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Utility and Mixed Trophic Analyses
This page illustrates how to use the enaUtility() and enaMTI() functions to find the integral or net impact of one species on another. These also characterize the resultant qualitative relationships.
The first step is to prepare the workspace.
rm(list = ls())
library(enaR)
library(network)
Then we can load the library of models and select one to use for this illustration.
# load data
data(enaModels) # load library of Ecosystem Networks
names(enaModels) # view model names
NET <- enaModels[[9]] # select the oyster NET
ssCheck(m)
Next, we apply the utility network analysis.
> u <- enaUtility(m) # perform the ENA flow analysis
> attributes(u)
$names
[1] "D" "SD" "U" "Y"
[5] "SY" "Relations.Table" "ns"
We can examine the througflow scaled integral utility matrix
> show(u$Y) # dimesionalized integral utiilty matrix
Filter Feeders Microbiota Meiofauna Deposit Feeders
Filter Feeders 34.5516009 3.21636398 1.76164548 0.002615238
Microbiota 2.9290686 6.05912271 0.01745223 1.096717767
Meiofauna 0.5320225 -1.63465748 8.02036899 0.417444025
Deposit Feeders -1.1206475 -0.49779890 -0.47764506 2.286340165
Predators -0.4863857 0.05982146 0.04660642 -0.154354794
Deposited Detritus -9.2412030 4.47185597 2.43467798 0.166693897
Predators Deposited Detritus
Filter Feeders 0.2895772 9.44904264
Microbiota 0.1746756 -4.31441404
Meiofauna 0.0469263 -0.79970117
Deposit Feeders 0.1216204 1.45166081
Predators 0.6693019 -0.02101919
Deposited Detritus -0.2985165 13.34522178
The related sign matrix is
> show(u$SY) # the sign matrix assoicated with U
Filter Feeders Microbiota Meiofauna Deposit Feeders Predators Deposited Detritus
Filter Feeders "+" "+" "+" "+" "+" "+"
Microbiota "+" "+" "+" "+" "+" "-"
Meiofauna "+" "-" "+" "+" "+" "-"
Deposit Feeders "-" "-" "-" "+" "+" "+"
Predators "-" "+" "+" "-" "+" "-"
Deposited Detritus "-" "+" "+" "+" "-" "+"
These elements are essentially intermediate results. The "Relations.Table" summarizes the key results
> u$Relations.Table
From To Direct Integral changed
1 Filter Feeders Filter Feeders (0,0) (+,+) *
2 Filter Feeders Microbiota (0,0) (+,+) *
3 Filter Feeders Meiofauna (0,0) (+,+) *
4 Filter Feeders Deposit Feeders (0,0) (+,-) *
5 Filter Feeders Predators (+,-) (+,-) -
6 Filter Feeders Deposited Detritus (+,-) (+,-) -
7 Microbiota Microbiota (0,0) (+,+) *
8 Microbiota Meiofauna (+,-) (+,-) -
9 Microbiota Deposit Feeders (+,-) (+,-) -
10 Microbiota Predators (0,0) (+,+) *
11 Microbiota Deposited Detritus (-,+) (-,+) -
12 Meiofauna Meiofauna (0,0) (+,+) *
13 Meiofauna Deposit Feeders (+,-) (+,-) -
14 Meiofauna Predators (0,0) (+,+) *
15 Meiofauna Deposited Detritus (-,+) (-,+) -
16 Deposit Feeders Deposit Feeders (0,0) (+,+) *
17 Deposit Feeders Predators (+,-) (+,-) -
18 Deposit Feeders Deposited Detritus (+,-) (+,+) *
19 Predators Predators (0,0) (+,+) *
20 Predators Deposited Detritus (+,-) (-,-) *
21 Deposited Detritus Deposited Detritus (0,0) (+,+) *
This table summarizes the pairwise relationship between each of the pairwise interactions in the network when considering just the direct interactions and the integral interactions, which consider all of the indirect interactions as well. Often these indirect interactions have the power to transform a relationship that it is different than it first appears.
Several whole network metrics are derived from this information.
> u$ns
lam1D relation.change.F synergism.F mutualism.F
r.change 0.8991676 61.9 4.915298 2.272727
The synergism.F parameter is a cost-benefit ratio. When it is greater than 1, it indicates that there is more integral positive utility in the system than negative utility. The mutualism parameter is a similar ratio. When it is greater than 1 in indicates that there are more integral positive relationships in the network than negative ones. The stars in the right hand column indicate if this relationship has changed.
The Mixed Trophic Impacts analysis of Ulanowicz and Puccia (1990) is executed with the enaMTI() function as follows.
> mti <- enaMTI(m, eigen.check=FALSE) # apply mixed trophic analysis
> attributes(mti)
$names
[1] "G" "FP" "Q" "M"
[5] "Relations.Table"
Like with the Utility analysis, we can ascertain the mixed impacts (integral) from the M matrix. Note that I have rounded the values to 3 decimal places for brevity.
> round(mti$M,3)
Filter Feeders Microbiota Meiofauna Deposit Feeders Predators Deposited Detritus
Filter Feeders -0.025 0.170 0.431 0.26 10.796 0.516
Microbiota -0.002 -0.307 -0.182 0.205 0.050 -0.295
Meiofauna 0.000 -0.474 -0.071 0.016 0.004 -0.002
Deposit Feeders -0.007 -0.268 -0.007 -0.103 0.220 0.177
Predators -0.030 0.020 -0.004 -0.076 -0.042 -0.020
Deposited Detritus -0.003 0.218 0.613 0.449 0.110 -0.251
Again, the key results are summarized in the Relations.Table
> mti$Relations.Table
From To Net (direct) Mixed (integral) changed
1 Filter Feeders Filter Feeders (0,0) (-,-) *
2 Filter Feeders Microbiota (0,0) (-,+) *
3 Filter Feeders Meiofauna (0,0) (-,+) *
4 Filter Feeders Deposit Feeders (0,0) (-,+) *
5 Filter Feeders Predators (-,+) (-,+) -
6 Filter Feeders Deposited Detritus (0,+) (-,+) *
7 Microbiota Microbiota (0,0) (-,-) *
8 Microbiota Meiofauna (-,+) (-,-) *
9 Microbiota Deposit Feeders (-,+) (-,+) -
10 Microbiota Predators (0,0) (+,+) *
11 Microbiota Deposited Detritus (+,-) (+,-) -
12 Meiofauna Meiofauna (0,0) (-,-) *
13 Meiofauna Deposit Feeders (-,+) (-,+) -
14 Meiofauna Predators (0,0) (-,+) *
15 Meiofauna Deposited Detritus (+,-) (+,-) -
16 Deposit Feeders Deposit Feeders (0,0) (-,-) *
17 Deposit Feeders Predators (-,+) (-,+) -
18 Deposit Feeders Deposited Detritus (+,+) (+,+) -
19 Predators Predators (0,0) (-,-) *
20 Predators Deposited Detritus (0,+) (+,-) *
21 Deposited Detritus Deposited Detritus (0,0) (-,-) *