Does scale‐dependent feedback explain spatial complexity in salt‐marsh ecosystems?

Complexity theory highlights scale-dependent feedback mechanisms as an explanation for regular spatial patterning in ecosystems. To what extent scale-dependent feedback clarifies spatial structure in more complex, non-regular systems remains unexplored so far. We report on a scale-dependent feedback process generating patchy landscapes at the interface of intertidal flats and salt marshes. Here, vegetation was characterized by Spartina anglica tussocks, surrounded by erosion gullies. To demonstrate the presence of a scale-dependent feedback, we determined if vegetation induced habitat modification resulted in local facilitation and large scale-inhibition of plant growth. Field surveys revealed that larger tussocks have deeper gullies, suggesting that gully erosion is caused by increased water flow around tussocks. This was confirmed by flume experiments, showing that feedback effects vary with current velocity and water depth. Transplantation of small Spartina units inside and just outside present tussocks revealed that the growth of Spartina transplants compared to transplant growth on bare sediment was higher within the raised Spartina tussocks, but lower in the gully just outside Spartina tussocks, providing clear evidence of scale-dependent feedback. Our results emphasize that scale-dependent feedback is a more general explanation for spatial complexity in ecosystems than previously considered.     

Scale-dependent feedback and regular spatial patterns in young mussel beds

In the past decade, theoretical ecologists have emphasized that local interactions between predators and prey may invoke emergent spatial patterning at larger spatial scales. However, empirical evidence for the occurrence of emergent spatial patterning is scarce, which questions the relevance of the proposed mechanisms to ecological theory. We report on regular spatial patterns in young mussel beds on soft sediments in the Wadden Sea. We propose that scale-dependent feedback, resulting from short-range facilitation by mutual protection from waves and currents and long-range competition for algae, induces spatial self-organization, thereby providing a possible explanation for the observed patterning. The emergent self-organization affects the functioning of mussel bed ecosystems by enhancing productivity and resilience against disturbance. Moreover, self-organization allows mussels to persist at algal concentrations that would not permit survival of mussels in a homogeneous bed. Our results emphasize the importance of self-organization in affecting the emergent properties of natural systems at larger spatial scales.     

Exploring stable pattern formation in models of tussock moth populations

1. The western tussock moth ( Orgyia vetusta ) at the University of California Bodega Marine Reserve (Sonoma County, California, USA) exhibits dense, localized populations in the midst of extensive habitats where variation in host plant quality or predator abundance is unable to explain the restricted extent of the outbreaks.
2. Two primary features suggest that the host patterning is intrinsically generated: (i) female tussock moths are wingless, producing a low effective dispersal distance for the hosts; and (ii) the tussock moth population is attacked by several species of widely dispersing wasp and fly parasitoids.
3. We consider a set of spatially explicit host–parasitoid models to examine whether intrinsically generated patterns are possible within this system. These models include a spatially extended Nicholson–Bailey model to examine general features of pattern formation in host–parasitoid systems, and two system-specific models, an individual-based simulation and a population-level analytic model, to examine the details of this empirical system.
4. Both stable patterning and rapid extinction of the host population are initial-condition dependent outcomes of the general and specific models, implying that an intrinsically generated stable host pattern is feasible within the tussock moth system.
5. Stable patterning is enhanced by a large parasitoid-to-host dispersal ratio, local host resource limitation, and increased parasitism at the host patch's edge.     

Regular pattern formation in real ecosystems

Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer-resource interactions, localized disturbance-recovery processes and scale-dependent feedback. Despite abundant theoretical literature, studies revealing spatial self-organization in real ecosystems are limited. Recently, however, many examples of regular pattern formation have been discovered, supporting the importance of scale-dependent feedback. Here, we review these studies, showing regular pattern formation to be a general phenomenon rather than a peculiarity. We provide a conceptual framework explaining how scale-dependent feedback determines regular pattern formation in ecosystems. More empirical studies are needed to better understand regular pattern formation in ecosystems, and how this affects the response of ecosystems to global environmental change.     

林冠结构是局域尺度木本植物功能性状beta多样性形成的重要驱动力

功能性状beta多样性反映了群落间功能性状组成的差异, 解析其形成机制是群落生态学研究的核心内容之一。本研究以云南西双版纳热带季节雨林20 ha动态监测样地为研究对象, 测定木本植物11个重要的功能性状, 采用多度加权的平均最近邻体性状距离度量不同取样尺度的功能性状beta多样性, 基于距离矩阵的多元回归方法解析林冠结构差异、环境异质性、空间距离在功能性状beta多样性格局形成中的相对作用。结果表明, 对于所有木本植物个体(DBH ≥ 1 cm)而言, 同时考虑林冠结构、环境和空间距离的模型为解释功能性状beta多样性格局的最优模型; 在3个不同取样尺度上, 林冠结构差异和环境距离都对功能性状beta多样性具有较大的解释力, 且随着取样尺度的增大而上升, 空间距离的作用基本可以忽略。本研究证实了林冠结构是局域尺度木本植物功能性状beta多样性格局形成的重要驱动力, 这一发现更新了环境异质性和空间距离是驱动功能性状beta多样性格局形成的主要因素的传统认知, 为将来研究功能性状beta多样性形成机制提供新的视角, 并证实了取样尺度在解析木本植物功能性状beta多样性格局形成机制中的重要性。     

Landscape as a model: the importance of geometry

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking.     

The spatial scaling of habitat selection by African elephants

1. Understanding and accurately predicting the spatial patterns of habitat use by organisms is important for ecological research, biodiversity conservation and ecosystem management. However, this understanding is complicated by the effects of spatial scale, because the scale of analysis affects the quantification of species-environment relationships. 2. We therefore assessed the influence of environmental context (i.e. the characteristics of the landscape surrounding a site), varied over a large range of scales (i.e. ambit radii around focal sites), on the analysis and prediction of habitat selection by African elephants in Kruger National Park, South Africa. 3. We focused on the spatial scaling of the elephants' response to their main resources, forage and water, and found that the quantification of habitat selection strongly depended on the scales at which environmental context was considered. Moreover, the inclusion of environmental context at characteristic scales (i.e. those at which habitat selectivity was maximized) increased the predictive capacity of habitat suitability models. 4. The elephants responded to their environment in a scale-dependent and perhaps hierarchical manner, with forage characteristics driving habitat selection at coarse spatial scales, and surface water at fine spatial scales. 5. Furthermore, the elephants exhibited sexual habitat segregation, mainly in relation to vegetation characteristics. Male elephants preferred areas with high tree cover and low herbaceous biomass, whereas this pattern was reversed for female elephants. 6. We show that the spatial distribution of elephants can be better understood and predicted when scale-dependent species-environment relationships are explicitly considered. This demonstrates the importance of considering the influence of spatial scale on the analysis of spatial patterning in ecological phenomena.     

Spatially explicit models of divergence and genome hitchhiking

Strong barriers to genetic exchange can exist at divergently selected loci, whereas alleles at neutral loci flow more readily between populations, thus impeding divergence and speciation in the face of gene flow. However, ‘divergence hitchhiking’ theory posits that divergent selection can generate large regions of differentiation around selected loci. ‘Genome hitchhiking’ theory suggests that selection can also cause reductions in average genome‐wide rates of gene flow, resulting in widespread genomic divergence (rather than divergence only around specific selected loci). Spatial heterogeneity is ubiquitous in nature, yet previous models of genetic barriers to gene flow have explored limited combinations of spatial and selective scenarios. Using simulations of secondary contact of populations, we explore barriers to gene flow in various selective and spatial contexts in continuous, two‐dimensional, spatially explicit environments. In general, the effects of hitchhiking are strongest in environments with regular spatial patterning of starkly divergent habitat types. When divergent selection is very strong, the absence of intermediate habitat types increases the effects of hitchhiking. However, when selection is moderate or weak, regular (vs. random) spatial arrangement of habitat types becomes more important than the presence of intermediate habitats per se. We also document counterintuitive processes arising from the stochastic interplay between selection, gene flow and drift. Our results indicate that generalization of results from two‐deme models requires caution and increase understanding of the genomic and geographic basis of population divergence.     

Spatial structure maintains diversity of pyocin inhibition in household Pseudomonas aeruginosa

Nearly all bacteria produce narrow-spectrum antibiotics called bacteriocins. Studies have shown that bacteriocins can mediate microbial interactions, but the mechanisms underlying patterns of inhibition are less well understood. We assembled a spatially structured collection of isolates of Pseudomonas aeruginosa from bathroom and kitchen sink drains in nine households. Growth inhibition of these P. aeruginosa by bacteriocins, known as pyocins in this species, was measured using pairwise inhibition assays. Carbon source usage of these isolates was measured, and genetic distance was estimated using multilocus sequencing. We found that as the distance between sites of isolation increased, there was a significantly higher probability of inhibition, and that pyocin inhibition and susceptibility vary greatly among isolates collected from different houses. We also detected support for other mechanisms influencing diversity: inhibition outcomes were influenced by the type of drain from which isolates were collected, and while we found no indication that carbon source utilization influences inhibition, inhibition was favoured at an intermediate genetic distance. Overall, these results suggest that the combined effects of dispersal limitation among sites and competitive exclusion within them maintain diversity in pyocin inhibition and susceptibility phenotypes, and that additional processes such as local adaptation and effects of phylogenetic distance could further contribute to spatial variability.     

Spatial scaling and transition in pneumatophore arthropod communities

Although most ecological variables are scale-dependent, few studies cover a broad range of spatial scales. Here, we consider South African mangrove pneumatophore arthropod communities (mites, crustaceans and insects), across seven spatial scales (from 10  cm to 100  km). We plot spatial autocorrelation in individual species, evaluate if resource and habitat availability determine spatial patterning, and identify the scales of community transition. Spatial autocorrelation in most ecological variables decreased with increasing spatial scale, with notable exceptions for the larger scales. Negative abundance autocorrelation was stronger at 10  km than at 100  km for common species, while the opposite was true for rare species. Spatial autocorrelation in species richness decreased from 1  m (strong positive) to 10  km (strong negative), but was not significant at the 100  km scale. These patterns reflect the patchy distribution of pneumatophores within mangrove forests, that of the forests along the coast, and the poor dispersal abilities of most of the arthropods sampled, in a highly dynamic environment. Although resource and habitat availability exhibited a similar autocorrelation pattern to that of the community, the total mass of pneumatophores did not appear to be an important determinant of community structure. Variations in the abundance of common species, as well as the restricted distribution of rare species caused assemblage structure to change gradually with increasing distance from 10 cm to 100 km, but only marginally from 10 to 100  km. We highlight the need for cross-scale studies in bridging the gap between two key ecological concepts: potential ecological niche and realized geographic range.     

Regular mosaic pattern development: A study of the interplay between lateral inhibition, apoptosis and differential adhesion

Background

A significant body of literature is devoted to modeling developmental mechanisms that create patterns within groups of initially equivalent embryonic cells. Although it is clear that these mechanisms do not function in isolation, the timing of and interactions between these mechanisms during embryogenesis is not well known. In this work, a computational approach was taken to understand how lateral inhibition, differential adhesion and programmed cell death can interact to create a mosaic pattern of biologically realistic primary and secondary cells, such as that formed by sensory (primary) and supporting (secondary) cells of the developing chick inner ear epithelium.

Results

Four different models that interlaced cellular patterning mechanisms in a variety of ways were examined and their output compared to the mosaic of sensory and supporting cells that develops in the chick inner ear sensory epithelium. The results show that: 1) no single patterning mechanism can create a 2-dimensional mosaic pattern of the regularity seen in the chick inner ear; 2) cell death was essential to generate the most regular mosaics, even through extensive cell death has not been reported for the developing basilar papilla; 3) a model that includes an iterative loop of lateral inhibition, programmed cell death and cell rearrangements driven by differential adhesion created mosaics of primary and secondary cells that are more regular than the basilar papilla; 4) this same model was much more robust to changes in homo- and heterotypic cell-cell adhesive differences than models that considered either fewer patterning mechanisms or single rather than iterative use of each mechanism.

Conclusion

Patterning the embryo requires collaboration between multiple mechanisms that operate iteratively. Interlacing these mechanisms into feedback loops not only refines the output patterns, but also increases the robustness of patterning to varying initial cell states.     

林分光照空间异质性对水曲柳更新的影响

 光照是森林更新动态中极为关键的环境因子。本研究在东北天然次生林中选择样地,应用地统计学理论结合实验生态学方法,定量分析林分光照空间异质性特征,同时进行林下播种水曲柳（Fraxinus mandshurica）的更新实验,探测更新格局特征。通过空间关联性分析,研究探讨是否林分光照的空间变异对水曲柳更新有重要影响作用。研究结果表明： 1）生长季林分平均光照仅为全光照的4.2%～4.6%,在空间分布上呈现非常明显的异质性特征,空间自相关变异（62.5%～78.2%）主要体现在10.9～12.4 m的尺度上。2）林分光照不同的空间样点上,水曲柳更新幼苗发生数量和秋季幼苗存活数量均存在显著差异,光照相对强的微生境中,更新苗发生数量较多且存活率高,而在光照较弱的微生境中则更新较差,更新具有十分明显的空间格局。3）更新格局与林分光照空间异质性特征紧密关联。在光照空间异质性程度较高、空间变异较复杂的条件下,更新相应呈现出较复杂的空间格局,自相关的变异表现在较小尺度范围（2.12～6.97 m）。在光照空间异质性程度较低、空间变异复杂性较小的条件下,更新格局的复杂程度明显变小,空间自相关变异（>83%）表现在较大的尺度上（30 m）,对更新格局起主要的影响作用,随机变异的影响很小（<17%）。这些研究结果说明,林分光照环境在水曲柳更新中的作用十分关键,林分光照的空间异质性对更新格局起决定性作用。     

Edaphic patchiness influences grassland regeneration from the soil seed‐bank in mountain grasslands of central Argentina

The soil seed‐banks in the main natural vegetation patches that make up mountain grasslands on granite substrates in central Argentina were studied. The main natural vegetation types are moist swards, tall‐tussock grasslands and stony grasslands. Ten compound soil samples from each community at two soil depths (0–5 and 5–10 cm) were taken. The density of soil seed‐banks was highest in moist swards, intermediate in stony grasslands and lowest in tall‐tussock grasslands. Low levels of similarity were found between the established vegetation and total soil seed‐bank in tall‐tussock grasslands and stony grasslands, but the similarity was higher in swards. In all three communities the seed‐bank was most frequently transient in nature. Short‐term persistent and long‐term persistent seed‐banks were less frequent. Regeneration from the seed‐banks after disturbance is expected to differ among communities on different edaphic patches. On the basis of the density and longevity of the soil seed‐banks and the similarity to the established vegetation, potential for in situ regeneration should be lower in tall‐tussock grasslands, intermediate in stony grasslands and higher in moist swards.     

Implications of self/non-self discrimination for spatial patterning of clonal plants

Many clonal plants are characterised by tussock growth forms, but the mechanisms that account for their formation and maintenance are still vague. Here we examine the possible effects of the recently identified phenomenon of self/non-self discrimination on the spatial distribution and patterning of ramets, tussocks and clones in stands of clonal plants. Spatially explicit ramet-based simulation modeling of growth and competition have shown that compact tussocks can be generated as a transient phenomenon that typically disappears at equilibrium. We introduced self/non-self discrimination into a spatial model by decreasing competition between neighbouring ramets on the same clonal fragment. The results demonstrate that self/non-self discrimination can have significant effects on clonal growth and architecture with a clear tendency to generate long-lasting and self-sustaining clumps. Interestingly, this effect was qualitatively independent of other architectural and growth attributes of the plants, making it a candidate mechanism of stable clumped growth forms observed in many clonal plants and communities. Furthermore, the introduction of self/non-self discrimination shifted competition from the level of ramets to that of clonal fragments, which in turns strongly increased genet extinction rates. Our results stress the need for greater attention to the rather neglected scaling up of physiological and morphogenetical controls to the population and community levels.     

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.     

整体大于部分之和: 生态自组织斑图及其涌现属性

近30年来, 自组织理论已经发展成为解释生态系统呈现规则空间格局的有效理论。伴随着生态系统自发有序空间格局的生成, 自组织过程产生一系列的涌现属性, 这些特征对生态系统功能至关重要。在此, 我们将介绍这一正蓬勃发展的研究领域的主要理论进展。首先, 叙述了自组织这一概念的发展历程与定义, 详细阐述了自组织理论的两个经典理论框架: 图灵原理与相分离原理。然后, 根据几个典型的生态自组织研究案例, 描述了图灵原理与相分离原理在不同生态系统中的具体数学模型表达形式。接着, 分别阐述了图灵原理的涌现属性对生态系统功能以及相分离原理的涌现属性对细胞功能的作用。最后, 从多尺度自组织斑图、瞬态斑图和生物个体行为自组织3个方面对未来生态自组织理论发展方向进行了探讨。自组织研究在生态学与生物学研究中方兴未艾, 希望更多的学者在未来关注与参与该领域的发展。     

The distance decay of similarity in ecological communities

Biological similartiy typically decreases with geographical distance. Despite the recent attention to the distance decay relationship, there is no consensus on how the relationship varies across organism groups, geographic gradients and environments. We first conducted a quantitative meta-analysis of 401 distance decay relationships across a wide range of organisms, ecosystems and geographical gradients, and then united the effects of categorical and continuous variables on the rate of distance decay using a general linear model (GLM). As effect sizes we used the similarity at one km distance (initial similarity) and the distance that halves the similarity from its value at one km distance (halving distance). Both the initial similarity and halving distance were significantly affected by variables characterizing the spatial scale, organism properties, study region and ecosystem concerned. The patterns appear robust as the results of meta-analysis and GLM only differed in marginal details. According to GLM with Akaike's information criterion, the most parsimonious models explained 55.3 and 37.6% of variance in initial similarity and halving distance, respectively. Across large scales, similarity was decreasing slightly faster at high latitudes than at low latitudes, while small-scale turnover was higher at low latitudes. We also found significant differences in initial similarity among the realms, with terrestrial systems showing higher small-scale beta diversity. The decrease in community similarity at large scales was higher among organisms that are actively mobile than among passively dispersed organisms. We conclude that regression of similarity against distance unites several ecological phenomena such as dispersal propensity and environmental structuring, and provides an effective approach for gauging the spatial turnover across sites. We also found that the patterns in beta-diversity are highly scale-dependent.     

Linking habitat modification to catastrophic shifts and vegetation patterns in bogs

Paleoecological studies indicate that peatland ecosystems may exhibit bistability. This would mean that these systems are resilient to gradual changes in climate, until environmental thresholds are passed. Then, ecosystem stability is lost and rapid shifts in surface and vegetation structure at landscape scale occur. Another remarkable feature is the commonly observed self-organized spatial vegetation patterning, such as string-flark and maze patterns. Bistability and spatial self-organization may be mechanistically linked, the crucial mechanism being scale-dependent (locally positive and longer-range negative) feedback between vegetation and the peatland environment. Focusing on bogs, a previous model study shows that nutrient accumulation by vascular plants can induce such scale-dependent feedback driving pattern formation. However, stability of bog microforms such as hummocks and hollows has been attributed to different local interactions between Sphagnum, vascular plants, and the bog environment. Here we analyze both local and longer-range interactions in bogs to investigate the possible contribution of these different interactions to vegetation patterning and stability. This is done by a literature review, and subsequently these findings are incorporated in the original model. When Sphagnum and encompassing local interactions are included in this model, the boundaries between vegetation types become sharper and also the parameter region of bistability drastically increases. These results imply that vegetation patterning and stability of bogs could be synergistically governed by local and longer-range interactions. Studying the relative effect of these interactions is therefore suggested to be an important component of future predictions on the response of peatland ecosystems to climatic changes.     

Finding the Missing Link between Landscape Structure and Population Dynamics: A Spatially Explicit Perspective

We construct and explore a general modeling framework that allows for a systematic investigation of the impact of changes in landscape structure on population dynamics. The essential parts of the framework are a landscape generator with independent control over landscape composition and physiognomy, an individual-based spatially explicit population model that simulates population dynamics within heterogeneous landscapes, and scale-dependent landscape indices that depict the essential aspects of landscape that interact with dispersal and demographic processes. Landscape maps are represented by a grid of 50x50 cells and consist of good-quality, poor-quality, or uninhabitable matrix habitat cells. The population model was shaped in accordance to the biology of European brown bears (Ursus arctos), and demographic parameters were adjusted to yield a source-sink configuration. Results obtained with the spatially explicit model do not confirm results of earlier nonspatial source-sink models where addition of sink habitat resulted in a decrease of total population size because of dilution of high-quality habitat. Our landscape indices, which describe scale-dependent correlation between and within habitat types, were able to explain variations in variables of population dynamics (mean number of females with sink home ranges, mean number of females with source home ranges, and mean dispersal distance) caused by different landscape structure. When landscape structure changed, changes in these variables generally followed the corresponding change of an appropriate landscape index in a linear way. Our general approach incorporates source-sink dynamics as well as metapopulation dynamics, and the population model can easily be modified for other species groups.