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SEEDless

Yesterday, while on a very long flight, I read the latest Seed Salon in Seed Magazine. It is a conversation between network theory guru Albert-Laszlo Barabasi (author of the bestseller “Linked”) and social scientist James Fowler (of the “Colbert Bump” fame). The two discuss the growing popularity of network representations of natural and human structures, including the internet, Facebook, and gene interaction networks. It is a very lively conversation, and quite good, with a few glaring exceptions. I’m going to highlight these.

About two-thirds of the way through the conversation, Barabasi points out that online social networks seem to differ fundamentally from “real-world” networks, in that online networks tend to have hub individuals. That is, they have popular individuals with many links, to whom are linked individuals with relatively fewer numbers of links. Similar patterns occur in many natural networks, such as metabolic and gene networks (though there are exceptions, and the jury is still out on many of these cases). But in real-world social networks, those hub or popular people tend to be linked to other popular people, not people with fewer links. Fowler then takes off with this, stating that recently, he and colleagues have found evidence that there’s a genetic basis for human social networks; the number of friends you possess is heritable. That is, if he is using the correct definition of heritability, the variance of the number of friends that individuals in a population possess, is largely explained by genetic variation among those individuals. Really?! Fowler goes on to list traits underlying “number of friends”, such as physical attractiveness, good communication skills, having assets, you know, all those things that we “know” to have a genetic basis in humans, and a genetic basis that we understand. Nevermind that earlier Barabasi pointed out the combinatoric basis of cancer in gene networks, in which more than 300 genes can be involved. Yet, Folwer implies that we can break down the possession of assets to genetic and Darwinian bases. I don’t disagree with Fowler when he says that Darwinian natural selection may play a role in the development of social networks, but that is a far cry from being able to list heritable traits, as well as understanding the strength of selection necessary for accomplishing this feat.

Gets worse, in my opinion. Barabasi is intrigued by Fowler’s idea,and goes on to give a somewhat counter-example. It has been noted that many biological (gene) networks are scale-free, and Barabasi points out that they are so, because of the constrained manner in which these networks grow. New genes tend to be added to a genome via duplication, and apparently in Barabasi’s hypothesis, only scale-free networks can emerge from this growth process. Fowler: “…if they’re all scale free, then that suggests that natural selection isn’t the cause.” Barabasi: “Right. … the scale-free state of the cell, the existence of hubs, is not because the cell has optimized itself to be resilient… It’s really coming from the way the cell… is created from the growth process.. Since hubs happen to be a desirable property, there is no reason for natural selection to delete them.” WHAT?!!! If anything, this is strongly suggestive of a role for selection in the evolution of the growth process itself. And, natural selection does not delete properties. If there is variation in a property, in this case the growth process or link distribution underlying a gene network, and that variation leads to a difference in performance, in this case resilience against gene disruption or deletion, then the variant that is borne by more offspring in the succeeding generation has been selected for. As simple as that. Otherwise, what would have constrained an ancient and ancestral molecular lineage from possessing a genome that grew as a random, Poisson network? It is absolutely premature to discount the role of selection here.

Okay, with my rant being over, Barabasi raises a very interesting question toward the end regarding a shift in the emphasis of scientific adventure to “humanity turning inward.” Fowler’s response is very insightful. If you’re interested, read the article; an online version is available here.

Hmmm…

I just can’t see how, in a topological secondary extinction-only situation, you could ever get higher levels of secondary extinction than you would in the presence of link strength compensation and top-down cascades. This really calls into question the previous results. Therefore, I’ve either overlooked something so far, or, I’m looking at the wrong set of results!

I’ve been out of the office and lab now for the better part of a month; just can’t seem to get healthy. I can’t check these results, really, without being able to sit down with the big computers. Hopefully, I’ll be back to work next week. A Miami Dolphins victory tomorrow could be just what the doctor ordered.

Next step

I’ve been reading one of Wolfram’s earliest papers on cellular automata, “Statistical mechanics of cellular automata“, and there are some striking similarities to themes and approaches that he utilized to explore elementary (and beyond) automata, and my attempts to understand some aspects of the CEG model, namely variance and criticality. The CEG model, however, while founded on necessary and sufficient ecological first principles, generates a level of complexity that does not allow the level of insight that Wolfram gets into the CAs. For example, I’ve looked at sensitivity to initial network configurations using an estimate of Hamming distance, but the relationship between Hamming distance and remains unclear. So, I’m going to begin again by deconstructing CEG and re-building incrementally. The first step is to implement the iterative matrix approach to topological extinction, to see how much of the full model is reproducible.

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Quick update

Frequent references are made to CEG, which stands for Cascading Extinction on Graphs. It is a model for examining the manner in which perturbations or species removals from a food web cascade or propagate through the web. The basics, and some application of CEG have already been published, and those references may be found here.

Metanetwork state space

Each metanetwork is a higher (than species) level representation of ecological/functional diversity within the community. Species sharing the same potential prey and predators are grouped into guilds. Trophic connections among guilds are certain. From each such metanetwork are derived species-level trophic networks, where links or interactions among individual species are specified. The CEG model derives these lower level networks stochastically, reflecting both uncertainty in the specific topology of the food web, as well as the fact that this topology is expected to vary on ecological spatial scales, and on evolutionary temporal scales. Stochastic derivation is controlled by drawing the number of in-links of any given consumer from a trophic link distribution assigned to that species guild. The link distributions are decay distributions (generally exponential, power law, or a mixed exponential-power law), reflecting the relative proportions and ranging of species within a guild from extreme specialists to generalists. The distributions are also truncated, with an upper limit set, of course, by the maximum number of prey species available to a guild.

Truncation of the link distributions therefore means that while derivation of a species-level network from is stochastic, the number of such networks is finite, defining a state space for . The size of the state space is calculated by first determining the in-degrees of all consumer species. Let the in-degree of species ( is a member of guild ) range , where is the element of ’s binary adjacency matrix. The sum is therefore the total species richness of all guilds that are prey to guild . Given a guild trophic link distribution , and an in-degree of equal to , the total number of configurations of ’s in-links is

Within a guild, the number of species of a particular in-degree is estimated discretely as

where is, again, the species richness of all ’s prey guilds. The total number of species-level topologies in is therefore the product of all in-link configurations possible for all species, and where represents a type or category of species within a guild , this total is

This blog

A brief introduction for anyone, besides myself, who might stumble across this blog. It really is a personal working blog. I’m a paleontologist and evolutionary ecologist at the California Academy of Sciences. One of my main areas of research is the reconstruction of paleocommunities and food webs, and the relationship(s) between those structures and extinction. It’s a very difficult topic for a number of reasons, some related to data availability, but mostly mathematical. I therefore tend to keep a series of notebooks, logging all my work. My working group and I also kept a wiki for awhile, but I simply didn’t upgrade it when I upgraded my lab server. As one of my other activities here at the Academy, I write the Climate Change Blog, and it occurred to me this morning, that perhaps I could use WordPress to blog my research notes! (duh). A quick search on Google told me that WordPress has capabilities, and so here I am.

There is a small danger in doing this blog. One of my colleagues always insisted that we keep our wiki private, and I agreed, because our unpublished scientific work is our own. So the danger is that by putting my thoughts and work out here in the blogosphere, I could open myself up to having my work misappropriated, or being scooped. On the other hand, if any of my thoughts are horribly wrong, then please, by all means, take them and run with them.

Okay, as a parting message from this introduction, here is a link sent to me by one of my graduate students yesterday (also see the video). It is a conversation involving Steve Strogatz, a mathematician whose work has been very valuable to my own. It pretty much sums up the difficulties with my own work, and is both uplifting and depressing. But, hard work never killed anyone! Wait, that’s probably not true.

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