John A. Ludwig

Statistical ecology: a primer on methods & computing

Ecological Community Data. SPATIAL PATTERN ANALYSIS. Distribution Methods. Quadrat-variance Methods. Distance Methods. SPECIES ABUNDANCE RELATIONS. Distribution Methods. Diversity Indices. SPECIES AFFINITY. Niche Overlap Indices. Interspecific Association. Interspecific Covariation. COMMUNITY CLASSIFICATION. Resemblance Functions. Association Analysis. Cluster Analysis. COMMUNITY COORDINATION. Polar Ordination. Principal Components Analysis. Correspondence Analysis. Nonlinear Ordinations. COMMUNITY INTERPRETATION. Classification Interpretation. Ordination Interpretation. References. Index. BASIC Programs.

VEGETATION PATCHES AND RUNOFF–EROSION AS INTERACTING ECOHYDROLOGICAL PROCESSES IN SEMIARID LANDSCAPES

Ecological and hydrological processes can interact strongly in landscapes, yet these processes are often studied separately. One particularly important interaction between these processes in patchy semiarid lands is how vegetation patches serve to obstruct runoff and then how this retained water increases patch growth that, in turn, provides feedbacks to the system. Such ecohydrological interactions have been mostly demonstrated for semiarid landscapes with distinctly banded vegetation patterns. In this paper, we use data from our studies and from the literature to evaluate how strongly four ecohydrological interactions apply across other patchy semiarid vegetations, and how these interactions are affected by disturbances. We specifically address four questions concerning ecohydrological interactions: (1) if vegetation patches obstruct runoff flows during rainfall events, how much more soil water is stored in these patches compared to open interpatch areas; (2) if inputs of water are higher in patches, how much stronger is the pulse of plant growth compared to interpatches; (3) if more soil water in patches promotes greater biological activity by organisms such as earthworms that create macropores, how much does this improve soil infiltrability; and (4) if vegetation patches are damaged on a hillslope, how much does this increase runoff and erosion and decrease biomass production? We used the trigger-transfer-reserve-pulse framework developed for Australian semiarid woodlands to put these four questions into a landscape context. For a variety of patchy semiarid vegetation types in Australia, Europe, and North America, we found that patches significantly stored more soil water, produced more growth and had better infiltrability than interpatches, and that runoff and erosion can markedly increase on disturbed hillslopes. However, these differences varied greatly and appeared to depend on factors such as the intensity and amount of input events (rainstorms) and type of topography, soils, and vegetation. Exper- imental and modeling studies are needed to better quantify how these factors specifically affect ecohydrological interactions. Our current findings do support the conclusion that vegetation patches and runoff-erosion processes do strongly interact in many semiarid landscapes across the globe, not just banded landscapes.

Spatial organisation of landscapes and its function in semi-arid woodlands, Australia

The spatial organisation of three major landscape types within the semi-arid woodlands of eastern Australia was studied by a detailed analysis of gradient-oriented transects (gradsects). The aim was to characterise the spatial organisation of each landscape, and to account for that organisation in functional terms related to the differential concentration of scarce resources by identifiable processes. Terrain, vegetation and soils data were collected along each gradsect. Boundary analysis was used to identify the types of landscape units at a range of scales. Soil analyses were used to determine the degree of differential concentration of nutrients within these units, and to infer the role of fluvial and aeolian processes in maintaining them. All three major landscape systems were found to be highly organised systems with distinctive resource-rich units or patches separated by more open, resource-poor zones. At the largest scale, distinct groves of trees were separated by open intergroves. At smaller-scales, individual trees, large shrubs, clumps of shrubs, fallen logs and clumps of grasses constituted discrete patches dispersed across the landscape. Our soil analyses confirmed that these patches act as sinks by filtering and concentrating nutrients lost from source areas (e.g., intergroves). We suggest that fluvial runoff-runon and aeolian saltation-deposition are the physical processes involved in these concentration effects, and in building and maintaining patches; biological activities also maintain patches. This organisation of patches as dispersed resource filters (at different scales) has the overall function of conserving limited resources within semi-arid landscape systems. Understanding the role of landscape patchiness in conserving scarce resources has important implications for managing these landscapes for sustainable land use, and for the rehabilitation of landscapes already degraded.

Stripes, strands or stipples: modelling the influence of three landscape banding patterns on resource capture and productivity in semi-arid woodlands, Australia

Abstract In the semi-arid open woodlands or savannas of eastern Australia banded vegetation is a common form of landscape patchiness. This banding can form relatively long strands or shorter stripes across the landscape, or small patches can occur in a stippled pattern. In degraded areas these patches can be completely removed from the landscape. This study addresses two related questions: does the type of patchiness (strands, stripes, or stipples) significantly influence how efficiently these semi-arid landscapes capture and store scarce soil resources; and how does this efficiency compare with landscapes that have lost all their patches? Results from a landscape simulation model, validated for a semi-arid woodland study site, demonstrated that the loss of landscape patchiness had the greatest influence on the capacity of the landscape to capture rainfall as soil water—reduced by about 25% compared to banded landscapes. This 25% loss of soil water reduced annual net primary productivity in these systems by about 40%. Banded patterns (stripes or strands) captured about 8% more rainfall as soil water than a stippled pattern; this increased their plant production by about 10%. However, these differences between banding patterns were relatively small compared to the impact of totally eliminating patchiness, which can occur with severe land degradation. This implies that preventing the loss of landscape patchiness is very important for managing savannas for production and conservation goals.

A Scaling Rule for Landscape Patches and How It Applies to Conserving Soil Resources in Savannas

ABSTRACT Scaling issues are complex, yet understanding issues such as scale dependencies in ecological patterns and processes is usually critical if we are to make sense of ecological data and if we want to predict how land management options, for example, are constrained by scale. In this article, we develop the beginnings of a way to approach the complexity of scaling issues. Our approach is rooted in scaling functions, which integrate the scale dependency of patterns and processes in landscapes with the ways that organisms scale their responses to these patterns and processes. We propose that such functions may have sufficient generality that we can develop scaling rules—statements that link scale with consequences for certain phenomena in certain systems. As an example, we propose that in savanna ecosystems, there is a consistent relationship between the size of vegetation patches in the landscape and the degree to which critical resources, such as soil nutrients or water, become concentrated in these patches. In this case, the features of the scaling functions that underlie this rule have to do with physical processes, such as surface water flow and material redistribution, and the ways that patches of plants physically “capture” such runoff and convert it into plant biomass, thereby concentrating resources and increasing patch size. To be operationally useful, such scaling rules must be expressed in ways that can generate predictions. We developed a scaling equation that can be used to evaluate the potential impacts of different disturbances on vegetation patches and on how soils and their nutrients are conserved within Australian savanna landscapes. We illustrate that for a 10-km2 paddock, given an equivalent area of impact, the thinning of large tree islands potentially can cause a far greater loss of soil nitrogen (21 metric tons) than grazing out small grass clumps (2 metric tons). Although our example is hypothetical, we believe that addressing scaling problems by first conceptualizing scaling functions, then proposing scaling rules, and then deriving scaling equations is a useful approach. Scaling equations can be used in simulation models, or (as we have done) in simple hypothetical scenarios, to collapse the complexity of scaling issues into a manageable framework.

A leakiness index for assessing landscape function using remote sensing

The cover, number, size, shape, spatial arrangement and orientation of vegetation patches are attributes that have been used to indicate how well landscapes function to retain, not ‘leak’, vital system resources such as rainwater and soil. We derived and tested a directional leakiness index (DLI) for this resource retention function. We used simulated landscape maps where resource flows over map surfaces were directional and where landscape patch attributes were known. Although DLI was most strongly related to patch cover, it also logically related to patch number, size, shape, arrangement and orientation. If the direction of resource flow is multi-directional, a variant of DLI, the multi-directional leakiness index (MDLI) can be used. The utility of DLI and MDLI was demonstrated by applying these indices to three Australian savanna landscapes differing in their remotely sensed vegetation patch attributes. These leakiness indices clearly positioned these three landscapes along a function-dysfunction continuum, where dysfunctional landscapes are leaky (poorly retain resources).

Theories on the Origins, Maintenance, Dynamics, and Functioning of Banded Landscapes

In this chapter, we explore the whys and hows of banded landscapes: (1) why do they form? (2) how are they maintained? (3) how do they move? (4) how do they work to conserve resources? In addition, we discuss how understanding these processes contributes to advancing heterogeneity theory in landscape ecology generally. Where banded landscapes occur and what forms they take were described in chapter 1. Such landscapes occur in Africa, Australia, and the Americas, and perhaps elsewhere, and are often called two-phase mosaics because they form bands of bare soil alternating with bands of perennial vegetation. They tend to be situated on low planar slopes and are characterized by the long axis of the bands being oriented along the contours of these slopes.

A comparison of paired- with blocked-quadrat variance methods for the analysis of spatial pattern

For the description of patterns in data from quadrats arranged in a belt or grid, a new ‘paired-quadrat variance’ (PQV) method is introduced. This and other published methods were applied to artificial data with known patterns and to two sets of field data. Hypotheses formed by other methods about patterns shown in the field data are tested by Goodalls method involving ‘random pairing of quadrats to obtain variances’ (RPQV). The advantages of using the PQV method and Hills new ‘two-term local quadrat variance’ (TTLQV) method over the earlier ‘blocked-quadrat variance’ (BQV) methods are discussed. It is recommended that quadrat data be divided into two subsets, and then the PQV method be applied to one and the RPQV method to the other. This new procedure for spatial pattern analysis would permit the separation of hypothesis formation (by the PQV method) from hypothesis testing (by the RPQV method), and would permit unambiguous significance tests.

Modelling the trade-off between fire and grazing in a tropical savanna landscape, northern Australia

As savannas are widespread across northern Australia and provide northern rangelands, the sustainable use of this landscape is crucial. Both fire and grazing are known to influence the tree-grass character of tropical savannas. Frequent fires open up the tree layer and change the ground layer from perennials to that dominated by annuals. Annual species in turn produce copious quantities of highly flammable fuel that perpetuates frequent, hot fires. Grazing reduces fuel loads because livestock consumes fuel-forage. This trade-off between fire and grazing was modelled using a spatially explicit, process-orientated model (SAVANNA) and field data from fire experiments performed in the Victoria River District of northern Australia. Results of simulating fire (over 40 years) with minimal or no grazing pressure revealed a reduction in the shrub and woody plants, a reduction in grasses, and no influence on the tree structure given mild fires. While mature trees were resistant to fire, immature trees, which are more likely associated with the shrub layer, were removed by fire. The overall tree density may be reduced with continual burning over longer time periods because of increasing susceptibility of old trees to fire and the lack of recruitment. Increases in stocking rates created additional forage demands until the majority of the fuel load was consumed, thus effectively suppressing fire and reverting to the grazing and suppressed fire scenario where trees and shrubs established.

Viewing rangelands as landscape systems

In this paper we take a fresh look at how to reach a predictable understanding of how rangelands work by viewing them as landscape systems3. What are the landscape structures and processes operating in rangelands that allow us to better understand how limited resources, such as water and soil nutrients, are naturally conserved within these systems? How can this understanding help us to better manage the use of rangelands so that degradation can be prevented? Can we distinguish between utilization and desertification? These kinds of questions can be addressed within a logical framework based on landscape ecology. This framework, labeled the trigger-transfer-reserve-pulse (TTRP) conceptual model, is built upon existing concepts applied to arid and semiarid, resource-limited rangelands. The TTRP framework focuses on how materials in short-supply such as water and soil nutrients (in sediments) are carried by runoff, or by winds, and are captured and concentrated within landscape patches (reserves). If the availability of these resources within a patch exceeds a critical threshold, a production ‘pulse’ occurs. The organic structures and materials produced in such pulses feedback to build on the integrity of landscape patches, and through them to the landscape as a whole, enabling them to capture more resources in the future. However, if patches are degraded by disturbances such as grazing, fewer scarce resources will be captured and landscapes can become dysfunctional. The relative ‘state’ of dysfunction for a rangeland unit can be measured and used to position the unit along a continuum of landscape functionality, from highly functional to highly dysfunctional. Whether this position on the continuum is acceptable for the current uses being made of the rangeland can then be evaluated. If an undesirable change in landscape functionality is detected by monitoring indicators on a unit of rangeland, then management recommendations and strategies can be developed to reverse this change by viewing the rangeland unit as a dynamic landscape system functioning to conserve resources.