Mantel-based tests have been the primary analytical methods for understanding how landscape features influence observed spatial genetic structure. Simulation studies examining Mantel-based approaches have highlighted major challenges associated with the use of such tests and fueled debate on when the Mantel test is appropriate for landscape genetics studies. We aim to provide some clarity in th...

The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Q n by utilizing spectral graph theory. More...

A new family of distances for graph vertices is proposed. These distances reduce to the shortest path distance and to the resistance distance at the extreme values of the family parameter. The most important property of them is that they are graphgeodetic: d(i, j)+d(j, k) = d(i, k) if and only if every path from i to k passes through j. The construction of the distances is based on the matrix f...

Resistance distance was introduced by Klein and Randić. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by Cat(n; t) the set of connected cacti possessing n vertices and t cycles. In this paper, we give the first three smallest Kirchhoff indices among gra...

The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...

The walk distances in graphs are defined as the result of appropriate transformations of the ∑∞ k=0(tA) k proximity measures, where A is the weighted adjacency matrix of a graph and t is a sufficiently small positive parameter. The walk distances are graphgeodetic; moreover, they converge to the shortest path distance and to the so-called long walk distance as the parameter t approaches its lim...

Isolation by adaptation increases divergence at neutral loci when natural selection against immigrants reduces the rate of gene flow between different habitats. This can occur early in the process of adaptive divergence and is a key feature of ecological speciation. Despite the ability of isolation by distance (IBD) and other forms of landscape resistance to produce similar patterns of neutral ...

Several studies have been conducted on resistance sources to improve the genetic resistance of farm-grown tomatoes to arthropod pests, including phytophagous mites. In the present study, we evaluate the behavior of the two-spotted spider mite on different cherry tomato accessions to identify possible sources of resistance (repellent effect) to this pest. Sixty-four accessions of cherry tomatoes...

Despite growing interest in the effects of landscape heterogeneity on genetic structuring, few tools are available to incorporate data on landscape composition into population genetic studies. Analyses of isolation by distance have typically either assumed spatial homogeneity for convenience or applied theoretically unjustified distance metrics to compensate for heterogeneity. Here I propose th...