Ecological networks: Pursuing the shortest path, however narrow and crooked

International audienceRepresenting data as networks cuts across all sub-disciplines in ecology and evolutionary biology. Besides providing a compact representation of the interconnections between agents, network analysis allows the identification of especially important nodes, according to various metrics that often rely on the calculation of the shortest paths connecting any two nodes. While the interpretation of a shortest paths is straightforward in binary, unweighted networks, whenever weights are reported, the calculation could yield unexpected results. We analyzed 129 studies of ecological networks published in the last decade that use shortest paths, and discovered a methodological inaccuracy related to the edge weights used to calculate shortest paths (and related centrality measures), particularly in interaction networks. Specifically, 49% of the studies do not report sufficient information on the calculation to allow their replication, and 61% of the studies on weighted networks may contain errors in how shortest paths are calculated. Using toy models and empirical ecological data, we show how to transform the data prior to calculation and illustrate the pitfalls that need to be avoided. We conclude by proposing a five-point checklist to foster best-practices in the calculation and reporting of centrality measures in ecology and evolution studies. The last two decades have witnessed an exponential increase in the use of graph analysis in ecological and conservation studies (see refs. 1,2 for recent introductions to network theory in ecology and evolution). Networks (graphs) represent agents as nodes linked by edges representing pairwise relationships. For instance, a food web can be represented as a network of species (nodes) and their feeding relationships (edges) 3. Similarly, the spatial dynamics of a metapopulation can be analyzed by connecting the patches of suitable habitat (nodes) with edges measuring dispersal between patches 4. Data might either simply report the presence/absence of an edge (binary, unweighted networks), or provide a strength for each edge (weighted networks). In turn, these weights can represent a variety of ecologically-relevant quantities, depending on the system being described. For instance, edge weights can quantify interaction frequency (e.g., visitation networks 5), interaction strength (e.g., per-capita effect of one species on the growth rate of another 3), carbon-flow between trophic levels 6 , genetic similarity 7 , niche overlap (e.g., number of shared resources between two species 8), affinity 9 , dispersal probabilities (e.g., the rate at which individuals of a population move between patches 10), cost of dispersal between patches (e.g., resistance 11), etc. Despite such large variety of ecological network representations, a common task is the identification of nodes of high importance, such as keystone species in a food web, patches acting as stepping stones in a dispersal network , or genes with pleiotropic effects. The identification of important nodes is typically accomplished through centrality measures 5,12. Many centrality measures has been proposed, each probing complementary aspects of node-to-node relationships 13. For instance, Closeness centrality 14,15 highlights nodes that are "near" to all othe

A MEASUREMENT OF ELECTROWEAK EFFECTS IN THE REACTION e+ e- ---> tau+ tau- at 35-GeV AND 42.4-GeV

We report on total cross section and forward backward charge asymmetry measurements of the reaction e+e- → τ+τ- at centre of mass energies of 35.0 GeV and 42.4 GeV using the TASSO detector. Including previous data an analysis in terms of electroweak parameters of the standard model is presented, and lower limits on mass scale parameters of residual contact interactions are given. A combined analysis of electroweak couplings using all our results on leptonic reactions e+e-→l+l- has been performed. © 1989 Springer-Verlag

PRODUCTION AND DECAY OF CHARMED MESONS IN e+ e- ANNIHILATION AT s**(1/2) > 28-GeV

We report on a study of inclusive production of D*± mesons in e+e- annihilation at c.m. energies between 28 and 46.8 GeV using the TASSO detector at the PETRA storage ring. A hard D*± energy spectrum is measured with a maximum near ED*±≃0.6 Ebeam. The measured cross section ratio {Mathematical expression} indicates that D* production accounts for a large fraction of the observed charm production. Two complementary methods have been used to determine the forward-backward asymmetry of charm pair production due to electroweak interference. Combining both measurements the product of the axial vector couplings of the electron and the charm quark to the weak neutral current was determined to be gAegAc=-(0.276±0.073), in agreement with the standard model prediction of -0.25. Using a sample of reconstructed D*± mesons, the relative strength of the strong interaction coupling of the c quark compared to that of an average of all flavours is measured as αs(c)/αs(all)=0.91±0.38±0.15, consistent with the coupling constant being flavour independent. An update of our D0 lifetime measurement is presented, based on a considerable increase in statistics, the final result being {Mathematical expression}. © 1989 Springer-Verlag

MEASUREMENT OF THE ASYMMETRY OF b QUARK PRODUCTION IN e+ e- ANNIHILATION OF s**(1/2) = 35-GeV

The forward-backward asymmetry in the reaction $e^+e^-→bb$ has been determined at centre of mass energies near 35 GeV using the TASSO detector. We report results from three different methods. The combined result of the measurements is $\bar A_b=−0.21±0.08 \bar A_b=−0.21±0.08$ ignoring $B^0\bar B^0B^0\bar B^0$ mixing. Taking mixing into account leads to a corrected asymmetry of $A_c$ or $\bar b=−0.28±0.11 \bar A{_b^{cor}}=−0.28±0.11$ . The axial vector coupling constant of the b quark as calculated from the corrected asymmetry isab=−1.2±0.5 to be compared with the valueabSM=−1 from the standard model

THE PRODUCTION AND DECAY OF TAU LEPTONS IN e+ e- ANNIHILATION AT PETRA ENERGIES

We have observed τ pair production at average CM energies of 13.9, 22.3, 34.5 and 43.1 GeV. The cross-sections are consistent with QED, the cut off parameters being Λ+>161 GeV and Λ-169 GeV (95% CL). The topological branching fraction of the τ to 1 charged particle, B1, is 0.847±0.011 (stat)-0.013+0.016(syst) and no decays to 5 charged particles were observed resulting in B5<0.007 (95% CL). Within the 3 charged track final state B(τ-→π-π+π- v)/(B(τ-→π- π+π- v)+B(τ-→π-π+π -π0v))=0.37-0.20+0.35 © 1985 Springer-Verlag

MEASUREMENT OF R AND SEARCH FOR THE TOP QUARK IN e+ e- ANNIHILATION BETWEEN 39.8-GeV AND 45.2-GeV

e+e- annihilation into hadrons was studied at CM energies between 39.8 and 45.2 GeV and a search was made for new heavy quarks. No evidence was found for the existence of a narrow state excluding the possible existence of the lowest vector toponium state in this mass range. A search for continuum production of heavy quarks led to lower mass limits for new quarks of 22.0 GeV (eQ = 2 3) and 21.0 GeV (eQ = 1 3). Quarks are found to be pointlike, the corresponding mass parameter being larger than 288 GeV. A fit of the QCD and the electroweak contributions to R=σtot/σμμ yielded sin2θW = 0.30-0.07+0.23. © 1984