A review of carcinization: from the biology to computational models

COURTESY: 10 Reasons to Celebrate Darwin Day, Paleontology World, February 14, 2018.

For Darwin Day 2025, I will talk about a form of convergent evolutionary phenomenon called carcinization. Carcinization is the convergent evolution of a crab phenotype. Crablike body plans (defined by a flat, rounded shell and a tail that is folded underneath the body) evolved independently at least five times over the course of Decopod evolution (Hamers, 2023; Wolfe et.al, 2021). This is an example of convergent evolution, where similar phenotypes (and by extension functional evolution) recur in different lineages with ostensibly different underlying molecular mechanisms.

From a phylogenetic perspective, carcinization (acquisition of a crablike body plan) and decarcinization (loss of a crablike body plan) are ubiquitous across marine invertebrates. Ecological selection for such a body type that has led to phenotypic integration of multiple traits, particularly the carapace shape and abdomen (Wolfe et.al, 2021). Figure 1 shows the phylogenetic origins of carcinization in the Brachyura and Anomura clades (infraorders).

Figure 1. A phylogeny showing a variety of crab phenotypes (left), and an illustration of transformation to different crab phenotypes (right). Left image: "How Does a Crustacean Become a Crab", Phys.org. Right image: The "hermit to king" transition within the infraorder Anomura (Tsang et.al, 2011). Click to enlarge.

The most interesting attributes of the carcinization body plan involves: 1) multiple paths to a basic phenotype (shape). Many alternate genotypes result in self-similar phenotype, 2) phenotypic elaboration not due to common ancestry, and 3) a generalized form of common ancestry not at the level of traits. There are varying definitions of carcinization (or brachyurization, see Footnote 1) across genera and orders. The strict definition of McLaughlin and Lemaitre (1997) is a reduction and folding of the abdomen beneath the thorax, or the evolution of a crab-like appearance. 

We can use molecular methods to discover the deep evolutionary relationships between various instances of crab-like phenotypes. Using a mitochondrial phylogeny based on genomic rearrangements of an arthropod protein-coding gene, Morrison et.al (2002) suggest that once they appear, the independent evolution of crab-like forms may be irreversible. Another study by Wolfe et.al (2019) utilize nuclear genes and the Anchored Hybrid Enrichment (AHE) method to confirm monophyletic (single origin) relationships between all infraorders of the clade Decopoda. They also demonstrate that monophyletic "lobster" and "crab" groups exist. In terms of developmental origins, carcinization involves Brachyury (T-box Genes): great detail for its pivotal role in the development of the notochord and posterior mesoderm (Papaioannou, 2014; see also Footnote 1). Carcinization results from several transcriptional mechanisms related to physiology and phenotype, including energy metabolism-related pathways, ventral nerve cord fusion and associated apoptosis, metamorphosis, and abdominal-specific Hox genes (Yang et.al, 2021).

The evolution and development of the crab-like body plan can be characterized computationally in order to expand our understanding of convergent evolution in the evolution of development. There are a number of means to build a computational model of this process. Ostachuk (2021) proposes a network-based topological model of crab metamorphic development. In this model, the stages of brachyuran metamorphosis are modeled as a series of complex networks. Figure 2 shows this process of defining morphological unit centroids as network nodes, and topological transformations between morphological units as the network edges. A topological overlap analysis was conducted to demonstrate changes in phenotypic complexity. Traditional measures of complexity, such as modularity and hierarchical organization, increase across the course of development. This corresponds to what Ostachuk (2021) defines as a transition from intensive to extensive complexity.

Figure 2. A network of morphological units derived from a crab-like phenotype. From Figure 1B, Ostachuk, 2021. Click to enlarge.

Figure 3. A comparison of developmental network topologies from egg to crab phenotype. From Figure 3 in Ostachuk, 2021. Click to enlarge.

Ostachuk (2021) uses morphological networks rather than gene regulatory networks (GRNs) because it is difficult to make a mapping from network outputs to topological transformations of the phenotype. Yet one benefit of using genomic representations is to allow for a further representation of canalized morphogenesis. This is consistent with Waddington's notion of reduced sensitivity to genetic or environmental perturbations (Agam and Braun, 2025) and is amenable to understanding via an epigenetic landscape model. The epigenetic landscape model (Wang et.al, 2011) in particular is useful for modeling the evo-devo of carcinization. According to our evolutionary examples, we should expect the landscape to converge during development. A prediction can be made that most stable points in the epigenetic landscape favor a path towards crab-like phenotypes. Molecular mechanisms such as Hsp90 can provide a mechanism for phenotypic divergence in cavefish. Yet phenotypic buffering mechanisms can also work the other direction: multiple configurations of genomic loci converge to the same phenotype (Kovuri et.al, 2023). This phenotype tends to become irreversible as other options are no longer developmentally viable. Indeed, evolutionary irreversibility can be represented as a saddle node, a pitchfork bifurcation where two developmental pathways diverge (Ferrell, 2012).

Carcinization can also be summarized in the form of a computational genotype-phenotype map (Figure 4). On such a map, we can approximate convergent evolution as multiple genotypic representations that converge to a single phenotype. Genotype-phenotype maps also allow convergent evolution to be viewed as a study in self-similarity. In the complexity literature, self-similarity is defined as a complex system with the same statistical properties at multiple powers of magnitude (Magnusson, 2023). Figure 4 demonstrates three different types of genotype-phenotype maps: GRNs to phenotypic modules (Figure 4A), a correspondence map that maps between domains (Figure 4B), and a genotypic representation that maps to a phenotypic representation (Figure 4C). In Figure 4A, the output of three GRNs (G1, G2, G3) are mapped to four phenotypic modules (P1, P2, P3, P4). Each GRN can map their outputs to multiple phenotypic modules, components of a phenotype that we observe in the crab-like body plan. This allows us to estimate the contribution of each GRN to each phenotypic module (Wagner et.al, 2007; see also Footnote 2). Figure 4B provides a means to understand the space of genotypic variation and how this corresponds to the space of all possible phenotypic configurations. While the example we give is not specific to crab-like body plans, in such a case a wide variety of GRN activities (W_g) will correspond to a constrained set of locations in the phenotypic map (W_p). This allows us to apply more sophisticated Computational Biology models such as joint manifolds (Munteanu and Sole, 2008). To conclude, Figure 4C demonstrates the concept of phenotypic redundancy (Ahnert, 2017), which is a common feature of phenotypic maps. Phenotypic redundancy can also help us understand how multiple genotypic representations can converge upon a self-similar phenotype. Our genotypic representation contains a simple chromosome with multiple loci, which in Figure 4C are recombined and mutated across our three examples. Our phenotype is a 2-D layer of black and white cells, which result from the expression of the genotypic representation. Based on an application of theory, the crab-like body plan can be said to exhibit robustness against gene duplication, mutation, and recombination events.

Figure 4. Genotype-Phenotype map components. A) discrete model of genomic elements (containing a GRN) with their outputs mapping to different phenotypic modules, B) correspondence map showing how genotypic elements in domain W_g map to phenotypic elements in domain W_p, C) genotypic representations that converge upon a single phenotypic representation. Click to enlarge.

Let us conclude with two items for further study. Wolfe et.al (2021) asks: can you predict a phenotype from ecology or genomics? In the case of carcinization, we observe repeated gain and loss of body plan: polyphyletic nature of crab phenotype. We might also be able to predict crab-like phenotypes from the results of computational models. The developmental network and epigenetic landscape approaches are particularly promising in this regard. Might carcinization be a form of developmental buffering as predicted by the epigenetic landscape model? Patterson and Klingenberg (2007) suggest that phenotypic buffering is triggered by Hsp90 activities in flies, fish, and plants. Genotype-phenotype maps are indeed possible but require a complete characterization of the genetic diversity underlying the multitude examples of crab-like phenotypes found in nature.

Footnotes:

1. Brachyurization is perhaps related to brachyury, which involves with the epithelial-mesenchymal transition in development. A description of this process is reviewed in Huang et.al (2022) and Haerinck et.al (2023).

2. Further discussion of conducting genotype-phenotype mapping using network approaches are presented in Kim and Przytycka (2013).

References:

Agam, O. and Braun, E. (2025). Stochastic morphological swings in Hydra regeneration: a manifestation of noisy canalized morphogenesis. PNAS, 122, e2415736121. 

Ahnert, S.E. (2017). Structural properties of genotype–phenotype maps. Royal Society Interface, 14(132), 20170275.

Ferrell, J.E. (2012). Bistability, Bifurcations, and Waddington's Epigenetic Landscape. Current Biology, 22(11), R458-R466.

Haerinck, J., Goossens, S., and Berx, G. (2023). The epithelial–mesenchymal plasticity landscape: principles of design and mechanisms of regulation. Nature Reviews Genetics, 24, 590–609.

Hamers, L. (2023). Why do animals keep evolving into crabs? LiveScience, June 1.

Huang, Z., Zhang, Z., Zhou, C., Liu, L., and Huang, C. (2022). Epithelial–mesenchymal transition: The history, regulatory mechanism, and cancer therapeutic opportunities. MedComm, 3(2), e144. doi:10. 1002/mco2.144.

Khodaee, F., Zandie, R., and Edelman, E.R. (2025). Multimodal learning for mapping genotype–phenotype dynamics. Nature Computational Science, doi:10.1038/s43588-024-00765-7.

Kim, Y-A. and Przytycka, T.M. (2013). Bridging the Gap between Genotype and Phenotype via Network Approaches. Frontiers in Genetics, 3, 227.

Kovuri, P., Yadav, A., and Sinha, H. (2023). Role of genetic architecture in phenotypic plasticity. Trends in Genetics, 39, 703-714.

Magnusson, M.S. (2023). Sudden bio-mathematical self-similarity and the uniqueness of human mass societies: from T-patterns and T-strings to T-societies. Frontiers in Psychology, 14, 1157315. 

McLaughlin, P.A. and Lemaitre, R. (1997). Carcinization in the Anomura: fact or fiction? I. Evidence from adult morphology. Contributions to Zoology, 67(2), 79-123.

Morrison, C.L., Harvey, A.W., Lavery, S., Tieu, K., Huang, Y., and Cunningham, C.W. (2002). Mitochondrial Gene Rearrangements Confirm the Parallel Evolution of the Crab-like Form. Royal Society B, 269(1489), 345-350.

Munteanu, A. and Sole, R. (2008). Neutrality and Robustness in Evo-Devo: Emergence of Lateral Inhibition. PLoS Computational Biology, 4(11), e1000226. 

Ostachuk, A. (2021). A network analysis of crab metamorphosis and the hypothesis of development as a process of unfolding of an intensive complexity. Scientific Reports, 11, 9551.

Papaioannou, V.E. (2014). The T-box gene family: emerging roles in development, stem cells and cancer. Development, 141(20), 3819–3833.

Patterson, J.S. and Klingenberg, C.P. (2007). Developmental buffering: how many genes? Evolution and Development, 9(6), 525–526.

Tsang, L-M., Chan, T-Y., Ahyong, S., and Chu, K-H. (2011). Hermit to King, or Hermit to All: Multiple Transitions to Crab-like Forms from Hermit Crab Ancestors. Systematic Biology, 60(5), 616-629.

Wagner, G.P., Pavlicev, M., and Cheverud, J.M. (2007). The road to modularity. Nature Reviews Genetics, 8, 921–931.

Wang, J., Zhang, K., Xu, L., and Wang, E. (2011). Quantifying the Waddington landscape and biological paths for development and differentiation. PNAS, 108(20), 8257–8262. 

Wolfe, J.M., Breinholt, J.W., Crandall, K.A., Lemmon, A.R., Moriarty Lemmon, E., Timm, L.E., Siddall, M.E., and Bracken-Grissom, H. (2019). A phylogenomic framework, evolutionary timeline and genomic resources for comparative studies of decapod crustaceans. Proceedings in Biological Science, 286(1901), 20190079.

Wolfe, J.M., Luque, J., and Bracken-Grissom, H.D. (2021). How to become a crab: Phenotypic constraints on a recurring body plan. BioEssays, 2100020.

Yang, Y., Cui, Z., Feng, T., Bao, C., and Xu, Y. (2021). Transcriptome analysis elucidates key changes of pleon in the process of carcinization. Journal of Oceanology and Limnology, 39, 1471–1484.

Gyrification of the Tree of Mammals

For this year's Darwin Day post, I will be reviewing the evolutionary origins and developmental emergence of gyrification of the Mammalian brain. Gyrification occurs when the neocortex, or six layered cortex on the dorsal surface of Mammalian brains, exhibits wrinkles and folds rather than a smooth surface (lissencephaly). Gyrification is measured using the gyrification index (or GI). GI can range from 5.6 in Pilot whales (Globicephala) to 3.8 in Elephants (Loxodonta) and 2.6 in Humans (Homo) [1]. A more extensive phylogenetic analysis (Figure 1) shows the evolutionary trajectory for this in Hominids, and a highly gyrified brain is associated with other traits that emerge as early as the divergence of Primates. 

Figure 1. A phylogeny of primate brain evolution (with Mammalian outgroups), with a focus on the origin of traits found in the human brain. COURTESY [2].

The evolutionary origins of gyrification may either be mono- or polyphyletic, as different genes have been identified as potential associated factors. Gyrification might also be a product of convergent evolution, as this trait may simply be a by-product of larger neocortical sheets. Steidter [3] points out that gyrification may simply be due to physical constraints related to fitting a vastly enlarged cortical sheet into a skull scaled to an organism's body size. 

Figure 2. Allometric scaling across select Mammalian brain, showing an increase in gyrification for larger brains. COURTESY [4].

In Figure 2, we see that in general larger brains also have a larger GI value. The curvilinear relationship shown in the figure is known as an allometric scaling. Allometry [5] is a convenient way to quantitatively assess relative growth across different species, and the resulting regression parameters are suggestive of underlying mechanisms that control and predict growth across evolution.

In this case, the allometric relationship is brain size versus tangential expansion. Tangential matter is expansion of gray matter relative to the constraints of white matter, or a grey-to-white matter proportion [4]. As the amount of gray matter increases, brain size also tends to increase, and so does the GI value. However, the proportion of gray to white matter saturates, while brain sizes continue to expand along with increasing GI values. 

Figure 3. Simulating gyrification as a by-product of physical processes. 3-D printed models based on MRI data for brains from different stages of development. COURTESY [6].

Genetic analyses implicate the role of specific genes in controlling brain volume, which then sets the stage for gyrification [7]. Developmental mutations in the human genetic loci collectively known as MCPH 1-18 [8] lead to a condition called microcephaly, where the mature microcephalic brain remains small and lacks gyrification. In a study of 34 species [9], the largest source of explained variance between species can be explained by random Brownian motion. Furthermore, the data within the order Primates shows that fold wavelength is stable (~12mm) despite a 20-fold difference in volume [9]. 

As an alternative hypothesis to evolutionary origins, gyrification can result from various physical processes in developmental morphogenesis (Figure 3). The gyrification process consists of gyral (ridge-like) and sulcal (groove-like) convolutions. In the earliest stages of development, no gyrification is expressed in the phenotype. However, as the neocortex grows faster relative to the rest of the brain, a mechanical instability results that leads to buckling [6]. Buckling thus creates gyrification, although the consistency of their localization and timing in development suggests underlying cellular and molecular mechanisms. Demonstration of biophysical mechanisms does not preclude a phylogenetic explanation, however. As we will see later on, surface physics relies upon the presence of certain cell types and growth conditions.

Figure 4. An overview of the evolution of development (Evo-Devo) of gyrification. Gyrification and lissencephaly occur through mechanisms that affect changes in brain size and GI relative to the last common ancestor (in this figure, transitional form). COURTESY [10].

There are also several cellular and molecular factors that contribute to neocortical growth, and thus towards gyrification. In Figure 4, we see four archetypes that result from increases and decreases of brain size coupled with increases and decreases of GI. For example, increases in basal radial ganglion (bRG) precursor cells and transit-amplifying progenitor cells (TAPs) contribute to increases of both brain size and GI [10]. Decreases in brain size and GI are controlled by changes in cell cycle timing and associated heterochronic changes. Heterochrony has to do with the timing of the rate and termination of growth in development and is but one factor that suggests lissencephaly is actually the derived condition. Thus, smooth brains would be an evolutionary reversal from the ancestral gyrified state that occurred multiple times across the tree of Mammals. 

Once again, an evolutionary conundrum. Happy evolutioning!

NOTES:

[1] Johnson, S. Number and Complexity of Cortical Gyrii. Center for Academic Research and Training in Anthropogeny. La Jolla, CA. Accessed: February 13, 2022. 

[2] Franchini, L.F. (2021). Genetic Mechanisms Underlying Cortical Evolution in Mammals. Frontiers in Cell and Developmental Biology, 9, 591017.

[3] Striedter, G. (2005). Principles of brain evolution. Sinauer, Sunderland, MA.

[4] Tallinen, T., Chung, J.Y. , Biggins, J.S., and Mahadevan, L. (2014). Gyrification from constrained cortical expansion. PNAS, 111(35), 12667-12672.

[5] Shingleton, A. (2010) Allometry: The Study of Biological Scaling. Nature Education Knowledge, 3(10), 2.

[6] Tallinen, T., Chung, J.Y., Rousseau, F., Girard, N., Lefevre, J., and Mahadevan, L. (2016). On the growth and form of cortical convolutions. Nature Physics, 12, 588–593.

[7] Zilles, K., Palomero-Gallagher, N., and Amunts, K. (2013). Development of cortical folding during evolution and ontogeny. Trends in Neurosciences, 36(5), 275-284. 

[8] Jayaraman, D., Bae, B-I., and Walsh, C.A. (2018). The Genetics of Primary Microcephaly. Annual Review of Genomics and Human Genetics, 19, 177-200.

[9] Heuer, K., Gulban, O.F., Bazin, P-L., Osoianu, A., Valabregue, R., Santin, M., Herbin, M., and Toro, R. (2019). Evolution of neocortical folding: A phylogenetic comparative analysis of MRI from 34 primate species. Cortex, 118, 275-291.

[10] Kelava, I., Lewitus, E., and Huttner, W.B. (2013). The secondary loss of gyrencephaly as an example of evolutionary phenotypical reversal. Frontiers in Neuroanatomy, 7, 16.

January is DevoWorm month!

Blossoms or fireworks to ring in the New Year?

Welcome to 2019! And welcome to OpenWorm Foundation's project of the month for January, featuring DevoWorm. Here I will briefly go over progress in the DevoWorm group over the last year and a half. If you would like to know more, we have a group Slack channel (#devoworm) in the OpenWorm team, a group website, and a Github repository.

For the uninitiated, the DevoWorm group has a multifaceted set of interests. We are interested in simulating and analyzing data related to worm development, but have an interest in the development of other model organisms as well. In terms of results, we have focused mostly on publications and open datasets, but as you will see from the website, we have also been involved in the creation of unique demos and software development.

The DevoWorm group is also interested in education. Our educational efforts have largely spread out over four types of pedagogy: digital badges, tutorials via interactive notebooks, public lectures, and one-on-one mentorship through the Google Summer of Code (GSoC) program. The OpenWorm Foundation has hosted a DevoWorm GSoC student for the past two years (2017 and 2018), and will be offering a third opportunity this year (2019). 

This is the 15th anniversary for the GSoC program, and it is always an excellent experience. The application process begins on February 25th. If you are interested in a mixture of computational biology, image processing, and machine learning, please contact us for more information.

COURTESY: Image from "One, Two, Three,....GSoC!" by Vipal Gupta

While GSoC is well-compensated opportunity to participate in DevoWorm, there are also less formal ways through which one can collaborate. One of these ways is through a conventional research pathway such as analyzing data, building a simulation, or curating a dataset. Another way to collaborate is to help create new types of educational content. We are particularly interested in creating virtual reality-based offerings in the near future. If you enjoy creating educational content, or simply enjoy learning, please get in touch!

Another new initiative is called DevoZoo. The DevoZoo site aggregates open datasets, methods, and techniques relevant to computational developmental biology and data science biology. We currently host open datasets for the following model organisms: C. elegans, Drosophila, Zebrafish, Ascidians, and Mouse. DevoZoo also hosts raw microscopy data in the form of movies for many of these model organisms as well as Spiders. As if this were not enough, we also try to engage learners and open scientists with artificial life models. The DevoZoo presents three: Morphozoans, developmental Braitenberg Vehicles, and Multicell Systems. The artificial life models in particular could use some further development. Check out the DevoZoo webpage or ask us if you would like to learn more.

Finally, you can participate by collaborating on a publication. The DevoWorm group has been featured in four publications in the past year. The OpenWorm article in the "Connectome to Behavior" special issue of Royal Society B provides a succinct description of the project and its current course. Some of our members served as editors and contributors to a special issue of BioSystems in honor of Dr. Lev Beloussov. This issue features 32 articles that provide a very broad and innovative look at the topic of morphogenesis. Our set of contributions (peer-reviewed papers) spanned from network models of the embryo to the developmental emergence of the connectome and quantitative approaches to organogenesis in the eye imaginal disc.

If you are interested in joining in on the discussion, we hold group meetings online every Monday at 9pm UTC. We are also starting to host hackathons on Fridays during the late morning/early afternoon North American time. Check out our scheduling page for more information. Hope to encounter you soon, and have a great month!

Rise of the Alt-Research Program

It is time for a new paradigm! In the past 5 years or so, a new type of research institute has arisen [1]. One that is flexible and open, without the constraints typical of a University or corporate labs. In a time of institutional change and funding uncertainty, such institutes provide a means for many non-conventional types of research to flourish. We can think of such facilities an "Alt-research Program" (after the "alt-academic" movement) [2], although stressing the open science and collaborative aspects are also important. So let's discuss some recent developments for one such organization, Orthogonal Research and Education Laboratory.

We have three recent developments: a new paper collaboration, a preprint mention, and a set of Google Summer of Code presentations. First up is a paper that was recently published with three co-authors. Orthogonal Research is a nexus for open science-enabled collaborations with University-based academics [3]. The paper “Network Dynamics of Attention During a Naturalistic Behavioral Paradigm” is now live at Frontiers in Human Neuroscience [4]. Learn about the what happens in attentional networks of the human brain during naturalistic behavior – in this case, high-resolution video game play with neural activity captured via “free-viewing” neuroimaging.

Here is how you build institutional credibility (or so I've heard). Notice the second affiliation.

From Figure 3 in the paper (drawings courtesy of Dr. Richard Huskey).

Screen shot of the first-person video game stimulus "Tactical Ops: assault on terror". Screenshot courtesy of Top Full Games and Software.

Orthogonal Lab was also recently mentioned in a preprint on scientific ecosystems [5] from members of the Ronin Institute. In the paper, Orthogonal Lab was described as a lab focusing on more specific research questions than a larger institute focused on enabling basic science initiatives (such as Neurolinx). This new scientific ecosystem paradigm proposed in the paper is focused on how to enable collaboration and open science outside of the formal University structure.

Thirdly, we have community period [6] presentations by three students in this year’s Google Summer of Code program (sponsored by INCF). There will be a presentation now, and a final presentation at the completion of the Summer. The idea is to keep students thinking about the project's progress, to develop their public speaking/presentation skills, and to build up the foundations for a paper or future research. Cheng-Hsun (Jim) Hsueh and Sam Felder are working on Contextual Geometric Structures project (Representational Brains and Phenotypes Group), while Arnab Banerjee is working with the OpenWorm Foundation (DevoWorm Group).

One way to enable Alt-research Programs is to embrace low carbon and location-free modes of doing and disseminating research. One such proposal (by Dr. Angel Goni-Moreno) has been made to provide low-carbon and researcher-accessible conferencing options to the annual ALife conference. In particular, distributed sessions would enable participation and collaboration across continents and research groups that would otherwise not interact.

The new research ecosystem paradigm path to field-specific and interdisciplinary community-building?

NOTES:

[1] See a previous Synthetic Daisies post on hosting theory hackathons through such as organization.

[2] While I find the prefix "alt-" to be a shallow marketing term (sometimes nefariously so), it does fit into existing descriptions of academic activity outside of or in parallel with Universities.

[3] The two main collaborators were the Media Neuroscience Laboratory at UCSB and the Cognitive Communication Science Laboratory at OSU.

[4] Here are the essential materials: Paper, Supplemental Materials, Open Dataset, Video Game Stimulus.

[5] Lancaster​​, A.K., Thessen​, A.E., Virapongse​, A. (2018). A new paradigm for science: nurturing the ecosystem. doi: 10.7287/peerj.preprints.26885v2.

[6] Typically, the community period is an opportunity for students to get acquainted with the community resources (open datasets, open codebase, community members) of their chosen open source/science organization. For more information on the Google Summer of Code community period, here are a few blog posts (1, 2, 3, 4, 5).

Upcoming Update on DevoWorm Project to OpenWorm

Next Friday (4/15) at 9:00am Pacific Time, I will be presenting an update to the OpenWorm Journal Club on advances in the DevoWorm subproject (How a Worm Develops). It has been a year and a half since the previous update [1], and we have made significant progress on a number of fronts:

* as of right now, our group consists of myself, Richard Gordon, Tom Portegys, Steve McGrew, and Gabriel Pascualy.

* DevoWorm now consists of three interests groups, all of which are fairly informal: Digital Morphogenesis, Developmental Dynamics, and Reproduction and Developmental Plasticity. It is hoped that as the project matures and attracts more collaborators, the interest groups will keep the subproject focused on specific goals.

Tom, Steve, and Gabriel have been taking the lead on the Morphozoic platform, which is part of the Digital Morphogenesis interest group. Morphozoic is a hybrid model (Cellular Automata/ANN) that can approximate morphogenetic processes. The Cellular Automata component utilizes an approach called nested neighborhoods that captures the action of cell-cell communication and signaling gradients in a way conventional Moore neighborhoods do not. Tom has also produced a number of demos ranging from simulating biological pattern formation to image processing. This work will be featured in an soon to be published book chapter [2].

Richard Gordon and myself have been taking the lead on the Developmental Dynamics interest group. To this end, we have worked out differentiation trees [3] for Caenorhabditis elegans [4] and Ciona intestinalis [5]. Differentiation trees are essentially reorganizations of the lineage tree based on the size differential of daughter cells after a cell division event, and may point us to subtle spatial patterns such as the precursors of tissue formation. More generally, we have been attempting to work out cross-species comparisons of early embryonic development, as well as novel computational characterizations of both mosaic and regulative development in multiple species. Some of this work will be featured in an upcoming publication in a special issue of the journal Biology [6].

The Reproduction and Developmental Plasticity interest group is focused on the evolution and development of C. elegans life-history, and stems from work I did in Nathan Schroeder's Laboratory at UIUC [7, 8]. So far, this interest group has involved experimental evolution and the induction of developmental plasticity resulting from L1 larval arrest in mutant genotypes. This is the newest area of DevoWorm, but is a necessary component of understanding for working towards whole-organism simulation.

All three DevoWorm project interest groups in their "2-cell phenotype". 

If you are interested in joining the DevoWorm group or just attending one of our group meetings, please attend the OpenWorm presentation or contact one of the current group members. More generally, the OpenWorm project is currently recruiting volunteers, so fill out an application and state your skills and specific interests. We are looking for people with a diversity of backgrounds, from hard-core programming and data analysis skills to science communication specialists and biologists with an interest in theoretical synthesis.


NOTES:
[1] Alicea, B., McGrew, S., Gordon, R., Larson, S., Warrington, T., and Watts, M. (2014). DevoWorm: differentiation waves and computation in C. elegans embryogenesis. bioRxiv, doi:10.1101/009993

[2] Portegys, T., Pascualy, G., Gordon, R., and Alicea, B. (2016). Morphozoic: cellular automata with nested neighborhoods as a novel representation for morphogenesis. Forthcoming in Multi-Agent Based Simulations Applied to Biological and Environmental Systems.

[3] Gordon, R. (1999). The Hierarchical Genome and Differentiation Waves: novel unification of development, genetics and evolution. World Scientific and Imperial College Press, Singapore and London.

[4] Alicea, B. and Gordon, R. (2016). Caenorhabditis elegans Embryonic Differentiation Tree (10 division events). doi:10.6084/m9. figshare.2118049.

[5] Alicea, B. and Gordon, R. (2016). Ciona intestinalis Embryonic Differentiation Tree (1- to 112-cell stage). doi: 10.6084/m9.figshare.2117152.

[6] Alicea, B. and Gordon, R. (2016). Quantifying mosaic development: towards an Evo-Devo Postmodern Synthesis via differentiation trees of embryos. Biology (Special Issue: beyond the modern evolutionary synthesis). Submitted.

[7] Alicea, B. (2016). Evolution in Eggs and Phases: experimental evolution of fecundity and reproductive timing in Caenorhabditis elegans. bioRxiv, doi:10.1101/042143.

[8] Alicea, B. (2016). Genotype-specific developmental plasticity shapes the timing and robustness of reproductive capacity in Caenorhabditis elegans. bioRxiv, doi:10.1101/045609.

Maps, Models, and Concepts, August edition

Walcome back, Maps, Models, and Concepts series! In this edition, with content cross-posted to Tumbld Thoughts, we take a tour of Artificial Intelligence reconsidered (I) and the visualization of Economic History (II). Enjoy!

I. Can you haz intelligent behavior, internet bot?

Here are a few recent readings on the modeling and simulation of intelligence, broadly defined. The first two [1, 2] are part of a series by Beau Cronin on alternative ways to model intelligence. How do we produce "better" (e.g. more intuitive, or more human) artificial intelligence? Perhaps it is the model that counts, or perhaps it is the definition of intelligence itself. 

COURTESY: Figure 3 in [3].

The authors of [3] take the former view, and present a review on how various computational architectures can produce intelligent outputs. One example demonstrates how hierarchical Bayesian models (HBMs) can be used to acquire intuitive theories for various knowledge domains. But one can also use biologically-based architectural models to produce intelligent behavior. In [4], it is shown that fabrication and cell culture techniques can produce outputs similar to purely computational connectionist models.

COURTESY: Figure 2 in [4].

II. Did it begin with a bang, a boom, or a bust?

Aha! The moment of economic creation was not at 1650 after all! Conventional economic theory sometimes gives the impression that economists are creationists in spirit. Many historical graphs [5] only offer useful information back to the year 1650. Around 1650 or so, most economic indicators enter their exponential phase, which renders graphical information about previous eras incomparable.

But economist and modeler Max Roser [6] offers a historical view of global GDP going back 2,000 years. His "Our World in Data" website is an attempt to characterize global economics and other social phenomena as a series of visualizations. This includes maps (spatial distributions) and charts that make long-term comparisons more than a series of bad graphs. If John Maynard Keynes were to look at these data, he might say: in the long run, we are all wealthier [7].

NOTES:

[1] Cronin, B.   In search of a model for modeling intelligence. O'Reilly Radar blog, July 24 (2014).

[2] Cronin, B.   AI's dueling definitions. O'Reilly Radar blog, July 17 (2014).

[3] Tenenbaum, J.B., Kemp, C., Griffiths, T.L., and Goodman, N.D.   How to Grow a Mind: Statistics, Structure, and Abstraction. Science, 331, 1279-1285 (2014).

[4] Tang-Schomera, M.D., White, J.D., Tien, L.W., Schmitt, L.I., Valentin, T.M., Graziano, D.J., Hopkins, A.M., Omenetto, F.G., Haydon, P.G., and Kaplan, D.L.   Bioengineered functional brain-like cortical tissue. PNAS, 10:1073/pnas.1324214111 (2014).

[5] The bottom three pictures are courtesy of: Roser, M.   GDP Growth Over the Very Long Run. Our World in Data (2014).

[6] Matthews, D.   The world economy since 1 AD, in a single chart. Vox blog, August 15 (2014).

[7] Based on the quote "in the long run, we are all dead".

Historical Contingencies at the Birthday Party

Historical contingencies are perhaps the most interesting outcomes of the evolutionary process. Stephen J. Gould spent a lot of time and energy making this idea popular, but evidence comes from both paleontology [1], extant populations [2], and experimental evolution [3]. However, the ubiquity of the contingency concept does not resolve its phylogenetic consequences. Is historical contingency highly specific (a hard constraint resulting in unique paths), or is it a softer constraint? And how can we understand the role of convergent evolution within this framework? We will approach this from a mathematical perspective, and answer the riddle of what evolution and birthdays have in common.

Definition of generative science (Wikipedia) and historical science (RationalWiki). 

Evolutionary Histories and Their Accidents

Like human history, evolutionary history is a product of many forces and causes. We often think of these factors as a series of chance events (sometimes unique) that lead to a given outcome [5]. Observers sometimes use this point to argue that history is not systematic and thus cannot be separated from context (and thus comparative history would be quite impossible) [5]. But this also assumes that the factors that make a given evolutionary history unique (its branching events) are "hard". Not only are they irreversible, but also should not have significant similarities. The outcomes of the evolutionary process (genotypes and phenotypes) are locked in to a specific trajectory. By itself, this constraint should favor some changes over others and disallow changes that resemble even closely-related lineages.

If historical contingency is a hard constraint, then this leads us to an evolutionary hypothesis: historical contingency creates irreversible paths to highly-unique phenotypes. While a bit simplistic, this nonetheless serves to understand the consequences of contingency. Recall that the evolutionary process occurs through branching, and results in a series of evolutionary outcomes (Figure 1). While these outcomes are individually different, their degree of uniqueness relies on the "hardness" of the branch that separates one outcome from another. Figure 1 not only shows the results of branching, but also assumes "hard" constraints. The contingencies generated by this model involve hard constraints that results in a unique, lineage-specific partition of the search space.

Figure 1. An example of a phylogeny with unique, non-recurrent evolutionary outcomes. The evolutionary changes act as hard constraints, and each terminal taxon occupies a distinct 1-dimensional subspace. 

In Figure 1, a conventional phylogenetic model demonstrates how a search space can be partitioned through evolutionary branching processes. However, when the constraints are softer, each branching event results in less distinction between the resulting alternative forms and increases the chances that traits or forms that resemble those of a related lineage (even distantly so) will emerge. Figure 2 demonstrates this difference using the analogy of the Plinko game [6]. In this case, the combination of the process and outcome of contingency creates an overlapping search space over time for a given lineage (see the distribution of Plinko balls at the bottom of Figure 2). 

Contingency also rests on the assumption that evolutionary randomness results in unique combinations of traits. One feature of historical contingency involves building upon previously-acquired traits. As complexity is built in this way, the total number of possibilities decreases. But while the stochastic nature of evolution is a matter of conditioned chance, branching is an assumption of theoretical intuition. Therefore, evolutionary outcomes can converge even when their forms nominally exist in different lineages. But given these constraints, shouldn't convergent evolution be impossible? Before we answer the question (and the answer is no) we must take an intellectual detour by way of birthday parties.

Figure 2. What it means to have an overlapping space of evolutionary outcomes enabled by soft historical constraints. COURTESY: Plinko Probability, version 2.02. PhET Interactive Simulations.

How are birthday parties at all relevant here? The birthday party paradox, a statistical curiosity, might help us establish a link between contingency and recurrence. But first, let us revisit our evolutionary process-as-hierarchical tree model. In this model, all possible combinations of n are classified using a tree-like structure. Given that the search space is much larger than the number of objects being classified, do they also end up in unique categories? Perhaps. But, as we will learn, it may not matter as much as does the size and complexity of the evolutionary landscape itself.

What is the Birthday Party paradox [7]? Amazingly, this did not make a Quora list of the most counterintuitive mathematical results [8]. But perhaps this result is not so intuitive after all. Say you were to survey a room of n people. Given that every day of the year has an equal chance of being a birthday, how many people will you need to sample in order to find at least two people with the same birthday? The answer you might give depends on your intuitions about randomness. With 365 days in a typical year, one might assume that you would need a lecture hall of at least 300 people. But in fact, once you reach a sample size of 47, the probability (95%) becomes asymptotic to 100%. See Figure 2 for a graphical representation.

Figure 2. Number of people surveyed (x-axis) vs. probability of at least two people having the same birthday (y-axis).

Evolutionary Histories and Their Coincidents

This outcome results from a mathematical principle called recurrence. This principle suggests that motifs and themes can recur at an unknown frequency -- it explains why you get runs of heads or tails in a series of coin flips. This recurrence has nothing to do with the outcomes being related to one another. They are merely conincidences inherent in a generative process. In the evolutionary outcome space example, this suggest that overlap can occur in the form of deep similarities. Can this be applied to the probability that n lineages will exhibit convergence?

Not exactly what we are talking about here, but an evolutionary birthday nonetheless.

Phylogenetic birthday (or contingency) paradox:

In the next few tables, I have shown how the mathematics and problem formulation of the standard birthday paradox can be used to understand a generative set of evolutionary configuration and the probability of a parallel evolutionary outcome. 

What the data should look like (standard Birthday Party paradox):

 What the data should look like (proposed evolutionary paradox):

In the case of the evolutionary paradox, an exceedingly small sample size of 60 possible configurations was used for demonstration purposes. It is of note that this model is scalable to very large numbers of distinct evolutionary configurations. However, it is clear that the probability of convergent evolution is nearly 100% well before a given lineage is locked in to a single point in the configuration space. As the number of changes increases, the number of possible configurations changes is correspondingly reduced. 

But....but.....there are assumptions!

This model makes a few general assumptions. One, while each change is assumed to be countable, there is no accounting of how hard or soft the constraint actually is. This could be resolved through using a soft classifier to characterize each change, although would not remove the effects of geographically-localized specialization. An example of this is in the supplemental Excel dataset (see Notes section below). Another is that all evolutionary configurations are countable in the same way (e.g. no modularity). Again, this can be resolved by generating a matrix for each component of an organism (e.g. phenotypic module). 

Despite these assumptions (for better or for worse), the general principle of recurrence should give us a somewhat useful model for estimating how plausible or implausible convergent evolution is for a given set of evolutionary relationships. Recurrence is a useful tool that is largely ignored in conventional discussions about evolutionary constraints and parallel evolution. Once again, recurrence (by way of Henri Poincare in Figure 3) allows us to use principles of complexity theory to better understand evolutionary phenomena [9].

Figure 3. An example of Poincare recurrence. In this example, an image of Henri Poincare has been permutated, with reconstruction of the original image (or a reasonable approximation) is reached well before the maximum number of possible combinations is reached.

UPDATE (6/30/2014):

It was pointed out to me by a reader that birthdays have a distribution of their own throughout the course of a year. For example, birthdates in the Summer months (June, July) are more common than those in the winter months. This is of course due to human mating preferences and seasonality (and so birthdays are actually a quasi-stochastic process). Hence, there is a clustering of more common (as opposed to less common) birthdates on the calendar (Figure 4).

Figure 4. Visualization of birthdate frequency (in heatmap form) distributed across the calendar year. COURTESY: VizWiz blog and NYTimes.

I imagine this type of probability density is also somewhat true for evolutionary data across the diversity of a genus, order, or domain. But this type of clustering is also an outcome of stochastic processes (and one reason why recurrence is possible). When sampled at a given point in time, the outcome of a stochastic process is often not uniformly distributed -- in fact, it reveals clusters which must be distinguished from clusters that result from non-random processes. The question would be whether or not birthdates (or confounding evolutionary processes) cluster so significantly as to override clusters that result from randomness. The birthday paradox equations don't explicitly take that into account, but that likely does not invalidate the larger pattern.

UPDATE (8/4/2014):
Here is a good recent article from Nautil.us Magazine on evolutionary contingency. Puts a lot of the contemporary support for the idea in perspective.

Zorich, Z.   If the World Began Again, Would Life as We Know It Exist? Nautil.us, June 19 (2014).

NOTES:

Mathematical notation courtesy Wolfram MathWorld (http://mathworld.wolfram.com). Implemented in Excel courtesy of eXcel eXchange (http://excelexchange.com). Excel workbook (computed using pseudo-data) located on Github (https://github.com/balicea/evo-birthdays).

[1] Vermeij, G.J.   Historical contingency and the purported uniqueness of evolutionary innovations. PNAS, 103(6), 1804-1809 (2006).

[2] Taylor, E.B. and McPhail, J.D.   Historical contingency and ecological determinism interact to prime speciation in sticklebacks, Gasterosteus. Proceedings of The Royal Society of London B, 267, 2375-2384 (2000).

[3] Blount, Z.D., Borland, C.Z., and Lenski, R.E.   Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli. PNAS, 105(23), 7899-7906 (2008).

[4] Travisano, M., Mongold, J.A., Bennett, A.F., and Lenski, R.E.   Experimental Tests of the Roles of Adaptation, Chance, and History in Evolution. Science, 267, 87-90 (1995).

[5] Fales, E.   Uniqueness and Historical Laws. Philosophy of Science, 47(2), 260-276 (1980).

[6] The Plinko analogy has also been used to describe the epigenetic landscapes of Waddington: Gordon, R. Introduction to differentiation waves Part 2. The evo-devo of epigenetic landscapes as differentiation trees. Embryogenesis Explained course (2013).

[7] Fletcher, J.   The Birthday Paradox at the World Cup. BBC News Magazine, June 15 (2014).

[8] Mathematics: what are some of the most counterintuitive mathematical results? Quora, March 27 (2014).

[9] Crutchfield, J., Farmer, J.D., Packard, N.H., and Shaw, R.S.   Chaos. Scientific American, December (1986).