A new family of standardized and symmetric indices for measuring the intensity and importance of plant neighbour effects

1. Measurements of competition and facilitation between plants often rely upon intensity and importance indices that quantify the net effect of neighbours on the performance of a target plant. A systematic analysis of the mathematical behaviour of the indices is lacking and leads to structural pitfalls, e.g. statistical problems detected in importance indices. 2. We summarize and analyse themathematical properties that the indices should display. We reviewthe properties of the commonly used indices focusing on standardization and symmetry, which are necessary to avoid compromising data interpretation.We introduce a new family of indices ‘Neighbour-effect Indices’ that meet all the proposed properties. 3. Considering the commonly used indices, none of the importance indices are standardized, and onlyRII (Relative Interaction Index) displays all the required mathematical properties. The existing indices show two types of symmetries, namely, additive or commutative, which are currently confounded, potentially resulting in misleading interpretations. Our Neighbour-effect Indices encompass two intensity and two importance indices that are standardized and have different and defined symmetries. 4. Our new additive intensity index, NIntA, is the first of its kind, and it is generally more suitable for assessing competition and facilitation intensity than the widely used RII, which may underestimate facilitation. Our new standardized importance indices solve the main statistical problems that are known to affectCimp and Iimp. Intensity and importance with the same symmetry should be used within the same study. The Neighbour-effect Indices, sharing the same formulation, will allow for unbiased comparisons between intensity and importance, and between types of symmetry.The research of R.D.S. was supported by funding from Ministry of Economy and Competitivity (AGL2015-69151-R). V.R.D. was supported by a Ram on y Cajal fellowship (RYC-2012-10970, MINECO, Spain). The research of M.B. and M.R. was supported by funding from the European Union’s Seventh Framework Programme (FP7/2007–2013), grant agreement 283068 (CASCADE). M.V. was supported by an NWO–ALW ‘open competition’ grant. (Netherlands Science Foundation – Earth and Life Sciences, project number 820.01.020.)

Topology and correlations in structured scale-free networks

We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small world properties in the whole parameters range. We discuss the physical properties of these networks in the light of the present detailed analysis.Comment: 10 pages, 9 figure

Steady-State Dynamics of the Forest Fire Model on Complex Networks

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.Comment: 13 pages, 9 figure

Class of correlated random networks with hidden variables

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an \textit{a priori} specified correlation structure. We also present an extension of the class, to map non-equilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

Mesoscopics and fluctuations in networks

We describe fluctuations in finite-size networks with a complex distribution of connections, $P(k)$. We show that the spectrum of fluctuations of the number of vertices with a given degree is Poissonian. These mesoscopic fluctuations are strong in the large-degree region, where $P(k) \lesssim 1/N$ ($N$ is the total number of vertices in a network), and are important in networks with fat-tailed degree distributions.Comment: 3 pages, 1 figur

Mixing patterns in networks

We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.Comment: 14 pages, 2 tables, 4 figures, some additions and corrections in this versio

Will a rising sea sink some estuarine wetland ecosystems?

Sea-level rise associatedwith climate change presents amajor challenge to plant diversity and ecosystemservice provision in coastal wetlands. In this study,we investigate the effect of sea-level rise on benthos, vegetation, and ecosystem diversity in a tidal wetland in westWales, the UK. Present relationships between plant communities and environmental variableswere investigated through 50 plots atwhich vegetation (species and coverage), hydrological (surface or groundwater depth, conductivity) and soil (matrix chroma, presence or absence ofmottles, organic content, particle size) data were collected. Benthic communities were sampled at intervals along a continuum from saline to freshwater. To ascertain future changes to the wetlands' hydrology, a GIS-based empirical model was developed. Using a LiDAR derived land surface, the relative effect of peat accumulation and rising sea levels were modelled over 200 years to determine how frequently portions of the wetland will be inundated by mean sea level, mean high water spring and mean high water neap conditions. The model takes into account changing extents of peat accumulation as hydrological conditions alter. Model results show that changes to the wetland hydrology will initially be slow. However, changes in frequency and extent of inundation reach a tipping point 125 to 175 years from2010 due to the extremely low slope of the wetland. From then onwards, large portions of the wetland become flooded at every flood tide and saltwater intrusion becomes more common. This will result in a reduction in marsh biodiversity with plant communities switching toward less diverse and occasionally monospecific communities that are more salt tolerant.IS