Paper: Hamilton's r vs. Ohtsuki's k

A recent paper by Wolf et al. in The American Naturalist looks at the relation between genetic relatedness and social structure from a new angle. The authors compare two parameters that should predict the level of cooperation in a society. Hamilton's rule of kin selection (1964) suggests that an individual A should cooperate with B if the benefit to B, relative to the cost to A, is more than the inverse of the genetic relatedness between them (b/c > 1/r), i.e. that you'll have a stronger will to help a closer relative. Studying (rather simple) model networks, Ohtsuki et al. (2006) suggested that cooperation is favorable when b/c > k, k being the average number of neighbors in the network, meaning you'll have a stronger will to help someone if the network is more sparse.

In a study of sea lions in the Galapagos, they compared r and k in different social levels: individual, clique, and community. They found a strong negative correlation between r and k in all social levels, meaning that k and r capture similar structural information in the population.
It is suggested that individuals may prefer associating with their relatives, although it's hard to understand how they "know" their relatedness to any other individual (I can think of some olfactory mechanisms that may facilitate this).

The  authors raise the concern that k may not reliably represent K, the "real" average for the population over longer timeframes (data was collected over a 3-month period). I also share this concern, especially since only one population was used. However, from my experience, if three months are enough for getting a "saturated" network in the sea lions, then more observations would contribute little to the analysis. One more concern considers their use of filtered binary networks, where a lot of information is lost, especially about weaker associations. This analysis seems like one that could gain more power from a weighted network, where the strength of each tie is taken into account.

Community Detection

Of all topics in general network theory, my favorite is community detection. For some reason I can't stop reading about new algorithms, analyzing them and trying them on my data.

So what is community detection? Every network can be subdivided into sub-units which are groups of closely connected nodes (or individuals). In animal populations, communities can be groups of animals, couples or even solitary individuals. As usual, the categorization is dependent on the definition of a connection in the network. In the past researchers were using their own intuition or very basic calculations in order to decide which individual belongs to each group. While in some species its simple and clear to make this decision, in others, like the hyrax, it's not trivial. Some hyraxes are clearly part of a group, while others are occasionally seen out of the group, or even with another group. In these cases, it's not easy to decide to what group they belong. This decision has many consequences, as any analysis at the group level, or comparison of individuals from different groups, will depend on the definition of group members.

Community detection algorithms try to solve this problem by taking into account the connections (edges) each node has with all other nodes. There are many algorithms out there, reviewed by Fortunato. I'm not going to exhaustively review them - I would like to mention 3 algorithms I found to do an accurate job, that are relatively easy to use. One thing that is important to the mathematicians who invent most of these algorithms is their complexity, or the time it will take to run. For animal researches this is usually not a real problem, as the numbers of individuals/relations are small. Therefore, I don't care if an algorithm is heavy on resources.

The first algorithm, and one of the most famous in the field, is called Girvan-Newman, and was published in PNAS in 2002. This algorithm computes the betweenness centrality of each edge, and then removes the edge with the highest betweenness, assuming that it connects communities and cannot be inside a community. In the next step the betweenness of all edges is recalculated, and again the edge with the highest value is removed. When the algorithm stops the result is a tree describing the levels of connectedness. Later, a stop mechanism was developed, based on a measure called modularity, to try and decide when should the algorithm stops if the "right" number of communities is unknown. Girvan-Newman can be calculated using UCINet. Although it performs very well, there is some critique on the use of modularity, and newer algorithms were developed.

The second algorithm is called CPM, or clique percolation method (published in Nature in 2005). This algorithm works in a different way, trying to connect more and more cliques of closely related nodes. In contrast to the Girvan-Newman algorithm, this one allows for community overlap, so that one node can be part of more than one community. It works by starting with cliques of a given size k, and then adding to them the members of other cliques that share k-1 nodes, until no more cliques can be added. One disadvantage is that you have to define k, or test which k gives the best results, which brings us back to the question of what is the best result. Another drawback is its inability to find communities of size 2, as cliques contain 3 or more members. There are versions of this algorithm that work on directed or weighted networks. A software named CFinder implements this algorithm.

A result of CPM

The last algorithm for today is called Link Communities and was published in Nature in 2010. This one also allows for community overlap. Its idea is that many nodes belong to more than one community (for example, a person might be part of his family, his workmates, his friends at the bar, etc), but the links between individuals usually represent only one kind of connection. The algorithm gets complex in finding the right links to join, and produces very accurate results. It has no resolution problem, meaning you can find any number of communities you wish, but calculates the best answer in terms of partition density. Rob Spencer from Scaled Innovation created a beautiful implementation, which shows the communities of each node, and the partition density function:

All of these algorithms performed well on my hyrax data, usually accurately identifying the "right" members of each group.
I am sure that the last word was not said yet, and new algorithms are about to be developed. It will be interesting to see if and when this field gets saturated, and what algorithms will "win" and become standard.

Paper: Social and Genetic Effects on Fitness

A recent paper by Frere et al. published in PNAS examines the interaction between social and genetic factors that affect fitness in dolphins. This is the first study to go beyond the social relations themselves, combining genetic data to form a more comprehensive perspective. The authors used data from a population of bottlenose dolphins in Shark Bay, Western Australia, that has been studied for more than 20 years. There are separate groups for females and males in this population.

The results show that genetic and social factors interact to influence female fitness, in terms of calving success. Although pairs of females that are closely related have similar fitness, and also pairs of females that are socially close, there is weak correlation between relatedness and social preference. Other factors, like time spent in a social group and home range size, were not found to correlate with calving success.
To summarize, this study shows the combined influence of relatedness and sociality on fitness. It is interesting that sociality seems to be more important here than genetic relatedness. Females with more strong associations with other females succeed more as mothers, although it's not clear if socializing contributes to maternal care or maybe better mothers tend to socialize more with one another.

Methodological highlights:
- The addition of genetic relatedness to social relations.
- The use of the pedigree-free animal model to quantify the effect of social relations.

Paper: Heritable Social Attributes

A recent paper by Lea et al. from Dan Blumstein's lab in UCLA states that while many morphological and behavioral traits of animals were shown to be heritable, the role of genetics in social interactions is not yet understood. The researchers constructed positive and negative networks based on different types of interactions between yellow-bellied marmots (Marmota flaviventris). The social traits of each individual were classified as agonistic or affiliative; direct (i.e., measure based only on interactions including the individual) or indirect; and initiated or received.

Surprisingly, agonistic in-degree and attractiveness, and affiliative in-degree were somewhat heritable, but not initiated properties. Measures based on direct interactions were more heritable than measures based on indirect ones.

The authors suggest that the lack of heritability in initiated agonistic traits may be due to the fact that these traits are already fixed in the population, i.e. that sociality caused the need to be aggressive in order to survive in a competitive social unit.

It was also found that marmots attacking more individuals lived longer. Individuals receiving more agonistic interactions had lower fitness in terms of reproductive success over lifetime. As receiving agonistic interactions is heritable, it shows that there are genes that lead to low social rank. Interestingly, marmots that are more central in the agonistic network have higher fitness and longevity. The authors state that "It is possible that a central and integrated position in the social group (which presumably results in more affiliative and agonistic partners and interactions) produces more benefits than the costs associated with the aggressive interactions themselves".

Personally, I believe that no one "wants" to receive agonistic interactions, and that the shown benefits of it in this paper actually point at the benefits of sociality, as negative and positive interactions were found to be highly correlated here. The results of this study surely call for further examination.

To summarize, the methodic highlights are:
1. First comparison of genetic vs. social attributes of animals.
2. The analysis of affiliative vs. agonistic networks.

Again, the importance of long-term studies on individually-identified animals proves its advantages.

Welcome

In this blog I intend to report and discuss the use of social network analysis in the study of animal behavior. The recent advances in the field of networks analysis in the last decade enable biologists studying animal behavior to quantify the social relations between individuals in a way that was not possible before. While in past you could only measure very basic properties of a social structure (e.g., group size, group sex composition), now you can quantify many more aspects of social living, both at the individual and group level.
Most past studies used social rank, or hierarchy, based solely on negative interactions. I believe that while negative interactions are important, in many species it is the positive ties that can tell us much more about the strong (and weak) individuals in a social system.

I came to learn about social networks while studying communication and social behavior of the rock hyrax in the Judean Desert in Israel. I found network methods to be extremely helpful in describing the social structure of my study population.

Hyraxes in Ein Gedi

While the first studies of animals using social networks were mostly descriptive, drawing the social interactions between individuals, recent studies revealed correlations between individual social attributes and fitness. These recent works emphasize the importance of the social relationships an animal has with its conspecifics in determining its life history and fitness. Such studies were not possible without applying social networks methods to data collected from animal observations.

I expect that the usage of network methods will change the way we view sociality in animals, as it has already began in humans. The next decade will bring with it a new thinking about the evolution of sociality and its role in animals' lives.

In my next posts I plan to discuss some relevant papers, and also some general issues like methodology, the kind of questions we can answer using social networks and the integration between animal and human studies, among other topics.