Analysis of a model for banded vegetation patterns in semi-arid environments with nonlocal dispersal

Journal of Mathematical Biology - Vegetation patterns are a characteristic feature of semi-arid regions. On hillsides these patterns occur as stripes running parallel to the contours. The...     

Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments

In many semi-arid environments, vegetation is self-organised into spatial patterns. The most striking examples of this are on gentle slopes, where striped patterns are typical, running parallel to the contours. Previously, Klausmeier [1999. Regular and irregular patterns in semiarid vegetation. Science 284, 1826-1828.] has proposed a model for vegetation stripes based on competition for water. Here, we present a detailed study of the patterned solutions in the full nonlinear model, using numerical bifurcation analysis of both the pattern odes and the model pdes. We show that patterns exist for a wide range of rainfall levels, and in particular for much lower rainfall than have been considered by previous authors. Moreover, we show that for many rainfall levels, patterns with a variety of different wavelengths are stable, with mode selection dependent on initial conditions. This raises the possibility of hysteresis, and in numerical solutions of the model we show that pattern selection depends on rainfall history in a relatively simple way.     

Natural vegetation phenology assessment by ground spectral measurements in two semi-arid environments

Natural vegetation in semi-arid regions is characterized by three ground features, in addition to bare surfaces - biological soil crusts, annuals, and perennials. These three elements have distinguishable phenological cycles that can be detected by spectral ground measurements and by calculating the weighted normalized difference vegetation index (NDVI). The latter is the product of the derived NDVI of each ground feature and its respective areal cover. Each phenological cycle has the same basic elements - oscillation from null (or low) to full photosynthetic status and back to a stage of senescence. However, they vary in phase. The biological soil crusts show the earliest and highest weighted NDVI peak during the rainy season, and their weighted NDVI signal lasts longer than that of the annuals. The annuals are dominant in late winter and early spring while the perennials predominate in late spring and during the summer.     

Spatial patterns of surface soil properties and vegetation in a Mediterranean semi-arid steppe

In arid and semi-arid areas with sparse vegetation cover, the spatial pattern of surface soil properties affects water and nutrient flows, and is a question of considerable interest for understanding degradation processes and establishing adequate management measures. In this study, we investigate the spatial distribution of vegetation and surface soil properties (biological crusts, physical crusts, mosses, rock fragments, earthworm casts, fine root accumulation and below-ground stones) in a semi-arid Stipa tenacissima L. steppe in SE Spain. We applied the combination of spatial analysis by distance indices (SADIE) and geostatistics to assess the spatial pattern of soil properties and vegetation, and correlation analyses to explore how these patterns were related. SADIE analysis detected significant clumped patterns in the spatial distribution of vegetation, mosses, fine root accumulation and below-ground stone content. Contoured SADIE index of clustering maps suggested the presence of patchiness in the distribution of earthworm casts, fine roots, below-ground stone content, mosses and biological crusts. Correlation analyses suggested that spatial pattern of some soil properties such as biological crusts, moss cover, surface rock fragments, physical crusts and fine roots were significantly related with above-ground plant distribution. We discuss the spatial arrangement of surface soil properties and suggest mechanistic explanations for the observed spatial patterns and relationships.     

Environmental determinants of woody and herbaceous riparian vegetation patterns in a semi-arid mediterranean basin

What environmental variables determine riparian vegetation patterns? Are there differences between woody and herbaceous species? To answer these questions, we first explored the composition and richness patterns of both riparian woody and herbaceous species in a semi-arid mediterranean basin. Then, we assessed the environmental factors (climate, geology, topography, hydrogeomorphology and land use) that best explain these patterns. We used the following methodological approaches: clustering analyses, distance-based linear models, generalised linear models and hierarchical partitioning procedures. Valley shape, drought duration, river habitat heterogeneity, water conductivity and agricultural land use were the most important variables explaining variation in species composition for both groups. Woody riparian richness was mainly influenced by flow conditions and valley shape, whereas herbaceous one was more dependent on substrate features. Thus, although some differences in the importance of individual variables were observed, we found a notable congruence in the composition and species richness of both groups and also in the main types of variables explaining these patterns (hydrogeomorphology and land use, especially agriculture). Our results show that both communities could be treated in a holistic way, since they respond similarly to the strong natural and anthropogenic environmental gradients present in mediterranean basins.     

Woody vegetation spatial patterns in a semi-arid savanna of Burkina Faso,West Africa

Spatial patterns of woody individuals were studied in a semi-arid savanna of West Africa located in Burkina Faso at and around 14° 12 N and 2° 27 W. The study was based upon a 10.24 ha plot within which individuals were mapped. Spatial pattern analysis was carried out using second order characteristics of point processes as K functions and pair correlations. The overall density amounted to 298 individuals ha^-1. The most abundant species were Combretum micranthum G. Don., Grewia bicolor Juss. and Pterocarpus lucens Lepr. Anogeissus leiocarpus (D.C.) G. et Perr. was also an important constituant of this vegetation type, owing to its taller stature. Clumped spatial distributions were identified for all species except for two, for which complete spatial randomness (CSR) was found (including P. lucens, a dominant woody plant). No regular pattern was found even when tall individuals were considered alone. Aggregation dominates interspecific relationships, resulting in multispecific clumps and patches. The overall aggregation pattern was constituted by two different structures. A coarse-grain pattern of ca. 30–40 m was based on edaphic features, and expresses the contrast between sparse stands on petroferric outcrops and denser patches on less shallow soils. A finer-grain pattern made of clumps ca. 5–10 m wide, with no obvious relation to pre-existing soil heterogeneity. There was no overall pattern for saplings (between 0.5 m and 1.5 m in height) irrespective of species, and thus no obvious common facilitation factor. For species with a high recruitment level there was no significant relationship between mature adult and saplings. The only case of clumped saplings with randomly distributed adults was found in P. lucens. However, this cannot be unequivocally interpreted as density dependent regulation since the existence of such a process was not consistent with the spatial distribution of dead P. lucens individuals (victims of the last drought). The mean density around dead P. lucens was lower than around surviving ones, indicating that the last drought tended to reinforce clumping rather than promote a regular pattern of trees. Spatial pattern analysis yielded no evidence supporting a hypothesis of stand density regulation through competition between individuals. Other processes, as surface sealing of bare soils or insufficient recruitment, may play a more important role in preventing a savanna-like vegetation from turning into denser woodlands or thickets.     

Spatial associations and patterns of perennial vegetation ina semi-arid steppe: a multivariate geostatistics approach

We investigated the spatial patterns of perennial species (Stipa tenacissima, Anthyllis cytisoidesGlobularia alypum, Brachypodium retusum and chamaephytes) in a 50 m × 50 m semi-arid steppe by using the combination of a linear model of coregionalization (LMC) and sampling units of varying size (1.25 m × 1.25 m, 2.5 m × 2.5 m, and 5 m × 5 m). The data-adjusted LMC showed the patchy structure of the vegetation, which was especially evident with the highest resolution grid. It also detected a periodic pattern in the distribution of S. tenacissima, as well as autocorrelation at two spatial scales for A. cytisoides and G. alypum. The latter species was negatively associated with the other species at both short and long distances. These negative associations were consistent for all sampling grids and suggest the presence of interference between G. alypum and the rest of the evaluated species. Despite species-specific differences, the LMC was fitted satisfactorily to all of them. This suggests a common variation pattern for all the species, which may be caused by an underlying environmental property driving the patterns of all the species or, alternatively, by the dominance of some species’ spatial pattern, or another kind of species association, over the rest. The spatial patterns found were profoundly affected by the observational scale. Our results reveal that the multivariate geostatistical approach introduced in this paper is a suitable technique for the spatial analysis of semi-arid plant communities. It allows plant ecologists to evaluate if the species forming the plant community of interest share a common spatial pattern, and to assess the spatial covariation between the species forming a plant community at different spatial scales independently.     

Self-organization and productivity in semi-arid ecosystems: implications of seasonality in rainfall

Spatial self-organization including striking vegetation patterns observed in arid ecosystems has been studied in models with uniform rainfall. In this paper, we present a fully seasonal rainfall model that produces vegetation patterns found in nature by including the natural adaptation of plants to scarcity of water and the consequent seasonal variation in their growth and metabolic rate. We present results for the mean-field and spatially extended versions of the model. We find that the patterns depend on the duration of the wet season even with fixed total annual precipitation (PPT) showing how seasonality affects spatial self-organization. We observe that the productivity can vary for fixed PPT as a function of the duration thereby providing another source of observed variations. We compute the maximum vegetation cover as function of PPT and find that the behavior is consistent with observations. We comment on the implications for regime shifts due to increased interannual fluctuations caused by climatic changes. Our specific model calculations provide more general conclusions for ecosystems with competition for scarce resources due to seasonal variations in the resource, especially for self-organization and productivity.     

Small-scale spatial soil-plant relationship in semi-arid gypsum environments

Studies on soil patterning on a small scale in arid and semi-arid regions have rarely been conducted. Many papers implicitly assume that plant distribution is controlled by some soil variables acting at small scales. We have directly tackled the relationships between soil and some biotic variables including plant distribution at small scales in an Iberian semi-arid gypsum environment. This has been carried out by means of Canonical Correspondence Analysis as a hypothesis-testing tool. CCA models show that the spatial data matrix is able to explain a relevant fraction of the soil data set (P < 0.001). The most important variable, as firstly selected in the CCA stepwise selection procedure, suggests the existence of a vegetation-elevation gradient in relation to soil physical properties; the rest of selected variables indicates the existence of other spatial trends which may be related to certain microgeomorphological features. On the other hand, only the cover of annuals and the cover of litter are selected in the case of the biotic data set as constraining matrix, but not the cover of any perennial plant. Partial CCA models indicated that the remaining information explained by the spatial data set after adjusting the biotic set as covariables is also significant (p < 0.001). This variability is not related to the existence of vegetation bands as shown by the two selected variables in the case of the partial CCA models. The primary source of spatial soil variation is related to the existence of three community bands and these differences are able to explain even the change of plant life forms in vegetated band. The soil parameters controlling the changes are mainly related to texture and surface features. However, we detected other sources of spatial soil variation out of this primary model. This hierarchical spatial pattern seems to be related to some geomorphological traits of the landscape, such as soil crust strength, presence of gypsum crystals or bare zones, and not to the presence of mature gypsophytes (at least the five most frequent) which might ameliorate the soil environment. Furthermore, the biotic data set is not able to explain any new fraction of soil variability out of that already explained by the spatial data set. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effects of local extinction of the plains vizcacha (Lagostomus maximus) on vegetation patterns in semi-arid scrub

We studied spatial and temporal effects of local extinction of the plains vizcacha (Lagostomus maximus) on plant communities following widespread, natural extinctions of vizcachas in semi-arid scrub of Argentina. Spatial patterns in vegetation were examined along transects extending outward from active and extinct vizcacha burrow systems. Responses of vegetation to removal of vizcachas were assessed experimentally with exclosures and by documenting vegetation dynamics for 6 years following extinctions. Transect data demonstrated clear spatial patterns in plant cover, particularly an increase in perennial grasses, outward from active vizcacha burrows. These patterns were consistent with predictions based on foraging theory and studies that document grasses as the preferred food of vizcachas. Removal of vizcachas, experimentally and with extinctions, resulted in an immediate increase in perennial and annual forbs indicating that intense herbivory can depress forb cover, as well as grasses. After a 1-year lag following cessation of herbivory, cover of grasses increased. Forbs declined as grasses increased. The long-term effect of extinction of vizcachas was a conversion of colony sites from open patches dominated by forbs to dense bunch grass characteristic of the matrix. Major changes in vegetation occurred within 2–3 years after extinction, resulting in a large pulse of landscape change. However, some species of grasses were uncommon until 5–6 years after the vizcacha extinction. With extinction and colonization, vizcachas generate a dynamic mosaic of patches on the landscape and create temporal, as well as spatial, heterogeneity in semi-arid scrub.     

Land management in semi-arid environments of New South Wales

Land of the semi-arid zone of Australia is generally managed to produce wool or beef. Past management has caused many changes in the land. These changes may be difficult to detect and assess. Much of the available information is at too coarse a scale to be really useful in assessing change. Graziers' perceptions of change are unknown but survey results from the agricultural zone suggest that their perceptions are probably incorrect. Apportioning the causes of change is very difficult as the main agents (climate, stocking rates, bushfires, legislation and economics) are not independent. Three different approaches to separating cause are described: use of historical information, integrating all information and using unpalatable plants as proxies for key economic species. Some difficulties with the historical approach are outlined. The major issues in semi-arid land management are social rather than technical. However, key aspects such as perceptions, motivation, and sources of information used by graziers are neglected research subjects. Recent research into an objective basis for assessing stocking rates from forage biomass production will replace traditional estimates based on extrapolating from similar country. This will significantly assist graziers in determining appropriate stocking rates to maximise their incomes. Other research by graziers has demonstrated the benefits of low stocking rates leading to increased incomes on both an animal and area basis. Such advances by graziers provide keys for future extension programs to achieve the desired goals of a stable grazing industry with good financial rewards, and improved land management.Abbreviations dse dry sheep equivalent. A standard animal unit equivalent to a medium sized wether or non-lactating ewe used to assess total grazing pressure on an area. All other vertebrates can be converted to dse using laboratory data. For this paper, I adopt the conversions factors of 1 beast (cattle, horse) =10 dse, 1.6 kangaroos =1 dse, 16 rabbits =1 dse.     

Small-scale species dynamics in semi-arid steppe vegetation in Inner Mongolia

Abstract. Small-scale species dynamics in semi-arid steppe vegetation under grazing and recovering from long-term grazing were followed during five years. Most species successively increased their frequency during the study period, whereas some early successional species decreased in frequency. Perennial Artemisia spp. dominated the vegetation and showed low mobility, whereas small annual or short-lived perennial species had a lower frequency and higher mobility. Significant associations between species were few.     

An analysis of the vegetation pattern in a semi-arid Eucalyptus populnea woodland in north-west New South Wales

Shrub invasion of Eucalyptus populnea woodland is of concern to the pastoral industry. As part of an ecosystem study, different analyses were used to identify spatial pattern and associations in the tree and shrub species, with the aim of identifying what factors were most influential on the ecosystem. The results suggested that there were no strong edaphic or topographic influences on the distribution of plants. The principal influence on the arrangement of trees and shrubs was the large Eucalyptus trees, which were randomly arranged, and the canopy of which covered 15% of the area. It is concluded that any disturbance of the large Eucalyptus trees would have intense effects on the whole ecosystem. Qualitative and quantitative measurements of the plant species in sample quadrats were subjected to a variety of pattern analyses including association analysis (DIVINF), correlation analysis, principal components analysis and several classification programs including POLYDIV and MULCLAS. A criticism of such analyses is that positive results are both inevitable and not subject to statistical proof, whilst their strength is that they can simplify complicated sets of data. In this case the patterns suggested by the results were visually apparent and no additional insights were achieved. The dangers inherent in relying on a single pattern analysis were revealed when the groups of quadrats produced by the different analyses were mapped. Even when the groupings derived from different analyses were based on a similar species content, their spatial arrangement was dissimilar.     

Herbivore regulation and irreversible vegetation change in semi-arid grazing systems

Models made to explain sudden and irreversible vegetation shifts in semi-arid grasslands typically assume that herbivore density is independent of the state of the vegetation, e.g., under the control of humans. We relax this assumption and investigate the mathematical implications of vegetation-regulated herbivore population dynamics. We show that irreversible vegetation change may also occur in systems where herbivore population dynamics are affected by changes in plant standing crop. Our analysis furthermore shows that irreversible vegetation change may occur for a larger set of soil and climatic conditions when herbivore numbers are independent of the vegetation, as compared to systems where vegetation density determines herbivore population size. Hence, our analysis suggests that irreversible vegetation change is less likely to occur in systems with natural herbivore population dynamics than in systems where humans control herbivore density.     

An analytical model for bidirectional reflectance factor of multicomponent vegetation canopies

Based on radiative transfer theory in vegetation and geometric-optical principles, an analytical physi-cal mode] for calculating multiangular, multispectral reflectance over a non-random, multiple component vegetation canopy is developed. This model is derived by taking advantages of the previous leaf canopy and multicomponent canopy BRF models. It quantitatively accounts for both the impact of foliage elements' orientation on the canopy hotspot through an innovative algorithm to estimate the hotspot function for any arbitrarily oriented foliage element and contributions of all foliage elements to the reflectance by multiple scattering. Thus, it is characterized by more com-pletely considering the integrative influence of spatial variations in optical and structural properties of all foliage ele-ments on canopy reflectance than any previous analytical BRF models. Simulation results from this model demonstrate that canopy hotspot becomes strongest when the mean inclination angle of foliage elements is ar     

A hierarchical model for analysing the stability of vegetation patterns created by grazing in temperate pastures

Questions: Does vegetation structure display any stability over the grazing season and in two successive years, and is there any correlation between the stability of these spatial patterns and local sward composition? Location: An upland grassland in the French Massif Central. Method: The mosaic of short and tall vegetation stands considered as grazed and ungrazed patches respectively is modeled as the realization of a Boolean process. This method does not require any arbitrarily set sward‐height thresholds to discriminate between grazed and ungrazed areas, or the use of additional variables such as defoliation indexes. The model was validated by comparing empirical and simulated sward‐height distributions and semi‐variograms. Results: The model discriminated between grazed and ungrazed patches at both a fine (1 m²) and a larger (500 m²) scale. Selective grazing on legumes and forbs and avoidance of reproductive grass could partly explain the stability of fine‐scale grazing patterns in lightly grazed plots. In these plots, the model revealed an inter‐annual stability of large‐scale grazing patterns at the time peak biomass occurred. At the end of the grazing season, lightly grazed plots showed fluctuating patch boundaries while heavily grazed plots showed a certain degree of patch stability. Conclusion: The model presented here reveals that selective grazing at the bite scale could lead to the creation of relatively stable patches within the pasture. Locally maintaining short cover heights would result in divergent within‐plot vegetation dynamics, and thus favor the functional diversity of vegetation.     

Models of vegetation dynamics in semi-arid vegetation: Application to lowland Central Otago, New Zealand

Predictions from three conceptual models of the dynamics of semi-arid vegetation (Clementsian succession, alternative stable states and annuation/pulse phenomena) are used to review the available evidence on changes in the vegetation of semi- arid lowland Central Otago, New Zealand. Evidence is presented from Central Otago that corresponds with Clementsian succession and with annuation/pulse phenomena, although there is so far no formal evidence of alternative stable states. A declining- productivity model, which combines aspects of the other models, is also shown to fit the process of vegetation change in vegetation dynamics in Central Otago are insufficient for the employment of management frameworks such as degradation gradient assessment and the state-and-transition model.     

Effects of Quercus emoryi on herbaceous vegetation in a semi-arid savanna

Ten trees (5–70 m² canopy area) were selected to determine effects of tree size (crown area) on herbaceous species composition and biomass in a Quercus emoryi savanna in southeastern Arizona. Consistent with most studies in temperate savannas, herbaceous biomass was reduced beneath the canopy relative to grassland areas. However, tree size appeared to exert no influence over herbaceous biomass. In contrast to most temperate savannas, Q. emoryi trees did not affect distribution of herbaceous species.