Angola dataset analysis

Marc Ohlmann

2023-05-26

Source: vignettes/angola.Rmd

Angola data set

An example using real data is accessible in metanetwork. It consists in the Angoala coastal trophic network from Angelini, R. & Vaz-Velho, F. (2011)., abundance data at different time steps (1986 and 2003) and a trophic table, indicating the groups to which species belong.

Loading the dataset 

data("meta_angola")
class(meta_angola)
## [1] "metanetwork"
print(meta_angola)
## metaweb has 28 nodes and 127 edges 
## 2 local networks 
## available resolutions are: Species Phylum

plot_trophic_table function

Contrary to the pyramid example, angola dataset do have a trophic table, describing nodes memberships in higher relevant groups. In angola dataset, two different taxonomic resolutions are available. Networks can be handled and represented at Species or Phylum level.
The plot_trophic_table function allows representing the tree describing species memberships.

ggnet.custom = ggnet.default
ggnet.custom$label.size = 2
plot_trophicTable(meta_angola,ggnet.config = ggnet.custom)

plot of chunk angola_plot_trophicTable

append_agg_nets method

The method append_agg_nets allows computing and appending aggregated networks (at the different available resolutions) to the current metanetwork.

meta_angola = append_agg_nets(meta_angola)
print(meta_angola)
## metaweb has 28 nodes and 127 edges 
## 2 local networks 
## available resolutions are: Species Phylum

Representing aggregated networks, adding a legend to networks

Once computed, ggmetanet function allows representing aggregated networks and legending local networks using trophic table. Do not forget to first compute trophic levels.

meta_angola = compute_TL(meta_angola)
ggmetanet(g = meta_angola$metaweb_Phylum,beta = 1,metanetwork = meta_angola)

plot of chunk angola_metaweb_phylum

Node sizes are proportional to relative abundances. Trophic table allows adding a legend to network at the finest resolution.

ggmetanet(g = meta_angola$metaweb,beta = 0.04,legend = 'Phylum',metanetwork = meta_angola)

plot of chunk angola_metaweb

The metaweb has two basal nodes, ‘Phytoplankton’ and ‘Detritus’, leading to a primary producer and detritus channel that mix up higher in the network. The ‘TL-tsne’ layout highlights these two distinct channels for both networks: the green channel, linked to primary producers, (phytoplankton) and the brown channel, linked to detritus.

diff_plot

To represent difference between local networks, use diff_plot() function.

diff_plot(g1 = meta_angola$X1986,g2 = meta_angola$X2003,beta = 0.04,metanetwork = meta_angola)

plot of chunk angola_diff_plot

vismetaNetwork function

metanetwork allows representing trophic networks in interactive way using visNetwork function and both layout algorithms. We highly recommend this function to explore large and dense networks. Since outputs of this functions cannot be rendered on this README, they are saved in ./vismetaNetwork in html format. x_y_range argument allows controlling the x-axis and y-axis scale.

vismetaNetwork(metanetwork = meta_angola,beta = 0.04,legend = 'Phylum',x_y_range = c(30,60))

Interactive visualisation of angola dataset and other trophic networks using vismetaNetwork are available at https://shiny.osug.fr/app/ecological-networks.

Additional features

attach_layout function

Since TL-tsne layout is stochastic and requires (a bit of) computation times, saving and using the the same layout (for a given \(\beta\) value) is recommended. Moreover, it makes easier visual network analysis and comparison since it is fixed. attach_layout function allows saving computed layouts by attaching them as a node attribute.

#attaching a layout to the metaweb
meta_angola = attach_layout(metanetwork = meta_angola,beta = 0.05)
#layout is saved as node attribute (only one component since the other one is trophic level)
igraph::vertex_attr_names(meta_angola$metaweb)
## [1] "name"            "ab"              "TL"              "layout_beta0.05"
#this is the computed layout
V(meta_angola$metaweb)$layout_beta0.05
##  [1]  -9.651342  -5.767532   5.194469  -3.823952 -18.572339  15.773919  21.064580   7.543386  25.917790  23.226553  11.649604  29.426068 -16.106680
## [14] -21.246919 -27.047448  -1.600164 -23.833696   2.788126   0.646412  18.443714 -14.331872 -31.772174   9.648135  13.705864  -7.831115 -12.831562
## [27] -10.993820  20.381996
#ggmetanet uses the computed layout
ggmetanet(meta_angola,beta = 0.05,legend = "Phylum")

plot of chunk angola_attach_layout1

Several layout can be computed and stored for the same \(\beta\) value. Argument nrep_ly allows selecting the desired computed layout for the focal \(\beta\) value.

#attaching a new layout for the same beta value
meta_angola = attach_layout(metanetwork = meta_angola,beta = 0.05)
#the two layouts are stored as node attribute
igraph::vertex_attr_names(meta_angola$metaweb)
## [1] "name"              "ab"                "TL"                "layout_beta0.05"   "layout_beta0.05_1"
#this is the new layout
V(meta_angola$metaweb)$layout_beta0.05_1
##  [1]  23.2884614   4.1340300  -4.8161359  15.5999164  10.4074526 -15.3107874 -20.5228096  -7.1625291 -25.3092535 -22.6558866 -11.2409679 -28.7714286
## [13]  13.2750092  18.0097423  26.7344642   1.9609046  20.4578198  -2.4228296  -0.2968211 -17.9566698   7.4907073  31.4329101  -9.2597165 -13.2684559
## [25]   6.1029551   8.6541160  11.3126872 -19.8668844
#ggmetanet with the new 'TL-tsne' layout
ggmetanet(meta_angola,beta = 0.05,legend = "Phylum",nrep_ly = 2)

plot of chunk angola_attach_layout2

Notice that even if the two layouts are quite different in term of global structure, they share some features in terms of local structure. For example, phytoplankton and zooplankton are close by as Detritus and benthic organisms. So, in this example, despite the stochasticity of the layout, the highlight of brown and green channels is stable.

Using metaweb layout

Using metaweb layout can ease the representation and comparison of multiple local networks.

#using metaweb layout to represent a local network
ggmetanet(g = meta_angola$X1986,metanetwork = meta_angola,
          legend = "Phylum",layout_metaweb = T,beta = 0.05)

plot of chunk angola_layout_metaweb

#using metaweb layout for diffplot
diff_plot(g1 = meta_angola$X1986,g2 = meta_angola$X2003,
          metanetwork = meta_angola,beta = 0.05,
          layout_metaweb = T)

plot of chunk angola_layout_metaweb

Computing network indices and metrics

Besides network representation, ‘metanetwork’ package can compute usual network metrics (weighted connectance, mean and max trophic level, mean shortest path length). Network diversity and dissimilarity indices based on Hill numbers are also implemented in order to quantitatively compare local networks at the different resolutions.

metrics_angola = compute_metrics(meta_angola)
metrics_angola$Species
##         connectance  mean_TL   max_TL mean_shortest_path_length
## metaweb  0.02921234 1.561919 2.739126                 0.2201667
## X1986    0.02859672 1.561919 2.739126                 0.2201667
## X2003    0.02918298 1.561919 2.739126                 0.2201667
metrics_angola$Phylum
##         connectance  mean_TL   max_TL mean_shortest_path_length
## metaweb  0.02925731 1.315389 2.229886                0.05117634
## X1986    0.02859672 1.319967 2.278338                0.04603361
## X2003    0.02918298 1.317792 2.206484                0.05471144

We now compute network diversity indices based on Hill numbers (cf. Ohlmann et al. 2019). The indices are based on node and link abundances are can be partitioned in \(\alpha\)-diversity, \(\beta\)-diversity and \(\gamma\)-diversity. A viewpoint parameter \(q\) allows giving more weight (see compute_div documentation)

div_angola = compute_div(meta_angola, q = 1)
div_angola$nodes
##                 Species   Phylum
## Gamma_P       13.666059 2.680737
## mean_Alpha_P  12.478328 2.669698
## Beta_P         1.095183 1.004135
## Alpha_X1986_P  9.027714 2.494158
## Alpha_X2003_P 17.247852 2.857593
div_angola$links
##                 Species   Phylum
## Gamma_L       54.570083 3.812301
## mean_Alpha_L  47.556571 3.791652
## Beta_L         1.147477 1.005446
## Alpha_X1986_L 35.532836 3.410505
## Alpha_X2003_L 63.648943 4.215394

We see a higher \(\alpha\)-diversity in 2003 compared to 1986 both on nodes and links and both at Species and Phylum resolution. Moreover, pairwise dissimilarity indices (both on nodes and links) are also implemented in metanetwork (see compute_dis documentation).

dis_angola = compute_dis(meta_angola)

#nodes and links dissimilarity at Species resolution
dis_angola$Species$nodes
##           X1986     X2003
## X1986 0.0000000 0.1311726
## X2003 0.1311726 0.0000000
dis_angola$Species$links
##           X1986     X2003
## X1986 0.0000000 0.1984655
## X2003 0.1984655 0.0000000
#nodes and links dissimilarity at Phylum resolution
dis_angola$Phylum$nodes
##             X1986       X2003
## X1986 0.000000000 0.005952805
## X2003 0.005952805 0.000000000
dis_angola$Phylum$links
##             X1986       X2003
## X1986 0.000000000 0.007835491
## X2003 0.007835491 0.000000000
#compute dissimilarity at Phylum resolution only
compute_dis(meta_angola,res = "Phylum")
## $Phylum
## $Phylum$nodes
##             X1986       X2003
## X1986 0.000000000 0.005952805
## X2003 0.005952805 0.000000000
## 
## $Phylum$links
##             X1986       X2003
## X1986 0.000000000 0.007835491
## X2003 0.007835491 0.000000000

We see that networks are more dissimilar at Species compared to Phylum resolution both on nodes and links. Moreover, at both resolutions, network are more dissimilar regarding link abundances compared to node abundances. To gain in efficiency, compute_dis uses parallel computation (see ncores argument in compute_dis documentation)

References

  • Angelini, R., & Vaz-Velho, F. (2011). Ecosystem structure and trophic analysis of Angolan fishery landings. Scientia Marina(Barcelona), 75(2), 309-319.

  • Ohlmann, M., Miele, V., Dray, S., Chalmandrier, L., O’connor, L., & Thuiller, W. (2019). Diversity indices for ecological networks: a unifying framework using Hill numbers. Ecology letters, 22(4), 737-747.