DOI: 10.5061/dryad.8sf7m0cwg
title: Density dependence only affects increase rates in baleen whale populations at high abundance levels

description: Most baleen whale populations are increasing after the end of industrial
 whaling, but their recovery patterns challenge long-standing assumptions
 about density dependence. It has long been assumed that
 population growth rates will decline with recovery, until reaching
 equilibrium (“carrying capacity”, K). Indeed, the International
 Whaling Commission assumes that growth rates will slow long before K is
 reached, with maximum productivity at 0.6K. This 0.6K population level is
 used as an international benchmark that forms the basis of whaling
 regulations and decisions about whether baleen whale populations are
 declared depleted. We fit models to four long-term datasets for
 baleen whales with multiple abundance estimates that span the range from
 low to high abundance, finding strong evidence that increase rates remain
 at near-maximal levels across a wide range of abundance levels, and only
 decline as the population nears K. As a result, maximum
 productivity occurs at 0.69–0.87 of K across these populations, which
 predicts more rapid recovery for baleen whale populations than currently
 assumed. The overall mean of these values (0.8K) would be a more sensible
 default choice than the 0.6K currently assumed. Synthesis and
 applications: Estimated recovery rates imply that management thresholds
 currently used are lower than actual maximum productivity, and that
 populations can increase rapidly even at high abundance. However, if
 population models continue to assume that maximum productivity is at 0.6K,
 they will estimate abundance relative to K to be lower than it is,
 providing conservative assessment results. Our results should stimulate
 further discussion about the role of maximum sustainable yield (MSY) as a
 fundamental concept in fisheries and wildlife management.
description: # Density dependence only affects increase rates in baleen whale
 populations at high abundance levels ## Overview of files hosted on Dryad
 Each file contains a time series of catch records by species/population
 and location, with two columns: 1. year, and 2. catch number. ***Models***
 "StanSimulation0.stan" (Stan code for the logistic model with
 fixed *z* =2.39) "StanSimulation.stan" (Stan code for the
 logistic model with estimating *z* value)   ## Overview of files hosted on
 Zenodo **Abundance time-series** "Abund.Bowhead.csv" (Abundance
 data for bowhead whales) "Abund.GR.csv" (Abundance data for gray
 whales) "Abund.Hbk.csv" (Abundance data for USWC humpback
 whales) "Abund.HbkAusNoad2019.csv" (Abundance data for EAUS
 humpback whales) "Abund.HbkAusSpueBb.csv" (Relative abundance
 data for EAUS humpback whales) "Abund.HbkAusSpueppc.csv"
 (Relative abundance data for EAUS humpback whales)
 "Abund.HbkAusSpuesol.csv" (Relative abundance data for EAUS
 humpback whales) ## Description of the data and file structure: Each file
 contains a time series of abundance estimates by species/population and
 location, with three columns: 1. year, 2. abundance estimate (or SPUE,
 sightings per unit effort), 3. cv (coefficient of variation), and
 reference information. **Catch time-series** "Catch.Bowhead.csv"
 (Catch data for bowhead whales) "Catch.GR.csv" (Catch data for
 gray whales) "Catch.Hbk.csv" (Catch data for USWC humpback
 whales) "Catch.HbkEAUS.csv" (Catch data for EAUS humpback
 whales) ## Context and References: ###### Bowhead whales
 (Bering-Chukchi-Beaufort Sea, BCB) Catch data are available for 1848 to
 2019 (Allison, 2020), and 13 abundance estimates are available during
 1978–2019 (Givens, George, & Suydam, 2015). Earlier abundance
 estimates from Zeh & Punt (2004) in 1978–2001, from Koski et al.
 (2010) in 2004, and from Givens et al. (2013) in 2011 were refined and
 updated in Givens et al. (2015). The latest two estimates, both for 2019,
 were estimated by Givens, George, Suydam, & Tudor (2021) and Ferguson
 *et al.* (2022). Abundance estimates were based on visual census, acoustic
 monitoring, and aerial surveys (or some combination of the three) during
 the spring migration. This population was severely depleted by the early
 1900s before a long period of recovery. Since the abundance data do not
 include the full recovery period, estimation might be unstable, and
 therefore we fitted three separate population models covering different
 time periods: 1848–2019, 1930–2019, and 1970–2019. ###### Gray whales
 (eastern North Pacific population, ENP) Catch statistics are available
 from 1930 to 2015 (Allison, 2020). Abundance estimates were based on
 shore-based count data of whales migrating south off the central
 California coast. Abundance estimates in 23 years among 1967–2006 were
 reported by Laake *et al.* (2012) and those in 2014 and 2015 were provided
 by Durban *et al.* (2017). Updated abundances in 2019, 2021, and 2022 were
 reported by Stewart & Weller (2021), Eguchi, Lang, & Weller
 (2022), and Eguchi, Lang, & Weller (2023), respectively. However,
 abundance suddenly declined from 2019 probably due to  variability in
 climate and prey abundance (Stewart et al., 2023). Our model does not
 focus on such fluctuation after reaching *K*, so that we simply fit the
 model time-series abundance up to 2015 assuming that the population has
 reached K at least by that year.     ###### Humpback whales (US west
 coast, USWC) Humpback whales off the US west coast are treated as a single
 unit for management purposes, even though they include whales that breed
 in different locations (Central America, Mexico, and Hawaii). There has
 been a moratorium on humpback whales in the North Pacific since 1966, and
 thus there were zero catches taken from this population during the period
 modeled (1970–2018). We used 33 abundance estimates from the period
 1989–2021 from an unpublished analysis (J. Calambokidis & J. Barlow,
 pers. comm. 11 June 2022) updated from Calambokidis and Barlow (2020).
 Those estimates were based on photo-identification mark-recaptures
 collected off the US west coast (Calambokidis and Barlow, 2020). Since
 there was a sudden jump in abundance from 2015–16, two models were fitted:
 (1) based on abundance estimates 1989–2014, and (2) based on abundance
 estimates 1989–2021. ###### Humpback whales (Eastern Australia, EAUS) No
 catches have been taken in the Southern Hemisphere since a moratorium in
 1963. We modeled abundance starting in 1973 by fitting to three distinct
 datasets based on long-term visual censuses conducted from Pt Lookout,
 North Stradbroke Island, south-eastern Queensland (Noad, Dunlop, Paton,
 & Cato, 2011; Noad, Kniest, & Dunlop, 2019). Only in 2004 did
 these surveys cover the entire migration and report an absolute abundance
 estimate, designated “N” (Noad *et al.* 2019). Additional independent
 long-term surveys producing relative indices of abundance from the peak
 migration period were conducted by M. Bryden and M. Brown (BB); and by R.
 Paterson, P. Paterson and H. Cato (PPC) (e.g. Paterson, Paterson, &
 Cato, 2004), designated *SPUE*BB for 1981–2004 (Noad et al., 2011) and
 *SPUE*PPC for 1984–2015 (Noad et al., 2019). A third relative abundance
 time series (*SPUE*Sol) is available from Cape Solander, Sydney, for
 1997–2017 (Pirotta et al., 2020). Since CVs were not provided for
 *SPUE*PPC and *SPUE*Sol, additional variance parameters were estimated in
 the population model for these datasets.   Allison, C. (2020). *IWC
 individual whale catch database Version 7.1, 23 December 2020.* Available
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