My last post looked at a very small, but well studied rocky intertidal ecosystem and was able to identify a keystone predator (Pisaster) in a network using centrality measures. I was worried, though, that this method would not work on a larger, more complicated system. Let’s try these same calculations on a slightly larger kelp forest ecosystem. These systems are commonly found on the west coast of continents and are characterized by the presence of large kelps. The sea otter, Enhydra lutris, is an important predator of herbivores (e.g., sea urchins) that eat macroalgae. In the absence of sea otters, sea urchin populations explode and overgraze the kelp. Will centrality measures be able to identify the sea otter as a keystone predator? In this network, I had trophic interactions, competition interactions, and new “habitatFor” interactions that described a relationship between two taxa wherein one provided habitat for the other. My initial list contained 69 interactions and the centrality measures were all pointing to the kelp as the keystone species. This is likely because the kelp provided habitat for nearly every species in the kelp forest.
This raises an interesting question regarding our definition of keystone species. Without the kelp there is no kelp forest and that’s why the centrality measures pointed to the kelp, but the sea otter is thought of as the keystone species is this system. An important part of the definition of a keystone species is its relative abundance. Keystone species are supposed to have a disproportionate effect on the ecosystem relative to its abundance. The kelp have a very large effect, but are also very abundant. The sea otters have a large effect and are nowhere near as abundant as the kelp. That is what makes the sea otter the keystone species and not the kelp. I can’t help but think that otters being cute and cuddly while kelp are cold and slimy has something to do with it.
An algorithm that identifies kelp as a keystone species of a kelp forest is not very helpful. The kelp are more of a foundation species. How can we identify the sea otter as a keystone species even though the kelp are far more influential? One strategy that is most direct is to include the relative biomass of each taxon, but this is often not known and not included in databases of networks and interactions. I am going to try and find a way to make the network calculations work, but the results of the various network measures are not very helpful (most point to the kelp as the most important) except for closeness vitality, which is highest for the sea otter. When I do the calculations on a network made up of only the trophic interactions, as I did with the rocky intertidal system, the sea otter comes out on top in all the centrality measures. This supports the importance of dividing the network by interaction type before analysis.
Two additional issues come to mind:
- How can I compare centrality measures across networks with different numbers of nodes, edges, and different degrees of connectivity?
- How does the size and granularity of a network affect the results of the connectivity calculations?
The first issue is relatively straightforward. The calculation results can be normalized against the highest value; thus, the highest result for each network is always 1. When I do this normlization, the values for Pisaster and the sea otter are both 1 and thus comparable.
To explore the second issue, I played a few games with the interactions in the kelp forest ecosystem. In the original list of 69 interactions, I have some that are a bit repetitive:
- Enhydra lutris, eats, Strongylocentrotus franciscanus
- Enhydra lutris, eats, Strongylocentrotus purpuratus
- Enhydra lutris, eats, Strongylocentrotus droebachiensis
Strongylocentrotus is a genus of sea urchin. Each species of sea urchin is listed as eating the same five species of macroalgae. So, the network has three nodes (the three Strongylocentrotus nodes) with identical edges. What happens to the results if I collapse these three identical species nodes into one genus node? The answer is not much. The kelp still has the highest connectivity in the network containing all the interactions and the sea otter still has the highest connectivity in the network with only trophic interactions. In the end, I collapsed the urchins into one genus, but the macroalgae was grouped by annual kelp and perennial kelp. Clearly, I need to develop some guidelines for lumping nodes consistently. Considering the high degree of taxonomic change in some groups, having genus- or family-specific nodes may be more desirable than species-specific nodes. In some cases a node defined by function instead of taxonomy may be better.
The data files for this work can be found in the github repo.
The sea otter image is CC-BY-NC from Biopix.