Inferring fishing intensity from contemporary and archaeological size-frequency data Michael J. Plank a, c, * , Melinda S. Allen b, c , Reno Nims b, c , Thegn N. Ladefoged b, c a School of Mathematics and Statistics, University of Canterbury, Christchurch 8140, New Zealand b Anthropology, School of Social Sciences, University of Auckland, Auckland 1010, New Zealand c Te P unaha Matatini, a New Zealand Centre of Research Excellence, New Zealand article info Article history: Received 8 August 2017 Received in revised form 23 January 2018 Accepted 29 January 2018 Keywords: Fisheries management fishing intensity Harvesting model Ichthyoarchaeology Resource depression Size-frequency data Size-structured population abstract Establishing whether pre-industrial societies caused significant harvesting impacts on fish stocks is often hindered by the paucity of historic evidence. Some archaeological assemblages contain information on the sizes and/or species of individuals in the catch, but this does not provide any direct evidence on the absolute size of the catch or comparative metrics. We develop a method for using size-frequency data to infer the intensity of fishing and the size-selectivity of the fishing gear in use. The model allows quan- titative estimates to be made for the depletion of snapper populations relative to the unexploited pre- human biomass. We evaluate this method using six modern and five archaeological datasets from northern New Zealand for a key commercial and artisanal species, Australasian snapper or silver seab- ream (Pagrus auratus). Our method uses two models for the size selectivity of fishing: one S-shaped, representing mobile fishing gear such as trawls or seines, and one dome-shaped, representing static fishing gear, such as hooks, longlines, or gillnets. The results show that the estimated fishing intensity is lower, and the size of fish being caught is larger, in the archaeological datasets than in the modern datasets, as might be expected. Nevertheless, some of the archaeological datasets show evidence that is consistent with substantial resource depression and depletion of the largest fish in the population, while others suggest only light exploitation. The method allows the five archaeological cases to be rank ordered in terms of exploitation pressures and the relative orderings are further assessed using independent information on site chronology, stratigraphy, and recovery procedures (i.e., screen size). Other factors that can affect size-frequency data are briefly considered, but require additional environmental and taphonomic data that are not currently available. The results provided by our new method support the hypothesis that the depletion of large fish and capture of progressively smaller ones occurred in the pre- European era, albeit in spatially localized areas and at a much less severe level than in modern times. The model results also help identify potential biases in the archaeological assemblages and directions for further research. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction The effects of human activity on nearshore marine fisheries today is uncontroversial. The impact of humans, particularly small- scale societies, in the past, however, is sometimes debated, was possibly variable, and is generally challenging to assess (e.g., Allen, 2002; Broughton, 1999; Butler, 2000; Field et al., 2016; Giovas et al., 2016; Grayson, 2001; Ono and Clark, 2010; Reitz, 2004). Nonetheless, there is increasing interest in archaeological evidence, not only for understanding local historical sequences, but also for the deep-time perspectives it might bring to contemporary resource management and conservation (e.g., Braje et al., 2017; Erlandson and Rick, 2010; Etnier, 2007; McKechnie et al., 2014). By its nature, archaeological evidence is often coarse-grained, incompletely sampled over time and space, and influenced by a range of factors that cannot always be controlled for. Analysts have thus occasionally turned to modelling as a complementary approach to aid understanding of zooarchaeological patterns and the underlying causes (e.g., Morrison and Addison, 2008; Morrison and Allen, 2015). In this paper, we present a mathematical method * Corresponding author. School of Mathematics and Statistics, University of Canterbury, Christchurch 8140, New Zealand. E-mail address: michael.plank@canterbury.ac.nz (M.J. Plank). Contents lists available at ScienceDirect Journal of Archaeological Science journal homepage: http://www.elsevier.com/locate/jas https://doi.org/10.1016/j.jas.2018.01.011 0305-4403/© 2018 Elsevier Ltd. All rights reserved. Journal of Archaeological Science 93 (2018) 42e53