Density dependence only affects increase rates in baleen whale populations at high abundance levels
Data files
Jul 17, 2024 version files 12.91 KB
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README.md
10.42 KB
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StanSimulation.stan
1.47 KB
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StanSimulation0.stan
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Abstract
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.
README: 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:
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.
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 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.
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 on request from statistics@iwc.int.
Calambokidis, J, Barlow, J., Flynn, K., Dobson, E., & Steiger, G. H. (2017). Update on abundance, trends, and migrations of humpback whales along the US West Coast. Paper SC/A17/NP/13 Presented to International Whaling Commission Scientific Committee.
Calambokidis, John, & Barlow, J. (2020). Updated abundance estimates for blue and humpback whales along the U.S. West Coast using data through 2018. U.S. Department of Commerce, NOAA Technical Memorandum NMFS-SWFSC-634, 16p.
Durban, J. W., Weller, D. W., & Perryman, W. L. (2017). Gray whale abundance estimates from shore-based counts off California in 2014/2015 and 2015/2016. Paper SC/A17/GW/06 Presented to International Whaling Commission Scientific Committee.
Eguchi, T., Lang, A. R., & Weller, D. W. (2022). Abundance and migratory phenology of eastern north Pacific gray whales 2021/2022. NOAA Technical Memorandum NMFS, NOAA-TM-NMFS-SWFSC-668 U.S., 1–10.
Eguchi, T., Lang, A. R., & Weller, D. W. (2023). Abundance of eastern North Pacific gray whales 2022/2023. NOAA Technical Memorandum NMFS, NOAA-TM-NMFS-SWFSC-680 U.S., 1–10.
Ferguson, M. C., Miller, D. L., Clarke, J. T., Brower, A. A., Amy, L., & Rotrock, A. D. (2022). Spatial modeling, parameter uncertainty, and precision of density estimates from line-transect surveys: a case study with Western Arctic bowhead whales. Paper SC/68d/ASI/01 Presented to International Whaling Commission Scientific Committee.
Givens, G. H., Edmondson, S. L., George, J. C., Suydam, R., Tudor, B., & DeLong, R. a. (2013). Estimate of 2011 abundance of the Bering-Chukchi-Beaufort Seas bowhead whale population. Paper SC/65a/BRG/01 Presented to International Whaling Commission Scientific Committee.
Givens, G. H., George, J. C., & Suydam, R. (2015). A population dynamics model and assessment of Bering-Chukchi-Beaufort Seas bowhead whales. Paper SC/66a/BRG/06 Presented to International Whaling Commission Scientific Committee.
Givens, G. H., George, J. C., Suydam, R., & Tudor, B. (2021). Bering Chukchi Beaufort Seas bowhead whale (Balaena mysticetus) abundance estimate from the 2019 ice based survey. Journal of Cetacean Research and Management, 22, 61–73.
International Whaling Commission. (2015). Report of the sub-committee on other southern hemisphere whale stocks. Journal of Cetacean Research and Management, Suppl. 16, 196–221.
Koski, W. R., Zeh, J., Mocklin, J., Davis, A. R., Rugh, D. J., George, J. C., & Suydam, R. (2010). Abundance of Bering-Chukchi-Beaufort bowhead whales (Balaena mysticetus) in 2004 estimated from photo-identification data. Journal of Cetacean Research and Management, 11, 89–99.
Laake, J. L., Punt, A. E., Hobbs, R., Ferguson, M., Rugh, D., & Breiwick, J. (2012). Gray whale southbound migration surveys 1967-2006: An integrated re-analysis. Journal of Cetacean Research and Management, 12, 287–306.
Noad, M. J., Dunlop, R. A., Paton, D., & Cato, D. H. (2011). Absolute and relative abundance estimates of Australian east coast humpback whales (Megaptera novaeangliae). Journal of Cetacean Research and Management, 3(Special Issue), 243–252.
Noad, M. J., Kniest, E., & Dunlop, R. A. (2019). Boom to bust? Implications for the continued rapid growth of the eastern Australian humpback whale population despite recovery. Population Ecology, 61, 198–209. doi: 10.1002/1438-390X.1014
Paterson, R., Paterson, P., & Cato, D. H. (2004). Continued increase in east Australian humpback whales in 2001, 2002. Memoirs of the Queensland Museum, 49, 712.
Pirotta, V., Reynolds, W., Ross, G., Jonsen, I., Grech, A., Slip, D., & Harcourt, R. (2020). A citizen science approach to long-term monitoring of humpback whales (Megaptera novaeangliae) off Sydney, Australia. Marine Mammal Science, 36, 472–485. doi: 10.1111/mms.12651
Stewart, J. D., Joyce, T. W., Durban, J. W., Calambokidis, J., Fauquier, D., Fearnbach, H., … Weller, D. W. (2023). Boom-bust cycles in gray whales associated with dynamic and changing Arctic conditions. Science, 382, 207–211. doi: 10.1126/science.adi1847
Stewart, J. D., & Weller, D. W. (2021). Abundance of eastern north Pacific gray whales 2019/2020. NOAA Technical Memorandum NMFS, NOAA-TM-NM-SWFSC-639, 1–5.
Zeh, J. E., & Punt, A. E. (2004). Updated 1978-2001 abundance estimates and their correlations for the Bering-Chukchi-Beaufort Seas stock of bowhead whales. Journal of Cetacean Research and Management, 7, 169–175.
Zerbini, A. N., Clapham, P. J., & Wade, P. R. (2010). Assessing plausible rates of population growth in humpback whales from life-history data. Marine Biology, 157, 1225–1236. doi: 10.1007/s00227-010-1403-y.