Modeling the influence of biotic interactions on the spread of the invasive vine Mikania micrantha: A graph theory approach
Invasive herbaceous vines are increasing in abundance in different parts of the World. In tropical regions these vines often form dense patches of multiple species that smother vegetation and human-made structures. These patches exhibit a large variation in species composition and abundance, and we hypothesized that invasion success of some vine species is driven by interactions with other vines. Specifically we ask how the strength of negative and positive vine interactions contributes to the large-scale spread of the invasive vine Mikania micrantha in the island of Puerto Rico. We used graph theory to 1) model the spread of M. micrantha as a network of potential habitats, 2) examine the influence of biotic interaction on the structure and connectivity of the network, and 3) examine the effect of different removal strategies on the spatial extent and connectivity of the networks. Focusing in the central region of Puerto Rico, we created three networks depicting competitive, facilitative and no interactions between M. micrantha and other vines. We measured the node degree distribution, connectance and clustering coefficient of each network to compare the structure and connectivity between networks.
Our results indicate differences in the size and connectivity of the three networks. The network that did not include biotic interactions was the largest with 2,935 nodes, followed by the networks depicting competition, and facilitation with 2,433 and 861 nodes, respectively. Including facilitation between M. micrantha and other vines resulted in a highly connected network consisting of only 2 connected components, whereas the absence of biotic interactions resulted in a network with 4 components. However, both networks are dominated by one large component of 859 and 2,929 nodes, respectively. Including competition resulted in a network of 66 components, with one large (2224 nodes) and 65 smaller components (2 -18 nodes). The total area covered by the networks was strongly influenced by biotic interactions. The networks depicting no interaction and facilitation spanned across most of the study area, while the network depicting competition restricted the spread of M. micrantha to a smaller area. These results show how a graph-theory approach can help us to understand the regulating effect that biotic interactions can exert on the spread of invasive species. Furthermore, our results can contribute to the development of plans for the management and control of invasive species.