Theme 3 | Functional Complex Networks

When looking at a forested landscape, one can see a patchwork of forest stands of different ages, composition, and physical contexts (slope, soil, etc.). While we might not see it with our human eyes, these forests are connected together in many ways, like in a huge network. In particular, forests can disperse the seeds of the trees they contain into adjacent forests, allowing for the transfer of biodiversity from one forest to the other.

It is not just biodiversity of forests that can propagate in such a way, but also their functional diversity. Indeed, as trees with different functions can migrate from neighboring forests, the forest they migrate to might see its functional diversity arise. There is more : if a forest suffers a disturbance which wipes out many tree species at once (like a disease), these same tree species might come back into it by dispersing from neighboring forests, offering resilience to the original forest.

In the past few years, several publications have developed the concept of the Functional Complex Network, as well as determining the configuration of such networks in several Canadian landscapes (see Aquilué et al., 2020). We’ll be using this concept as another way to quantify the resilience of the forests in our 22 research sites.

In Theme 3, we will assess the resilience of forests through 5 indicators. The first two indicators are the same ones used in theme 1, being the functional diversity and functional redundancy of the forests in our research sites. The three other measures are computed once the functional network for the area is determined, by looking at the configuration of forests in the landscape, and at the dispersal capabilities of the tree species they contain : the probability of connectivity (PC), the Betweenness Centrality Index (BCI) and the modularity of the network (all explained below).

Following this, we will produce maps of resilience for each research site, using the R Shiny package to present them as interactive web applications. These maps will show how the functional diversity, functional redundancy and BCI change across the forests of the site, as well as showing the PC and modularity of the network. These maps will presente guidance as to what forest operations to use in order to increase these different measures, which should increase the resilience of the forests in the research sites.

The first step will be to determine the Functional Complex Network inside each of our research sites. The network takes the form of “nodes” (representing forest stands), connected to all surrounding nodes with “links”. Each link is associated with a value representing how much of the functional diversity of one node can disperse to the other, depending on the distance between the two nodes and on the functional diversity and redundancy of the forests in each of them (as calculated in Theme 1).

Then, once the functional network is identified in the area, the first measure that we will compute from it in each research site is the probability of connectivity (PC). PC is the probability that two random points in the landscape might be able to share the functional diversity of the forests in which the points are, whether because the two points are in the same forest or in two forests well connected to each other. While its definition is complex, the consequences are simple : the higher its value, the more the forests of the research site can transfer their functional diversity to each other, ensuring a form of forest resilience. The second measure computed from the network is the Betweenness Centrality Index (BCI). BCI estimates the importance of each node in the network, by measuring how often the nodes serve as a stepping stone to connect other nodes. The nodes with the highest BCI can therefore be identified as being crucial to the transfer of functional diversity in the landscape.

We will end by computing what is called the “modularity” of the network. Modularity expresses how much a network is composed of “clusters”, meaning nodes that are highly connected together, but not very much to the rest of the network. Imagine two cities that are linked by a single road : one can move from house to house very easily inside each city, but if you want to go to a house in the other city, only a single road is available to you. In this example, the cities are clusters; the houses are nodes; and the roads are links. Having a “modular” or “clustered” structure is not such a bad thing, however; as forests can suffer from diseases that transmit from host tree to host tree, a modular structure can slow down the propagation of the disease in many ways.

With all of these computations done, we will create a R Shiny web app that will allow the visualization of these measures for each of our research sites in an easy way.