Fisheries Research 240 (2021) 105956 Available online 4 April 2021 0165-7836/© 2021 Elsevier B.V. All rights reserved. A gaussian feld approach to generating spatial age length keys Jonathan Babyn a, *, Divya Varkey b , Paul Regular b , Danny Ings b , Joanna Mills Flemming a a Dalhousie University, Department of Mathematics & Statistics, 6316 Coburg Road, PO Box 15000, Halifax NS B3H 4R2, Canada b Fisheries and Oceans Canada, Northwest Atlantic Fisheries Center, St. John’s, Newfoundland and Labrador, Canada A R T I C L E INFO Handled by Prof. A.E. Punt Keywords: Spatial age-length keys Smooth age-length keys Age estimates ABSTRACT Estimating the age composition of a fsh population is a critical frst step in all stock assessments that apply age- structured models. Often this is done through the use of an Age Length Key (ALK), which links a subsample of fsh that have had their ages determined to those that have only had their lengths measured in order to obtain an estimate of the age structure of the entire sample. ALKs can suffer from data gaps and sampling artifacts and are limited in both how they can refect spatial variability and how spatial information can be incorporated. We propose a novel spatial ALK model that uses an approximation of a Gaussian Field and has the ability to account for physical barriers (e.g. islands, coastlines) in the study area. Our approach is compared with a pre- viously suggested spatial ALK model as well as non-spatial approaches using both real and simulated survey data. We fnd that spatial ALK approaches reduce errors in stratifed estimates of abundance at age over non-spatial approaches and that incorporating physical barriers can deliver more realistic results. 1. Introduction Stock assessments are tools that can allow us to understand the overall health of a fsh stock. They enable quantifying the abundance, age and length compositions of the population and determine in- dications of whether the stock is facing overexplotation (Worm et al., 2009). They play a key part in helping to rebuild and maintain fsheries around the world (Worm et al., 2009; Hilborn and Ovando, 2014). Stock assessment methods have evolved from simple methods based only on catch data to models that integrate additional sources of data, to modern state-space approaches (Aeberhard et al., 2018) that allow for increasing levels of inference and precision. Age structured methods can greatly simplify stock assessment models as ages link directly to the numbers of survivors in each year. However, for most species accurately and easily determining the age of a fsh can be a time consuming and expensive process that often requires an expert counting the number of growth rings on an otolith or similar procedure. Measuring the length of a fsh is much easier, less lethal and it can be done on site for low cost. In order to take advantage of the benefts of age structured methods, approaches for estimating the age of a fsh from its cheaply measured length are commonly used, like Age Length Keys (ALKs) (Aanes and Vølstad, 2015). ALKs have been used to estimate the age of fsh for over 80 years (Fridriksson, 1934). They are based on the idea that the proportion of fsh at age a, p a is equal to p a = ∑ K i=1 k i p a|i (1) where i indexes discrete length bins i = 1 to K and k i is the proportion of fsh in length bin i, p a|i is the observed conditional probability (or pro- portion) of being age a given membership in length bin i. An ALK is then simply a matrix of proportions of fsh at age a given length i. To convert the sampled length frequencies to estimates at age, the length fre- quencies are multiplied by the ALK to get the numbers at age. An example of a traditional ALK along with an example of a smooth model based ALK is shown in Table 1. ALKs are often constructed separately for different covariates such as sex, time of year and gear type depending on the species and application. Traditional ALKs can easily suffer from data gaps resulting in some fsh not being assigned an age estimate. ALKs also suffer from low sample numbers particularly for rarer older age classes. An example of such a sampling artifact can be seen in Table 1a where any fsh assigned to the 49 cm length bin will automatically be assumed to be age 9 despite the existence of shorter older fsh. Smooth ALKs have non-zero proportions at every possible length bin ensuring that all fsh are assigned an age estimate. Kvist et al. (2000) * Corresponding author. E-mail addresses: jn805248@dal.ca (J. Babyn), Divya.Varkey@dfo-mpo.gc.ca (D. Varkey), Paul.Regular@dfo-mpo.gc.ca (P. Regular), Danny.Ings@dfo-mpo.gc.ca (D. Ings), Joanna.Flemming@dal.ca (J. Mills Flemming). Contents lists available at ScienceDirect Fisheries Research journal homepage: www.elsevier.com/locate/fishres https://doi.org/10.1016/j.fshres.2021.105956 Received 13 August 2020; Received in revised form 19 March 2021; Accepted 21 March 2021