John W. Hearne

Effects of fire and herbivory on the stability of savanna ecosystems

Savanna ecosystems are characterized by the co-occurrence of trees and grass- es. In this paper, we argue that the balance between trees and grasses is, to a large extent, determined by the indirect interactive effects of herbivory and fire. These effects are based on the positive feedback between fuel load (grass biomass) and fire intensity. An increase in the level of grazing leads to reduced fuel load, which makes fire less intense and, thus, less damaging to trees and, consequently, results in an increase in woody vegetation. The system then switches from a state with trees and grasses to a state with solely trees. Similarly, browsers may enhance the effect of fire on trees because they reduce woody biomass, thus indirectly stimulating grass growth. This consequent increase in fuel load results in more intense fire and increased decline of biomass. The system then switches from a state with solely trees to a state with trees and grasses. We maintain that the interaction between fire and herbivory provides a mechanistic explanation for observed discontinuous changes in woody and grass biomass. This is an alternative for the soil degradation mechanism, in which there is a positive feedback between the amount of grass biomass and the amount of water that infiltrates into the soil. The soil degradation mechanism predicts no discontinuous chang- es, such as bush encroachment, on sandy soils. Such changes, however, are frequently ob- served. Therefore, the interactive effects of fire and herbivory provide a more plausible explanation for the occurrence of discontinuous changes in savanna ecosystems.

Spatial Heterogeneity and Irreversible Vegetation Change in Semiarid Grazing Systems

Recent theoretical studies have shown that spatial redistribution of surface water may explain the occurrence of patterns of alternating vegetated and degraded patches in semiarid grasslands. These results implied, however, that spatial redistribution processes cannot explain the collapse of production on coarser scales observed in these systems. We present a spatially explicit vegetation model to investigate possible mechanisms explaining irreversible vegetation collapse on coarse spatial scales. The model results indicate that the dynamics of vegetation on coarse scales are determined by the interaction of two spatial feedback processes. Loss of plant cover in a certain area results in increased availability of water in remaining vegetated patches through run‐on of surface water, promoting within‐patch plant production. Hence, spatial redistribution of surface water creates negative feedback between reduced plant cover and increased plant growth in remaining vegetation. Reduced plant cover, however, results in focusing of herbivore grazing in the remaining vegetation. Hence, redistribution of herbivores creates positive feedback between reduced plant cover and increased losses due to grazing in remaining vegetated patches, leading to collapse of the entire vegetation. This may explain irreversible vegetation shifts in semiarid grasslands on coarse spatial scales.

Relationship between vegetation growth rates at the onset of the wet season and soil type in the Sahel of Burkina Faso: implications for resource utilisation at large scales

In the Sahel, poor soil quality and rainfall levels have a great influence on pasture production and hence on secondary output. In areas where rainfall is the limiting factor for primary production, recovery of primary and secondary production after the dry season depends on soil type. On sandy soils a large fraction of rainfall infiltrates and becomes available for plant growth, stimulating fast herbage growth, while on clayey and loamy soils low infiltration rates generate runoff, leading to slower herbage growth rates. The very different moisture retention characteristic of sands and clays is another possible cause for the observed differences in growth rates. In this paper we investigate the herbage growth rate from the onset of the rainy season. We hypothesise that, in areas where rainfall is the limiting factor for primary production, the vegetation growth rate on clayey soils is lower than that on sandy soils. We will test this hypothesis using long-term rainfall, soil types and satellite derived normalised difference vegetation index data. This research shows that the growth rates on sandy soil are significantly greater than that on clayey soils during the early part of the rainy season. We also show that these differences can be detected at large scales using satellite imagery. We also conclude that, at this scale, movement strategies of pastoralists would be intrinsically linked to not only rainfall patterns and distribution, but also to the underlying soil types in the region as this affects the quality and quantity of fodder available.

A mathematical model of an estuarine seagrass

Abstract A discrete simulation model for the dynamics of a submerged macrophyte, Zostera capensis Setchell, is presented. The model describes the vegetative spread of Zostera sp. which occurs through runners. The model can be used to analyse the response of Zostera sp. to various freshwater-related scenarios. The model shows how reduced freshwater inflow and associated stable salinities have contributed to the increased Zostera sp. population. The effect of floods and dry conditions are simulated. The dynamics of Zostera sp. was investigated for various mouth breaching scenarios.

Evaluating the effects of freshwater inflow on the distribution of estuarine macrophytes

A mathematical model is used to analyse the role of freshwater inflow on spatial patterns and biomass of estuarine macrophytes. A cellular automaton is used, where the updating rules are deterministic. Environmental heterogeneity is defined by salinity, water level fluctuations and freshwater inflow rates. The model is used to project the impact of freshwater release patterns on the distribution of macrophytes in two South African estuaries. Preliminary work on the development of a non-spatial model demonstrated the necessity of introducing a spatial component in the model.

Optimal translocation strategies for saving the black rhino

Abstract Over the past 30 years the black rhinoceros (Diceros bicornis) populations in Africa have dwindled dramatically. To enhance the survival prospects of the species, a national conservation strategy has been developed in South Africa. Its main goal is to formulate and implement policies to increase the southern African rhino population as rapidly as possible. This involves translocating animals from areas where the population is approaching the ecological carrying capacity and establishing new viable populations in other suitable reserves. A non-linear differential equation model for a population of black rhino was developed. The model is used with a combination of analytical and numerical techniques to investigate a number of issues relating to the translocation of rhino from well-stocked, high-density areas to low-density areas with small herds or no herds. Firstly, the model is used to determine the maximum sustainable yield from the well-stocked reserves. The model is then applied to a newly established population to determine optimal import policies. Finally, the model is extended to include both an established exporting population and a new understocked importing population. Simulations are performed to give an indication of the number and age of animals which should be translocated to maximise the growth rate of the total rhino population in southern Africa.

Compelling Reasons for Game Ranching in Maputaland

The last decade has seen a considerable increase in the area of land devoted to wildlife in South Africa. In this chapter we argue that this has been driven by economic rather than conservation reasons. A strong local and overseas market within the right political and legal framework have made game ranching an economically attractive proposition for many landowners in certain areas of South Africa such as Maputaland.

Optimising the offtake of large herbivores from a multi-species community

Abstract The Natal Parks Board annually sells hunting licences for the Controlled Hunting Area (CHA) adjacent to the Mkuzi Game Reserve. A management objective is to maximise the revenue obtained from these hunting activities while ensuring that the population of each species is kept above some minimum level. This management problem is formulated as a linear programming problem and solved for the fourteen different species in the CHA. The LP problem is formulated in such a way as to utilise the same data that is the basis for present management decision-making. The objective function takes into account that animals are hunted for both meat and trophies. Only a fraction of each population is suitable for trophy hunting and higher prices are usual for such animals. The model considers fourteen species divided according to their food preferences into four groups. There is a carrying capacity constraint which limits the weighted sum of the populations in each of these groups. Further constraints relate to the specific growth rates of each species. The optimal equilibrium population levels were calculated to serve as goals or targets. However, droughts and other natural phenomena which affect population numbers are frequently encountered at Mkuze. A number of experiments were therefore performed where the populations were set to reduced levels. The optimal control problem which steers the populations towards the target levels in an optimal way was formulated. Some illustrative solutions are presented.

Determining strategies for the biological control of a sugarcane stalk borer

Abstract The African stalk borer, Eldana saccharina , has become a serious pest to the sugar industry in southern Africa. Over the past decade the South African Sugar Association (SASA) has been investigating numerous indigenous and exotic parasitoids as a means of biologically controlling Eldana infestations in sugarcane. Laboratory results indicate Goniozus natalensis to be one of the most promising parasitoids for this purpose. To aid in analysis its efficacy a mathematical model was constructed. The model comprises a system of different equations governing the populations in the various stages of the E. saccharina life cycle and their interaction with the parasitoid G. natalensis . Using the model, various management strategies relating to the release of parasitoids were simulated. Relationships between the reduction in crop damage and the magnitude and frequency of releases were obtained. It was also found that a change in farming practices could lead to a self-sustaining parasitoid population with a 60% reduction in crop damage.

Modelling to optimise consumptive use of game

There has been a rapid increase in the number of private game ranches established in South Africa in recent years. These ranches are good for conservation but many are driven by the profit motive. A number of models have been used to help managers formulate strategies for achieving their economic objectives. These models are discussed and their use illustrated.A detailed sex and age structured model is presented first with an illustration of its use in attaining two different management objectives. For a given management objective this model generates the returns per unit of food consumed for each species. These returns are then fed into a model to determine the relative abundance of each species in a multispecies herbivory that is required to maximise income.Finally, some problems with the use of these models are discussed. Suggestions and current modelling activities towards improving the tools available to African game ranch managers are presented.