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.

Sperry, Darwin, and the Evolution of Reference Frames

It's all about deforming the phenotype. COURTESY: DiPaola, Evolving Darwin's Gaze (click to enlarge).

For this year's Darwin Day (February 12), I will be discussing a classic Neuroscience experiment by Roger Sperry [1]. This was discussed recently on Twitter (Figures 1 and 3), along with a movie (Movie 1) that demonstrates the behavioral effect of this manipulation. In the movie, we can see before and after behaviors with respect to prey capture. Before the manipulation, the frog seamlessly captures flies with a flick of the tongue. Afterward, the frog flicks in precisely the opposite direction of the fly. What is the biology behind this manipulation, and why does the manipulation produce seemingly maladaptive behavior?  

Figure 1. Tweet on Sperry's eye rotation experiment and chemosensory hypothesis (click to enlarge). 

Movie 1. Video demonstration of Sperry's eye rotation experiment (click to enlarge). 

In conducting this experiment, a frog's eyes are surgically rotated 180 degrees about each socket (see Figure 2). Due to this treatment, the normal course of axonogenesis between the eyeball and the tectum (part of the frog brain) is distorted [2]. As a result, the connections are shifted and the visual information is mapped to different regions of the tectum. The tectum serves as a visuospatial map of the environment, and maps visual stimuli to a reference frame used to generate motor behavior. As the reference frame is than systematically rotates, so is the frog's movement behavior. Thus, our manipulated frog produces a tongue flick that is 180 degrees in the opposite direction of the prey it is trying to capture. 

Figure 2. Cartoon demonstrating chemosensory hypothesis and behavioral effects of eye rotation experiment (click to enlarge). 

What is known as the chemosensory hypothesis (see Figure 2) also provided support for another concept, that of experience-dependent plasticity. The second tweet (below) discusses how this concept explains (and does not explain) what we see in the frog tectum and its modified behavior.

Figure 3. Part of response to tweet in Figure 1, with an assessment of the functional consequences (click to enlarge). 

Roger Sperry is also known for another set of experiments conducted a few years later [3] that asked whether neuroplasticity was a real phenomenon (as opposed to an epiphenomenon). This was done by either abnormally innervating muscle or placing end-effectors (limbs) in maladaptive locations on the body. If the organism could overcome these changes, such changes could be overcome via adaptation. As in the case of the eye rotation experiment, motor patterns are not plastic, even when neuronal connections are non-specific. This is why the eye rotated frog cannot adjust its behavior to adaptation in the spatial representation of visual input. 

Figure 4. A demonstration of conduction delay in the quadruped hindlimb in relation to multiple components of the sensorimotor loop. COURTESY: Figure 1 in [7] (click to enlarge).

So what does this have to do with evolution by natural selection [4]? It turns out that there are scaling laws that govern the coordination of the nervous system and phenotype as they both emerge in development [5]. Specifically, there are characteristically proportional relationships between motor neuron innervation and target tissue size in different parts of the organism [5, Note 1]. This developmental relationship (which holds true across related species) leads to interesting functional consequences. More et.al [6] suggests a trade-off in sensorimotor systems between responsiveness (temporal respond to stimuli) and resolution (sensory discrimination translated into muscle force production) results from size variation across phylogeny. 

Figure 5. Scaling of various sources of delay across species. Scaling comparison is in terms of mass (kg) versus delay (ms). COURTESY: Figure 2 in [7] (click to enlarge).

This relationship between size and a responsiveness-resolution trade-off also affects behavior. More and Donelan [7] show that conduction delay (an indicator of reaction time) also scales with variation in organismal size (Figure 4). The delay in force production (behavioral output) can be explained mostly in terms of nerve conduction delay rather than a delay in the sensory or synaptic components of the sensorimotor loop (Figure 5). This suggests a fundamental constraint on motor behavior that is independent of sensory inputs or their neural representation. But notice what is said about frog tectum in Figure 3: while eye saccades and tongue movement that produce the movement itself are not controlled by the tectum, a triggering threshold results from the active representation of visual information. 

Through the efficiency of population coding [8], this representation determines the timing of movement execution, which occurs in spatial context along with an appropriate amount of force. Perhaps the rotated eye manipulation (and associated phenomena like the prism experiment) presents an interesting exception to the responsiveness/resolution trade-off. Perhaps an intervening variable, representational alignment, also affects the linearity of the primary trade-off for specific movement behaviors. Across different species with common ancestry [9], this could become quite variable, and even provide an evolutionary-based account of neural plasticity.

NOTES:

[1] Sperry, R.W. (1943). Effect of 180 Degree Rotation of the Retinal Field on Visuomotor Coordination. Journal of Experimental Zoology, 92(3), 263–279.

[2] the reference to chemoaffinity in the first tweet refers to the process of axons finding their way to a target tissue. This is the basis for Sperry's "chemoaffinity hypothesis". Please see: Meyer, R.L. (1998). Roger Sperry and his chemoaffinity hypothesis. Neuropsychologia, 36 (10), 957–980.

[3] Sperry, R.W. (1945). The Problem of Central Nervous Reorganization After Nerve Regeneration and Muscle Transposition. Quarterly Review of Biology, 20(4), 311-369.

[4] For more on this topic, please see the following Synthetic Daisies posts:

     The Evolution and Neuromechanics of very-fast movements. January 24, 2012

     The Neuromechanics and Evolution of Very Slow Movements. April 18, 2012

     Perceptual Time and the Evolution of Informational Investment. September 24, 2013

[5] Striedter, G.F. (2004). Principles of Brain Evolution. Oxford University Press, Oxford, UK.

[6] More, H.L., Hutchinson, J.R., Collins, D.F., Weber, D.J., Aung, S.K.H., and Donelan, J.M. (2010). Scaling of sensorimotor control in terrestrial mammals. Royal Society of London B, 277(1700), 3563-3568.

[7] More, H.L. and Donelan, J.M. (2018). Scaling of sensorimotor delays in terrestrial mammals. Royal Society of London B, 285(1855), 20180613.

[8] Shamir, M. (2014). Emerging principles of population coding: in search for the neural code. Current Opinion in Neurobiology, 25, 140-148 AND Pouget, A., Dayan, P., & Zemel, R. (2000). Information processing with population codes. Nature Reviews Neuroscience, 1, 125–132.

[9] Quian Quiroga, R. (2019). Neural representations across species. Science, 363(6434), 1388-1389.

Darwin as a Universal Principle

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

8-bit Darwin. COURTESY: Diego Sanches.

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


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

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

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

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

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

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

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

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

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

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

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

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

From Toy Models to Quantifying Mosaic Development

Time travel in the Terminator metaverse. COURTESY: Michael Talley.

Almost two years ago, Richard Gordon and I published a paper in the journal Biosystems called "Toy Models for Macroevolutionary Patterns and Trends" [1]. Now, almost exactly two years later [2], we have published a second paper (not quite a follow-up) called "Quantifying Mosaic Development: towards an evo-devo postmodern synthesis of the evolution of development via differentiation trees of embryos". While the title is quite long, the approach can be best described as computational/ statistical evolution of development (evo-devo).

Sketch of a generic differentiation tree, which figures prominently in our theoretical synthesis and analysis. COURTESY: Dr. Richard Gordon.

This paper is part of a special issue in the journal Biology called "Beyond the Modern Evolutionary Synthesis- what have we missed?" and a product of the DevoWorm project. The paper itself is a hybrid theoretical synthesis/research report, and introduces a variety of comparative statistical and computational techniques [3] that are used to analyze quantitative spatial and temporal datasets representing early embryogenesis. Part of this approach was previewed in our most recent public lecture to the OpenWorm Foundation.

The comparative data analysis involves investigations within and between two species from different parts of the tree of life: Caenorhabditis elegans (Nematode, invertebrate) and Ciona intestinalis (Tunicate, chordate). The main comparison involves different instances of early mosaic development, or a developmental process that is deterministic with respect to cellular fate. We also reference data from the regulative developing Axolotl (Amphibian, vertebrate) in one of the analyses. All of the analyses involve the reuse and analysis of secondary data, which is becoming an important part of the scientific process for many research groups.

One of the techniques featured in the paper is an information-theoretic technique called information isometry [4]. This method was developed within the DevoWorm group, and uses a mathematical representation called an isometric graph to visualize cell lineages organized in different ways (e.g. a lineage tree vs. a differentiation tree). This method is summarized and validated in our paper "Information Isometry Technique Reveals Organizational Features in Developmental Cell Lineages" [4]. Briefly, each level of the cell lineage is represented as an isoline, which contains points of a specific Hamming distance. The Hamming distance is the distance between that particular cell in two alternative cell lineage orderings (the forementioned lineage and differentiation trees).

An example of an isometric graph from Caenorhabditis elegans, taken from Figure 12 in [5]. The position of a point representing a cell is based on the depth of its node in the cell lineage. The positions of all points are rotated 45 degrees clockwise from a bottom-to-top differentiation tree (in this case) ordering, where the one-cell stage is at the bottom of the graph.

A final word on the new Biology paper as it related to the use of references. Recently, I ran across a paper called "The Memory of Science: Inflation, Myopia, and the Knowledge Network" [6], which introduced me to the statistical definition of citation age. This inspired me to calculate the citation age of all journal references from three papers: Toy Models, Quantifying Mosaic Development, and a Nature Reviews Neuroscience paper from Bohil, Alicea (me), and Biocca, published in 2011. This was used as an analytical control -- as it is a review, it should contain papers which are older than the contemporary literature. Here are the age distributions for all three papers.

Distribution of Citation Ages from "Toy Models for Macroevolutionary Patterns and Trends" (circa 2014).

Distribution of Citation Ages from "Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development Via Differentiation Trees of Embryos" (circa 2016).

Distribution of Citation Ages from "Virtual Reality in Neuroscience Research and Therapy" (circa 2011).

What is interesting here is that both "Toy Models" and "Quantifying Mosaic Development" show a long tail with respect to age, while the review article shows very little in terms of a distributional tail. While there are differences in topical literatures (the VR and associated perceptual literature is not that old, after all) that influence the result, it seems that the recurrent academic Terminators utilize the literature in a way somewhat differently than most contemporary research papers. While the respect for history is somewhat author and topically dependent, it does seem to add a extra dimension to the research.

NOTES:
[1] the Toy Models paper was part of a Biosystems special issue called "Patterns in Evolution".

[2] This is a Terminator metaverse reference, in which the Terminator comes back every ten years to cause, effect, and/or stop Judgement Day.

[3] Gittleman, J.L. and Luh, H. (1992). On Comparing Comparative Methods. Annual Review of Ecology and Systematics, 23, 383-404.

[4] Alicea, B., Portegys, T.E., and Gordon, R. (2016). Information Isometry Technique Reveals Organizational Features in Developmental Cell Lineages. bioRxiv, doi:10.1101/062539

[5] Alicea, B. and Gordon, R. (2016). Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development Via Differentiation Trees of Embryos. Biology, 5(3), 33.

[6] Pan, R.K., Petersen, A.M., Pammolli, F., and Fortunato, S. (2016). The Memory of Science: Inflation, Myopia, and the Knowledge Network. arXiv, 1607.05606.

New Paper on Experimental Evolution (with Nematodes!)

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

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

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

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

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

Darwin Day, Past and Present

For this year's Darwin Day (his 207th posthumous birthday), we take a tour of Darwin Day features from both the past and present.

Panel discussion at the Darwin Centennial Celebration, University of Chicago circa 1959.

First stop: last year's Synthetic Daisies post for Darwin Day, featuring portraits of Charles Darwin throughout the course of his lifetime.

Second stop: 2009, and Nature's special issue for Darwin's 200th birthday, which includes many nice multimedia features.

Third stop: Google's Doodle from February 12, 2009 and  a Doodle-like short movie from 2014. Link to the Doodle design and animated movie can be found below. The movie is quite elaborate, as each letter making up "Google" are treated as terminal taxa in a prototypical tree of life.

Darwin Birthday Google Doodle from 2009.

Darwin Day Google Doodle from 2014. COURTESY: Vimeo and Devone Paul

Final stop: The Selfish Gene. This year's Darwin Day roughly coincides with the 40th anniversary of "The Selfish Gene" by Richard Dawkins. This work established the gene as the fundamental unit of natural selection, and provided a strong defense of Darwinian ideas. Enjoy these readings by John Brockman ("About Richard Dawkins") and Matt Ridley ("In Retrospect: The Selfish Gene").

Happy Darwin Day!

Talk to UIUC Fly/Worm Club

Here is a link to the slides (short, 20 minute talk) I presented last week to the Fly/Worm Club [1] at the University of Illinois Urbana-Champaign. The talk (an evo-devo perspective on Nematode life-history) is entitled "Natural Variation, Development, and Adaptive Phenotypes in C. elegans".

[1] the Fly/Worm club is hosted by the Smith-Bolton lab in the Department of Cell and Developmental Biology, and includes people interested in flies (Drosophila) and worms (Nematodes, Planaria) from across campus. It meets occasionally.

Reading Carnival, April Edition

A new feature here on Synthetic Daisies, which features a variety of readings from blogs, the popular press, and journals of both immediate and long-term interest. This edition features six pieces ranging topically from intellectual property and data analysis to evolutionary biology and complexity theory.


Haydari, S. and Smead, R.   Does Longer Copyright Protection Help of Hurt Scientific Knowledge Creation? JASSS, 18(2), 23 (2015).

An agent-based modeling approach (featuring a type of spatial lattice called an epistemic plane) is used to better understand how copyright protections can both enable and hinder knowledge creation. The model represents knowledge creation in two ways: knowledge can either either "discovered" by agents or remain "undiscovered". Discovered knowledge can be disseminated in either a high-access (proprietary) or open-access (freely-distributable) fashion. This distributed model of scholar behavior has revealed that extended periods of intellectual property protection can act to hinder innovation. While open-access can serve the public good, there is also a role for individual incentives which are served by limited periods of proprietary protection. Whether these returns are served through monetary compensation or social capital accumulation go unexplored.


Lind, P.A., Farr, A.D., and Rainey, P.B.   Experimental evolution reveals hidden diversity in evolutionary pathways. eLife, 10.7554/eLife.07074 (2015).

By examining 28 morphs of the wrinkly spreader phenotype in Pseudomonas fluorescens (a gram-negative bacterium), the authors were able to discover a number of new pathways through which diversity is generated. These unique pathways involved unique, uncharacterized mutations that provided variation to the existing taxonomic group. As instances of parallel evolution, they provided a means to suggest a set of principles that involve changing the regulation of genes followed by a change of function for those genes.

Kiers, E.T. and West, S.A.   Evolving new organisms via symbiosis. Science, 348(6233), 392-394 (2015).

A mini-review on the evolution of symbiont species and how it may account for major transitions in the tree of life.


Dennett, D. and Roy, D.   Our Transparent Future: No secret is safe in the digital age. Scientific American, 312(3), 32-27 (2015).

This essay compares the rise of information transparency, enabled through internet technologies, to the explosion of life's complexity as it occurred during the Cambrian explosion. As a result, the practice of information-handling by individuals and organizations will change due to key innovations. These innovations are analogous to the camera-like retinas, claws, jaws, and shells that emerged amongst animals during the Cambrian. A very Rodney Brooks-esque style argument for internet-enabled (or -forced, depending on your point of view) cultural evolution.


Ellenburg, J.   The Amazing, Autotuning Sandpile. Nautil.us, 23(1) (2015).

A popular science take on the Abelian Sandpile model and its role in pattern formation. The beginning of the article presents a neccessary contrast with the domino model of causality. Unlike a linear model of system dynamics (one event leads to another with a predictable timing), the sanpile model produces nonlinear dynamics with unpredictable timing. While both models involve a simplistic physical structure, but only one produces a highly complex output. Latter portions of the article focus on geometric abstractions (cellular automata) which produce self-organizing and "life-like" behavior.

Brown, C.T.   Cultural confusions about data - the intertidal zone between two styles of biology. Living in an Ivory Basement blog, April 2 (2015).

An interesting blog post (with links and comments) on the cultural meaning of data and what constitutes useful datasets when comparing both academic fields (e.g. computational biology vs. molecular biology) and research outputs (e.g. genome sequences vs. experimental outcomes).

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).