A graph-based approach to investigating the influence of the landscape on population spread processes

Modelling of landscape connectivity is a key point in the study of the movement of populations within a given landscape. For studies focused on the preservation of biodiversity, graph-based methods provide an interesting framework to investigate the landscape influence on population spread processes. Such an approach is described here, based on the mapping of landscape categories in habitat patches, including a diachronic data set describing the population spread within the habitat patches. A minimum planar graph was built by computing spatial distances between all pairs of neighbouring patches. From this structure, two types of analysis are proposed: one focused on the links of the graph and consists in correlating spatial distances and gap indicators computed from the diachronic data. The other was based on the correlations between population data and connectivity metrics at the patch level. As an example, this approach was applied to the spread of the fossorial water vole on the Jura plateau (France), with annual population data covering eleven years from 1989 to 2000. Link analysis allowed to find an optimal set of resistance values used in the least-cost distances computations, and thus to build a relevant graph. From this graph, patch analysis displayed a cyclic correlation between a metric based on potential dispersal flux and the population density, outlining the strong role of landscape connectivity in the population spread. The present study clearly shows that landscape modelling and graph-based approach can produce parameters which are consistent with field observations and thus pave the way to simulating the effect of landscape modification on population dynamics.     

Functional connectivity as an indicator for patch occupancy in grassland specialists

Habitat specialists living in metapopulations are sensitive to habitat fragmentation. In most studies, the effects of fragmentation on such species are analyzed based on Euclidean inter-patch distances. This approach, however, ignores the role of the landscape matrix. Recently, therefore, functional distances that account for the composition of the landscape surrounding the habitat patches have been used more frequently as indicators for patch occupancy. However, the performance of functional and non-functional connectivity measures in predicting patch occupancy of such species has never been compared in a multi-species approach.Here we evaluate the effect of habitat connectivity on the patch occupancy of 13 habitat specialists from three different insect orders (Auchenorrhyncha, Lepidoptera, Orthoptera) in fragmented calcareous grasslands. In order to calculate functional distances we used four different sets of resistance values and rankings. We then modelled species’ occurrence using both Euclidean and functional (based on least-cost modelling) inter-patch distances as predictors.We found that functional connectivity measures provided better results than the non-functional approach. However, a functional connectivity measure that was based on very coarse land-cover data performed even better than connectivity measures that were based on much more detailed land-use data.In order to take into account possible effects of the landscape matrix on patch occupancy by habitat specialists, future metapopulation studies should use functional rather than Euclidean distances whenever possible. For practical applications, we recommend a ‘simple approach’ which requires only coarse land-cover data and in our study performed better than all other functional connectivity measures, even more complex ones.     

Grassland connectivity explains entomophilous plant species assemblages in an agricultural landscape of the Pampa Region,Argentina

The Pampa grassland of Argentina is one of the most highly threatened biomes in the world. A high proportion of the original grassland cover has been transformed into land for agriculture or degraded. In the southern part of the region, fragmented semi‐natural grasslands over exposed rock still persist and connectivity between them is assumed to be crucial for maintaining viable populations. We quantified overall connectivity of grassland patches in a sector of the Southern Pampa region, and investigated the degree to which landscape connectivity explains entomophilous plant species assemblages in a subset of patches. We characterized each of the 301 patches in the landscape by their degree of intra‐patch and inter‐patch connectivity based on graph theory, and considering threshold dispersal distances from 100 to 1000 m. We surveyed entomophilous plant species in 39 grassland patches and classified the species in three categories (annual herbs, perennial herbs and shrubs) considering their different growth form and longevity. The influence of connectivity variables on entomophilous plant species assemblages variation was explored using Canonical Correspondence Analysis. Although grassland patches were poorly connected at all threshold distances, some of them were found to be critical for global connectivity. Connectivity significantly explained total, annual‐biennial and shrub assemblages for all threshold dispersal distances (6–13% of total variation). Variation in annual species assemblages was associated with intra‐patch and inter‐patch connectivity at short distance (100 m), while variation in shrub species assemblages was explained by intra‐patch and inter‐patch connectivity for distances between 100 m and 1000 m. This study evidenced the low connectivity of the study system, allowed the identification of critical areas for conservation, and provided valuable information to develop management strategies in increasingly human‐dominated landscapes.     

Gene flow and functional connectivity in the natterjack toad

Functional connectivity is a key factor for the persistence of many specialist species in fragmented landscapes. However, connectivity estimates have rarely been validated by the observation of dispersal movements. In this study, we estimated functional connectivity of a real landscape by modelling dispersal for the endangered natterjack toad (Bufo calamita) using cost distance. Cost distance allows the evaluation of 'effective distances', which are distances corrected for the costs involved in moving between habitat patches in spatially explicit landscapes. We parameterized cost-distance models using the results of our previous experimental investigation of natterjack's movement behaviour. These model predictions (connectivity estimates from the GIS study) were then confronted to genetic-based dispersal rates between natterjack populations in the same landscape using Mantel tests. Dispersal rates between the populations were inferred from variation at six microsatellite loci. Based on these results, we conclude that matrix structure has a strong effect on dispersal rates. Moreover, we found that cost distances generated by habitat preferences explained dispersal rates better than did the Euclidian distances, or the connectivity estimate based on patch-specific resistances (patch viscosity). This study is a clear example of how landscape genetics can validate operational functional connectivity estimates.     

Effects of landscape features on gene flow of valley oaks (<Emphasis Type="Italic">Quercus lobata</Emphasis>)

Landscape features affect habitat connectivity and patterns of gene flow and hence influence genetic structure among populations. We studied valley oak (Quercus lobata), a threatened species of California (USA) savannas and oak woodlands, with a distribution forming a ring around the Central Valley grasslands. Our main goal was to determine the role of topography and land cover on patterns of gene flow and to test whether elevation or land cover forms stronger barriers to gene flow among valley oak populations. We sampled valley oaks in 12 populations across the range of this species, genotyped each tree at eight nuclear microsatellite loci, and created a series of resistance surfaces by assigning different resistance values to land cover type and elevation. We also estimated recent migration rates and evaluated them with regard to landscape features. There was a significant but weak relationship between Euclidian distance and genetic distance. There was no relationship between genetic distances and land cover, but a significant relationship between genetic distances and elevation resistance. We conclude that gene flow is restricted by high elevations in the northern part of the valley oak range and by high elevations and the Central Valley further south. Migration rate analysis indicated some gene flow occurring east–west but we suggest that the high connectivity in the northern Central Valley is facilitating the formation of these links. We predict that southern populations may become more differentiated in the future through genetic isolation and local adaptation taking place in the face of climate change.     

Improving landscape connectivity for the Yunnan snub-nosed monkey through cropland reforestation using graph theory

Habitat fragmentation is a threat to biodiversity because it restricts the ability of animals to move. Maintaining landscape connectivity could promote connections between habitat patches, which is extremely important for the preservation of gene flow and population viability. This paper aims to evaluate the landscape connectivity of forest areas as it relates to the conservation of the Yunnan snub-nosed monkey (Rhinopithecus bieti), an emblematic and endemic endangered primate species. Specifically, this study seeks to model ways to improve connectivity via cropland reforestation scenarios which incorporate graph theory and genetic distances. The connectivity improvement assessment is performed at two nested scales. At the regional scale, the aim is to quantitatively assess the gain in connectivity from different reforestation scenarios, in which croplands are replaced by different kinds of forest habitats. At the local scale, the goal is to prioritize and to locate croplands based on the gain in connectivity that they would provide if they were reforested. The results indicate that the four reforestation scenarios have different impacts on connectivity; the fourth scenario, in which reforestation is accomplished with plant species that provide optimal monkey habitat, yields the greatest increase in connectivity (+24% versus less than +2% for the others). Prioritization of the 1482 cropland patches shows that the 10 best patches increase connectivity from 0.04% to 9.1% as the isolation threshold distance increases. This kind of graph theoretic approach appears to be a useful tool for connectivity assessment and the development of conservation measures for species impacted by human activities.     

Identifying potential conservation areas in the Cuitzeo Lake basin,Mexico by multitemporal analysis of landscape connectivity

Lake Cuitzeo basin is an important ecological area subjected to strong human pressure on forest covers that are key elements for the long-term support of biodiversity. We studied landscape connectivity changes for the years 1975, 1996, 2000, 2003 and 2008 to identify potential conservation areas in the basin. We modeled potential distributions of the Mexican bobcat (Lynx rufus escuinapae) and the ringtail (Bassariscus astutus) – two terrestrial mammal focal species with contrasting dispersal capacities – and we determined their habitat availability and suitability in the basin. We then identified their optimal habitat patches and produced landscape cumulative resistance maps, estimated least-cost paths (graph theory approach), and elaborated current flow maps (circuit theory approach). For evaluation of landscape connectivity, we applied an integral index of connectivity (IIC) to each study period, and determined individual habitat patch contribution to the overall landscape connectivity. The IIC index had very low values associated with reduced availability of focal species habitat. However, our study showed the conservation importance of the surface of optimal habitat patch areas. The combined application of a graph-based approach and current flow mapping were useful, and complementary both in terms of estimating potential dispersal corridors and identifying high probability dispersal areas. This indicated that landscape connectivity analysis is a useful tool for identification of potential conservation areas and for local landscape planning.     

Spatial graphs highlight how multi-generational dispersal shapes landscape genetic patterns

Current approaches that compare spatial genetic structure of a given species and the dispersal of its mobile phase can detect a mismatch between both patterns mainly due to processes acting at different temporal scales. Genetic structure result from gene flow and other evolutionary and demographic processes over many generations, while dispersal predicted from the mobile phase often represents solely one generation on a single time-step. In this study, we present a spatial graph approach to landscape genetics that extends connectivity networks with a stepping-stone model to represent dispersal between suitable habitat patches over multiple generations. We illustrate the approach with the case of the striped red mullet Mullus surmuletus in the Mediterranean Sea. The genetic connectivity of M. surmuletus was not correlate with the estimated dispersal probability over one generation, but with the stepping-stone estimate of larval dispersal, revealing the temporal scale of connectivity across the Mediterranean Sea. Our results highlight the importance of considering multiple generations and different time scales when relating demographic and genetic connectivity. The spatial graph of genetic distances further untangles intra-population genetic structure revealing the Siculo-Tunisian Strait as an important corridor rather than a barrier for gene flow between the Western- and Eastern Mediterranean basins, and identifying Mediterranean islands as important stepping-stones for gene flow between continental populations. Our approach can be easily extended to other systems and environments.     

Patch quality and connectivity influence spatial dynamics in a dune wolfspider

The spatial population dynamics of the wolfspider Pardosa monticola, inhabiting patchily distributed grasslands in the Flemish coastal dunes of Belgium and Northern France were investigated with incidence function models using field survey data from 1998 and 2000. Vegetation height and patch size were related to habitat quality. Mark-recapture experiments revealed maximum cursorial dispersal distances of 280 m for moss dunes and 185 m for higher dune grassland. Higher shrub vegetation appeared to be dispersal barriers. These habitat-dependant cursorial distances and the theoretically estimated ballooning distance were included with patch distances into a connectivity index for both dispersal modes. Forward multiple regression indicated that patch occurrence was influenced by habitat quality and ballooning connectivity. Habitat quality and cursorial connectivity explained patterns in short-term colonisation. Extinction appeared to be stochastic and not related to habitat quality and connectivity. Genetic differentiation and variability was low. The discrepancy between the estimated low dispersal capacity and the indirect estimate of gene flow ( F(ST)) indicates that historical population dynamics and/or historical ballooning dispersal influence the genetic structure in this species.     

Why everything is connected to everything else

In Earth surface systems (ESS), everything is connected to everything else, an aphorism often called the First Law of Ecology and of geography. Such linkages are not always direct and unmediated, but many ESS, represented as networks of interacting components, attain or approach full, direct connectivity among components. The question is how and why this happens at the system or network scale. The crowded landscape concept dictates that linkages and connections among ESS components are inevitable. The connection selection concept holds that the linkages among components are (often) advantageous to the network and are selected for, and thereby preserved and enhanced. These network advantages are illustrated via algebraic graph theory. For a given number of components in an ESS, as the number of links or connections increases, spectral radius, graph energy, and algebraic connectivity increase. While the advantages (if any) of increased complexity are unclear, higher spectral radii are directly correlated with higher graph energy. The greater graph energy is associated with more intense feedback in the system, and tighter coupling among components. This in turn reflects advantageous properties of more intense cycling of water, nutrients, and minerals, as well as multiple potential degrees of freedom for individual components to respond to changes. The increase of algebraic connectivity reflects a greater ability or tendency for the network to respond to changes in concert.     

Insecticide resistance in the dengue vector Aedes aegypti from Martinique: distribution, mechanisms and relations with environmental factors

Dengue is an important mosquito borne viral disease in Martinique Island (French West Indies). The viruses responsible for dengue are transmitted by Aedes aegypti, an indoor day-biting mosquito. The most effective proven method for disease prevention has been by vector control by various chemical or biological means. Unfortunately insecticide resistance has already been observed on the Island and recently showed to significantly reduce the efficacy of vector control interventions. In this study, we investigated the distribution of resistance and the underlying mechanisms in nine Ae. aegypti populations. Statistical multifactorial approach was used to investigate the correlations between insecticide resistance levels, associated mechanisms and environmental factors characterizing the mosquito populations. Bioassays revealed high levels of resistance to temephos and deltamethrin and susceptibility to Bti in the 9 populations tested. Biochemical assays showed elevated detoxification enzyme activities of monooxygenases, carboxylesterases and glutathione S-tranferases in most of the populations. Molecular screening for common insecticide target-site mutations, revealed the presence of the "knock-down resistance" V1016I Kdr mutation at high frequency (>87%). Real time quantitative RT-PCR showed the potential involvement of several candidate detoxification genes in insecticide resistance. Principal Component Analysis (PCA) performed with variables characterizing Ae. aegypti from Martinique permitted to underline potential links existing between resistance distribution and other variables such as agriculture practices, vector control interventions and urbanization. Insecticide resistance is widespread but not homogeneously distributed across Martinique. The influence of environmental and operational factors on the evolution of the resistance and mechanisms are discussed.     

Spatial graphs as templates for habitat networks in boreal landscapes

Network topology serves as a useful model for biological systems at various scales. Contrary to many biological systems, spatial reference is crucial for habitat networks. Boreal forest landscapes provide a wide gradient of spatial patterns and, thus, unique network structures. Assuming forest-dwelling organisms in general aim to minimize travel distances during foraging, dispersal, etc., linear links across the landscape matrix constitute expected movement routes among forested areas in boreal landscapes. We quantified the number and length of links in a set of 57 boreal forest landscapes for four hierarchically nested graphs in order to compare the incremental changes in characteristics of resulting graph measures. The forest cover graphs consisted of the same set of forest patches, and hierarchical link types extracted from real landscapes: nearest neighbour graph (NN), minimum spanning tree (MST), Gabriel graph (GG) and minimum planar graph (MPG). Most of the links in graphs were NN and GG links. Commonly links were 100–200?m in length, but link lengths particularly in the GG and MPG shorten when the proportion of forest in landscapes increased. Most nodes had 3–5 links each, but the number of links per node depended on node size and the proportion of forest cover. GG and MPG graphs retain the topology of the underlying node layout. Changes in node pattern alter the NN and MST graphs more than GG and MPG. Variation in regional network topologies is likely to affect connectivity patterns in a landscape and, thus, many ecological processes that occur at a local scale. An appropriate network analysis enables the discovery and comparison of distinctive network patterns. Understanding network topologies provide practical tools for land use planning and biodiversity management of broader areas that target functional habitat networks.     

Incorporating landscape connectivity into household pond configuration in a hilly agricultural landscape

Manmade ponds are common landscape features in rural areas and also important habitats for maintaining biodiversity. However, they are vulnerable to anthropogenic activities, land-use changes, and habitat degradation; many ponds being filled or (re)created arbitrarily. Little attention has been paid to quantifying the spatial structure of these manmade ponds at a landscape scale, nor to their potential functional benefits in promoting ecological flows and interactions between habitats for whole-ecosystem integrity. In this study, we investigated the patch-based landscape connectivity of household ponds, a particular type of domestic pond prevalent in hilly rural areas of China, by using least-cost path modelling and graph theory based network analysis. A hierarchical network was modelled consisting of 4606 individual ponds, 373 pond patches and 772 potential links within a 1.5-km threshold distance. Network importance analysis revealed that the largest pond patch contributes 24.5 % to network building and that patches with larger areas are generally more important. In contrast, the importance of the simulated links is only 2.3 % at most, indicating that the network has spatial redundancy which can strengthen resilience to uncertain disturbances. Our study moves beyond network simulation and importance assessment by directly relating the connectivity analysis to a real construction context through the incorporation of a spatially explicit land suitability analysis. This approach systematises the analysis of pond landscapes and guides integration with the wider landscape matrix. It provides operational spatial suggestions for holistic landscape planning across local to regional scales.     

Uterine Synchronization Analysis During Pregnancy and Labor Using Graph Theory,Classification Based on Neural Network and Deep Learning

1) ObjectivesPreterm birth caused by preterm labor is one of the major health problems in the world. In this article, we present a new framework for dealing with this problem through the processing of electrohysterographic signals (EHG) that are recorded during labor and pregnancy. The objective in this research is to improve the classification between labor and pregnancy contractions by using a new approach that focuses on the connectivity analysis based on graph parameters, representative of uterine synchronization, and comparing neural network and machine learning methods in order to classify between labor and pregnancy.2) Material and methodsafter denoising of the 16 EHG signals recorded from pregnant women abdomen, we applied different connectivity methods to obtain connectivity matrices; then by using the graph theory, we extracted some graph parameters from the connectivity matrices; finally, we tested different neural network and machine learning methods on the features obtained from both graph and connectivity methods in order to classify between labor and pregnancy.3) ResultsThe best results were obtained by using the logistic regression method. We also evidence the power of graph parameters extracted from the connectivity matrices to improve the classification results.4) ConclusionThe use of graph analysis associated with machine learning methods can be a powerful tool to improve labor and pregnancy classification based on the analysis of EHG signals.     

Graph models of habitat mosaics

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights.     

Emergent functional properties of neuronal networks with controlled topology

The interplay between anatomical connectivity and dynamics in neural networks plays a key role in the functional properties of the brain and in the associated connectivity changes induced by neural diseases. However, a detailed experimental investigation of this interplay at both cellular and population scales in the living brain is limited by accessibility. Alternatively, to investigate the basic operational principles with morphological, electrophysiological and computational methods, the activity emerging from large in vitro networks of primary neurons organized with imposed topologies can be studied. Here, we validated the use of a new bio-printing approach, which effectively maintains the topology of hippocampal cultures in vitro and investigated, by patch-clamp and MEA electrophysiology, the emerging functional properties of these grid-confined networks. In spite of differences in the organization of physical connectivity, our bio-patterned grid networks retained the key properties of synaptic transmission, short-term plasticity and overall network activity with respect to random networks. Interestingly, the imposed grid topology resulted in a reinforcement of functional connections along orthogonal directions, shorter connectivity links and a greatly increased spiking probability in response to focal stimulation. These results clearly demonstrate that reliable functional studies can nowadays be performed on large neuronal networks in the presence of sustained changes in the physical network connectivity.     

Functional Brain Networks: Random, “Small World” or Deterministic?

Lately the problem of connectivity in brain networks is being approached frequently by graph theoretical analysis. In several publications based on bivariate estimators of relations between EEG channels authors reported random or “small world” structure of networks. The results of these works often have no relation to other evidence based on imaging, inverse solutions methods, physiological and anatomical data. Herein we try to find reasons for this discrepancy. We point out that EEG signals are very much interdependent, thus bivariate measures applied to them may produce many spurious connections. In fact, they may outnumber the true connections. Giving all connections equal weights, as it is usual in the framework of graph theoretical analysis, further enhances these spurious links. In effect, close to random and disorganized patterns of connections emerge. On the other hand, multivariate connectivity estimators, which are free of the artificial links, show specific, well determined patterns, which are in a very good agreement with other evidence. The modular structure of brain networks may be identified by multivariate estimators based on Granger causality and formalism of assortative mixing. In this way, the strength of coupling may be evaluated quantitatively. During working memory task, by means of multivariate Directed Transfer Function, it was demonstrated that the modules characterized by strong internal bonds exchange the information by weaker connections.     

Current approaches using genetic distances produce poor estimates of landscape resistance to interindividual dispersal

Landscape resistance reflects how difficult it is for genes to move across an area with particular attributes (e.g. land cover, slope). An increasingly popular approach to estimate resistance uses Mantel and partial Mantel tests or causal modelling to relate observed genetic distances to effective distances under alternative sets of resistance parameters. Relatively few alternative sets of resistance parameters are tested, leading to relatively poor coverage of the parameter space. Although this approach does not explicitly model key stochastic processes of gene flow, including mating, dispersal, drift and inheritance, bias and precision of the resulting resistance parameters have not been assessed. We formally describe the most commonly used model as a set of equations and provide a formal approach for estimating resistance parameters. Our optimization finds the maximum Mantel r when an optimum exists and identifies the same resistance values as current approaches when the alternatives evaluated are near the optimum. Unfortunately, even where an optimum existed, estimates from the most commonly used model were imprecise and were typically much smaller than the simulated true resistance to dispersal. Causal modelling using Mantel significance tests also typically failed to support the true resistance to dispersal values. For a large range of scenarios, current approaches using a simple correlational model between genetic and effective distances do not yield accurate estimates of resistance to dispersal. We suggest that analysts consider the processes important to gene flow for their study species, model those processes explicitly and evaluate the quality of estimates resulting from their model.     

Explicit distance geometry: identification of all the degrees of freedom in a large RNA molecule.

An alternative approach to distance geometry ("explicit" distance geometry) is being developed for problems, such as the modeling of RNA folding in the ribosome, where relatively few distances are known. The approach explicitly identifies minimal sets of additional distances that can be added to a distance matrix in order to calculate structures that are consistent with all the known information without distorting the original input data. These additional distances are bounded to the extent possible by the known distances. These explicitly added distances can be treated as degrees of freedom and used to explore the full range of alternative foldings consistent with the original input in an organized way. The present paper establishes that it is practical to explicitly determine such degrees of freedom for even very large RNAs. To demonstrate the feasibility of the approach tRNA was represented as a simple undirected graph containing all relevant information represented in the usual cloverleaf secondary structure and nine base-base tertiary interactions. Using a three atom representation for each residue a total of 206 degrees of freedom are explicitly identified. To accomplish this a graph theoretic approach was used in which a minimal covering cycle basis was determined.     

Landscape genetic analyses reveal fine‐scale effects of forest fragmentation in an insular tropical bird

Within the framework of landscape genetics, resistance surface modelling is particularly relevant to explicitly test competing hypotheses about landscape effects on gene flow. To investigate how fragmentation of tropical forest affects population connectivity in a forest specialist bird species, we optimized resistance surfaces without a priori specification, using least‐cost (LCP) or resistance (IBR) distances. We implemented a two‐step procedure in order (i) to objectively define the landscape thematic resolution (level of detail in classification scheme to describe landscape variables) and spatial extent (area within the landscape boundaries) and then (ii) to test the relative role of several landscape features (elevation, roads, land cover) in genetic differentiation in the Plumbeous Warbler (Setophaga plumbea). We detected a small‐scale reduction of gene flow mainly driven by land cover, with a negative impact of the nonforest matrix on landscape functional connectivity. However, matrix components did not equally constrain gene flow, as their conductivity increased with increasing structural similarity with forest habitat: urban areas and meadows had the highest resistance values whereas agricultural areas had intermediate resistance values. Our results revealed a higher performance of IBR compared to LCP in explaining gene flow, reflecting suboptimal movements across this human‐modified landscape, challenging the common use of LCP to design habitat corridors and advocating for a broader use of circuit theory modelling. Finally, our results emphasize the need for an objective definition of landscape scales (landscape extent and thematic resolution) and highlight potential pitfalls associated with parameterization of resistance surfaces.