mat.model: Functions for matrix population model
In Lobz/facilitation: A C++ Framework for Plant-Plant Interaction IBMs

These functions produce the matrix population model matrices for a continuous time structured population model. Function mat.model receives as an input the result of a simulation (from function community), or a data.frame containing the model parameters If there is more than one population, returns a list of matrices, or one block-diagonal matrix created by the combination. The solution.matrix function returns the solution to a linear ODE of the form P' = MP, which is merely P(t) = exp(Mt)p0 where p0 is the initial condition. The function limiting.rate returns the real dominant eigenvalue of a Matrix Population Model matrix. That is a real number that corresponds to the per-capita growth rate that a population approaches as time passes, in a model with no interactions. A structured population can grow at exactly this rate if the distribution between stages corresponds exactly to the distribution of the dominant eigenvector. The models that can be simulated by this package are of a class that always has a real dominant eigenvector. Note that these are continuous-time models, in which r > 0 means the population will grow, and r < 0 means it will decrease. This function doesn't throw errors, instead it returns 'NA'.

mat.model(data, ns, combine.matrices = FALSE)

solution.matrix(p0, mat, times = c(1:10))

limiting.rate(mat)

`data`	Either the result of a simulation, to extract the parameters from, or a data.frame containing the parameters.
`ns`	an array of numbers of stages. Use when `data` is a data.frame and the is more than one population.
`combine.matrices`	Logical. Combine the matrices into a single, multi-population matrix?
`p0`	initial condition, as an array
`mat`	a square matrix
`times`	an array containing the times in which to calculate the solution

# Generating a mat model from random parameters and exploring the solution matrix
mat <- mat.model(create.parameters(n=4))
solution.matrix(c(1,0,0,0),mat)

# Extracting the mat model from a simulation object and checking the limiting rate
data(malthusian)
mat <- mat.model(malthusian)
limiting.rate(mat)

# Working with more than one species
data(twospecies)
mat.model(twospecies,combine.matrices=TRUE)