Vegetation pattern formation in a fog-dependent ecosystem

Vegetation pattern formation is a striking characteristic of several water-limited ecosystems around the world. Typically, they have been described on runoff-based ecosystems emphasizing local interactions between water, biomass interception, growth and dispersal. Here, we show that this situation is by no means general, as banded patterns in vegetation can emerge in areas without rainfall and in plants without functional root (the Bromeliad Tillandsia landbeckii) and where fog is the principal source of moisture. We show that a simple model based on the advection of fog-water by wind and its interception by the vegetation can reproduce banded patterns which agree with empirical patterns observed in the Coastal Atacama Desert. Our model predicts how the parameters may affect the conditions to form the banded pattern, showing a transition from a uniform vegetated state, at high water input or terrain slope to a desert state throughout intermediate banded states. Moreover, the model predicts that the pattern wavelength is a decreasing non-linear function of fog-water input and slope, and an increasing function of plant loss and fog-water flow speed. Finally, we show that the vegetation density is increased by the formation of the regular pattern compared to the density expected by the spatially homogeneous model emphasizing the importance of self-organization in arid ecosystems.     

Intraspecific competition in models for vegetation patterns: Decrease in resilience to aridity and facilitation of species coexistence

Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high biomass and patches of bare soil. Nevertheless, intraspecific competition dynamics other than competition for water over long spatial scales are commonly ignored in mathematical models for vegetation patterns. In this paper, I address the impact of local intraspecific competition on a modelling framework for banded vegetation patterns. Firstly, I show that in the context of a single-species model, neglecting local intraspecific competition leads to an overestimation of a patterned ecosystem’s resilience to increases in aridity. Secondly, in the context of a multispecies model, I argue that local intraspecific competition is a key element in the successful capture of species coexistence in model solutions representing a vegetation pattern. For both models, a detailed bifurcation analysis is presented to analyse the onset, existence and stability of patterns. Besides the strengths of local intraspecific competition, also the difference between two species has a significant impact on the bifurcation structure, providing crucial insights into the complex ecosystem dynamics. Predictions on future ecosystem dynamics presented in this paper, especially on pattern onset and pattern stability, can aid the development of conservation programs.     

Numerical investigation of spatial pattern in a vegetation model with feedback function

The vegetative cover in semi-arid lands typically occurs as patches of individual species more or less separated from one another by bare ground. Klausmeier [1999. Regular and irregular patterns in semiarid vegetation. Science 284 (5421), 1826-1828] reported that the vegetation striped patterns can grow lying along the contours of gentle slopes. He has proposed a model of vegetation stripes based on competition for water. In this paper, our main aim is to study the positive feedback effects between the water and biomass on the vegetation spatial pattern formation within a nonsaturated soil, which arises from the suction of water by the roots and processes of water resource redistribution. According to the dispersion relation formula, we discuss the changes of the wavelength, wave speed, as well as the conditions of the spatial pattern formation. Our numerical results show that trees are more sensitive than grasses to the positive feedback function to format the spatial heterogenous pattern, and the stronger positive feedback increases the parameters region where vegetation bands occur, which indicates that the positive feedback raises the possibility of shift from green to desert states in semi-arid areas for the long term. Our numerical results also show that the positive feedback can increase the migration velocity of the vegetation stripes.     

Nonlinear pattern selection in a mechanical model for morphogenesis

We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.     

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.      

Beyond Turing: The response of patterned ecosystems to environmental change

Spatially periodic patterns can be observed in a variety of ecosystems. Model studies revealed that patterned ecosystems may respond in a nonlinear way to environmental change, meaning that gradual changes result in rapid degradation. We analyze this response through stability analysis of patterned states of an arid ecosystem model. This analysis goes one step further than the frequently applied Turing analysis, which only considers stability of uniform states. We found that patterned arid ecosystems systematically respond in two ways to changes in rainfall: (1) by changing vegetation patch biomass or (2) by adapting pattern wavelength. Minor adaptations of pattern wavelength are constrained to conditions of slow change within a high rainfall regime, and high levels of stochastic variation in biomass (noise). Major changes in pattern wavelength occur under conditions of either low rainfall, rapid change or low levels of noise. Such conditions facilitate strong interactions between vegetation patches, which can trigger a sudden loss of half the patches or a transition to a degraded bare state. These results highlight that ecosystem responses may critically depend on rates, rather than magnitudes, of environmental change. Our study shows how models can increase our understanding of these dynamics, provided that analyses go beyond the conventional Turing analysis.     

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.     

Vegetation patterns generated by a wind driven sand-vegetation system in arid and semi-arid areas

Wind has been proposed as a driving factor in determining vegetation patterns, but there are few dynamic models that include both vegetation and wind. In this paper, we present a dynamic model to investigate how a vegetation pattern is generated and affected by wind. In the model, the effects of prevailing wind and non-prevailing wind on sand and vegetation are modeled respectively as advection terms and diffusion terms. With these considerations and proper parameter values that satisfy Turing bifurcation conditions, labyrinth and banded vegetation patterns are obtained in two situations of wind. By changing wind transportation capacity, we simulate the adaptation process from one vegetation pattern to another. With environmental changes of large amplitude, the width of vegetation bands varies while the wavelength can increase but does not decrease in our simulation. Then we describe the difference between simulated patterns and real patterns. And in the discussion, we explain the mechanism that forming patterns and the consistency of this research with other studies.     

A putative mechanism for bog patterning

The surface of bogs commonly shows various spatial vegetation patterning. Typical are "string patterns" consisting of regular densely vegetated bands oriented perpendicular to the slope. Here, we report on regular "maze patterns" on flat ground, consisting of bands densely vegetated by vascular plants in a more sparsely vegetated matrix of nonvascular plant communities. We present a model reproducing these maze and string patterns, describing how nutrient-limited vascular plants are controlled by, and in turn control, both hydrology and solute transport. We propose that the patterns are self-organized and originate from a nutrient accumulation mechanism. In the model, this is caused by the convective transport of nutrients in the groundwater toward areas with higher vascular plant biomass, driven by differences in transpiration rate. In a numerical bifurcation analysis we show how the maze patterns originate from the spatially homogeneous equilibrium and how this is affected by changes in rainfall, nutrient input, and plant properties. Our results confirm earlier model results, showing that redistribution of a limiting resource may lead to fine-scale facilitative and coarse-scale competitive plant interactions in different ecosystems. Self-organization in ecosystems may be a more general phenomenon than previously thought, which can be mechanistically linked to scale-dependent facilitation and competition.     

广东省2004-2016年植被冠层降雨截留模拟及时空变化特征

评价植被冠层降雨截留能力,是生态系统水循环的重要研究内容。以广东省中小流域为例,结合地面监测站点的降雨量数据和MODIS叶面积指数遥感数据,利用植被冠层降雨截留模型,定量模拟和分析了广东省流域尺度2004-2016年的地表植被冠层降雨截留能力及其时空变化特征。结果表明：（1）2004-2012年广东省年均植被冠层降雨截留率持续下降,2016年略有上升,并且随着时间的推移,流域之间的植被冠层降雨截留率差异越来越小。（2）广东省植被冠层降雨截留能力呈现山区东西两翼高,山区中部以及沿海地区低的显著空间差异格局,这种空间格局与植被覆盖LAI主要呈现由珠三角向外围递增的圈层空间格局特征密切相关,而与由南向北逐渐递减的降雨空间格局特征相关性不大。（3）森林覆盖对流域植被冠层降雨截留能力有着一定的影响,其中流域内阔叶林占森林面积的比例对这种影响的程度起着最为关键的作用。     

Short‐term propagation of rainfall perturbations on terrestrial ecosystems in central California

Question: Does vegetation buffer or amplify rainfall perturbations, and is it possible to forecast rainfall using mesoscale climatic signals? Location: Central California (USA). Methods: The risk of dry or wet rainfall events was evaluated using conditional probabilities of rainfall depending on El Niño Southern Oscillation (ENSO) events. The propagation of rainfall perturbations on vegetation was calculated using cross‐correlations between monthly seasonally adjusted (SA) normalized difference vegetation index (NDVI) from the Advanced Very High Resolution Radiometer (AVHRR), and SA antecedent rainfall at different time‐scales. Results: In this region, El Niño events are associated with higher than normal winter precipitation (probability of 73%). Opposite but more predictable effects are found for La Niña events (89% probability of dry events). Chaparral and evergreen forests showed the longest persistence of rainfall effects (0‐8 months). Grasslands and wetlands showed low persistence (0‐2 months), with wetlands dominated by non‐stationary patterns. Within the region, the NDVI spatial patterns associated with higher (lower) rainfall are homogeneous (heterogeneous), with the exception of evergreen forests. Conclusions: Knowledge of the time‐scale of lagged effects of the non‐seasonal component of rainfall on vegetation greenness, and the risk of winter rainfall anomalies lays the foundation for developing a forecasting model for vegetation greenness. Our results also suggest greater competitive advantage for perennial vegetation in response to potential rainfall increases in the region associated with climate change predictions, provided that the soil allows storing extra rainfall.     

Vegetation change in semiarid communities

In arid regions, the effects of grazing or sparing management on natural communities of long-lived plants generally take decades to become evident. Event-driven dynamic behavior, unpredictable and low rainfall and complicated interactions between species make it difficult to assess probabilities and time scales of vegetation change.To gain a better understanding of the main processes and mechanisms involved in vegetation change, we have developed a spatially explicit individual based model that simulates changes in plant communities over long time spans. The model, based on life-history attributes of the five dominant component plant species of a typical Karoo shrub community, follows the fate of each individual plant within the community, the sum of which is community dynamics. The model explores the differential effects of a realistic range of rainfall pattern on the abilities of these species to compete, survive, grow and reproduce.The specific aim of the model is to identify key processes of vegetation change and to calculate probabilities and timespans for transitions between different vegetation states. Such knowledge is needed for species conservation and sustained animal production.We show that the time-scale for changes of the dynamic state of the system are long compared with human lifespans. Employing the full range of possible rainfall scenarios showed that short-term community dynamics (years to decades) and species composition depend strongly on the short-term (years) sequence of rainfall events. In all simulation experiments the final vegetation state varied by more than 37% after a 60 year simulation period. Simulating resting of an overgrazed part of the shrub community indicated that little improvement in rangland condition was likely during a period of 60 years. Even such active management, as (simulated) clearing of unpalatable shrubs, resulted in only a 66% probability that degraded shrubland would be in good condition after 60 years resting. Simulated overgrazing of a rangeland in good initial condition only became obvious 40 or 50 years after the initiation of heavy grazing, and after 70 years the mean vegetation state eventually reached that of an overgrazed rangeland.     

A model for colour pattern formation in the butterfly wing of Papilio dardanus

The butterfly Papilio dardanus is well known for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a geometrically accurate wing domain produce spatial patterns that are consistent with many of those observed on the butterfly. Our results suggest that the wing coloration is due to a simple underlying stripe-like pattern of some pigment-inducing morphogen. We focus on the effect of key factors such as parameter values for mode selection, threshold values which determine colour, wing shape and boundary conditions. The generality of our approach should allow us to investigate other butterfly species. The relationship between these key factors and gene activities is discussed in the context of recent biological advances.     

Mode-doubling and tripling in reaction-diffusion patterns on growing domains: A piecewise linear model

 Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system. Received: 19 December 2000 / Revised version: 24 May 2001 / Published online: 7 December 2001     

Rainfall and habitat interact to affect the condition of a wintering migratory songbird in The Bahamas

On the subtropical and tropical wintering grounds of migratory birds, variation in moisture levels and habitat can influence the availability of food resources and subsequently impact overwintering birds. Using stable carbon isotopes in blood samples as a measure of moisture, we assessed the interactive effects of rainfall, vegetation, and moisture on the demographics and condition of Prairie Warblers (Setophaga discolor) wintering in The Bahamas. Carbon isotopes in Prairie Warbler blood were more depleted in taller, wetter habitats; we additionally detected novel temporal effects of rainfall on isotope values. During a winter with more rainfall, most birds maintained mass and pectoral muscle regardless of the habitat type occupied. In a winter with less rainfall, birds lost mass and pectoral muscle, and this effect was more pronounced in birds with enriched isotope values and birds that occupied drier, shorter habitat. Prairie Warblers exhibited strong patterns of sexual habitat segregation with males disproportionately observed in areas with taller vegetation and females in shorter vegetation. During the drier winter, older males had better maintenance of pectoral muscle compared to females and younger individuals. Also in the drier winter, daily rainfall patterns explained more of the variation in body condition compared to the date of capture; pectoral muscle was best explained by recent precipitation (during the previous 30 days), while size‐corrected mass was more a function of longer‐term (90‐day) rainfall and habitat moisture. Our findings along with other studies suggest that Prairie Warblers and other migratory birds are sensitive to interactions between annual variation in winter rainfall, within‐season daily rainfall patterns, and habitat quality. Increasing drought and habitat loss in the Caribbean may be having a negative impact on wintering bird populations. To best conserve Nearctic–Neotropical migratory passerines in the region, we recommend prioritizing the protection of the least drought‐prone wintering areas.     

植被与水土流失关系研究进展

水土流失是世界性的环境问题之一,对人类社会可持续发展构成威胁,控制水土流失成为迫切需要,有许多水土流失控制措施,而生物措施尤其植被一直是人们研究的焦点.根据前人的研究,从斑块、坡面和流域/区域尺度总结了植被与水土流失的关系.斑块尺度植被对降雨和径流侵蚀能量具有很大的减弱或消除作用,可以改变植株底部的土壤性质,改善其结构,进而降低土壤可蚀性,增加入渗能力,从而减轻土壤侵蚀程度.不同植被类型、植被的不同层次结构,不同植被的形态结构具有不同的土壤侵蚀控制作用.坡面尺度主要从坡位、坡度、坡向对植被生长和分布格局的影响、对水土流失过程和格局的影响以及裸地-植被镶嵌格局、植被的条带格局对水土流失的影响和反映水土流失过程的景观格局指数的构建等方面进行了研究.更多是从植被恢复及其水土流失效应方面进行了探讨,为退化生态系统恢复和格局设计提供了极其有用的信息.流域/区域尺度植被与水土流失的关系更大程度上受到气候、地貌特征的影响,因此研究多从一定气候条件控制的土地覆盖（植被覆盖）及其格局的水土流失效应方面进行的.由于大尺度监测非常困难,研究多从遥感监测、GIS集成和模型模拟方面开展,是流域、区域等大尺度生态安全格局设计的有力支持.前人的研究为生态环境建设和保护提供了大量参考信息,但仍有一些问题需要进一步探讨,对此进行了初步的概括和归纳,希望能够对植被和水土流失关系的研究起到一定促进作用.     

A collocation approach to the numerical calculation of simple gradients in reaction-diffusion systems

Reaction diffusion equations are frequently used to model pattern formation problems in biology, but numerical experiments in two or three space dimensions can be expensive in computing time. We show that the spectral method with collocation is a particularly efficient method for the numerical study of the evolution of simple patterns in such models. In many cases of interest, the scheme is sufficiently simple and efficient for calculations to be carried out on a micro-computer.     

Environmental and anthropogenic determinants of vegetation distribution across Africa

Aim To assess the influence of natural environmental factors and historic and current anthropogenic processes as determinants of vegetation distributions at a continental scale. Location Africa. Methods Boosted regression trees (BRTs) were used to model the distribution of African vegetation types, represented by remote‐sensing‐based land‐cover (LC) types, as a function of environmental factors. The contribution of each predictor variable to the best models and the accuracy of all models were assessed. Subsequently, to test for anthropogenic vegetation transformation, the relationship between the number of BRT false presences per grid cell and human impact was evaluated using hurdle models. Finally, the relative contributions of environmental, current and historic anthropogenic factors on vegetation distribution were assessed using regression‐based variation partitioning. Results Deserts and evergreen forests were best predicted by environmental variables, though most other LC classes were also relatively well predicted by the environment. Annual precipitation emerged as the most important determinant of all LC classes. At low rainfall levels, LC classes with increasing woody cover replaced each other as rainfall increased, while LC class rainfall optima overlapped at high rainfall levels. With some exceptions, anthropogenic factors had a relatively small influence on the distribution of most LC classes. However, anthropogenic factors did have an influence on the inaccuracies in BRT models, and these models provided an indication of which LC classes have been most reduced by transformation. Main conclusions Here we show, for the first time, how environmental and anthropogenic factors influence vegetation distribution across Africa. LC classes at rainfall extremes are best predicted by the environment. In addition, we corroborate, also for the first time, the much‐stated claim that rainfall is the most important variable for the distribution of African vegetation for all African vegetation types. Finally, we indicate how anthropogenic drivers affect LC distributions.     

Rainfall manipulation experiments as simulated by terrestrial biosphere models: Where do we stand?

Changes in rainfall amounts and patterns have been observed and are expected to continue in the near future with potentially significant ecological and societal consequences. Modelling vegetation responses to changes in rainfall is thus crucial to project water and carbon cycles in the future. In this study, we present the results of a new model‐data intercomparison project, where we tested the ability of 10 terrestrial biosphere models to reproduce the observed sensitivity of ecosystem productivity to rainfall changes at 10 sites across the globe, in nine of which, rainfall exclusion and/or irrigation experiments had been performed. The key results are as follows: (a) Inter‐model variation is generally large and model agreement varies with timescales. In severely water‐limited sites, models only agree on the interannual variability of evapotranspiration and to a smaller extent on gross primary productivity. In more mesic sites, model agreement for both water and carbon fluxes is typically higher on fine (daily–monthly) timescales and reduces on longer (seasonal–annual) scales. (b) Models on average overestimate the relationship between ecosystem productivity and mean rainfall amounts across sites (in space) and have a low capacity in reproducing the temporal (interannual) sensitivity of vegetation productivity to annual rainfall at a given site, even though observation uncertainty is comparable to inter‐model variability. (c) Most models reproduced the sign of the observed patterns in productivity changes in rainfall manipulation experiments but had a low capacity in reproducing the observed magnitude of productivity changes. Models better reproduced the observed productivity responses due to rainfall exclusion than addition. (d) All models attribute ecosystem productivity changes to the intensity of vegetation stress and peak leaf area, whereas the impact of the change in growing season length is negligible. The relative contribution of the peak leaf area and vegetation stress intensity was highly variable among models.     

Factors influencing the distributional abundance of two trophic guilds of Peruvian cricetid rodents

The distributional abundance of 13 species of southern Peruvian rodents is significantly correlated with altitude and patterns of vegetation but vegetation is a better predictor than altitude. Coincidental reversals in the altitudinal trends of both vegetation and rodents demonstrate that rodents are responding to vegetation patterns. Abundance and diversity of rodents are greatest around 4000 m elevation which coincides with the region of greatest vegetational abundance and seasonally heavy rainfall.
The rodent communities consist of two separate feeding guilds, omnivores and insectivores and these guilds show distinctly different distributional patterns. Insectivorous species are strongly associated with the zone of seasonally heavy rainfall (4000 m) whereas omnivorous rodents are relatively abundant over a broader spectrum of elevations and habitats. In a previous study of these same communities, we showed a correspondence between rodent morphology and their diets. This study reveals a correspondence between distributional abundance of the various species and their diets. We conclude that the distributional abundance of southern Peruvian rodents is related to the physiological constraints imposed by altitude (climate) and the distributional abundance of food resources.