G:P:C (Genotype:Phenotype:Culturtype) Maps

For Darwin Day 2026, I will introduce a method and theory for multiple types of inheritance called Genotype:Phenotype:Culturtype (G:P:C) Maps. While dubious attempts at understanding culture in Darwinian terms were advanced in the 19th century, it wasn't until the 20th century that evolutionary approaches to culture matured [1]. These approaches, advanced by Boyd and Richerson [2] and Cavalli-Sforza and Feldman [3] identified cultural evolution as units of inheritance subject to mutation and recombination. These approaches are influenced by biological evolution, while also serving as a metaphor that brings cultural change in line with biological evolutionary change. What goes on inside of a population of organisms ultimately ties together culture and biology, there are additional factors and types of explanation necessary that allow us to map from biology (both genotypic and phenotypic aspects) to culture [4].

The approach sketched out here expands on the concept of Genotype: Phenotype (G:P) maps which provide a means to characterize a mapping of the genotype to a phenotype [5]. Let us take a very small G:P example (Figures 1 and 2). We might think that the simplest relationship would be a 1:1 mapping, with the genome collectively serving as a blueprint for the phenotype. But this simplistic mapping scheme results in a linear, low-resolution phenotype. In such cases, mutations or recombination in each gene have direct effects in the phenotype. The resulting linearity also works against evolvability of the G-P map [6], as every new trait would require a new gene. Simply duplicating genes might appear to solve the problem, but this ultimately results in an extremely large genome.

Figure 1. Five examples of relationships between Genotype (G), Phenotype (P), and Culturtype (C) featuring the convergence and divergence of braided structures and 1:1 mappings. From left: 1) 1:1 mapping between G and P, divergence between P and G; 2) divergence between G and P, convergence between P and C; 3) terminal effects at P; 4) convergence between G and P, divergence between P and C; and 5) convergence between G and P, 1:1 mapping between P and C.  

Another issue is the information content of a 1:1 mapping. Mapping one gene to one phenotypic trait results in a blocky, 1 bit representation. While we can specify as much detail as we would like in a single gene, it can only be turned on or off in a switchlike fashion. This is a common feature across the tree of life, and basic regulatory mechanisms exhibit common ancestry among bacteria (start sites and modulation) and in the Last Universal Common Ancestor (LUCA; an RNAP that predates DNA replication) [7, 8].

A much more realistic scenario is a G-P map where multiple genes contribute to a single trait, and each trait is the product of epistatic interactions between genes [9]. This not only provides compensatory routes to a partial phenotype in case of functional loss yet also provides a source of regulation resulting in phenotypic variation. Such a nonlinear approach moves us away from the “genes as blueprint” view, and towards a different view of G-P maps. This alternative view enables an emergent approach to gene regulation, where different versions of a phenotype can arise from the same set of genes. The G-P map is thus defined by pleiotropic interactions, which can be mapped out as the translation from one gene to many phenotypes.

G-P maps are defined by convergence as well as emergence. Convergence can be characterized by phenocopying or buffering, or where a single phenotype can result from multiple genotypic interactions. Genotype networks possess a small-world network architecture with assortativity [10].  

Figure 2. An example of a G:P:C mapping. Each dot is a unit that corresponds with its level: red dots (G, or genotype) are equivalent to alleles, blue dots (P, or phenotype) are equivalent to affordances, and green dots (C, or culturtype) are equivalent to cultural variants.

In Figure 2, we can see that a G-P map (and by extension the G-P-C map) is constructable as a set of topological braids: branching and convergence patterns between two 1-D physical maps of the genotype (bottom) and phenotype (top). We are interested in a level above the phenotype, however, and this is where our third physical map (culturtype, Figure 2B) comes into play. A culturtype is the culture in which a phenotype operates. Each culturtype is a distinct form of practices and behaviors that shares attributes with other culturtypes. Culturtypes also have a connection to both the genotype and phenotype, offering a means to adapt to environmental conditions when genotypes cannot. From an embodied perspective, collective behaviors can be shaped by the phenotype, which should then map to the culturtype. The mapping between the phenotype and culturtype is similar in nature to the genotype-phenotype mapping. In particular, the relation between phenotypes composed of affordances and culturtypes composed of variants allows us to understand embodied, embedded, and extended cognition in the context of biological diversity [11]. The equivalent of epistasis is a more generic one-to-many mapping, typified by differences in cultural practice. This is typified by branching patterns. By contrast, convergence is defined by functional buffering and similar cultural practices derived from different phenotypes.  

Topological braids [12] consist of strands that represent single pathways that map between different sets. In our example, each genotype:phenotype path is defined by a subset of braids, each braid being assigned a braid word as a means of credit assignment. Likewise, each phenotypic component has a subset of braids leading to a culturtype. The G:P:C map is an open braid system in which the number of braids nor number of units at each level remain constant, connecting the open nature of genotype, phenotype, and cultural diversity.  Future work might incorporate a phylogenetic approach where braids are mapped to a reticulating phylogenetic tree, where temporal relationships can also be addressed.

References:

[1] Lewens, T. and Buskell, A. (2013). Cultural evolution. Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/evolution-cultural/

[2] Boyd, R. and Richerson, P.J. (1985). Culture and the Evolutionary Process. University of Chicago Press.

[3] Cavalli-Sforza, L.L. and Feldman, M. (1981). Cultural Transmission and Evolution: a quantitative approach. Princeton University Press.

[4] Claidière, N., Scott-Phillips, T.C., and Sperber, D. (2014). How Darwinian Is Cultural Evolution? Royal Society B, 369(1642), 20130368.

[5] Alberch, P. (1991). From genes to phenotype: dynamical systems and evolvability. Genetica, 84, 5–11.

[6] Wagner, G.P. and Zhang, J. (2011). The pleiotropic structure of the genotype-phenotype map: the evolvability of complex organisms. Nature Reviews Genetics, 12(3), 204-213.

[7] Kuo, S-T., Chang, J.K., Chang, C., Shen, W-Y., Hsu, C., Lai, S-W., and Chou, H-H.D. (2025). Unraveling the start element and regulatory divergence of core promoters across the domain bacteria.  Nucleic Acids Research, 53, gkaf1310.

[8] Koonin, E.V., Krupovic, M., Ishino, S., and Ishino, Y. (2020). The replication machinery of LUCA: common origin of DNA replication and transcription.  BMC Biology, 18, 61. 

[9] Pigliucci, M. (2010). Genotype–phenotype mapping and the end of the ‘genes as blueprint’ metaphor. Royal Society London B: Biological Sciences, 365(1540), 557–566.

[10] Aguilar‐Rodríguez, J., Peel, L., Stella, M., Wagner, A., and Payne, J.L. (2018). The architecture of an empirical genotype‐phenotype map. Evolution, 72(6), 1242–1260.

[11] Alicea, B., Gordon, R., and Parent, J. (2023). Embodied Cognitive Morphogenesis as a Route to Intelligent Systems. Royal Society Interface Focus, 13(3), 20220067.

[12] Weisstein, E.W. (2025). Braid. Wolfram MathWorld. https://mathworld.wolfram.com/ Braid.html AND Artin, E. (1950). The Theory of Braids. American Scientist, 38, 112-119, 1950.

What if there had been a Chaos/Fractals bubble?

 

Why does one research culture drive a bubble while another does not? COURTESY: Soap Bubbles and Chaos, Journal of Pneumatic Adventures Medium.

 

Modern Artificial Intelligence (AI) research is currently at the heart of a massive financial bubble. It might pop soon, and it might not. "AI" is seemingly everywhere, although its actual value is yet to be determined. I remember learning how to program GPUs in the period around 2010 for applications to computational biology, never thinking that an esoteric research topic could become elemental in propping up the tech economy.

This got me to thinking about what it would look like if we switched out one research area for another, just to highlight any potential absurdities of the situation. So imagine if the field of Chaos and Fractals, quite popular to the point of cliche in the 1980s, was the subject of a financial bubble. It is of note that chaos and fractals were definitely hyped in their time, being featured in movies such as Star Trek: the Wrath of Khan (the Genesis Effect scene) and Ian Malcolm's rhetoric in Jurassic Park. Interestingly, advances in chaos and fractals in particular relied on advances in computing power, initially with supercomputing, and later with GPUs, parallel computing, and quantum computing [1].

In the formative years of chaos, people such as the Eds (Ott and Lorenz) [2, 3] produced a paradigm shift in how complex systems were viewed. The visualization of chaos in the form of fractals were advanced by Benoit Mandelbrot [4]. Fractals were likewise a paradigm shift in how complex phenomena were visualized. In particular, fractals visualize various aspects of chaos using non-Euclidean geometries and relatively simple sets of equations. Their popularity was advanced by a convenient shorthand: visualizations that captured the imagination. While slogans and pretty pictures captured the imagination, the popular imagination got quite far ahead of methodological rigor. This is reminiscent of claims that ascribe properties like sentience or superintelligence to AI systems.

Is this science, or inspiration, or both? Please don't financialize this. COURTESY: Moss and Fog blog.

Eventually, enthusiasm for chaos and fractals regressed back into the fields of physics and mathematics, while also becoming specialized tools for fields like finance. In short, the field matured without the irrational influx of cash, roughly following a Gartner hype cycle. This is curious in light of the limits of AI that people discuss today: regardless of whether or not AI exhibits "true" intelligence, AI systems require intense computational resources to merely be evocative of biological intelligence. But what if there is not a missing component of the intelligence simulation, but of the way in which the underlying system is modeled? Chaos and fractals are not the product of reductionist relationships (as science had been done before), but rather the product of system dynamics, recursivity, and a sensitivity to initial condition. This was the main insight of chaos and fractals, but apparently those insights are not worth a large-scale financial bubble [5].

In their time, fractals were derided as "pretty pictures", and eventually, the pretty pictures could not keep up with methodological trends across the different sciences. But fractals did provide at least one serious insight: systems that look regular at one scale exhibit irregularities apparent at other scales. This has been popularized by the Powers of 10 idea, and further applied to ideas like the coastline paradox. What is particularly interesting to a person who likes complexity approaches to science is that standard hypothesis testing was exposed to many of the same criticisms as chose and fractals. This is despite much more serious consequences of the unaddressed issues with NHST, and has persisted as the scientific norm in spite of superior methods. Quite an interesting exercise in methodological inertia. 

In the current era, AI has partially been driven by advances in methodology, but also by advances in hardware. Central to this has been NVIDIA and their GPU architecture. While GPUs have done much of the heavy lifting in the current AI summer, it is important to remember the origins of GPUs: as a graphical processing tool. This parallels how advances in computing and computational power suddenly opened up our ability to solve and plot the equations of fractal growth and other structures. Perhaps the experience of chaos and fractals will guide AI research after the bubble bursts.

References:

[1] Kaboudian, A., Cherry, E.M., and Fenton, F.H. (2019). Large-scale interactive numerical experiments of chaos, solitons and fractals in real time via GPU in a web browser. Chaos, Solitons & Fractals, 121, 6-29.

[2] Motter, A. and Campbell, D.K. (2013). Chaos at Fifty. Physics Today, 66(5).

[3] Viswanath, D. (2004). The fractal property of the Lorenz attractor. Physica D, 190, 115–128.

[4] Mandelbrot, B.B. and Blumen, A. (1989). Fractal Geometry: What is it, and What Does it do? Royal Society A, 423(1864), 3–16.

[5] Notice that I said "large-scale", which is the distinction between overeager commercialization and financialization. Perhaps financialization is a feature of 21st century popularity, but there does seem to be a difference that makes its way into scientific practice. Fractals are used extensively in attempts to understand the stochastic nature of markets, and have been commercialized in line with that expectation. 

The connections between fractals, efficient markets, and to a lesser extent chaotic behavior is exemplified in books such as:  Peters, E. (1994). Fractal Market Analysis. Wiley.

OpenWorm Annual Meeting 2025 (DevoWorm update)

Here are the slides for the DevoWorm group's report to the OpenWorm Annual Meeting (2024). You can watch Bradly Alicea present the talk on YouTube.

Thanks again to all of our contributors over the past year, all of our Github contributors, and all of our Google Summer of Code applicants. If you are interested in participating, join one of our meetings or contribute to our Github repo and organization.

OA Week: The Troubling U-turn of Open Access

 

Who Owns Our Knowledge? Troubling trends have emerged.

As academics, media producers, and authors: Who Owns Our Knowledge? I present two troubling scenarios. Each of these have happened in the past few decades and is a heady mix of hypocrisy and gross power imbalance.

Intellectual Property Rights!

2006: RIAA Persecutes people for downloading music.

2013: Aaron Schwartz is persecuted for downloading JSTOR articles, resulting in his suicide.

2025: Technology companies use intellectual property without author permissions to train Large Language Models (LLMs). Everyone celebrates tech company profit margins, and LLMs can drive some people to suicide. 

Which of these things is not like the other? To be fair, the final example (in red text) is at the expense of legacy publishers and intellectual property laws. But that is the point. Intellectual property rights are enforced in ways that totally benefit the largest entity. 

Open Access to the.....logical endpoint?

Once upon a time, people were excited about radical open access. Post a preprint, post-peer review, and eliminate the bias of prestige journals. Now, it is the prestigious journals that enjoy Gold (!!) open access (for an exorbitant fee).

Although there are a number of options outside of this paradigm (e.g. Green Open Access), the goals of the open access reform movement seem to have become obscured. More specifically, the transition from words and slogans to institutional normalization has not been smooth.

So is the highlighted scenario the logical endpoint for open access? Probably not, but more work is needed. Not the easy work, but the harder work of changing systems and institutions.

That is all.

Can these scenarios be stopped? This is up to us.

Welcome to our Google Summer of Code scholars for 2025!

 

The Orthogonal Research and Education Laboratory is pleased to welcome three students to the lab as Google Summer of Code (GSoC) scholars. Two (Lalith Baru and Jayadratha Gayen) will be joining the DevoWorm group and one (Vidhi Rohira) will be joining the Open-source Sustainability project.

Lalith and Jayadratha will be working on different aspects of our DevoGraph project (Github). Lalith’s successful project proposal is called “NDP-HNN: Modelling Neural Developmental Programs of C. elegans Using Growing Hypergraph Neural Networks”, while Jayadratha’s successful project proposal is called “DevoTG: Dynamic Graph Neural Networks for Modeling C. elegans Development”. Good luck to both of them! They will be working with the DevoWorm group and active in our weekly meetings. They will also be hosted by the OpenWorm Foundation and contributing to their mission.

Vidhi will be contributing to OREL's Open-source Sustainability project (Github) by working at the intersection of Reinforcement Learning and Agent-based Modeling. Vidhi’s successful project proposal is called “SustainHub: Adaptive Agent-Based Model for Open-Source Community Sustainability”. Check out her updates as part of the Saturday Morning NeuroSim meeting series.

We have also invited our unsuccessful candidates to join our Open-source interest group. We host this meeting every Friday at 12 Noon Eastern time, and cover promoting open-source practices, project development, and project management education.