Darwin meets Category Theory in the Tangential Space

For this Darwin Day (February 12), I would like to highlight the relationship between evolution by natural selection and something called category theory. While this post will be rather tangential to Darwin's work itself, it should be good food for thought with respect to evolutionary research. As we will see, category theory also has relevance to many types of functional and temporal systems (including those shaped by natural selection) [1], which is key to understanding how natural selection shapes individual phenotypes and populations more generally.

This isn't the last you'll hear from me in this post!

Category Theory originated in the applied mathematics community, particularly the "General Theory of Natural Equivalence" [2]. In many ways, category theory is familiar to those with conceptual knowledge of set theory. Uniquely, category theory deals with the classification of objects and their transformations between mappings. However, category theory is far more powerful than set theory, and serves as a bridge to formal logic, systems theory, and classification.

A category is defined by two basic components: objects and morphisms. An example of objects are a collection of interrelated variables or discrete states. Morphisms are things that link objects together, either structurally or functionally. This provides us with a network of paths between objects that can be analyzed using categorical logic. This allows us to define a composition (or path) by tracing through the set of objects and morphisms (so-called diagram chasing) to find a solution.

In this example, a pie recipe is represented as a category with objects (action steps) and morphisms (ingredients and results). This monoidal preorder can be added to as the recipe changes. From [3]. Click to enlarge.

Categories can also consist of classes: classes of objects might include all objects in the category, while classes of morphism include all relational information such as pathways and mappings. Groupoids are functional descriptions, and allow us to represent generalizations of group actions and equivalence relations. These modeling-friendly descriptions of a discrete dynamic system is quite similar to object-oriented programming (OOP) [4]. One biologically-oriented application of category theory can be found in the work of Robert Rosen, particularly topics such as relational biology and anticipatory systems.

Animal taxonomy according to category theory. This example focuses on exploring existing classifications, from species to kingdom. The formation of a tree from a single set of objects and morphisms is called a preorder. From [3]. Click to enlarge.

One potential application of this theory to evolution by natural selection is to establish an alternate view of phylogenetic relationships. By combining category theory with feature selection techniques, it may be possible to detect natural classes that correspond to common ancestry. Related to the discovery of evolutionary-salient features is the problem of phylogenetic scale [5], or hard-to-interpret changes occurring over multiple evolutionary timescales. Category theory might allow us to clarify these trends, particularly as they relate to evolving life embedded in ecosystems [6] or shaped by autopoiesis [7]. 

More relevant to physiological systems that are shaped by evolution are gene regulatory networks (GRNs). While GRNs can be characterized without the use of category theory, they also present an opportunity to produce an evolutionarily-relevant heteromorphic mapping [8]. While a single GRN structure can have multiple types of outputs, multiple GRN structures can also give rise to the same or similar output [8, 9]. As with previous examples, category theory might help us characterize these otherwise super-complex phenomena (and "wicked" problems) into well-composed systems-level representations.

NOTES:
[1] Spivak, D.I. (2014). Category theory for the sciences. MIT Press, Cambridge, MA.

[2] Eilenberg, S. and MacLane, S. (1945). General theory of natural equivalences. Transactions of the American Mathematical Society, 58, 231-294. doi:10.1090/S0002-9947-1945-0013131-6 

[3] Fong, B. and Spivak, D.I. (2018). Seven Sketches in Compositionality: an invitation to applied category theory. arXiv, 1803:05316.

[4] Stepanov, A. and McJones, P. (2009). Elements of Programming. Addison-Wesley Professional.

[5] Graham, C.H., Storch, D., and Machac, A. (2018). Phylogenetic scale in ecology and 
evolution. Global Ecology and Biogeography, doi:10.1111/geb.12686.

[6] Kalmykov, V.L. (2012). Generalized Theory of Life. Nature Precedings, 10101/npre.2012.7108.1.

[7] Letelier, J.C., Marin, G., and Mpodozis, J. (2003). Autopoietic and (M,R) systems. Journal of Theoretical Biology, 222(2), 261-272. doi:10.1016/S0022-5193(03)00034-1.

[8] Payne, J.L. and Wagner, A. (2013). Constraint and contingency in multifunctional gene regulatory circuits. PLoS Computational Biology, 9(6), e1003071. doi:10.1371/journal.pcbi.1003071.

[9] Ahnert, S.E. and Fink, T.M.A. (2016). Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space. Journal of the Royal Society Interface, 13(120), 20160179. doi:10.1098/rsif.2016.0179.

Darwin as a Universal Principle

Background Diagram: Mountian-Sky-Astronomy-Big-Bang blog.

For this year's Darwin Day post, I would like to introduce the concept of Universal Darwinism. To understand what is meant by universal Darwinism, we need to explore the meaning of the term as well as the many instances Darwinian ideas have been applied to. The most straightforward definition of Universal Darwinism is a Darwinian processes that can be extended to any adaptive system, regardless of their suitability. Darwinian processes can be boiled down to three essential features:

1) production of random diversity/variation (or stochastic process).  

2) replication and heredity (reproduction, historical contingency). 

3) natural selection (selective mechanism based on some criterion). 

A fourth feature, one that underlies all three of these points, is the production and maintenance of populations (e.g. population dynamics). These features are a starting point for many applications of universal Darwinism. Depending on the context of the application,these four features may be emphasized in different ways or additional features may be added.

Taken collectively, these three features constitute many different types of process, encompassing evolutionary epistemology [1] to cultural systems [2], neural systems [3, 4], physical systems [5, 6], and informational/cybernetic systems [7, 8]. Many of these universal applications are explicitly selectionist, and do not have uniform fitness criteria. In fact, fitness is assumed in the adaptive mechanism. This provides a very loose analogy to organismal evolution indeed.

Universal computational model shaped by Darwinian processes. COURTESY: Dana Edwards, Universal Darwinism and Cyberspace.

Of these, the application to cybernetic systems is the most general. Taking inspiration from both cybernetics theory and the selectionist aspects of Darwinian models, Universal Selection Theory [7, 8] has four basic claims that can be paraphrased in the following three statements:

1) "operate on blindly-generated variation with selective retention". 

2) "process itself reveals information about the environment". 

3) "processes built atop selection also operate on variation with selective retention".

The key notions are that evolution acts to randomly generate variation, retains only the most fit solutions, then builds upon this in a modular and hierarchical manner. In this way, universal Darwinian processes act to build complexity. As with the initial list of features, the formation and maintenance of populations is an important bootstrapping and feedback mechanism. Populations and heredity underlie all Darwinian processes, even if they are not defined in the same manner as biological populations. Therefore, all applications of Darwinian principles must at least provide an analogue to dynamic populations, even at a superficial level.

There is an additional advantage of using universal Darwinian models: capturing the essence of Darwinian processes in a statistical model. Commonalities between Darwinian processes and Bayesian inference [3, 5] can be proposed as a mechanism for change in models of cosmic evolution. In the Darwinian-Bayesian comparison, heredity and selection are approximated using the relationship between statistical priors and empirical observation. The theoretical and conceptual connections between phylogeny, populations, and Bayesian priors is a post-worthy topic in and of itself.

At this point, we can step out a bit and discuss the origins of universal Darwinian systems. The origin of a Darwinian (or evolutionary) system can take a number of forms [9]. There are two forms of "being from nothingness" in [9] that could be proposed as origin points for Darwinian systems. The first is an origin in the lowest possible energetic (or in our case also fitness) state, and the other is what exists when you remove the governance of natural laws. While the former is easily modeled using variations of the NK model (which can be generalized across different types of systems), the latter is more interesting and is potentially even more universal.

An iconic diagram of Cosmic Evolution. COURTESY: Inflation Theory by Dr. Alan Guth.

An iconic diagram of Biological Evolution. COURTESY: Palaeontological Scientific Trust (PAST).

So did Darwin essentially construct a "theory of everything" over 200 years ago? Did he find "42" in the Galapagos while observing finches and tortoises? There are a number of features from complexity theory that might also fit into the schema of Darwinian models. These include concepts from self-organization not explicitly part of the Darwinian formulation: scaling and complexity, dependence on initial condition, tradeoffs between exploitation and exploration, and  order arising from local interactions in a disordered system. More explicitly, contributions from chaos theory might provide a bridge between nonlinear adaptive mechanisms and natural selection.

The final relationship I would like to touch on here is a comparison between Darwinian processes and Universality in complex systems. The simplest definition of Universality states that the properties of a system are independent of the dynamical details and behavior of the system. Universal properties such as scale-free behavior [10] and conformation to a power law [11] occur in a wide range of systems, from biological to physical and from behavioral to social systems. Much like applications of Universal Darwinism, Universality allows us to observe commonalities among entities as diverse as human cultures, organismal orders/genera, and galaxies/universes. The link to Universality also provides a basis for the abstraction of a system's Darwinian properties. This is the key to developing more representationally-complete computational models.

8-bit Darwin. COURTESY: Diego Sanches.

Darwin viewed his theory development of evolution by natural selection as an exercise in inductive empiricism [12]. Ironically, people are now using his purely observational exercise as inspiration for theoretical mechanisms for systems from the natural world and beyond.


NOTES:
[1] Radnitzky, G.,‎ Bartley, W.W., and Popper, K. (1993). Evolutionary Epistemology, Rationality, and the Sociology of Knowledge. Open Court Publishing, Chicago. AND Dennett, D. (1995). Darwin's Dangerous Idea. Simon and Schuster, New York.

[2] Claidiere, N., Scott-Phillips, T.C., and Sperber, D. (2014). How Darwinian is cultural evolution? Philosophical Transactions of the Royal Society B, 36(9), 20130368.

[3] Friston, K. (2007). Free Energy and the Brain. Synthese, 159, 417-458.

[4] Edelman, G.M. (1987). Neural Darwinism: the theory of neuronal group selection. Oxford University Press, Oxford, UK.

[5] Campbell, J. (2011). Universal Darwinism: the path to knowledge. CreateSpace Independent Publishing.

[6] Smolin, L. (1992). Did the universe evolve? Classical and Quantum Gravity, 9, 173-191.

[7] Campbell, D.T. (1974). Unjustified Variation and Selective Retention in Scientific Discovery. In "Studies in the Philosophy of Biology", F.J. Ayala and T. Dobzhansky eds., pgs. 139-161. Palgrave, London.

[8] Cziko, G.A. (2001). Universal Selection Theory and the complementarity of different types of blind variation and selective retention. In "Selection Theory and Social Construction", C. Hayes and D. Hull eds. Chapter 2. SUNY Press, Albany, NY.

[9] Siegal, E. (2018). The Four Scientific Meanings Of ‘Nothing’. Starts with a Bang! blog, February 7.

[10] Barabási, A-L. (2009). Scale-Free Networks: a decade and beyond. Science, 325, 412-413.

[11] Lorimer, T., Gomez, F., and Stoop, R. (2015). Two universal physical principles shape the power-law statistics of real-world networks. Scientific Reports, 5, 12353.

[12] Ayala, F.J. (2009). Darwin and the Scientific Method. PNAS, 106(1), 10033–10039.

War of the Inputs and Outputs

Earlier this Summer, I presented a talk on sub-optimal cybernetic systems at NetSci 2017. While the talk was a high-level mix of representational modeling and computational biology, there were a few loose ends for further discussion.

One of these loose ends involves how to model a biological system with boxes and arrows when biology is a multiscale, continuous process in both space and time [1]. While one solution is to add as much detail as possible, and perhaps even move to hybrid multiscale models, another solution involves the application of philosophy.

In the NetSci talk, I mentioned in passing a representational technique called metabiology. Our group has recently put out a preprint on the cybernetic embryo in which the level of analysis is termed metabiological. In a metabiological representation, the system components do not need to map isomorphically to the biological substrate [2]. Rather, the metabiological representation is a model of higher-order processes that result from the underlying biology.

From a predictive standpoint, this method is imprecise. It does, however, get around a major limitation of black box models -- namely what a specific black box is representative of. It makes more sense to black box an overarching feature or measurement construct than to constrain biological details to artificial boundaries.

A traditional cybernetic representation of a nonlinear loop. Notice that the boxes represent both specific (sensor) and general (state of affairs) phenomena.

The black box also changes through the history of a given scientific field or concept. In biology, for example, the black box is usually thought of as something to ultimately break apart and understand. This is opposed to understanding how the black box serves as a variable that interacts with a larger system. So it might seem odd to readers who assume a sort of conceptual impermanence by the term "black box".

A somewhat presumptuous biological example: in the time of Darwin, heredity was considered to be a black box. In the time of Hunt Morgan, a formal mechanism of heredity was beginning to be understood (chromosomes), but the structure was a black box. By the 1960s, we were beginning to understand the basic function and structure of genetic transmission (DNA and gene expression). Yet at each stage in history, the "black box" contained something entirely different. In a fast moving field like cell biology, this becomes a bit more of an issue.

A realted cultural problem in biology has involves coming to terms with generic categories. This goes back to Linnean classification, but more generally this applies to theoretical constructs. For example, Alan Turing's morphogen concept does not represent any one biological agent, but a host of candidate molecules that fit the functional description. Modern empirical biology involves specification rather than generalization, or precisely the opposite goal of theoretical abstraction [3].

The relationship between collective morphogen action and a spatial distribution of cells. COURTESY: Figure 4 in [4]. 

A related part of the black box conundrum is what the arcs and arrows (inputs and outputs) represent. Both inputs and outputs can be quite diverse. Inputs bring things like raw materials, reactants, free energy, sources of variation, components, while outputs include things like products, transformations, statistical effects, biological diversity, waste products, bond energy. While inputs and outputs can be broadly considered, the former (input signals) provide information to the black box, while the latter (output signals) provide samples of the processes unfolding within the black box. Inputs also constrain the state space representing the black box.

Within the black box itself, processes can create, destroy, or transform. They can synthesize new things out of component parts, which hints towards black box processes as sources of emergent properties [5]. Black boxes can also serve to destroy old relationships, particularly when a given black box has multiple inputs. Putting a little more detail to the notion of emergent black boxes involves watching how the black box transforms one thing into another [6]. This leads us to ask the question: do these generic transformational processes contribute to increases in global complexity?

COURTESY: http://jolyon.co.uk

Perhaps it does. The last insight about inputs and outputs comes from John Searle and his Chinese Room problem [7]. In his model of a simple message-passing AI, an input (in this case, a phrase in Chinese) is passed into a black box. The black box processes the input either by mere recognition or more in-depth understanding. These are referred to as weak and strong artificial intelligence, respectively [7]. And so it is with a cybernetic black box -- the process within the unit can be qualitatively variable, leading to greater complexity and potentially a richer representation of biological and social processes.

NOTES:
[1] certainly, systems involving social phenomena operate in a similar manner. We did not discuss social systems in the NetSci talk, but things discussed in this post apply to those systems as well.

[2] for those whom are familiar, this is quite similar to the mind-brain problem from the philosophy of mind literature, in which the mind is a model of thought and the brain is the mechanism for executing thought.

[3] this might be why robust biological "rules" are hard to come by.

[4] Lander, A. (2011). Pattern, Growth, and Control. Cell, 144(6), 955-969.

[5] while it is not what I intend with this statement, a good coda is the Sidney Harris classic "then a miracle happens..."

[6] 

[7] Searle, J. (1980). Minds, Brains, and Programs. Cambridge University Press, Cambridge, UK.

New Paper on Experimental Evolution (with Nematodes!)

Here is a new paper from the bioRxiv on experimental evolution in Nematodes titled "Evolution in Eggs and Phases: experimental evolution of fecundity and reproductive timing in Caenorhabditis elegans". This represents work done during 2015 in Nathan Schroeder's laboratory at UIUC [1], and is published as part of the new Reproduction and Developmental Plasticity theme in the DevoWorm group (currently consisting of just myself). Here is the abstract:

To examine the role of natural selection on fecundity in a variety of Caenorhabditis elegans genetic backgrounds, we used an experimental evolution protocol to evolve 14 distinct genetic strains over 15-20 generations. Beginning with three founder worms for each strain, we were able to generate 790 distinct genealogies, which provided information on both the effects of natural selection and the evolvability of each strain. Among these genotypes are a wildtype (N2) and a collection of mutants with targeted mutations in the daf-c, daf-d, and AMPK pathways. The overarching goal of our analysis is two-fold: to observe differences in reproductive fitness and observe related changes in reproductive timing. This yields two outcomes. The first is that the majority of selective effects on fecundity occur during the first few generations of evolution, while the negative selection for reproductive timing occurs on longer timescales. The second finding reveals that positive selection on fecundity results in positive and negative selection on reproductive timing, both of which are strain-dependent. Using a derivative of population size per generation called the reproductive carry-over (RCO) measure, it is found that the fluctuation and shape of the probability distribution may be informative in terms of developmental selection. While these consist of general patterns that transcend mutations in a specific gene, changes in the RCO measure may nevertheless be products of selection. In conclusion, we discuss the broader implications of these findings, particularly in the context of genotype-fitness maps and the role of uncharacterized mutations in individual variation and evolvability.

 C. elegans adults, juveniles, and eggs in an unsynchronized culture. COURTESY: Bowerman Lab, University of Oregon.

The entire dataset (genealogies for fecundity and reproductive carry-over measurements) is publically available. Below is a heat map (Figure 6 in the paper) featuring the distribution of that measurement for 14 wildtype and mutant genotypes.

NOTES
[1] For related work, please see "An Experimental Evolution Approach to Understanding C. elegans Adaptability", Poster 766C at the 20th International C. elegans Meeting (2015), Los Angeles, CA.

The Pace of Paper Construction

I recently found this graph amngst my files, having done this about a year ago to gauge the revisions of two papers [1, 2] published by myself and co-authors in 2014. The plotted function represents the number of words at a certain timepoint (draft completed every month). The plateaus represent a lack of development during that period.

[1] RED: Alicea, B.   Animal-oriented Virtual Environments: illusion, dilation, and discovery. F1000 Research, 3:202. doi: 10.12688/f1000research.3557.1 (2014).​

[2] BLUE: Alicea, B. and Gordon, R.   Toy Models for Macroevolutionary Patterns and Trends. Biosystems, 122, 25-37 (2014). Special Issue: Patterns of Evolution.

Posters at the International C. elegans Meeting

UCLA and Los Angeles. COURTESY: UCLA Department of Physiology.

I just returned from the International C. elegans Meeting in Los Angeles (being hosted on the UCLA campus). There are posters, talks, workshops, and much fun to be had. I will give a more detailed discussion of some of the sessions in a future post.

Some people (not me) took turns wearing the "worm suit".

COURTESY: #worm15 Twitter feed.

There were several days of talks and posters, plus the famous C. elegans art and variety shows. Talks ranged from Physiology to Evolution and Development. The worm art show is somewhat unique to the conference, The OpenWorm group was able to meet up and discuss research strategies. 

There was also a worm art show. Here are some of the entries. 

Aside form partaking in the intellectual and social festivities, I also presented two posters on Saturday night. One was in the area of experimental evolution, and the other on the DevoWorm project.

Sample of the Experimental Evolution poster. Full poster can be viewed/downloaded here.

Sample of the DevoWorm poster. Full poster can be viewed/downloaded here.

My week was not all worm biology. I also sampled some botany, courtesy of the Mildred Mathias Botanical Garden, UCLA.

Ratchets, Constructions, Games, and Borg in the Reading Queue

Here are a few new (or new to me) papers that are evolution-related from my reading queue. There is a loose theme to these papers (indicated in the title of this post). I will give you my impressions and insights as the post proceeds.

Varieties of uni- and multicellular relationships amongst different species of green algae. COURTESY: Figure 1 in [1].

1. Libby, E. and Ratcliff, W.C.   Ratcheting the Evolution of Multicellularity. Science, 346, 426-427 (2014).

This short paper in a recent issue of Science deals with the transition to multicellularity and associated "ratcheting" mechanisms in what is a complexity theory take on evolutionary transitions and ratchets. According to Libby and Ratcliff's model, the transition to multicellularity involved a transfer of fitness costs from individual cells to groups of cells. This could also be seen as an overall change in the level of selection from individual cells to cell populations [2]. In this case, a so-called ratcheting mechanism is also proposed that provide a mechanism for how such transitions occur. Group living allows for certain group traits to emerge and limits reversion to the single-celled state, a so-called "de-Darwinization" of individual-level cell behaviors [3].

While individual cells transition from being autonomous to being mutually reliant, this occurs only in the context of its fitness effects. For the complexity ratchet to work, there must be opposite effects on fitness. Group living in the form of a colony formation provides a fitness benefit that is not at all present with individualistic cells. Social arrangements such as division of labor can encourage these fitness effects. The authors point to apoptosis as a trait which, while having a high fitness cost to the individual, can be beneficial to the group. Namely, relaxed group selection on apoptosis allows for the growth and nutrient constrains of a population to be circumvented. There are other traits for which individual and group selection differ -- changes in these selective pressures (much like what one would see in a shift to a new environmental niche) are what drive the evolutionary transition.

Do cultural practices (such as dietary innovations) have an influence on human evolution? COURTESY: Frank Stockton, Smithsonian Mag.

2. Laland, K.N., Odling-Smee, J., and Myles, S.   How culture shaped the human genome: bringing genetics and the human sciences together. Nature Review Genetics, 11, 137-148 (2010).

Transitions to group living also involve new sources of fitness costs, distinct from those that exist at the individual level. In this lengthy review article (from 2010), Laland, Odling-Smee, and Myles argue that culture can modify fitness costs for a given trait. The article authors are also advocates of niche construction theory and a post-synthesis evolutionary theory [4], which is clearly seen in their treatment of how culture interfaces with evolution. The mediating effects of culture on population genomics and evolutionary dynamics can be seen in gene-culture coevolution, but also suggests that there is another dimension to group selection in animal species that possess culture. These authors might also argue that cultural selection pressure is a key factor in human uniqueness, something we will come back to in the next section.

While the examples given in the article are muddied with more standard environmental selection pressures, the argument for cultural selection is that some environmental pressures are specifically related to cultural construction [5]. For example, natural selection due to dietary practices are reinforced by human modification of the environment (e.g. harvesting animal milk for general consumption). While genes and culture are viewed as interacting forms of inheritance, it is not so clear as to how they can be disentangled. In cases where cultural boundaries shape population genetics, the answer is relatively easy. However, in cases where cultural dynamics influence the frequency of host-pathogen interactions or heat shock genes, removing the signal from the noise is less clear.

Chimps playing the Prisoner's Dilemma. COURTESY: Science Magazine.

3. Martin, C.F., Bhui, R., Bossaerts, P., Matsuzawa, T., and Camerer, C.   Chimpanzee choice rates in competitive games match equilibrium game theory predictions. Scientific Reports, 4, 5182 doi:10.1038/srep05182 (2014).

3a. Lopata, J.   How Star Trek may show the emergence of human consciousness. Nautil.us, November 18 (2014).

3b. Helbing, D., Yu, W., Opp, K-D., and Rauhut, H.   Conditions for the Emergence of Shared Norms in Populations with Incompatible Preferences. PLoS One, 9(8), e104207 doi:10.1371/ journal.pone. 0104207 (2014).

Here is an interesting collection of readings, which make sense in the context of the Martin et.al paper. In Martin et.al, the authors compare equilibrium expectations for Prisoner's Dilemma (PD) game [6] play with actual outcomes for both humans and chimps. It was found that when chimps play the game, the result is closer to the theoretical expectation than when humans play the game. This suggests that chimpanzee decision-making is more homogeneous than human decision-making, at least in the context of interactions that involve theory of mind. While the result is curious, there are two more recent items that might provide useful speculation about these outcomes.

In a recent article published in Nautil.us (3a), it is postulated that early human cognition (and perhaps cognition in the human-chimp common ancestor) resembled that of the Borg from Star Trek. It is argued that our ancestors were Borg-like in their ability exhibit little individuality across populations. In terms of the PD game, the theoretical equilibria often results from a convergence upon pure strategies. This may not so much a improvement upon an individual's ability to predict what their opponent will do next as the lack of heterogeneity in behavior over time. Thus, a species that exhibits much heterogeneity with respect to behavioral innovation (e.g. humans) would deviate from the theoretical expectation [7].

But does that mean the PD model is not really valuable in modeling human behavior? After all, the original formulation was modeled on human behavior. In addition, the model implicitly relies upon behavioral traits possibly unique to human cognition (such as theory of mind). In 3b, we can see that even though humans have a great diversity of preferences, sets of shared norms may emerge that serve to unify the behavioral outcomes of a population [8]. Despite our great individuality, some aspects of human culture can serve to reduce human heterogeneity.

We were a bit like the Borg (sans hive mind-style collective consciousness), once... COURTESY: Star Trek Online Pictures.

NOTES:
[1] Michod, R.E.   Evolution of individuality during the transition from unicellular to multicellular life. PNAS, 104(S1), 8613-8618 (2007).

[2] Of course, there is plenty of debate regarding the role of group and multilevel selection in the evolutionary process. For more on the virtues of these types of selection, please see: Traulsen, A. and Nowak, M.A.   Evolution of cooperation by multilevel selection. PNAS, 103(29), 10952–10955 (2006) AND Goodnight, C.J.   Multilevel selection: the evolution of cooperation in non-kin groups. Population Ecology, 47, 3-12 (2005).

[3] The term "de-Darwinization" refers to the relaxation of selection for a given trait or level of selection. Please see: Godfrey-Smith, P.   Darwinian Populations and Natural Selection. Oxford University Press, New York (2009).

[4] Laland, K., Uller, T., Feldman, M., Sterelny, K., Muller, G.B., Moczek, A., Jablonka, E., Odling-Smee, J., Wray, G.A., Hoekstra, H.E., Futuyma, D.J., Lenski, R.E., Mackay, T.F.C., Schluter, D., and Strassmann, J.E.   Does evolutionary theory need a rethink? Nature, October 8 (2014).

[5] Richerson, P.J. and Boyd, R.   Natural Selection and Culture. BioScience, 34(7), 430-434 (1984) AND Bell, A.V.   Why cultural and genetic group selection are unequal partners in the evolution of human behavior. Communicative and Integrative Biology, 3(2), 159–161 (2010).

[6] Johnson, D.D.P., Stopka, P., and Bell, J.   Individual variation evades the Prisoner's Dilemma. BMC Evolutionary Biology, 2, 15 (2002).

[7] Herbert-Read, J.E., Krause, S., Morrell, L.J., Schaerf, T.M., Krause, J., and Ward, A.J.W.   The role of individuality in collective group movement. Proceedings of the Royal Society B, 280(1752), 1-8 (2013).

[8] Such norms, such as sharing, exhibit species differences in children. For an example, please see: Hamann, K., Warneken, F., Greenberg, J.R., and Tomasello, M.   Collaboration encourages equal sharing in children but not in chimpanzees. Nature 476, 328–331 (2011).

C. elegans as an Evolutionary Model

In the past year, I have been starting to use the nematode Caenorhabditis elegans (roundworm) as a model organism. Not only have I helped to establish the DevoWorm project, I am also starting to engage with C. elegans in a wet-lab setting. As a consequence, I am learning about multiple facets of C. elegans biology. C. elegans is a well-established model organism, having well-characterized neural and developmental systems. The nervous system contains just 302 cells, with a full accounting of the connectome (synaptic connections) [1]. The developmental system is also well-characterized, with a lineage tree [2] having been worked out for the entire organism. While a lineage tree relies upon deterministic mechanisms (and thus cannot be applied to organisms such as Mammals), it does provide us with a clear accounting of cell differentiation and organ formation during development. Thus, C. elegans is a tractable model for whole-organism investigations (Figure 1).

Figure 1. Anatomy of the adult hermaphrodite. COURTESY: WormAtlas.

But what about evolution? At first pass, it seems as though asking evolutionary questions is not a tractable feature of roundworm biology. Nevertheless, we can use this worm to answer several outstanding questions in evolution [4]. I will use information from a recent review by Jeremy Gray and Asher Cutter [5] to discuss these potential research advances (Figure 2). The actual future applications of C. elegans as an evolutionary model might turn out to investigate other issues. As it turns out, the roundworm provides a happy medium between more traditional models of experimental evolution (microbes) and complex organisms with long generation times (humans). While C. elegans have a relatively short generation time (~50 hours), they also have complex phenotypes with organs.

Figure 2. The life cycle and means of experimental manipulation for evolution experiments. COURTESY: Figure 1 in [5].

The most common means of experimental evolution proposed in [5] is the mutation accumulation (MA) approach. MA may also serve as a weak factor in determining life-history traits in a species [6]. In experimental evolution, the MA approach allows us to observe the role of mutational variation in evolution. One way to apply this method might be to manipulate a single gene (using directed mutagenesis, gene editing, or RNAi -- see Figure 2) and then place it in a genetic background. Rather than waiting for a series of mutations to emerge in a population, mutation is induced to maximize the variation upon which evolution can act upon [7].

Another means of experimental evolution discussed in [5] is co-evolution between worms and pathogens. This can done by culturing worms in ecological context over several generations. One prediction involves the evolution of tradeoffs observed in already co-evolved relationships such as C. elegans growth rate and pathogenic resistance [8]. A secondary means of understanding the ecology of evolution involves introducing environmental fragmentation through introducing spatial variation (physical barriers or agar gradients) on a culture dish. This can produce to genetic bottlenecks and other effects related to population structure and neutral processes.

A third strategy discussed in [5] involves examining different reproductive strategies and degrees of adaptability between species of Caenorhabditis. The latter topic might include a better understanding of how the degeneracy [9] of neuronal and genetic circuits that lead to observable behaviors and phenotypes evolves. Yet there is also great potential for C. elegans to be used as an eco-evo-devo [10] model which integrates to response of environmental stimuli by cell and molecular mechanisms of development over evolutionary time (Figure 3). While I do not have plans on establishing my own C. elegans experimental evolution program in the near future, stay tuned.

Figure 3. A fledgling eco-evo-devo approach to C. elegans.

NOTES:
[1] Jarrell, T.A., Wang, Y., Bloniarz, A.E., Brittin, C.A., Xu, M., Thomson, J.N., Albertson, D.G. Hall, D.H., and Emmons, S.W.   The Connectome of a Decision-Making Neural Network. Science, 337, 437-444 (2012).

Please also see The Connectome Project website.

[2] Sulston, J.E., Schierenberg, E., White, J.G., and Thomson, J.N.   The Embryonic Cell Lineage of the Nematode Caenorhabditis elegans. Developmental Biology, 100, 64-119 (1983).

[3] Jovelin, R., Dey, A., Cutter, A.D.   Fifteen Years of Evolutionary Genomics in Caenorhabditis elegans. eLS, doi:10.1002/9780470015902.a0022897 (2013).

[4] For a review of Caenorhabditis phylogeny and evolutionary biology, please see: Fitch, D.H.A. and Thomas, W.K.   Evolution. In "C. elegans II", Chapter 29. Cold Spring Harbor Laboratory, Woods Hole, MA (1997).

[5] Gray, J.C. and Cutter, A.D.   Mainstreaming Caenorhabditis elegans in experimental evolution. Proceedings of the Royal Society B, 281, 20133055 (2014).

[6] Danko, M.J., Kozlowski, J., Vaupel, J.W., and Baudisch, A.   Mutation Accumulation May Be a Minor Force in Shaping Life History Traits. PLoS One,  7(4), e34146 (2011).

[7] Thompson, O., Edgley, M., Strasbourger, P., Flibotte, S., Ewing, B., Adair, R., Au, V., Chaudhry, I., Fernando, L., Hutter, H., Kieffer, A., Lau, J., Lee, N., Miller, A., Raymant, G., Shen, B., Shendure, J., Taylor, J., Turner, E.H., Hillier, L.W., Moerman, D.G., and Waterston, R.H.   The million mutation project: a new approach to genetics in Caenorhabditis elegans. Genome Research, 23(10), 1749-1762 (2013).

[8] Schulte, R.D., Makus, C., Hasert, B., Michiels, N.K., and Schulenburg, H.   Multiple reciprocal adaptations and rapid genetic change upon experimental coevolution of an animal host and its microbial parasite. PNAS USA, 107, 7359 –7364 (2010).

[9] Degeneracy involves structurally different elements (such as functional neuronal networks) that converge upon the same output. An example of this within C. elegans: Trojanowski, N.F., Padovan-Merhar, O., Raizen, D.M. and Fang-Yen, C.   Neural and genetic degeneracy underlies Caenorhabditis elegans feeding behavior. Journal of Neurophysiology, 112, 951-961 (2014).

[10] Abouheif, E., Fave, M.J., Ibarraran-Viniegra, A.S., Lesoway, M.P., Rafiqi, A.M., and Rajakumar, R.   Eco-evo-devo: the time has come. Advances in Experimental Medicine and Biology, 781, 107-125 (2014).

Flash Lecture for "Toy Models for Macroevolution"

Or, more toys at the Carnival.....

Last summer, I did a series of "flash lectures" on Human Augmentation on my Tumblr site, which was subsequently cross-posted to Synthetic Daisies [1]. Flash lectures are short, 5 minute lectures that are either multimedia-rich or presented in the form of a very quick summary. Sometimes they meld two or three disparate topics together around a single theme. In this post, I have chosen to present a new Biosystems paper from myself and Richard Gordon in such a format [2].

The first part of the paper introduces the toy model as a unified concept. From a writing perspective, this was the most challenging part of the paper, as we re-interpreted a diverse set of biological and evolutionary models. Some of these models are more traditional (e.g. Hardy-Weinberg and fitness landscapes), while others are more novel (e.g. coupled avalanches/evolutionary dynamics and self-organized adaptive change). 

In the end, however, we were able to define toy models as set of tools that summarize, represent, and allow for a prepared description of evolutionary change. Think of this strategy as a short-cut to complexity. While biological systems are extremely complex, we can nonetheless find much more compact and lower-dimensional representations that aid us in extracting useful patterns and trends.

We present 13 different toy models, loosely grouped into three functional categories. These include: the dynamic aspects of evolution, the hereditary aspects of evolution, and the adaptive and conserved features of populations in a small number of dimensions. Aside from these categories, there are three archetypes of toy model: hybrid, classical, and heuristic/phenomenological (see the slide above for details). 

Toy models are not simply theoretical concerns. They can be used in tandem with statistical tools to provide a sort of deep context to an analysis. This is particularly important in terms of big data-type analyses (e.g. high-throughput sequence data). Yet such context can also be useful when multiple types of data are used in the same analysis. The kinds of debates that surround gene trees and species trees will likely be replicated for studies that involve genome sequences vs. transcriptional patterns, or genomic and behavioral analyses. Combining several different toy models to act as "filters" of datasets that can aid in how these data are understood.

For supplemental information, there is also an emerging Github repository which will feature code for many of the toy models presented in this paper plus additional models.

NOTES:

[1] I also did a series of flash lectures for each episode of the "Cosmos" reboot. The entire compilation can be downloaded here.

[2] The paper was previously mentioned as a standalone publication, but now the paper has been reassigned to a special issue of Biosystems called "Patterns of Evolution".

Six Degrees of the Alpha Male: breeding networks to understand population structure

This post is part of a continuing series on ways to think more deeply about human biological diversity. In last month's post (One Evolutionary Trajectory, Many Processes), I discussed how dual-process models (such as the DIT model) might be used to include a new dimension to more traditional studies of population genetics. This example did not spend too much time on the specifics of what such a model would look like. Nevertheless, a dual-process model provides a broader view of the evolutionary process, particularly for highly social (and cultural) species like humans.

In this post, I will lay out another idea briefly mentioned in the "Long Game of Human Biological Variation" post. This involves the use of complex network theory to model the nature of structure in populations. To review, the null hypothesis (e.g. no structure) is generally modeled using an assumption of panmixia [1]. In this conception, structure emerges from interactions between individuals and demes (semi-isolated breeding populations). Thus, a deviation from the null model involves the generation of structure via selective breeding, reproductive isolation, or some other mechanism.

One way to view these types of population dynamics is to use a population genetics model such as the one I just described. However, we can also use complex network theory to better understand how populations evolve, particularly when populations are suspected to deviate from the null expectation [2]. Complex networks provide us with a means to statistically characterize the interactions between individual organisms, in addition to rigorously characterizing sexual selection and the long-range effects of mating patterns.

An example of a small-world network with extensive weak ties. Importantly, this network topology is not random, but instead feature shortcuts and extensive structure. Data represents the human brain. COURTESY: Reference [3].

Since attending the Network Frontiers Workshop (Northwestern University) last December, I have been toying around with a new approach called "breeding networks". The breeding network concept [2] involves using multilayered, dynamical networks to characterize breeding events, the creation of offspring, the subsequent breeding events for those offspring, and macro-scale population patterns that result. This allows us to characterize a number of parameters in one model, such as the effects of animal social networks on population dynamics [4]. This includes traditional network statistics (e.g. connectivity and modularity parameters) that translate into theoretical measures of fecundity, the diffusion of genotypic markers within a population, and structural independence between demic populations. But these statistics are determined by a meta-process, one that is explicitly social and behavioral.

Before we continue, it is worth asking why complex networks are relevant. No doubt you have heard of the "small-world network" phenomenon, which postulates that given a certain type of network topology, networks with many nodes and connections can be traversed in a very small number of steps [5]. This is the famous "six degrees" phenomenon in action. But complex networks can range from random connectivity to various degrees of concentration. This approach, which comes with its own mathematical formalisms, allows us to neatly characterize the behavior, physiology, and other non-genetic factors that result in the population dynamics that produces structured genetic variation.

An example of regular, small-world, and random networks, ordered by to what extent their connectivity is determined by random processes [6]. In breeding networks, non-random connectivity is determined by sexual selection (e.g. selective breeding). As sexual selection increases or decreases, it can change the connectivity of a population.

As complex networks are made up of nodes and connections, the connections themselves are subject to
connection rules. In some networks, these rules can be observed as laws of preferential attachment [7].
But in general, each node or class of nodes can have simple rules for preferring (or ignoring) association with one node over another. If this sounds like an informal selection rule, this is no accident. While complex network theory does not approach connectivity rules in such a way, breeding networks are expected to be influenced by sexual selection at a very fundamental (e.g. dyadic interaction) level.

The complex network zoo, and the three parameters (heterogeneity, randomness, and modularity) that define the connectivity of a network topology. Examples of specific network types are given in the three-dimensional example above, but breeding networks could fall anywhere within this space. COURTESY: Reference [8].

Another feature of breeding networks involves connectivity trends over time. For example, a founder population with a small effective population size might indeed be panmictic (in this case represented by a random network topology). However, as the population size increases and connectivity rules change, this topology can evolve to one with scale-free or even small-world properties. This is not only due to the selective nature of producing offspring, but difference in the fecundity of individual nodes.

Once you start paying around with this basic model, a number of alternative network structures [9] can be used to represent the null model. Types of configuration such as star topologies, hyperbolic trees, and cactus graphs can approximate inherent geographic structure in a population's distribution. These alternative graph topologies are the product of factors such as geography or migration, and may have pre-existing structure. The key is to use these features as the null hypothesis as appropriate. This will provide us with a better accounting of the true complexity involved in shaping the structural features of an evolving population.

A map showing the seasonal migration of shark populations in the Pacific, including aggregation points. COURTESY: The Fisheries' Blog.

NOTES:
[1] One model organism for understanding local and global panmixia is the aquatic parasite Lecithochirium fusiforme. For more, please see: Criscione, C.D., Vilas, R., Paniagua, E., and Blouin, M.S.   More than meets the eye: detecting cryptic microgeographic population structure in a parasite with a complex life cycle.
Molecular Ecology, 20(12), 2510-2524 (2011).

[2] The idea of breeding networks is similar to the idea of sexual networks, except that breeding networks are more explicitly tied to population genetics. This paper give good insight into how sexual selection factor into the formation of structured, complex networks: McDonald, G.C., James, R., Krause, J., and Pizzari, T.   Sexual networks: measuring sexual selection in structured, polyandrous populations. Proceedings of the Royal Societiy B, 368, 20120356 (2013).

[3] Gallos, L.K., Makse, H.A., and Sigman, M.   A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. PNAS, 109(8), 2825-2830 (2012).

[4] For more on animal social networks and their relationship to evolution, please see the following references:

a) Oh, K.P. and Badyaev, A.V.   Structure of social networks in a passerine bird: consequences for sexual selection and the evolution of mating strategies. American Naturalist, 176(3), E80-89 (2010).

b) Kurvers, R.H.J.M., Krause, J., Croft, D.P., Wilson, A.D.M., Wolf, M.   The evolutionary and ecological consequences of animal social networks: emerging issues. Trends in Ecology and Evolution, 29(6), 326–335 (2014).

[5] For a definition of network diameter in context, please see: Porter, M.A.   Small-world Network. Scholarpedia, 7(2), 1739 (2012).

[6] This classification of idealized graph models is based on the Watts-Strogatz model of complex networks. For more information, please see: Watts, D.J. and Strogatz, S.H.   Collective dynamics of 'small-world' networks. Nature, 393, 440-442 (1998).

[7] This property of idealized graph models is based on the Barabasi-Albert model of complex networks. For more information, please see: Barabasi, A-L. and Albert, R.   Emergence of scaling in random networks. Science, 286(5439), 509–512 (1999).

[8] Sole, R.V. and Valverde, S.   Information Theory of Complex Networks: On Evolution and Architectural Constraints, Lecture Notes in Physics, 650, 189–207 (2004).

[9] Oikonomou, P. and Cluzel, P.   Effects of topology on network evolution. Nature Physics 2, 532-536 (2006).