 2008), and maturing later (L/A50 61 cm/15 years vs. 44 cm/8 years; Morgan et al, 2003; Yan et al, 2022) than males (estimates from the Institute of Marine Research (IMR) database). Mark–recapture studies have shown that Greenland halibut can be a highly migratory species (Albert & Vollen, 2015; Boje, 2002; Vihtakari et al, 2022).…”