nam(input, rounding = TRUE)cleavogram, which is a list with components:
input contains an element $sm, i.e. a sympatry matrix S of
order n (= number of species). Each entry Sij is 1 if there is a
sympatric link between species i and j, while Sij is 0 if
allopatry is suggested. The diagonal elements are 1 because sympatry is reflexive.
Furthermore, sympatry matrix is symmetric due to reciprocal nature of this relationship. Sympatry matrices are adjacency matrices, and finding the connection patterns in
the associated network is the scope of nam function. In a given
sympatry network, nodes represent species and edges sympatric links. nam
is an iterative process of node removal to isolate subsets of nodes with within-group
sympatry and between-group allopatry (units of co-occurrence). Units of co-occurrence
are generally embedded into a global network due to connecting intermediary nodes.
nam identifies and removes nodes with the highest intermediacy score.
Intermediacy is evaluated with the betweenness measure (Freeman, 1977). After the
node removal, a sub-network is generated and the process is repeated until it arrives
at a sub-network with all nodes with zero betweenness. In this way, nam
produces a series of sub-networks.
Dos Santos et al. (2011) describes a new graphical tool, called a cleavogram,
that depicts the structural changes of the network along the removal process.
This function also retrieves the necessary information to plot a cleavogram.
The older version of NAM method focused on the structure of a single sub-network Dos Santos et al. (2008). Now, the interest relies on the cohesiveness of the various components emerging during the removal process. The density describes the general level of linkage among the vertices (or nodes) in a network. A 'complete' graph (density = 1) is one in which all the actors are adjacent to one another. The density of a graph is the fraction of edges it actually has out of all possible vertex pairs.
Transitivity measures the probability that the adjacent vertices of a vertex are connected. This sometimes is also called the global clustering coefficient. It calculates the number of existing transitive triangles proportional to the number of connected triples.
In graph theory, the distance between two vertices in a graph is the number of edges in the shortest path connecting them (i.e., the geodesic distance). If there is no path connecting the two vertices, they belong to different connected components. The eccentricity of a vertex v is the greatest geodesic distance between v and any other vertex. It can be thought of as how far a node is from the node most distant from it in the graph. The diameter of a graph is the maximum eccentricity of any vertex in the graph. That is, it is the greatest distance between any pair of vertices. Groups of vertices tightly connected is expected to have a small diameter.
Dos Santos D.A., Fernandez H.R., Cuezzo M.G., Dominguez E. 2008. Sympatry Inference and Network Analysis in Biogeography. Systematic Biology 57:432-448.
Dos Santos D.A., Cuezzo M.G., Reynaga M.C., Dominguez E. 2011. Towards a Dynamic Analysis of Weighted Networks in Biogeography. Systematic Biology (in press). Freeman L. C. 1977. A Set of Measures of Centrality Based on Betweenness. Sociometry 40:35-41.
Newman M. E. J. 2001. Scientific Collaboration Networks. II. Shortest Paths, Weighted Networks and Centrality. Phys. Rev. E 64:016132.
Seidel R. 1995. On the All-Pairs-Shortest-Path Problem in Unweighted Undirected Graphs.In Proceedings of J. Comput. Syst. Sci.: 400-403.
cleavogram.
data(sciobius2x2)
mtx <- gridinfer(dntable = sciobius2x2, reciprocity = FALSE) # Infers the sympatry network
cleavosciobius <- nam(mtx) # Performs NAM analysis and create cleavogram called 'cleavosciobius'
## Not run:
# cleavogram()
# ## End(Not run)
# Choose the previous cleavogram and dissect it!
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