SoV 1.3 Modelling cannibalism and inter-species predation for the Cape hake species Merluccius capensis and M. paradoxus Andrea Ross-Gillespie A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy University inof the Cape Town Department of Mathematics and Applied Mathematics University of Cape Town May 2016 Supervisor: Douglas S. Butterworth The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non- commercial research purposes only. Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. University of Cape Town Declaration of Authorship I know the meaning of plagiarism and declare that all of the work in the thesis, save for that which is properly acknowledged (including particularly in the Acknowledgements section that follows), is my own. Special men- tion is made of the model underlying the equations presented in Chapter 4, which was developed by Rademeyer and Butterworth (2014b). I declare that this thesis has not been submitted to this or any other university for a degree, either in the same or different form, apart from the model underlying the equations presented in Chapter 4, an earlier version of which formed part of the PhD thesis of R. Rademeyer in 2012. ii Acknowledgements Undertaking a PhD is as much an emotional challenge and test of character as it is an intellectual pursuit. I definitely could not have done it without the support of a multitude of family, friends and colleagues. First, thanks go to my supervisor, Doug Butterworth, for his constant guidance and advice over the last four and a half years, but in particular for his dedicated input, patience and willingness to sacrifice time over the last few months in order to bring this PhD to completion. Thanks also go to all my colleagues at MARAM for their support over the years and their willingness to proof-read chapters, but in particular to Rebeccca Rademeyer for tolerating my frequent badgering and for her ever-willingness to provide various bits of output from her hake assessment model. Many thanks also go to Di Loureiro for the gracious way in which she always deals with our various administrative requests, and without whom MARAM would undoubtedly function much less efficiently. There are of course countless people who have provided input of various kinds on this work over the years; too numerous to all be mentioned. But I would like to express particular thanks to the following people. First Tracey Fairweather from DAFF for not only the provision of the diet data but for all the emails and phone calls to answer my questions. Similarly thanks go to Larvika Singh, Rob Leslie and Deon Durholtz from DAFF for their advice and responses to requests for information, and for their friendly words of encouragement. Much of the progress made during the development of the predation model presented in this thesis is as a result of the input provided by the panels for the annual NRF-DAFF International Stock Assessment workshops organised by MARAM, whose members continue to volunteer their time (in some cases year after year) to provide valuable expert advice on the assessment and management of fisheries in a different part of the world to their own. I would like to express my thanks to all the panellists who have provided input on the hake predation model over the years, but in particular to Andr´ePunt, who has taken the time to respond to numerous questions over the course of the last four years. I would like to express my sincerest gratitude to my family and friends for their continued love, support and most importantly their prayers over the years. In particular I would like to mention my parents and my in-laws | I feel much humbled by the love and support that they have shown. And to my husband Vere, without whose constant love, presence and advice this PhD would have been much less bearable. It is is a privilege to have someone with whom to share ALL the ups and downs. Lastly and most importantly I thank my heavenly father for bringing me to this point. Financial support from the David and Elaine Potter Foundations is gratefully acknowledged, as is the use of the facilities provided by the University of Cape Town's ICTS High Performance Computing team (http://hpc.uct.ac.za) | the computations for this thesis would most certainly not have been possible without the use of the HPC! iii Abstract The hake fishery is South Africa's most valuable and harvests two morphologically similar species, the shallow- water Cape hake Merluccius capensis and the deep-water Cape hake M. paradoxus. Since 1948, annual catches have exceeded 50 000 tons and the current total allowable catch (TAC) is about 150 000 tons, a quantity informed by assessments of the hake resource. Current assessments on which management is based use single-stock models that ignore food-web effects. Usually including such interactions in assessments is problematic because of the complexity of food webs. In the case of Cape hake, however, cannibalism and inter-species predation form a very large component of hake mortality and food consumption, thus making a multi-species model not only more feasible but also likely more reliable. A comprehensive multi-species model incorporating these interactions was last investigated in 1995. Since then, substantially more data have become available, and hake single-species assessments have developed considerably, inter alia now including the ability to take careful account of species differentiation. Additionally, with increased computer processing power, more sophisticated modelling can now be attempted than was possible 20 years ago, rendering an update and refinement of the 1995 analyses timeous. The thesis uses mathematical methods to model hake-on-hake predation and cannibalism in hake populations explicitly by incorporating an additional mortality term to account for these interactions. Information from stomach samples obtained on hake research surveys on predator and prey lengths, as well as on the proportion of hake in the diet of hake predators, is then included when fitting the model to data. Chapter 1 contains a brief introduction to the work. Chapter 2 provides background information on the Cape hake fishery and its management, as well as pertinent information on the biology and diet of the hake (and related fish) from the literature that is relevant to the development of the model constructed in this thesis. Chapter 3 lays out the data available for assessing the Cape hake populations: abundance indices together with catch and catch-at-size data for the standard non-predation model, and hake stomach content data for the years 1999-2013 to inform the predation component of multi-species model developed. Chapter 4 provides the details for the standard hake assessment model used at present to inform management of the stocks. This model forms the basis for the multi-species model developed incorporating predation, which is presented in Chapter 5. The remaining Chapters of the thesis present the results and discussions (Chapter 6), possible future development of this model (Chapter 7) and a brief summary of the main findings of the thesis (Chapter 8). The hake predation model is able to take hake-on-hake predation and cannibalism into account explicitly and still provide a reasonable fit to the various sources of data available. There are, however, some indications of data conflicts as well as of potential model over-parameterisation, which need to be addressed. When cannibalism and predation are taken into account, the M. paradoxus population exhibits a predation release in first half of the 20th century in response to a M. capensis predator population reduced by the early fishery. The M. capensis population shows an increase in the 1960s that is not evident to the same extent in the non-predation models, suggesting that the M. capensis population also experienced a predation release as a result of reduced cannibalism by M. capensis. Despite these predation releases, the predation model estimates similar, even slightly higher, extents of depletion for M. paradoxus. The chief reason for this is the requirement to reflect the large drop in the ICSEAF CPUE data from the mid-1950s to mid-1970s. Higher predation levels give greater predation release, but show stronger oscillatory behaviour which is unable to also mimic the ICSEAF CPUE decline. This finding is contrary to the hope expressed by some stakeholders in the fishery that this predation release would result in estimates of a substantially less depleted M. paradoxus resource. While the predation model still needs to be developed further, it shows good potential as a tool to improve the assessment and management of what is South Africa's most valuable fishery. Contents Declaration of Authorship ii Acknowledgements iii Abstract iv Contents v 1 Introduction 1 2 Assessing the Cape hake stocks - why a multi-species model? 5 2.1 Introduction: the Cape hake stocks . 5 2.1.1 Fisheries and Management . 6 2.1.2 Status of the Cape hake stocks . 7 2.1.3 Stock structure . 8 2.1.4 Overview of aspects of the biology . 8 2.1.5 Diet and feeding habits of the Cape hake . 9 2.2 Developing a predator-prey model . 11 2.2.1 Functional response . 11 2.3 Cape hake multi-species models . 12 2.3.1 The Punt (1994) analyses . 12 2.3.1.1 The overall approach . 12 2.3.1.2 The hake predation component .