) r.\ .å'so Mathematical Apptications for Conservation Ecology: The Dynamics of Tree Hollows and the Design of Nature Reserves Ian R Ball Submitted in partial fulfilment of the requirements of a PhD University of Adelaide, Department of Applied Mathematics Table of Contents TOC I Abstract lll Acknowledgments iv Declaration v Papers arising from work vi Part L: HOLSIM the tree hollow simulator Seeing the Hollows for the Trees Section 1 Introduction 1 Section 2 The Model 5 Section 3 The Scenarios 23 Section 4 Results 4.1 Null run (Introducing the Scenarios) 25 4.2 ProportionalHarvesting 27 4.3 Retaining a Fixed Number of Trees with Hollows 31 4.4 Retaining Trees with or without Hollows 34 4.5 Retained Tree MortalitY 37 4.6 More Detailed Regimes 40 Section 5 Sensitivity Analysis 45 Section 6 Conclusions 57 Part 2: The Nature of Reserve Design and the Design of Nature Reserves Section 1: Introduction 63 Section 2: Literature Review 66 Section 3: Formal Problem Statement 81 Section 4: Methods used in this Thesis 93 Section 5: Data sets 105 Section 6: Comparison of Different Solution Methods. 111 Section 7: Cost Threshold 123 Section 8: Incremental Reserve Design 134 Section9: Fragmentation t4t Section 10: Spatial Rules 150 Section I 1: Conclusions 158 Bibliography Tree Hollow Dynamics Bibliography t7t Nature Reserve Design Bibliography 176 Abstract The first pan of this thesis describes a deterministic computer model for simulating forest dynamics. The model predicts the long term dynamics of hollow bearing trees which occur in a single species (monotypic) forest stand under an array of different timber harvesting regimes over a time scale of centuries. It is applied to a number of different timber harvesting scenarios in the mountainash(Eucalyptus regnans F.Muell.) forests of Victoria, south-eastern Australia. The results have far-reaching implications for forest management. These include: l) When the harvest rotation time is 100 years or less, a supply of trees with hollows cannot be ensured by only retaining trees which already have hollows; and 2) When some retained trees are lost through logging related mortality, the effect on the number of trees with hollows is exaggerated. For instance if half of the retained trees are lost via logging related mortality, it is not sufficient to double the number of trees retained in order to maintain the same number of hollow bearing trees. The second part of the thesis looks at a number of new mathematical problems in the design of nature reserve systems. The basic problem is to select a set of sites from a list to try to meet the representation requirements of a set of species which occur on these sites for as small a cost or number of sites as possible. After comparing a number of methods for solving basic problems a number of new problems are introduced. These include: Fixing the cost or size of the reserve system and then trying to maximise species coverage; Building a reserve system up in stages with species requirements incremented - this is another way of controlling the size or cost of the reserve system and also allows the cost - biodiversity trade-off to be examined; Controlling fragmentation of the reserve system by trying to minimise the boundary length as well as the size of the reserve; and introducing spatial requirements for each species. These requirements are that individual patches with the species be large enough to be viable on their own, as well as having some patches separated by a great enough distance that they are not all likely to be destroyed in a local catastrophe. llt Acknowledgments This work was in part funded by Environment Australia. I would like to thank Andrew Taplin from Environment Australia, David Lindenmayer, Drew Tyre, Hugh Possingham (of course) and Donna, Callum and Ethan. Now small fowls flew screaming over the yet yawnins gulf; a sullen white surf beat against its steep sides; then aII collapsed, and the great shroud of the sea rolled on as it rolled fiv e thousand years ago. Herman Melville, Moby Dick lv Declaration This work contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to this copy of my thesis, when deposited in the University Library, being available for load and photocopying. Ian Ball Date at ^3-Zoao Publications arising from this work Already Published Ball, I. R., Lindenmayer, D. 8., Possingham, H, P., (1997) "4 tree hollow simulation model for forest managers: The dynamics of the absence of wood in trees." Proceedings International Congress on Modelling and Simulation (MODSIM 97) Eds: McDonald, A. D., and McAleer, M. Ball, I. R., Possingham, H. P., and Lindenmayer, D. 8., (1996) "Modelling of retained trees in logged forests" (ANCA: Canberra) Ball,I. R., Lindenmayer, D. B., Possingham H. P. (1999) "A tree hollow dynamics simulation model for forest managers: Seeing the hollows for the trees." Forest Ecology and Management, 123,179-t94. ln Press Ball, I. R., Smith, 4., Day, J. R., Pressey, R. L., Possingham, H. "Comparison of mathematical algorithms for the design of a reserve system for nature conservation: An application of genetic algorithms and simulated annealing." In press: Journal of Environmental Management. Possingham, H., Ball,I. R., Andelman, S. (2000) "Mathematical methods for identifying representative reserve networks" in Quantitative methods for conservation biology. Ferson, S., and Burgman, M. (eds). Springer-Verlag, New York. Submitted Leslie, H., Ruckelshaus, M., Ball, I. R., Possingham, H. P. "Using siting algorithms in the design of marine reserve networks", submitted to Ecological Applications vl Part 1 HOLSIM the tree hollow simulator: Seeing the Hollows for the Trees Section I Introduction The potential impacts of timber harvesting operations on the conservation of biodiversity has become a major planning and policy issue in the management of Australian Eucalypt forests (Resource Assessment Commission,1992; Commonwealth of Australia, 1992;Department of the Environment, Sports and Territories, 1995). In a typical unharvested forest there will be trees representing all stages in the life cycle including trees with hollows. Tree hollows include fissures, and cracks in trees, holes and hollow branches, and they are occasionally termed cavities in the literature (Lindenmayer et al. 1993). These hollows are extremely important in the maintenance of animal diversity as a wide of animal species use them. In Australia alone it is estimated that approximately 400 vertebrate species need hollows (Ambrose, 1982). Trees with hollows are a characteristic component of forest ecosystems, not only in Australia, (Scotts, 1991; Lindenmayer et al.,1993) but in many places around the world (Newton, 1994). They provide a key habitat component for a wide array of vertebrate and invertebrate taxa (Gibbons and Lindenmayer, 1996) and provide nesting and denning sites as well as places for animals to roost and perch (Lindenmayer and Franklin, 1998) for a wide range of purposes including shelter, protection and breeding Species which use hollows in trees are considered to be among those most vulnerable to the impacts of timber harvesting (Mcllroy, 1978; Recher et a|.,1980; Lindemayer et al', L990a, I99La,l99lb; Scotts, 1991; Gibbons and Lindenmayer, 199ó). This is because hollows suitable for occupation by wildlife may take several hundred years to develop (Ambrose, 1982; Saunders et a\.,1982; Lindenmayer et a\.,1991c; 1993; Gibbons 1994), this and the type of logging operations used, as well as the interval between harvesting events, may prevent or severely impair the development of trees with hollows (Lindenmayer et aI., 1990b; Recher, 199ó; Gibbons and Lindenmayer,1996). Logging typically results in substantial changes to forest structure (Shaw, 1983; Recher, 1985a, 1985b, 1995; Lindenmayer et al., 1990b; Lindenmayer 1992a, I992b, 1994; Ough and Ross, 1992), such as a smaller size-class distribution (Recher, 1985a; Lindenmayer, 1995). Such changes typically lead to a reduction in the numbers of hollow-bearing trees (Mcllroy, 1978; Smith, 1985; Mackowski, 1988; Lindenmayer et al., l99tc). In Australian Eucalypt forests the short period of time between 1 logging operations (typically 4O-I2O years) (Government of Victoria, 1986; van Saane and Gorden, 1991; State Forests of New South Wales, 1994) severely impedes the recruitment of hollow bearing trees. This has a negative effect on the large number of vertebrate and invertebrate taxa that are obligate or facilitate hollow-using species (Gibbons and Lindenmayer,Igg6). As hollow ontogeny in Australian eucalypt trees takes a long time, rectifying hollow shortages in wood production forests will take a long time (Lindenmayer and Possingham, 1995; Recher, 1995). Tree retention strategies can help avoid shonages in hollow bearing trees and mitigate the impact of logging on hollow dependent fauna. (Gibbons and Lindenmayer 1996). Such approaches may enable those stand attributes which are essential for wildlife to be maintained within logged forests. These key attributes can then be perpetuated through many harvest rotation cycles to maintain essential habitat components for wildlife. Consequently tree retention strategies could help maintain the populations of those species that might otherwise be permanently eliminated from logged areas, or even lost from the entire wood production forest. Studies of a range of different types of eucalypt forest have highlighted the value of retained trees in facilitating the recolonisation of logged sites by birds (for example Loyn et al., 1980; Recher et a\.,1980; Smith, 1985; Kavanagh and Turner, 1994 ). A detailed review of a range of aspects of tree retention strategies has indicated that many key issues remain to be resolved (Gibbons and Lindenmayer,1996). For example, in most Australian wood production forests, there is insufficient field data to determine the number, type and spatial arrangement of trees that should be retained (Gibbons and Lindenmayer, 1996).