Reducing the Complexity of Ecological Interactions
- scottmorello
- Sep 27, 2017
- 8 min read
In nature, the interactions between species can be incredibly complex. For instance, let’s say we have 3 species living on a rocky shore (of course I chose “rocky shore”). All 3 of these species might interact directly with each other in at least one of many ways. For example:
1) Species A and Species B competing over a resource, like food, or attachment space on the rock
2) Species A gets eaten by Species C
3) Species C eats Species A
Each of these interactions controls each species’ abundance on the rocky shore to some degree. Beyond these direct interactions, species might also interact indirectly through other species. For example:
4) If Species C eats Species A, then Species C indirectly benefits competitors of Species A (i.e. Species B)
An ecologist’s job is to figure out which of these interactions are changing over space and time, and how they are leading to different abundances and groupings of species - known as species “communities”. As you can see from the examples above, this process is difficult enough when only 3 species are involved, and ecologists are typically dealing in systems with far more than 3 species. With every additional species added to the mix, the number of possible interactions an ecologist needs to account for increases exponentially, requiring a proportional exponential increase in number of experiments needed to tease apart each interaction’s effects on species. This quickly becomes unsustainable, and so ecologists often focus on a very reduced subset of the total possible interactions in nature - typically the ones involving the most abundant species, and based on the current understanding of an ecosystems natural history. For example:
- An ecologist looks at a rocky shore and thinks “hey- there is a lot of Seaweed A here. I know Snail B eats Seaweed A, and Crab C eats Snail B. I think I’ll just look at the interactions between Seaweed A, Snail B, and Crab C.”
There are usually more complex thoughts and designs surrounding ecological experiments, but typically nothing accounting for the entire complexity of the ecosystem. Ignoring species and interactions, even if they are rare, can bias your results though - oftentimes due to those less obvious indirect interactions I mentioned earlier (i.e., C —> A —> B). To most comprehensively determine which changes in species interactions are most important to changes in species communities, we need to study as many species and interactions as possible then… and preferably do so in the simplest way possible.
During my PhD, I developed a new approach to simply, but quantitatively, determine which species interactions within complex interaction webs change as you travel across large distances. In my case, I looked at species interactions in the rocky intertidal, and how they change as you travel across New England (from Cape Ann, Massachusetts to Pemaquid, Maine, to Bar Harbor, Maine). Central to my approach was building Markov Chain Models (which I’ll refer to hereafter as MCMs) for multiple rocky shores (sites) within those afformentioned regions spread across New England. MCMs are matrix models that use tables describing the probability of changing from one thing to another over a fixed period of time. For instance, and an example relevant to my research, if there is a mussel sitting on this rock right now, what is the probability that there will be a barnacle in its place when I come back in a month? I can quantify this probability by just monitoring a single spot on a single rock every month. I take that data describing what species was occupying that spot every month, then only look at the times I saw a mussel at that spot. I then calculate the frequency a mussel changed to a barnacle by the next month as:
# of times a mussel changed to a barnacle / total # of times there was a mussel at the spot
If you do this for every combination of species, you can calculate a full table of “transition probabilities” that describe the probability of transitioning from any species on a rocky shore to any other species possible on the rocky shore. Somewhat interesting, but who cares? Well, these individual probabilities can correspond to those complex species interactions I described before! Transitions from a mussel to the same mussel (#1 in the figure) reflect the mussel surviving. Transitions from bare rock to a mussel (#2 in the figure) can reflect a baby mussel settling on the shore (i.e., mussel recruitment). Transitions from that same mussel back to bare rock (#3 in the figure) can reflect the mussel dying (but we wouldn’t know if it died because it was eaten by a crab, or knocked off by a wave or something, because we didn’t see it die). The transition from a mussel to a barnacle (#4 in the figure) could represent the barnacle outcompeting the mussel for space on the rock. So, this large table of probabilities can be used to simulate complex interactions among species in a model (i.e., a Markov chain model).
I quantified this table of transition probabilities for 3 rocky shores at each of 3 different regions across New England (Cape Ann, Massachusetts = CA; Pemaquid, Maine = PQ; Bar Harbor, Maine = BH) by monitoring 150 spots at each shore every two months for around 3 years. In total, 14 different species groups were found, meaning each table had 14 things a point could possibly transition from or two, yielding 196 transition probabilities for each shore!
After quantifying the transition probability tables, we needed to make sure the probabilities accurately captured the complex species interactions at each shore. We let the Markov chain model predict what species community should develop on each shore according to the transition probabilities, and then compared the predictions to measurements of the actual species community on each shore. The MCMs did a great job predicting actual species communities, on average capturing over 97% of the variation in species abundance on a shore.
Confident that transition probabilities were accurately capturing the species interactions for each rocky shore, we looked at how probabilities varied across New England. Based on prior research, we knew that rocky shore species communities can change drastically as you travel from southern to northern New England, and that changes in transition probabilities over this spatial scale can dramatically alter the Markov chain model predictions. Comparing the transition probabilities across these spatial scales would thus help us understand which species interactions were changing and leading to different rocky shore communities across New England!
We analyzed differences in the transition probabilities in a variety of ways (log-linear analysis, permutational MANOVA, individual ANOVAs on properties and dynamics of the probability tables). The most intuitive way to visualize differences between Cape Ann, Pemaquid, and Bar Harbor transition probabilities was with a combination of a CAP analysis (Canonical Analysis of Principle-coordinates), and a network visualization. The CAP analysis uses a combination of two analyses (principle coordinates analysis and a discriminant function analysis) to take data with lots of variables that might be correlated (i.e., the 196 possible transitions reflecting species interactions) and reduce it so we can view the vast majority of variation on a few (in our case, 2) axes on a plot. Each point in the plot reflects a transition probability table from a rocky shore we looked at, and the points disperse themselves around the graph according to how similar their transition probability tables are to each other - the closer they cluster to each other, the more similar the transition probabilities. In the figure below, we also use color to depict our different regions (Cape Ann = Blue, Pemaquid = Red, and Bar Harbor = Black), and shape to depict transition probability tables from different seasons (spring/summer = triangle, fall/winter = square, with a dotted line connecting the two seasons for the same shore), so we can more easily visualize differences.
These CAP analysis results display how transition probabilities from rocky shores in the same region were similar, no matter the season, but were very different from transition probabilities in other regions. The CAP analysis also showed us which transitions, out of all the 196 possible, changed the most among our regions. Taking just those most important transitions (the top 20%), we visualized how probabilities changed between regions with networks. In each network below, each node (circle) represents a different species (the two letter codes refer to species group names), and the arrows connecting the nodes represent the direction of the transition. The thickness of an arrow indicates how different the two probabilities were between two regions (thin arrow = only a little different, thick arrow = very different), and the color of the arrow indicates the region with the higher probability (e.g., in a Cape Ann vs Bar Harbor comparison, a blue arrow indicates Cape Ann had the higher probability).
To focus in on one very noticeable difference between Cape Ann, Massachusetts and Bar Harbor, Maine in the spring/summer, Cape Ann (blue) has higher probabilities of transitioning to a blue mussel (ME, Mytilus edulis) from other species, and from bare rock (BS and EC, two different types of settlement surfaces). Bar Harbor (red), on the other hand, has higher probabilities of transitioning to an acorn barnacle (SB, Semibalanus balanoides) and the barnacle persisting. Based on prior research, we know that mussels are very good at outcompeting barnacles (and just about everything else) for space on rocky shores (they settle on top of barnacles and other species and smother them). The transition probabilities are telling us that Cape Ann seems to have lots of mussels settling in the spring and summer (transitons from bare rock to mussels, BS—>ME and EA —> ME), and that mussels then outcompe other species for space on the rocks (all the arrows going to ME). By contrast, in Bar Harbor, mussels don’t seem to be settling in as high numbers, and so they are not outcompeting other species like barnacles for space. Barnacles are thus surviving much longer in Bar Harbor (SB —> SB) and not giving up any space. Over a long enough time, this allows barnacles to take over the rocky surface. The results of these dynamics are very clear if you actually look at the species communities at Cape Ann and Bar Harbor rocky shores.
So there you go. There are a lot of other uses for transition probabilities in ecology, but my research demonstrates how they can be very effective at reducing the complexity of species interactions in nature, and help us determine exactly which interactions are changing across space and leading to different species communities. Any conclusions you generate from the probabilities will eventually need to be tested with experimental manipulations of different species - this is the best way to really develop an understanding of causal relationships in science. Nevertheless, the simple framework I briefly outlined above can be used to focus those more in-depth experiments in a very quantitative way, rather than based on what species is most abundant, and qualitative assessments of natural history.
For more on my transition probability research feel free to checkout some of the work I’ve published on the topic… or email me and ask!
Or, feel free to read some manuscript drafts (one in review, one in press, one published):
Comments