Transition from connected to fragmented vegetation across an environmental gradient: scaling laws in ecotone geometry

A change in the environmental conditions across space—for example, altitude or latitude—can cause significant changes in the density of a vegetation type and, consequently, in spatial connectivity. We use spatially explicit simulations to study the transition from connected to fragmented vegetation. A static (gradient percolation) model is compared to dynamic (gradient contact process) models. Connectivity is characterized from the perspective of various species that use this vegetation type for habitat and differ in dispersal or migration range, that is, “step length” across the landscape. The boundary of connected vegetation delineated by a particular step length is termed the “ hull edge.” We found that for every step length and for every gradient, the hull edge is a fractal with dimension 7/4. The result is the same for different spatial models, suggesting that there are universal laws in ecotone geometry. To demonstrate that the model is applicable to real data, a hull edge of fractal dimension 7/4 is shown on a satellite image of a piñon‐juniper woodland on a hillside. We propose to use the hull edge to define the boundary of a vegetation type unambiguously. This offers a new tool for detecting a shift of the boundary due to a climate change

Similar self-organizing scale-invariant properties characterize early cancer invasion and long range species spread

Occupancy of new habitats through dispersion is a central process in nature. In particular, long range dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves spread to new tissues. We show that the early spread of cancer cells is similar to the species individuals spread and that both processes are represented by a common spatio-temporal signature, characterized by a particular fractal geometry of the boundaries of patches generated, and a power law-scaled, disrupted patch size distribution. We show that both properties are a direct result of long-distance dispersal, and that they reflect homologous ecological processes of population self-organization. Our results are significant for processes involving long-range dispersal like biological invasions, epidemics and cancer metastasis.Comment: 21 pages, 2 figure

Homologous self-organising scale-invariant properties characterise long range species spread and cancer invasion

The invariance of some system properties over a range of temporal and/or spatial scales is an attribute of many processes in nature1, often characterised by power law functions and fractal geometry2. In particular, there is growing consensus in that fat-tailed functions like the power law adequately describe long-distance dispersal (LDD) spread of organisms 3,4. Here we show that the spatial spread of individuals governed by a power law dispersal function is represented by a clear and unique signature, characterised by two properties: A fractal geometry of the boundaries of patches generated by dispersal with a fractal dimension D displaying universal features, and a disrupted patch size distribution characterised by two different power laws. Analysing patterns obtained by simulations and real patterns from species dispersal and cell spread in cancer invasion we show that both pattern properties are a direct result of LDD and localised dispersal and recruitment, reflecting population self-organisation

The Principle of Similitude in Biology: From Allometry to the Formulation of Dimensionally Homogenous `Laws'

Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the $\rm \Pi$ theorem (Vaschy 1892; Buckingham 1914). However, most relations in allometry do not satisfy this basic requirement, including the `3/4 Law' (Kleiber 1932) that relates the basal metabolic rate and body mass, which it is sometimes claimed to be the most fundamental biological rate (Brown et al. 2004) and the closest to a law in life sciences (West \& Brown 2004). Using the $\rm \Pi$ theorem, here we show that it is possible to construct a unique homogeneous equation for the metabolic rates, in agreement with data in the literature. We find that the variations in the dependence of the metabolic rates on body mass are secondary, coming from variations in the allometric dependence of the heart frequencies. This includes not only different classes of animals (mammals, birds, invertebrates) but also different exercise conditions (basal and maximal). Our results demonstrate that most of the differences found in the allometric exponents (White et al. 2007) are due to compare incommensurable quantities and that our dimensionally homogenous formula, unify these differences into a single formulation. We discuss the ecological implications of this new formulation in the context of the Malthusian's, Fenchel's and the total energy consumed in a lifespan relations.Comment: A accepted for publication in Theoretical Ecology. Comments are welcome ([email protected]

Fractal-cluster theory and thermodynamic principles of the control and analysis for the self-organizing systems

The theory of resource distribution in self-organizing systems on the basis of the fractal-cluster method has been presented. This theory consists of two parts: determined and probable. The first part includes the static and dynamic criteria, the fractal-cluster dynamic equations which are based on the fractal-cluster correlations and Fibonacci's range characteristics. The second part of the one includes the foundations of the probable characteristics of the fractal-cluster system. This part includes the dynamic equations of the probable evolution of these systems. By using the numerical researches of these equations for the stationary case the random state field of the one in the phase space of the $D$, $H$, $F$ criteria have been obtained. For the socio-economical and biological systems this theory has been tested.Comment: 37 pages, 20 figures, 4 table

Power-law behavior reveals phase transitions in landscape controls of fire regimes

In low-severity fire regimes of the American West and elsewhere, landscape memory of fire events is registered in fire-scarred trees, with temporal record lengths often exceeding 200 years^1-5^. Understanding the environmental controls on historical wildfires, and how they changed across spatial scales, is difficult because there are no surviving explicit records of either weather or vegetation (fuels). We show how power laws associated with fire-event time series arise in limited domains of parameters that represent critical transitions in the controls on landscape fire. We used stochastic simulations iteratively with Monte Carlo inference to replicate the spatio-temporal structure of historical fire-scar records in forested watersheds of varying topographic complexity. We find that the balance between endogenous and exogenous controls on fire spread shifts with topographic complexity, where in the most complex landscapes the endogenous controls dominate and the pattern exhibits criticality. Comparison to an self-organized criticality (SOC) model^6,7^ shows that the latter mimics historical fire only in a limited domain of criticality, and is not an adequate mechanism to explain landscape fire dynamics, which are shaped by both endogenous and exogenous controls. Our results identify a continuous phase transition in landscape controls, marked by power laws, and provide an ecological analogue to critical behavior in physical and chemical systems^8-11^. This explicitly cross-scale analysis provides a paradigm for identifying critical thresholds in landscape dynamics that may be crossed in a rapidly changing climate

Recruitment Facilitation and Spatial Pattern Formation in Soft-Bottom Mussel Beds

Mussels (Mytilus edulis) build massive, spatially complex, biogenic structures that alter the biotic and abiotic environment and provide a variety of ecosystem services. Unlike rocky shores, where mussels can attach to the primary substrate, soft sediments are unsuitable for mussel attachment. We used a simple lattice model, field sampling, and field and laboratory experiments to examine facilitation of recruitment (i.e., preferential larval, juvenile, and adult attachment to mussel biogenic structure) and its role in the development of power-law spatial patterns observed in Maine, USA, soft-bottom mussel beds. The model demonstrated that recruitment facilitation produces power-law spatial structure similar to that in natural beds. Field results provided strong evidence for facilitation of recruitment to other mussels—they do not simply map onto a hard-substrate template of gravel and shell hash. Mussels were spatially decoupled from non-mussel hard substrates to which they can potentially recruit. Recent larval recruits were positively correlated with adult mussels, but not with other hard substrates. Mussels made byssal thread attachments to other mussels in much higher proportions than to other hard substrates. In a field experiment, mussel recruitment was highest to live mussels, followed by mussel shell hash and gravel, with almost no recruitment to muddy sand. In a laboratory experiment, evenly dispersed mussels rapidly self-organized into power-law clusters similar to those observed in nature. Collectively, the results indicate that facilitation of recruitment to existing mussels plays a major role in soft-bottom spatial pattern development. The interaction between large-scale resource availability (hard substrate) and local-scale recruitment facilitation may be responsible for creating complex power-law spatial structure in soft-bottom mussel beds

Understanding drivers of species distribution change: a trait-based approach

The impacts of anthropogenic environmental change on biodiversity are well documented, with threats such as habitat loss and climate change identified as causes of change in species distributions. The high degree of variation in responses of species to environmental change can be partly explained through comparative analyses of species traits. I carried out a phylogenetically informed trait-based analysis of plant range change in Britain, discovering that traits associated with competitive ability and habitat specialism both explained variation in range changes. Competitive, habitat generalists out-perform ed species specialised to nutrient-poor conditions; a result which can be attributed to the impact of agricultural intensification in Britain. A limitation of the comparative approach is that the models do not directly test the impact of environmental change on species distribution patterns, but instead infer potential impacts. I tested the potential of comparative analyses from a spatial context by conducting a spatial analysis of plant distribution change in Britain, examining the direct impact of environmental change on the spatial distribution of the trait characteristics of species that have gone locally extinct. I discovered a loss of species associated with nitrogen poor soils in regions that had an increase in arable land cover, a result that supports the results from the trait-based analysis of plant range change and demonstrates that comparative studies can accurately infer drivers of distribution change. I found that the cross-region transferability of trait-based models of range change to be related to land cover similarity, highlighting that the trait-based approach is dependent on a regional context. Additionally, I discovered that traits derived from distribution data were significant predictors of range shift across many taxonomic groups, out-performing traditional life history traits. This thesis highlights the potential of the data accumulated through the increased public participation in biological recording to address previously unanswerable ecological research questions.Open Acces

Macaques preferentially attend to visual patterns with higher fractal dimension contours.

Animals' sensory systems evolved to efficiently process information from their environmental niches. Niches often include irregular shapes and rough textures (e.g., jagged terrain, canopy outlines) that must be navigated to find food, escape predators, and master other fitness-related challenges. For most primates, vision is the dominant sensory modality and thus, primates have evolved systems for processing complicated visual stimuli. One way to quantify information present in visual stimuli in natural scenes is evaluating their fractal dimension. We hypothesized that sensitivity to complicated geometric forms, indexed by fractal dimension, is an evolutionarily conserved capacity, and tested this capacity in rhesus macaques (Macaca mulatta). Monkeys viewed paired black and white images of simulated self-similar contours that systematically varied in fractal dimension while their attention to the stimuli was measured using noninvasive infrared eye tracking. They fixated more frequently on, dwelled for longer durations on, and had attentional biases towards images that contain boundary contours with higher fractal dimensions. This indicates that, like humans, they discriminate between visual stimuli on the basis of fractal dimension and may prefer viewing informationally rich visual stimuli. Our findings suggest that sensitivity to fractal dimension may be a wider ability of the vertebrate vision system