1331 Ecological Applications, 15(4), 2005, pp. 1331���1341 q 2005 by the Ecological Society of America A MODEL-FRAMED EVALUATION OF ELEPHANT EFFECTS ON TREE AND FIRE DYNAMICS IN AFRICAN SAVANNAS PETER W. J. BAXTER1,3 AND WAYNE M. GETZ1,2 1Department of Environmental Science, Policy and Management, 201 Wellman Hall, University of California, Berkeley, California 94720-3112 USA 2Mammal Research Institute, Department of Zoology and Entomology, University of Pretoria, Pretoria 0002 South Africa Abstract. There is a concern that high densities of elephants in southern Africa could lead to the overall reduction of other forms of biodiversity. We present a grid-based model of elephant���savanna dynamics, which differs from previous elephant���vegetation models by accounting for woody plant demographics, tree���grass interactions, stochastic environ- mental variables (fire and rainfall), and spatial contagion of fire and tree recruitment. The model projects changes in height structure and spatial pattern of trees over periods of centuries. The vegetation component of the model produces long-term tree���grass coexis- tence, and the emergent fire frequencies match those reported for southern African savannas. Including elephants in the savanna model had the expected effect of reducing woody plant cover, mainly via increased adult tree mortality, although at an elephant density of 1.0 elephant/km2, woody plants still persisted for over a century. We tested three different scenarios in addition to our default assumptions. (1) Reducing mortality of adult trees after elephant use, mimicking a more browsing-tolerant tree species, mitigated the detrimental effect of elephants on the woody population. (2) Coupling germination success (increased seedling recruitment) to elephant browsing further increased tree persistence, and (3) a faster growing woody component allowed some woody plant persistence for at least a century at a density of 3 elephants/km2. Quantitative models of the kind presented here provide a valuable tool for exploring the consequences of management decisions involving the manipulation of elephant population densities. Key words: African savanna herbivory Loxodonta africana plant demography spatial model tree���grass coexistence woody plants. INTRODUCTION Savannas occupy 60% of sub-Saharan Africa. They are typified by the coexistence of woody plants and grasses, with the relative (and wide-ranging) propor- tions of each being influenced predominantly by water availability, fire, nutrients, herbivory, and people (Scholes and Walker 1993, Solbrig et al. 1996, Ruth- erford 1997, Scholes 1997). Many mechanisms have been proposed for tree���grass coexistence in savannas, from equilibrial niche partitioning via rooting-zone competition for available moisture (Walter 1971, Walk- er and Noy-Meir 1982), to nonequilibrial stability via disturbance (Higgins et al. 2000) and state-and-tran- sition (Westoby et al. 1989) dynamics. African elephants (Loxodonta africana) have major ecological effects on savanna dynamics, playing sig- nificant roles in nutrient cycling, seed dispersal, and the provision of space for new germinants (Lewis 1987, Owen-Smith 1988). Despite their overall endangered status, extensive protected areas and effective control Manuscript received 2 December 2002 revised 5 November 2004 accepted 19 November 2004 final version received 24 Jan- uary 2005. Corresponding Editor: R. J. Scholes. 3 Present address: Australian Research Centre for Urban Ecology, School of Botany, University of Melbourne, Park- ville, VIC 3010 Australia. E-mail: pbaxter@unimelb.edu.au of poaching in southern Africa have led to the success of elephant conservation in the region (Douglas-Ham- ilton 1987). Continued increase of elephant populations may lead to a decrease in other species: it is argued that the present spatial restriction of elephant popula- tions by fenced nature reserves or external human pres- sures exacerbates their impact on woody plants (Laws 1970, Lewis 1986, Hoare 1999, Pamo and Tchamba 2001). The habitat modification that results, particu- larly at high elephant densities, has altered the com- positional, structural, and possibly functional diversity of ecosystems (Buechner and Dawkins 1961, Dublin et al. 1990, Cumming et al. 1997). Loss of canopy trees may imperil the woody plant population in the absence of recruits (Barnes 1983), or be followed by a transition to bushland (i.e., shrub-dominated vegetation) due to the prevention, by elephants, fire, or other browsers, of tree recruitment (Leuthold 1977, Pellew 1983, Jach- mann and Bell 1985, Smallie and O���Connor 2000). While most attempts at modeling elephant���savanna interactions have ignored spatial heterogeneity (Caugh- ley 1976, Pellew 1983, van Wijngaarden 1985, Dublin et al. 1990, Ben-Shahar 1996a, b, Duffy et al. 1999, 2000), it has been argued that nonspatial models are inadequate to describe a system defined by heteroge- neous vegetation (Jeltsch et al. 2000). Recent attempts

1332 PETER W. J. BAXTER AND WAYNE M. GETZ Ecological Applications Vol. 15, No. 4 at modeling savanna vegetation dynamics (without el- ephants) have acknowledged the importance of space in ecological processes (Menaut et al. 1990, Hochberg et al. 1994, Jeltsch et al. 1996, Simioni et al. 2000). Most of these spatial vegetation models have been in- dividual-based models (IBMs), or grid-based approx- imations to IBMs, exploring tree���grass coexistence processes by modeling very localized plant environ- ments and operating at a spatial resolution of 0.3���5.0 m sided cells. While such models are useful in con- sidering fine-scale drivers of tree���grass coexistence, they are not readily expandable for considering the action of megaherbivores such as elephants and not necessarily appropriate for application to management (also see Getz and Haight 1989). Other larger scale multilayered models such as the Coughenour SAVAN- NA model (Kiker 1998, Ludwig et al. 2001, Boone et al. 2002) are less amenable to testing a wide range of scenarios. In this paper we develop a savanna model sufficiently broad in scale to explore elephant impacts usefully while still capturing the essential underlying vegetation processes. We use a set of interrelated pop- ulation models, each representing the dynamical pro- cesses occurring in a 1-ha cell of a 1-km2 block of 100 such cells. While elephant impacts on woody plants may leave the species composition of woodlands unchanged, the structural composition may be considerably altered (Jachmann and Bell 1985, Trollope et al. 1998). Some models of elephant���vegetation interactions have ig- nored this vertical structuring of the woody community (Caughley 1976, Duffy et al. 1999, 2000). Others (Pel- lew 1983, Dublin et al. 1990, Ben-Shahar 1996b) have modeled the effects of elephants and fire on height- structured populations, but excluded the effects of cli- mate, grass, competition, and density dependence. The elephant���trees���grass���grazers model produced by van Wijngaarden (1985) included woody plant structure at a coarse level (trees and shrubs) but not rainfall vari- ability or fire. Starfield et al. (1993) used frame-based modeling to track broad-scale qualitative shifts be- tween woodland, bushland, and grassland states, as driven by elephant, fire, and rainfall levels, but this approach lacked the detailed, quantitative information provided by a demographic model. Here we present a spatial elephant���vegetation model, which has a realistic vegetation component, taking into account a height- structured woody plant population operating in com- petition with grass, and affected by key environmental variables (water and fire). Our objective was to produce a model with a sufficient level of realism to investigate the impacts of elephants on savanna structure while maintaining enough flexibility to be adaptable to a va- riety of savanna ecosystems. THE MODEL Our model links 100 1-ha cells in a 10 3 10 grid, to maintain a reasonable scale for modeling plant com- petition and fire events and to produce smooth and predictable dynamics (Hochberg et al. 1994). We as- sume uniform water and nutrient distribution across the resulting 1-km2 area. Each hectare cell consists of a tree���grass community that, we assume, experiences uniform fire intensity and herbivory. The cells are linked spatially by seed dispersal and fire contagion. A cell���s neighbors are defined as those cells immedi- ately to the north, south, east, or west, with cells on the edge having fewer neighbors (i.e., dissipative boundary conditions). A flow diagram outlining the progression of the mod- el is given in Fig. 1. The model is simulated using discrete, half-year time steps (denoted by t), reflecting annual wet and dry seasons characteristic of savannas (Solbrig et al. 1996), although some savanna ecologists (e.g., Starfield et al. 1993) recognize three seasons: hot���wet, cold���dry, and hot���dry. In southern Africa, rainfall has a component of ������quasi 20-year oscillation������ of relatively wet and dry periods (Tyson and Dyer 1978, Gertenbach 1980), which we also include in the model. The rainfall is applied evenly over the entire grid this is a reasonable assumption, given the size of our representative plot (du Toit et al. 1990). In our model, fire is assumed to occur only in the dry season. Although timing of burning can be important (partic- ularly with reference to whether woody plants have produced new shoots yet or not Frost and Robertson 1987, Enslin et al. 2000), our resolution of time into biannual units does not permit us to account explicitly for this subtlety (rather, the effect is averaged into the parameter values). Although woody vegetation attributes can be mea- sured using aboveground biomass, canopy cover, or stem diameter, elephant use of woody plants is often measured with reference to tree height. Therefore, we use height to demarcate nine stage classes of woody plant (1 # i # 9), which in turn represent four broader classes (metaclasses): seedlings are ,15 cm tall (i 5 1), saplings (i 5 2, . . . , 5) are ,1 m tall, two shrub- sized classes of 1���2 m (i 5 6) and 2���3 m (i 5 7 i.e., up to fire escape height Pellew 1983), and two tree classes of 3���5 m (i 5 8) and .5 m (i 5 9 beyond browsing height). We use four sapling classes as a de- vice to prevent seedlings entering the shrub metaclass within two years, and so individuals advance auto- matically through classes i 5 2, . . . , 5 subject to suf- ficient rainfall. We employ a 10th vegetation class to record grass biomass. We also track area covered by woody plants and grass. An individual in each of the woody metaclasses is assumed to control a ������resource area������ of 0.01, 1, 9, and 25 m2, respectively (after Kiker 1998). Rather than using the 23/2 self-thinning rule (Yoda et al. 1963, Westoby 1977), we follow other spatial models of savannas by assuming a linear rela- tionship between height and neighborhood extent (Menaut et al. 1990, Higgins et al. 2000).