README.md
In ECGen/coNet: Model and analyze co-occurrence based networks
conetto
A toolbox for co-occurrence based network modeling
Network models are a useful representation of systems (Woodward et al.
2010). Because it is not always possible to directly observe
relationships (i.e. ecological interactions) spatial or temporal
patterns of co-occurrence can be used to render models of interaction
networks (Araújo et al. 2011). conetto adapts a method previously
developed for ecological networks (Araújo et al. 2011) with the
application of Bayesian probability to generate network models and
provides several functions useful for comparative analysis of sets of
co-occurrence based networks.
Installation
Currently, the package is still in beta but it can be installed via the
devtools package.
install.packages("devtools")
devtools::install_github("ECGen/conetto")
How to use the package
The basic usage of the conetto package is to generate network models.
To do this, we need a matrix of co-occurrence values, which will be
passed into the coNet function:
A <- c(1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1)
B <- c(1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1)
C <- c(1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)
D <- c(0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0)
M <- data.frame(A, B, C, D)
coNet(M)
#> A B C D
#> A 0.0000000 0.4090909 0.0000000 0.0000000
#> B 0.2922078 0.0000000 0.0000000 0.0000000
#> C 0.0000000 0.0000000 0.0000000 -0.3181818
#> D 0.0000000 0.0000000 -0.4370629 0.0000000
The coNet function returns of square matrix with the same number of
rows and columns equal to the number of columns in the co-occurrence
matrix. There are a couple of features that are useful to note here:
- First, the matrix is not symmetric, that is, the top and bottom
halves are not equal. This is because the dependency of two
variables is based on both their independent occurrences and their
co-occurrences: P(A|B) = P(A, B)/P(B) and
P(B|A) = P(A, B)/P(A).
- Some of the values in the network are zero. This is because
coNet
conducts a test that compares the observed co-occurrences to a
theoretical “null” co-occurrence interval. If the observed
co-occurrences are within the interval, the conditional probability
is set equal to the joint probability. Then, when relativized, the
resulting values are zero (i.e. P(A, B) − P(A, B) = 0).
The threshold for the null interval test can be adjusted using the
ci.p argument (DEFAULT = 95).
- Also, some values are negative. This is because the network is
comprised of the difference between the interval adjusted
conditional probabilities and the observed independent probabilities
(i.e. P(A|B) − P(A)). The “raw”, un-relativized, values
can be returned via the raw argument.
Network comparisons
The coNet function was developed for use with replicated datasets,
where multiple networks have been observed. Two other functions were
written to provide a way to analyze these network sets.
One function, meanNet, will calculate the “mean” or average of a set
of networks. The result is the cell-wise summation of all matrices
divided by the total number of matrices. This function requires that the
set of networks all have the same dimensionality and that they are
organized into a list.
net.l <- lapply(1:3, function(x) matrix(runif(9), nrow = 3))
net.l
#> [[1]]
#> [,1] [,2] [,3]
#> [1,] 0.1774681 0.9657068 0.29029980
#> [2,] 0.7242745 0.1201478 0.09624685
#> [3,] 0.8448571 0.8808937 0.23259419
#>
#> [[2]]
#> [,1] [,2] [,3]
#> [1,] 0.1622999 0.8386214 0.9518285
#> [2,] 0.5160295 0.9816857 0.6515049
#> [3,] 0.3204079 0.3763381 0.6507989
#>
#> [[3]]
#> [,1] [,2] [,3]
#> [1,] 0.6478331 0.4237671 0.024558929
#> [2,] 0.4435030 0.7917245 0.398837226
#> [3,] 0.5865592 0.4493110 0.001135512
meanNet(net.l)
#> [,1] [,2] [,3]
#> [1,] 0.07288982 0.1644444 0.09348774
#> [2,] 0.12427323 0.1397539 0.08462390
#> [3,] 0.12929323 0.1259512 0.06528256
Another function, distNet, facilitates the calculation of a distance
matrix for a set of networks. Two metrics are provided, Euclidean and
Bray-Curtis. The resulting matrix is the distance among all networks in
the set. Similar to meanNet, distNet requires that all matrices have
the same dimensionality. The result is a distance, or dissimilarity in
the case of Bray-Curtis, matrix that can now be used for multivariate
analyses, such as ordination.
net.d <- distNet(net.l)
net.d
#> 1 2
#> 2 1.442174
#> 3 1.219601 1.480388
Method: Co-occurrence based network models
The network modeling is based on conditional probability. Ultimately, we
are interested in an estimate of how much one variable (A) affects
another (B), and visa-versa. conetto approaches this by calculating
the difference between the conditional and independent probabilities of
species paris using the observed occurrences (A and B) and
co-occurrences (A, B) of the variables of interest from a set of
observations (N).
- Independent probabilities (P(A) = A/N and
P(B) = B/N)
- Joint probabilities P(A, B) = (A, B)/N
- Conditional probabilities
P(A|B) = P(B|A)P(A)/P(B)
Since there is uuncertainly in whether or not two species are dependent,
conetto uses a interval based test to determine whether or not to use
the observed joint probability O[P(A, B)] = (A, B)/N or
the expected probability using an analytical null model
E[P(A, B)] = P(A)P(B). Via the Chain Rule of
probabililty P(A, B) = P(B|A)P(A), such that if
E[P(A, B)] is used then
P(A|B) = P(A)P(B)/P(B), which reduces to
P(A|B) = P(A) and A is conditionally independent from B. We
can then subtract the independent probability matrix from the interval
test modified conditional probability matrix, which produces a matrix of
the dependency among the variables of interest.
References
Araújo, Miguel B., Alejandro Rozenfeld, Carsten Rahbek, and Pablo A.
Marquet. 2011. “Using species co-occurrence networks to assess the
impacts of climate change.” Ecography 34: 897–908.
Woodward, Guy, Jonathan P Benstead, Oliver S Beveridge, Julia Blanchard,
Thomas Brey, Lee E Brown, Wyatt F Cross, et al. 2010. “Ecological
Networks in a Changing Climate.”
https://doi.org/10.1016/S0065-2504(10)42002-4.
ECGen/coNet documentation built on Sept. 14, 2019, 5:24 a.m.
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conetto
A toolbox for co-occurrence based network modeling
Network models are a useful representation of systems (Woodward et al. 2010). Because it is not always possible to directly observe relationships (i.e. ecological interactions) spatial or temporal patterns of co-occurrence can be used to render models of interaction networks (Araújo et al. 2011). conetto adapts a method previously developed for ecological networks (Araújo et al. 2011) with the application of Bayesian probability to generate network models and provides several functions useful for comparative analysis of sets of co-occurrence based networks.
Installation
Currently, the package is still in beta but it can be installed via the devtools package.
install.packages("devtools")
devtools::install_github("ECGen/conetto")
How to use the package
The basic usage of the conetto package is to generate network models.
To do this, we need a matrix of co-occurrence values, which will be
passed into the coNet function:
A <- c(1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1)
B <- c(1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1)
C <- c(1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)
D <- c(0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0)
M <- data.frame(A, B, C, D)
coNet(M)
#> A B C D
#> A 0.0000000 0.4090909 0.0000000 0.0000000
#> B 0.2922078 0.0000000 0.0000000 0.0000000
#> C 0.0000000 0.0000000 0.0000000 -0.3181818
#> D 0.0000000 0.0000000 -0.4370629 0.0000000
The coNet function returns of square matrix with the same number of
rows and columns equal to the number of columns in the co-occurrence
matrix. There are a couple of features that are useful to note here:
- First, the matrix is not symmetric, that is, the top and bottom halves are not equal. This is because the dependency of two variables is based on both their independent occurrences and their co-occurrences: P(A|B) = P(A, B)/P(B) and P(B|A) = P(A, B)/P(A).
- Some of the values in the network are zero. This is because
coNetconducts a test that compares the observed co-occurrences to a theoretical “null” co-occurrence interval. If the observed co-occurrences are within the interval, the conditional probability is set equal to the joint probability. Then, when relativized, the resulting values are zero (i.e. P(A, B) − P(A, B) = 0). The threshold for the null interval test can be adjusted using the ci.p argument (DEFAULT = 95). - Also, some values are negative. This is because the network is comprised of the difference between the interval adjusted conditional probabilities and the observed independent probabilities (i.e. P(A|B) − P(A)). The “raw”, un-relativized, values can be returned via the raw argument.
Network comparisons
The coNet function was developed for use with replicated datasets,
where multiple networks have been observed. Two other functions were
written to provide a way to analyze these network sets.
One function, meanNet, will calculate the “mean” or average of a set
of networks. The result is the cell-wise summation of all matrices
divided by the total number of matrices. This function requires that the
set of networks all have the same dimensionality and that they are
organized into a list.
net.l <- lapply(1:3, function(x) matrix(runif(9), nrow = 3))
net.l
#> [[1]]
#> [,1] [,2] [,3]
#> [1,] 0.1774681 0.9657068 0.29029980
#> [2,] 0.7242745 0.1201478 0.09624685
#> [3,] 0.8448571 0.8808937 0.23259419
#>
#> [[2]]
#> [,1] [,2] [,3]
#> [1,] 0.1622999 0.8386214 0.9518285
#> [2,] 0.5160295 0.9816857 0.6515049
#> [3,] 0.3204079 0.3763381 0.6507989
#>
#> [[3]]
#> [,1] [,2] [,3]
#> [1,] 0.6478331 0.4237671 0.024558929
#> [2,] 0.4435030 0.7917245 0.398837226
#> [3,] 0.5865592 0.4493110 0.001135512
meanNet(net.l)
#> [,1] [,2] [,3]
#> [1,] 0.07288982 0.1644444 0.09348774
#> [2,] 0.12427323 0.1397539 0.08462390
#> [3,] 0.12929323 0.1259512 0.06528256
Another function, distNet, facilitates the calculation of a distance
matrix for a set of networks. Two metrics are provided, Euclidean and
Bray-Curtis. The resulting matrix is the distance among all networks in
the set. Similar to meanNet, distNet requires that all matrices have
the same dimensionality. The result is a distance, or dissimilarity in
the case of Bray-Curtis, matrix that can now be used for multivariate
analyses, such as ordination.
net.d <- distNet(net.l)
net.d
#> 1 2
#> 2 1.442174
#> 3 1.219601 1.480388
Method: Co-occurrence based network models
The network modeling is based on conditional probability. Ultimately, we are interested in an estimate of how much one variable (A) affects another (B), and visa-versa. conetto approaches this by calculating the difference between the conditional and independent probabilities of species paris using the observed occurrences (A and B) and co-occurrences (A, B) of the variables of interest from a set of observations (N).
- Independent probabilities (P(A) = A/N and P(B) = B/N)
- Joint probabilities P(A, B) = (A, B)/N
- Conditional probabilities P(A|B) = P(B|A)P(A)/P(B)
Since there is uuncertainly in whether or not two species are dependent, conetto uses a interval based test to determine whether or not to use the observed joint probability O[P(A, B)] = (A, B)/N or the expected probability using an analytical null model E[P(A, B)] = P(A)P(B). Via the Chain Rule of probabililty P(A, B) = P(B|A)P(A), such that if E[P(A, B)] is used then P(A|B) = P(A)P(B)/P(B), which reduces to P(A|B) = P(A) and A is conditionally independent from B. We can then subtract the independent probability matrix from the interval test modified conditional probability matrix, which produces a matrix of the dependency among the variables of interest.
References
Araújo, Miguel B., Alejandro Rozenfeld, Carsten Rahbek, and Pablo A. Marquet. 2011. “Using species co-occurrence networks to assess the impacts of climate change.” Ecography 34: 897–908.
Woodward, Guy, Jonathan P Benstead, Oliver S Beveridge, Julia Blanchard, Thomas Brey, Lee E Brown, Wyatt F Cross, et al. 2010. “Ecological Networks in a Changing Climate.” https://doi.org/10.1016/S0065-2504(10)42002-4.
R Package Documentation
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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