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.

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).

One Evolutionary Trajectory, Many Processes

Two months ago, I wrote a post on how we might think more deeply about human biological variation. This post also involved a discussion about the recent Nicholas Wade book (A Troublesome Inheritance), which has engendered its own rancor on the internet [1]. In the second part of the post, I discussed some potential ways we can more effectively model human variation. This was decidedly exploratory, the intent of which was to follow-up on the discussion. In this post, I will discuss the need for taking cultural evolution and other factors into account when interpreting genetic variation.

To understand where I am coming from here, consider the difference between population genetics and behavioral ecology approaches. In population genetics, the concern is over observing the patterns of standing variation in a population. We discuss topics such as allele frequencies, admixture, and the mechanisms of genetic differentiation. But populations also behave, and in behavioral ecology topics such as sexual selection, foraging patterns, and strategic behaviors are also taken into account.

While there is indeed implicit overlap between these two fields in the literature, there is little direct theoretical synthesis in this direction. For example, if one takes species concepts into account [2], we can see the issue rear its head: one can apply a host of species concepts which explain both the behavioral and genealogical dynamics of a population, but a unified conceptual framework (e.g. one that is not contradictory) is elusive.

Yet even when only taking behavioral dynamics into account, there are a multitude of factors that make direct comparisons between populations difficult. Species differ in both their sociality and acquisition of culture. This differentiation is even more profound in terms of how culture has shaped a species' ability to adaptively radiate and persist over multiple generations. Humans are not only an intensely eusocial species, but also fall into the latter category of being shaped by culture as much as by environmental selection.

One might simply refer to this as "cultural selection", but a better approach is to model the process of genealogical and cultural (or social) evolution as nominally separate but interrelated processes. In "Playing the Long Game of Human Biological Variation", I advocated for the use of dual process models. Such models treat the same population as being subject to two or more distinct processes simultaneously. In a Synthetic Daisies post re-published at Humanity+ [3], I introduced a dual process Artificial Life-based model that integrates genealogical dynamics and biogeographic processes (specifically changes in geomorphology).

There are a good number of examples of dual process models in the literature which integrate cultural and biological evolution. A good starting point is the work of Richerson, Boyd, McElreath, and Henrich [4, 5], who use a dual inheritance model (DIT) with similar genetical and cultural inheritance mechanisms. While this does not distinguish between the mode transmission for genetical units (genealogy) and cultural units (social learning), it does allow for their dynamics to differ within a population.

This provides us with a conceptual expression of "nature" not being equivalent to "nurture", even though we end up in a place similar to the species concept example. But this does not necessarily solve a key issue; namely, that culture and genetics do not simply have the potential to follow divergent trajectories. Culture might also provide a coherent and context-dependent evolutionary constraint [6] which can influence "fast" human evolution [7]. Specifically, culture might influence genetic evolution indirectly through evolutionary constraints (EC) on admixture, migration, local environmental genetic polymorphisms, and demographic fluctuations [8].

One example of a dual process model (in this case, an example from niche construction). COURTESY: Niche Construction page, Semiotics Encyclopedia Online.

Notice that this is quite a bit different than claims of genetics influencing cultural evolution, or culture acting as a multiplier of genetic differences. In fact, the effect is not a feedback or other type of causal mechanism at all, but rather an incongruence [9]. Evolutionary incongruence (EI) occurs when the evolutionary trajectory of the genome and the cultural environment do not lead in the same direction [8].

For example, even though you might possess a genotype that makes you very unfit for a certain environment, possessing a cultural adaptation on top of this genotype might make you fit enough (or even very fit). EI and EC can also determine more general outcomes in a dual process model. In the case of humans, where culture enables humans to survive in environments beyond what is enabled by genes alone, EI is much more dominant than EC. You can still find genetic variants that result from adaptation to a specific local environment, but they are not the determining factor in survival. In a very different context, for example in the case of a solitary species, EC might dominate over EI.

In summary, accounting for variation within and between human groups might best be done using a sophisticated theoretical framework. This framework includes 1) the use of a dual process model that represents cultural and genetic evolutionary processes, and 2) the identification of how culture contributes to genetic variation, namely either through constraint (which enables feedback between genes and culture) or incongruence (where the variation contributed by genetic and cultural evolutionary processes point in different directions). In the case of eusocial species that possess culture (example: Homo sapiens), incoherence will be predominant, although constraint can drive forward local genetic adaptation when needed.

 Examples of eusocial (left) and solitary (right) species.

In a future post, I will explore another theme in the original "Long Game" blog post, namely the idea that panmixia might not be the best way to assess the absence of population subdivision. Instead of using a traditional population genetics model, using scale-free networks to represent the null hypothesis might give us a more profound theory and more realistic results. Look forward to it.

NOTES:
[1] I'm not particularly interested in ideological debates. But be aware that this post will be largely theoretical and perhaps a bit too speculative. That's the way theoretical advances are made!

[2] Wheeler, Q. and Meier, R.   Species Concepts and Phylogenetic Theory: a debate. Columbia University Press (2000).

[3] Alicea, B.   Artificial Life meets Geodynamics (EvoGeo). Humanity+ Magazine, December 7 (2012).

[4] Richerson, P.J. and Boyd, R.   Not By Genes Alone: How Culture Transformed Human Evolution. University of Chicago Press (2005).

[5] McElreath, R. and Henrich, J.   Dual inheritance theory: the evolution of human cultural capacities and cultural evolution. In "Oxford Handbook of Evolutionary Psychology", R. Dunbar and L. Barrett eds., Oxford University Press (2007).

[6] Boyd, R. and Richerson, P.   The cultural transmission of acquired variation: effects on genetic fitness. Journal of Theoretical Biology, 100, 567-596 (1983).

[7]  Hawks, J., Wang, E.T., Cochran, G.M., Harpending, H.C., and Moyzis, R.K.   Recent acceleration of human adaptive evolution. PNAS, 104(52), 20753–20758 (2007).

[8] NOTE: The terms and abbreviations for evolutionary constraint (EC) and evolutionary incongruence (EI) are of my own coinage.

[9] Laland K. and Brown, G.   Sense and Nonsense: Evolutionary Perspectives on Human Behavior. Oxford: Oxford University Press (2002).

Four Readings and an Open Science Argument

Here are some papers from my reading queue. Four readings on human culture, behavior, and evolution, and one feature (set of readings) on Open Science. 

Four Readings......

Here are four readings from the reading queue on human culture, behavior, and evolution. The picture below (only tangentially related to the first paper) is from [1].

The first paper [2] is on the genetic architecture of economic and political preferences. Using a SNP analysis, the authors demonstrate that such traits have a polygenicarchitecture (e.g. many genes, small effect size for each). Studies that are underpowered (and no one really knows what the appropriate sample sizes should be) can potentially generate many false positive associations between genes and behavior. Nevertheless, understanding the presence of key variants for social preferences might help us understand why some people seem to be inherently "liberal" or "conservative".

The second paper [3] presents us with a premise that equates (or perhaps confounds) the psychophysiology of political ideologies with the roots of more general ideological bias. Are we really looking at "natural" differences between liberals and conservatives? Or does this simply demonstrate that high-profile social issues with already polar liberal and conservative positions [4] are undergirded by strong emotional responses? The standard evolutionary psychology explanation is a bit contrived as well. But it goes well with the previous article.

Crossmodal and cross-cultural comparisons, unite! In this study [5], people from several different cultures were asked to make both "congruent" and "incongruent" associations between smells and colors. The authors come to the conclusion that cultural context through experience has both statistical (covariance) and semantic (linguistic) components.

The fourth article [6] is a gateway article to several recent studies in the area of neuroplasticity. The gateway leads to the work being done in the laboratory of Michael Stryker [7]. Learn about the "neural volume control knob" and much, much more.

.....And An Open Science Argument

Here are some additional readings on networking and open science from my reading queue. The first is a paper on the life-cycle of a preprint on the arXiv [8] The top image is Figure 2 in the paper. The other two readings advocate for the use of open access protocols and social media to disseminate research [9] and counter cultural biases towards keeping research behind laboratory doors [10].

NOTES:

[1] Top picture courtesy: http://www.ucsf.edu/news/2009/01/8225/study-powerful-genes-and-cancer-points-vitamin-d-inflammation.

[2] Benjamin, D.J. et.al    The genetic architecture of economic and political preferences. PNAS, 10:1073/ pnas.1120666109 (2014).

[3] Mooney, C.   Scientists Are Beginning To Figure Out Why Conservatives Are ...... Conservative. Mother Jones, July 15 (2014).

[4] Related to this is the concept of the news filter bubble. One recent paper on this phenomenon: Koutra, D., Bennett, P., and Horvitz, E.   Events and Controversies: influences of a shocking news event on information seeking. arXiv, 1405.1486 (2014).

[5] Ren et.al   Cross-Cultural Color-Odor Associations. PLoS One, 9(7), e101651 (2014).

[6] Stix, G.   Neuroplasticity: new clues to just how much the adult brain can change. Scientific American blog, July 14 (2014).

[7] Two notable publications:

a) Fu, Y., Tucciarone, J.M., Espinosa, S., Sheng, N., Darcy, D.P., Nicoll, R.A., Huang, J., and Stryker, M.P.   A Cortical Circuit for Gain Control by Behavioral State. Cell, 156, 1139–1152 (2014).

b) Niell, C.M. and Stryker, M.P.   Modulation of Visual Responses by Behavioral State in Mouse Visual Cortex. Neuron, 65, 472-479 (2010).

[8] Shuai, X., Pepe, A., and Bollen, J.   How the Scientific Community Reacts to Newly Submitted Preprints: Article Downloads, Twitter Mentions, and Citations. PLoS One, 7(11), e47523 (2012).

[9] Allen , E.   “All research should be OA”. We agree! ScienceOpen blog, July 14 (2014).

[10] Konkiel, S.   How to become an academic networking pro on LinkedIn. ImpactStory blog, April 24 (2014).

Intra- and Inter-generational Physiological Evolution: three case studies

Evolutionary processes are crucial to driving forward physiological processes. While inter-generational adaptation is considered to be the "gold standard" of evolutionary change, natural selection-driven adaptive processes can also act on intra-generational timescales. Like many epigenetic mechanisms, intra-generational adaptive processes are not known to transmit nor retained over many generations.

In this post, we will discuss three cases of how evolutionary processes (two explicitly intra-generational, one extensively inter-generational) affect the operation of physiological systems. In the case of our inter-generational examples (I and III), physiological processes exhibit their own adaptive dynamics. In the case of our inter-generational example, the macro-evolutionary distribution of gene variants provides a basis for intra-generational adaptation.

I. Role of Intra-generational Selection in tRNA Availability and Translation

Mahlab, S. and Linial, M.   Speed Controls in Translating Secretory Proteins in Eukaryotes: an Evolutionary Perspective. PLoS Computational Biology, 10(1), e1003294 (2014).

This paper deals with transcription and the production of secretory molecules (production of the secretome) as an intra-generational evolutionary process. The secretome involves a vast array of peptides produced via a special ribosomal structure located at the cell membrane (Figure 1). The resulting peptides (manufactured on the outside of this membrane) are then involved in cell-cell communication.

Figure 1. The specialized translational pathway that leads to the production of signaling peptides.

The authors focus on role of tRNA (or transfer RNA) adaptation and the N' terminal of secretory proteins. tRNAs are internal to the translational process, and serve to translate open reading frames of DNA into amino acids. As adaptors, tRNAs are specialized by codon and function. Each type of specialization results in a population (or pool) which has a certain degree of diversity. This results in something called codon usage bias, a concept to which we will return. The N' terminal regions of the signaling peptide are associated with the so-called "fast" tRNAs. Secretory proteins made in this fashion are also found to contain segmental information that allow for various signaling functions. The signaling functionality is in turn a product of adaptation by natural selection within a single human generation (and perhaps even within a single cellular generation). "Fast" tRNAs are just one type of specialized tRNA molecule that exist in different proportions depending on various factors. The consequences of selection on these ratios is to affect the production of some codons (and thus peptides) over others.

Changes in the proportion of tRNA types requires an adaptive mechanism. While the specifics of this mechanism are unknown (but see Figure 2), the amount of diversity is governed by the number of tRNA molecules of a certain specialized type. To illustrate this, I use a conceptual model of translation called the "Hungry, Hungry Hippos" model, named after the popular children's board game (see Figure 3). The game begins with four hippos and a game board full of freely-moving marbles. Then, each hippo eats as many marbles as they can before the marbles are all eaten. This race exemplifies how tRNAs are utilized in the process of translation: mRNA is moved through the ribosome at different speeds, which tRNA molecules compete to bind to the incoming sequence and replicate their information in a new generation of peptides.

Figure 2. The site of translation and the trade-offs inherent in tRNA selection. COURTESY: Figure 1 (a and b) from [2].

Figure 3. The game "Hungry, Hungry Hippos", a model for transcription?

While one might think of this as a stochastic process, tRNA pools adapt to the needs of a given cell, including the speed of translation and amino acid bias. One measure of how these pools evolve is the tRNA adaptation index [1], which is based on the concept of codon usage bias (Figure 4).

Figure 4. the tRNA (codon) adaptation index, a intra-generational natural selection index. CAI is a weighted geometric mean for all categories of codon.

The premise of tRNA adaptation and the potential role of natural selection is that gene expression is correlated with codon bias [3]. Depending on the needs of the cell, the production of proteins can be biased towards certain amino acids through controlling both the speed of translation and the (perhaps more importantly) the composition of tRNA pools. The consequences of this codon bias can be observed when plotted against gene expression (e.g. the production of mRNAs -- see Figure 5). In general, when gene expression (or transcriptional noise) is more active, the greater the bias in codon-specific tRNA activity (in the form of codon frequency).

Figure 5. Changes in codon frequency with respect to gene expression. Figure 2 from [4]. 

II. Inter-generational Selection for Antigens

Forni, D., Cagliani, R., Tresoldi, C., Pozzoli, U., De Gioia, L., Filippi, G., Riva, S., Menozzi, G., Colleoni, M., Biasin, M., Lo Caputo, S., Mazzotta, F., Comi, G.P., Bresolin, N., Clerici, M., and Sironi, M. An Evolutionary Analysis of Antigen Processing and Presentation across Different Timescales Reveals Pervasive Selection. PLoS Genetics, 10(3), e1004189 (2014).

The human immune system is a complex system that consists of recognition and defense mechanisms (Figure 6). These mechanisms operate both intracellularly and extracellularly. In addition (see Figure 7), there is both an innate system (which is evolutionarily conserved) and an adaptive system (which is derived but shared among vertebrates). Given this complexity, it is often hard to find the inter-generational underpinnings of intra-generational adaptation. One form of intra-generational adaptation in the immune system involves antigen processing and presentation. This is determined by both the inter-generational evolutionary history of antigen-specific genes and the role of selection within and between generations.

Figure 6. A quick refresher on the human immune system architecture. COURTESY: [5].

In this study, the authors examined the evolutionary history of 45 antigen-specific genes in Homo sapiens. In doing so, they and looked at both the intra-specific variation and inter-specific diversity of genes related to antigen-related processes. This study also used a comparative genomic approach to better understand the evolutionary history of antigen-specific genes in humans. This was done in two different ways. The first was to use several different statistical tests to identify the target of selection. Then, the targets were characterized using low-coverage, whole-genome Sanger sequencing (e.g. high-throughput analysis using next-gen sequencing). In the end, it was found that 9 genes in the antigen processing and presentation (APP) pathway have undergone adaptation within Homo sapiens. Taken collectively, this study gives us a structural view of diversity in the immune system that may predict variation in immune-related physiological responses.

Figure 7. Evolution of adaptive immunity in the Tree of Life. COURTESY: [6]

III. Intra-generational Selection in Tumor Survival (Cancer Evolution)

Ostrow, S.L., Barshir, R., DeGregori, J., Yeger-Lotem, E., and Hershberg, R.   Cancer Evolution Is Associated with Pervasive Positive Selection on Globally Expressed Genes. PLoS Genetics, 10(3), e1004239 (2014).

Much like Evolutionary Psychology, evolutionary views of cancer has become increasingly popular as conceptual models. Unlike Evolutionary Psychology, however, evolutionary views of cancer are not based on attempts to broadly characterize human behavior. The evolutionary view of cancer is similar to the population dynamics of organismal evolution by natural selection. Except that in this case, population processes are intra-generational and occur within specific tissues. What makes them "evolutionary"? For one, cancer can be characterized as a genealogical (branching) process, with many cancer cells originating from a single deleterious mutant (Figure 8).

Figure 8. Oncogenesis as a branching bush (evolution from common descent). COURTESY: [8].

In fact, one could think of evolutionary models of cancer as an instance of evolutionary dynamics rather than the outcome of reproductive fitness. Nevertheless, the usual suspects still participate in the process. For example, genetic variation in the form of standing variation or somatic mutations is selected upon through the process of tumorigenesis [7]. Mutations that are robust to positive selection contribute to the proliferation and microenvironmental maintenance of tumors (Figure 9). This is distinct from the natural selection that acts on germ line cells. Nevertheless, reproductive fitness is still the criterion for selection.

Figure 9. LEFT: Schematic showing the role of selection on cell populations and their microenvironmental ecosystem. RIGHT: comparison of clonal populations and their evolution with organismal species and their evolution. COURTESY: [9].

One important but often overlooked aspect of treating cancer as an intra-generational evolutionary process is that the constituent cells of a tumor can be viewed as replicators. Figure 10 demonstrates how lineages bud from single mitotically-dividing cells given various environmental and microenvironmental triggers. Yet single- cell replicators are also theoretical units upon which selection acts. In the case of Eukaryotic somatic and stem cells, variants can compete to determine the intensity or metastatic ability or a given type of cancer. These replicators also operate in an environmental context that often acts as a source of selection.

Figure 10. Evolutionary process in a single body (e.g. intra-generational cell population). COURTESY: Figure 2 in [10].

Despite some conceptual difficulties, these three studies give us a window into intra-generational adaptive and evolutionary processes. Far from being a black box, these processes are often distinct from but are influenced by inter-generational evolution. While these studies ignore the role of currently hyped adaptive mechanisms such as epigenetics and the microbiome, there is a lesson for interpreting the true contribution of these types of mechanisms on the long-term evolutionary process.

NOTES:
[1] dos Reis, M., Savva, R., and Wernisch, L.   Solving the riddle of codon usage preferences: a test for translational selection. Nucleic Acids Research, 32(17), 5036–5044 (2004).

[2] Pechmann, S. and Frydman, J.   Evolutionary conservation of codon optimality reveals hidden signatures of co-translational folding. Nature Structural and Molecular Biology, 20, 237–243 (2013).

[3] Neame, E.   Structure vs. Codon Bias. Nature Reviews Microbiology, 7, 406 (2009).

[4] Shah, P. and Gilchrist, M.A.   Explaining complex codon usage patterns with selection for translational efficiency, mutation bias, and genetic drift. PNAS, 108(25), 10231-10236 (2011).

[5] The Human Immune System. The Molecules of HIV website (2006).

[6] Danilova, N.   Evolution of the Immune System. MIT OpenCourseWare, Spring (2005).

[7] Anderson, A.R.A., Weaver, A.M., Cummings, P.T., and Quaranta, V.   Tumor Morphology and Phenotypic Evolution Driven by Selective Pressure from the Microenvironment. Cell, 127, 905-915 (2006) AND Magiliocco, A.M.   Tumor Heterogeneity in Breast Cancer, Concepts, and Tools. Figshare.

[8] Looi, M-K.   Cancer, genomes, evolution, and personalized medicine - it's complicated. Wellcome Trust blog, March 7 (2012).

[9] Greaves, M. and Maley, C.C.   Clonal Evolution and Cancer. Nature, 481, 306-313 (2012).

[10] Yates, L.R. and Campbell, P.J.   Evolution of the Cancer Genome. Nature Review Genetics, 13, 795-806 (2012).

On Bet-hedging and Evolutionary Futures

When someone mentions "bet-hedging", the first thing that comes to mind is an economic investment or gambling strategy, one that maximizes a human's return on their investment. This necessitates cognitive mechanisms for decision-making and valuation. For example, a bet-hedger might keep their investments in two places (e.g a rowboat and a hang-glider). When the return on one potential source of income is exhausted (e.g. rowboat goes over the falls), the other investment can be drawn upon to pick up the slack. Overall, total losses are minimized and potential gains are maximized.

Bet-hedging as a human investment strategy. Hence the rowboat and hang-glider analogy.

But bet-hedging has also been used as a means to explain biological "decision-making" with respect to adaptive changes in genotype and/or phenotype. In this case, decision-making refers to directed changes in a lineage that emerge from stochastic mechanisms. There is no need for a set of formal cognitive mechanisms (or a designer), because in this case natural selection plays the role of a brain (e.g. information processing). In the case of biological bet-hedging, an organism hedges between two or more phenotypic/genotypic states (or behavioral strategies), one becoming predominant only when encouraged by environmental conditions.

Figure 1. A statistical view of biological bet-hedging. COURTESY: Discussion of bet-hedging and adaptation to environmental stresses in [1].

To understand how biological bet-hedging might work, we can use a Venn diagram to take a statistical view of the process (Figure 1). Some form of switching (phenotypic, genotypic) is induced by a subset of environmental stimuli. A smaller subset of positive responses are triggered by environmental stress. This relatively small resulting set of adaptive responses (switching due to an environmental stress signal) should (in theory) be the outcomes of highest fitness value. 

There are many ways this bet-hedging can be accomplished, as the existing literature is quite diverse. I will focus on two candidate mechanisms from the literature: selection on random noise and selection on standing variation.

Selection on random noise is driven by inherent oscillations in gene expression. Gene expression differences (e.g. differential gene expression) are usually thought to define distinct biological processes and cell types. However, gene expression also exhibits wide-band fluctuations [2] and "bursty" changes over time [3], even within the same process or cell type. A recent review in Science on oscillating gene expression over time (e.g. gene expression noise) and biological bet-hedging [4] discusses these mechanisms in more detail.

Figure 2. Type A transcriptional oscillations, sensu [4]. One example of genotypic bet-hedging.

The first type of bet-hedging (type A) is indirect, and involves retaining two or more context-dependent mechanisms for the expression of a single gene. In Figure 2, the successful transcription of a downstream target gene depends on the synchronized activity of two upstream transcription factors. In this case, each upstream gene fluctuates with respect to time. Only when their fluctuations become coordinated in-phaseare they capable of activating a downstream target. In fact, in order to exhibit this selective synchronization, the upstream gene expression must be oscillatory. Otherwise, the downstream gene would not be sensitive to environmental context.

Figure 3. Type B transcriptional oscillations, sensu [4]. Another example of genotypic bet-hedging.

By contrast, type B bet-hedging (direct) is a matter of selecting between alternating genotypic or phenotypic states. In this case, upstream genetic mechanisms create a bistable switch which allows the organism to switch between states given an environmental signal. In the case of stochastic bet-hedging, switching can be like a roulette wheel, in which all possible states are generated spontaneously. The most (as opposed to transient) stable states are those which are most strongly supported by the environment. This is a candidate model for how cells acquire and maintain their identity in microenvironmental niches. Yet it is also relevant to evolutionary change.

Instead of individual phenotypes being the focus of selection, perhaps the ability to switch between phenotypes itself is selected as a trait. For example, stochastic phenotype switching in bacteria results in persistence in the face of rapid environmental variation [5]. Using Pseudomonas fluorescens lineages, phenotypic switching can be experimentally evolved. In fact, the capacity for switching can be isolated to a single gene mutation (CarB), which is both sufficient and necessary for the colony switching trait.

Although stochastic switching is a single trait, it is by no means a simple one. Not only does CarB enable colony switching, but lineages that carry this mutation have a higher fitness compared to those that do not among mixed cultures in a static environment. In the experiments of [5], it took multiple rounds of selection to evolve the CarB mutant. This may also be due to enabling mutations and lineage-specific dependencies which set up the transition to a CarB mutant phenotype.

CarB mutation, examined within a single bet-hedging lineage. TOP: fitness, MIDDLE: genotypes, BOTTOM: phenotypes.

Now we will jump to a highly-speculative infographic [6] on future events in Earth's history. "Timeline of the Far Future" proposes events from the present to Earth's best-case scenario astrological death. In 100 quadrillion (10²⁰) years, the Earth's orbit is predicted to fall into the Sun, if the red giant Sun does not engulf the Earth before then.

In any case, five events on this timeline are relevant to the future of life and worthy of discussion. Keep in mind that this infographic is not sequentially consistent, as it is based on multiple sources of data and overlapping potential scenarios. These events include:

* end of Eukaryotic life, in 1.3 billion years.

* end of Prokaryotic and Archean life, in 2.8 billion years.

* end of C₃ photosynthesis, in 600 million years.

* end of C4 photosynthesis, in 800 million years.

* Earth's temperature rises to 47C due to an increase in solar luminosity, in 1 billion years.

Some of the predictions are provocative, such as the extinction of the Y chromosome [7]. However, one set of predictions intersect with the literature on bet-hedging: the end of photosynthesis. What we know about the possible end of photosynthesis comes from studies [8, 9] that examine the instability and breakdown of photosynthetic reactions at high temperatures. A primary producer's photosynthesis rate becomes unstable above a threshold temperature [8]. When temperature is lowered, this rate returns to normal.

When applied in a laboratory or experienced during heat waves, severe heat stress can cause cellular damage. In fact, large-scale process-based models of photosynthesis assumes that the rate returns to normal after environmental shocks [9]. However, what happens in cases where the average temperature reaches or exceeds this threshold? In such cases, extreme temperatures are not experienced as shocks, but as the physiological set-point.

View of a "red giant" Sun from a now-barren (far future) Earth. Humans, the oceans, and perhaps all extremophiles are all gone at this point.

According to the infographic's predictions, in 0.6 to 2.8 billion that will be that (although I'm not sure why primary producers would be the first type of life to die out). Yet there might be three fundamental changes to life's complexity as we reach a red giant Sun that enable it to survive until perhaps the physical end of the Earth (and/or Sun): 

* the radical restructuring of organismal physiology to suit temperatures that will approach the boiling point of water. This might include hard insulating shells, smaller areas of exposed surface, and "interesting" changes to metabolism. The hedging concept could come into play here, as the expression of genes and phenotypes associated with metabolic function in all organisms (not just single-celled ones) could fluctuate significantly across life-history.

* the radical restructuring of food webs so as to reduce any one source of primary or secondary production. Bets would be hedged in order to survive ever increasing extreme conditions. The increase of energy in the biosphere could lead to more energy being available in general. But of course there could be biospheric tradeoffs (atmospheric composition) which could limit ecological complexity. The sources of primary production would of course need to adapt to take advantage of this situation.

* the evolution of primary production itself. Like complex organisms, we should not expect photosynthesis to simply disappear. Recall that C4 photosynthesis was dominant in the Paleozoic era, only to be eclipsed by the C₃ variety during the Mesozoic era. And this transition occurred despite C4 photosynthesis being more efficient than C₃ in times of heat stress and draught [10]. It might turn out that a new type of hyper-efficient and multiphasic photosynthesis could evolve that takes advantage of late solar system conditions.

These points are speculative as well, but remember -- fully-functioning ecosystems that are gradually exposed to extreme conditions will likely adapt instead of coming to an abrupt end. It would be hard to transplant existing organisms (even extremophiles) into these conditions, but it might not be as hard to evolve responses to the extremities of late Earth. 

NOTES:
[1] Mostowy, R.   Evolution of Stress Response in the Face of Unreliable Environmental Signals. Rafal Mostowy blog, August 20 (2012).

[2] Eldar, A. and Elowitz, M.B.   Functional roles for noise in genetic circuits. Nature, 467, 167-173 (2010).

[3] Goh, K-I. and Barabasi, A-L.   Burstiness and Memory in Complex Systems. arXiv:0610233.

[4] Levine, J.H., Lin, Y., and Elowitz, M.B.   Functional Roles of Pulsing in Genetic Circuits. Science, 342, 1193 (2013).

[5] Beaumont, H.J.E., Gallie, J., Kost, C., Ferguson, G.C., and Rainey, P.B.   Experimental evolution of bet hedging. Nature, 462, 90-93 (2009).

[6] Timeline of the Far Future. BBC Future, January 6 (2014).

[7] This is an example of a scientific debate disguised as persistent myth in the popular press. For two perspectives (the former Y-optimist, the latter Y-pessimist), please see:

a) Hughes, J.F. et.al   Strict evolutionary conservation followed rapid gene loss on human and rhesus Y chromosomes. Nature, 483, 82-86 (2012).

b) Aitken, R.J. and Marshall-Graves, J.A.   Human Spermatozoa: the future of sex. Nature, 415, 963 (2002).

[8] Sage, R.F. and Kubien, D.S.   The temperature response of C₃ and C₄ photosynthesis. Plant, Cell, and Environment, 30, 1086-1106 (2007).

[9] Huve, K., Bichele, I., Rasulov, B., and Niinemets, U.   When it is too hot for Photosynthesis: heat-induced instability of photosynthesis in relation to respiratory burst, cell permeability changes and H₂O₂ formation. Plant, Cell, and Environment, 34, 113-126 (2011).

[10] Liu, Z., Sun, N., Yang, S., Zhao, Y., Wang, X., Hao, X., and Qiao, Z.   Evolutionary transition from C3 to C4 photosynthesis and the route to C4 rice. Biologia, 68(4), 577-586 (2013).