From Beverton and Holt and Back Again. ICES CM 2011/D:02
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Not to be cited without Prior Reference to the Author ICES ASC Gdansk 2011 ICES CM 2011/D:02 Movement Modeling in Stock Assessment: From Beverton and Holt and Back Again Daniel R. Goethel Steven X. Cadrin In the computer age of modern fisheries science, it is difficult to imagine working on today‟s models by hand. This is especially true in stock assessment where a laptop computer has become the only tool most assessment scientists ever use. However, Beverton and Holt developed the foundations for much of fisheries science in their 1957 „fisheries bible,‟ using little more than slide rules and adding machines. As models grow in complexity, it becomes easy to forget their origins and basic assumptions. On the forefront of assessment science is the use of tag-integrated models, which allow fish movement between sub-populations by including tagging data within the objective function. Although current tag-integrated models are more complex than could ever be imagined 50 years ago, it is important to remember that the basis for these models were first developed by Beverton and Holt in their seminal work. A review of Beverton and Holt‟s original movement models shows that the assumptions are essential for the successful application of their models. Although these models were largely forgotten in stock assessment, advancements in computation power, data collection techniques, and cooperative research have led to a resurgence of movement models and the successful application of tag- integrated models. In today‟s world of instant computing it is often easy to take for granted what one‟s predecessors have accomplished, thereby undervaluing their work but simultaneously overlooking important lessons learned along the way. Keywords: Beverton and Holt, movement models, tagging models, tag-integrated models Contact Author: Daniel Goethel UMASS-Dartmouth School for Marine Science and Technology 200 Mill Rd., Suite 325 Fairhaven, MA 02719 [email protected] 1 1. Introduction In his foreword to the 1993 reprint of Beverton and Holt‟s On the Dynamics of Exploited Fish Populations (1957), Daniel Pauly (1993) muses: “I wonder what example will be used for illustrating Beverton and Holt‟s anticipation of ideas when, in a few years or decades, another reprint…is presented to a new generation of fishery scientists?” Although the possibilities are almost infinite, it appears that over the last two decades the honor should be given to Beverton and Holt‟s views on incorporating the effects of fish movement on population dynamics. Section 10 of the „fisheries bible‟, titled „Spatial Variation in the Values of Parameters: Movement of Fish within the Exploited Area,‟ takes up less than 30 of the over 500 pages in Beverton and Holt‟s (1957) book. However, the work presented in this section has been the basis for the recent development of spatially explicit stock assessment models. The most advanced of which, termed tag-integrated models due to the ability to incorporate a tagging component directly in the objective function, represent one of the biggest advancements in stock assessment since the development of statistical catch-at-age (SCAA) models. Even though these models are much more complex than even Beverton and Holt envisioned, the basic tenets and simplifying assumptions used in these models all can be traced back to their 1957 work (Schwarz, 2005). A review of their ideas on incorporating movement along with a brief historical trace of how these simple models have developed into today‟s complex statistical stock assessment models is presented. Additionally, a short discussion of the data, computational, and research advancements that have led to the ability to build and successfully apply tag-integrated models is provided. Many people agree with Isaac Newton‟s quote that scientific progress is only possible by „standing on the shoulders of giants‟ (i.e., our scientific predecessors). While this claim is certainly true, the rate of progress and data assimilation in modern science appears to have developed a tendency to move forward without completely understanding where current research originated. This often results in a lack of understanding and an inability to properly analyze the intricacies of modern scientific models, while simultaneously devaluing the work of one‟s predecessors. In the case of fisheries science and especially stock assessment understanding the past necessitates going back to Beverton and Holt once again. 2. History 2.1 Early Migration Research Although fishery scientists have understood that most marine fish species are capable of long range movements, the extent and details of many fish migrations remain unknown. The temporal changes in fish abundance due to migrations have intrigued scientists since the days when the field of ecology was first emerging. Johann Anderson (1746) presented the idea of panmictic stocks that underwent large-scale migrations. The main thesis was that herring would partake in migrations from their „home‟ under the polar ice cap in search of food when the population outgrew the available prey sources, and would arrive at the various worldwide fishing grounds at different periods during this migration (Wegner, 1996; Chambers and Trippel, 1997; Sinclair 2009). The „migration‟ theory remained a prominent viewpoint well into the early stages of the 20th century when work by Heincke (1898) with herring and by Hjort (1914) with cod 2 demonstrated that different spawning „races‟ or populations existed within a given species, which underwent much shorter spawning and feeding migrations than proposed by Anderson (1746). This research undermined and refuted the „migration‟ theory and ushered in the slow transition to „population thinking.‟ This theory claimed that fishery fluctuations were caused by year-class variability within geographically distinct populations and not long scale migrations of the entire species (Chambers and Trippel, 1997; Secor, 2002; Sinclair, 2009). The importance and baffling nature of fish movements was reflected during the inaugural meeting of the International Council for the Exploration of the Seas (ICES) in 1902. During this initial meeting one of first three committees established was to investigate the “Migrations of the Principal Food-fishes of the North Sea” (Anderson, 2002). Despite the committee focusing primarily on recruitment variability, the cause and effect of migrations remained an important research priority for many fisheries institutions worldwide. 2.2 The Initial Stages of Fisheries Modeling In the 1920s ecology slowly began to turn towards mathematics in order develop modeling tools to predict and understand nature in much the same way as physics had done to understand the physical world. The transition was slow and many ecologists felt, as Russian scientist Nikolai Knipowitsch stated, that “it is completely unacceptable…as a biologist, to reach a conclusion on the basis of formulae” (Smith, 1994). However, the trend towards theoretical modeling in biology had begun and could not be reversed. In fisheries, the stage was set by F. I. Baranov (1918) with the publication of his catch equation, although it was not seen by the western world until decades later. Russell (1931) built on Baranov‟s theory resulting in his energy balance equation regarding fish population growth. Thompson and Bell (1934) further investigated the potential fishery yield from a given stock and calculated what the expected yield should be based on different combinations of natural and fishing mortality. This was followed by von Bertalanffy‟s (1938) growth equation, Michael Graham‟s (1939) introduction of maximum sustainable yield (MSY), and Ricker‟s (1944) work on instantaneous mortality rates. Finally, a short publication in Nature by Henry Hulme, Raymond Beverton and Sidney Holt (Hulme et al., 1947) synthesized much of the previous work into a single yield equation. At this point the stage was set for the biggest breakthrough, and what many consider the foundation of, theoretical fisheries science in the form of Beverton and Holt‟s (1957) On the Dynamics of Exploited Fish Populations (Hilborn, 1994; Anderson, 2002; Angelini and Moloney, 2007) [for a full review of the history of modeling in fisheries see: Smith, 1994 or Angelini and Moloney, 2007] 2.3 The Fisheries ‘Bible’ Mathematical modeling was not a well accepted approach by many in the contentious field of fisheries science. In fact, one of the pioneers of population dynamics modeling, F. I. Baranov, was attacked by the Russian fisheries community following the publication of his catch equation. This resulted in his being ostracized by the scientific community with some going as far as to call him a „saboteur‟ (Ben-Yami, 2010). As is the case with many famed scientists--such as Galileo--whose ideas predate the public and scientific community‟s ability to comprehend and accept them, history has exonerated and proven Baranov a visionary. Luckily, in 1957 when Beverton and Holt published their seminal work, the trend of incorporating mathematics into 3 biology had become a standard practice, albeit one that was accepted begrudgingly by many biologists. This was portrayed by Cren‟s (1959) critique: “Whether we like it or not, however, this book is another demonstration that it is becoming increasingly difficult to make fundamental contributions to ecology without invoking the aid of at least some mathematics.” Instead of facing alienation by the scientific community, Beverton and Holt, who open the book by stating “we make no apology for the fact that much of what is to follow is mathematical in nature,” have been exalted as pioneers and founders of quantitative fisheries science (Pitcher and Pauly, 1998). The original publication run took over three years to typeset and required the head of the Lowesoft Fisheries Laboratory, Michael Graham, threatening to retire in order to convince the United Kingdom Stationary Office to print it (Anderson, 2002; Holt, 2008). Initially, 1,500 copies were printed and sold for ₤6 6s (~US $17.64; Cren, 1959; Rounsefell, 1959; Anderson, 2002). Critiques at the time of first publication were generally positive, but weary of the “highly theoretical and purely mathematical approach” (Rounsefell, 1959).