A graph theoretic approach to assess vulnerability of lakes to species invasions

Background/Question/Methods

Quantifying the connectivity of fragmented landscapes is essential to modeling and mitigating the spread of non-native species. A key element of the connectivity of a landscape is the degree and extent to which organisms disperse through natural and built environments with human assistance. The goal of this study was to determine how the interaction between the connectivity of the landscape and the environmental suitability of receiving habitats affects the vulnerability to invasion of lakes in Wisconsin and the Upper Peninsula of Michigan, using a graph theoretic approach. The primary mechanism of spread of many non-native species through these lakes, including Eurasian watermilfoil (Myriophyllum spicatum) and zebra mussels (Dreissena polymorpha), is by propagules "hitchhiking" on recreational boating gear. We used graph theoretic indices to quantify connectivity of a network of almost 5200 lakes given contemporary boater activity. Using an empirical distribution of recreational boater movements from the literature, we calculated the number of sub-components, the number of links and the probability of connectivity in the network to identify lakes that are important hubs of connectivity and those that may be vulnerable to the arrival of non-native species.  We combined this information with the predicted environmental suitability of each lake from logistic regression analysis to quantify the probability of invasion by the non-native species.

Results/Conclusions

Analysis of the probable connectivity given the empirical distribution of boater movements identified 13 separate components in the network (with an empirical interval of 1 – 61 components).  The degree distribution of the contemporary network approached that of a random network which indicates that within each component, the majority of lakes had a similar number of connections given recreational boater movements.  However, six lakes, three of which were artificial impoundments, were identified as key hubs in the network acting as intermediate nodes between what would be otherwise spatially isolated network components.  Combining the probability of connectivity with the predicted environmental suitability of each lake to the non-native species, identified the vulnerability to invasion of each lake.  Identifying vulnerable lakes in the region given these two elements of the invasion process is an important step to slowing and possibly stopping the spread of invasive species into as yet uninvaded lakes. Combining graph theoretic approaches with statistical models can help identify specific lakes at which efforts to mitigate the invasion process may have the greatest effect while accounting for uncertainty due to network structure and statistical model uncertainty.