Development shapes the evolutionary diversification of rodent stripe patterns

Significance

How and why did diverse animal color patterns evolve? Explanations for pattern diversification typically emphasize the ecological forces that select for color patterns (e.g., camouflage or sexual selection). However, pattern diversification may also critically depend on the developmental mechanisms that provide the substrate for pattern evolution. Here, drawing on empirical advances, we explore theoretically how development shapes rodent pattern diversification. We show that pattern diversification can indeed be partly explained by underlying developmental mechanisms. Specifically, development can both facilitate and constrain pattern evolution by enabling evolutionary changes in stripe number while limiting changes in stripe positioning. Thus, by integrating developmental data, models of pattern formation, and empirical data on pattern diversity, our work helps bridge the gap between pattern evolution and pattern development.

Abstract

Vertebrate groups have evolved strikingly diverse color patterns. However, it remains unknown to what extent the diversification of such patterns has been shaped by the proximate, developmental mechanisms that regulate their formation. While these developmental mechanisms have long been inaccessible empirically, here we take advantage of recent insights into rodent pattern formation to investigate the role of development in shaping pattern diversification across rodents. Based on a broad survey of museum specimens, we first establish that various rodents have independently evolved diverse patterns consisting of longitudinal stripes, varying across species in number, color, and relative positioning. We then interrogate this diversity using a simple model that incorporates recent molecular and developmental insights into stripe formation in African striped mice. Our results suggest that, on the one hand, development has facilitated pattern diversification: The diversity of patterns seen across species can be generated by a single developmental process, and small changes in this process suffice to recapitulate observed evolutionary changes in pattern organization. On the other hand, development has constrained diversification: Constraints on stripe positioning limit the scope of evolvable patterns, and although pattern organization appears at first glance phylogenetically unconstrained, development turns out to impose a cryptic constraint. Altogether, this work reveals that pattern diversification in rodents can in part be explained by the underlying development and illustrates how pattern formation models can be leveraged to interpret pattern evolution.

Various groups of vertebrates have evolved color patterns that have long fascinated biologists for their widespread occurrence, adaptive significance, and striking diversity (1–4). Because color patterns play important roles in intra- and interspecific signaling, their evolution is thought to be largely driven by the ecological forces that select for patterns with particular adaptive functions (5–10). However, by providing the substrate upon which ecological forces can operate, developmental processes have the potential to facilitate and/or constrain pattern evolution (11–21). To understand whether and how developmental mechanisms have shaped pattern evolution, it is critical to bridge the gap between evolutionary analyses of pattern diversification and the underlying developmental mechanisms. Taking such an integrative approach is possible in groups where diverse patterns have evolved and insights into the underlying developmental mechanisms have been obtained.

Rodents have evolved a wide range of stripe patterns that vary in the color, number, and positioning of stripes (Fig. 1A). Although the molecular mechanisms generating these patterns remain largely unknown, recent work has provided key insights into the processes underlying pattern formation in the African striped mouse, Rhabdomys pumilio. The coat pattern of African striped mice consists of two longitudinal light stripes, each flanked by two dark stripes (Fig. 1A). This adult pattern is foreshadowed by a molecular prepattern that is established during mid-embryogenesis in part by a dorsoventral gradient of the Wnt modulator Sfrp2 (22). Moreover, mathematical simulations showed that coupling this gradient to a downstream reaction–diffusion mechanism suffices to recapitulate the observed prepattern (22). This empirical understanding of stripe formation in R. pumilio, together with the marked variety of color patterns across rodents, provides a foundation to explore the potential role of development in shaping pattern diversification in rodents.

Fig. 1.

Independent evolutionary origins have given rise to diverse rodent patterns. (A) Examples of striped rodents. (B) Genus-level phylogeny of rodents with colors indicating ancestral reconstruction of pattern evolution. The clades Sciuridae (3) and Murinae (13), in which origins of patterns are concentrated, are highlighted; other numbers correspond to Gliridae (1), Aplodontiidae (2), Diatomyidae (4), Ctenodactylidae (5), Phiomorpha (6), Caviomorpha (7), Anomaluromorpha (8), Spaclacidae (9), Lophiomyinae (10), Gerbillinae (11), Deomyinae (12), Cricetidae (14), Nesomyidae (15), Calomyscidae (16), Platacanthomyidae (17), Dipodoidea (18), Geomyoidea (19), and Castoridae (20). (C) Catalog of pattern diversity. One representative example for each independently evolved pattern is shown; most examples represent multiple closely related species with the same pattern. The number of pattern origins in the genera Funisciurus and Paraxerus is unclear.Photo credit: Wikipedia users C. R. Selvakumar (Rhabdomys pumilio), Krazytea (Ictidomys tridecemlineatus), C. J. Sharp (Funambulus pennantii) (CC-BY-SA license), and iNaturalist user P. Kungurov (Apodemus agrarius) (CC-BY license).

To do so, we first reconstruct the evolutionary history of pattern diversification and catalog the evolved diversity of patterns. Then, drawing inspiration from insights in R. pumilio, we develop a simple developmental model that turns out to be sufficiently flexible to recapitulate the diverse patterns that have evolved. Guided by the model, we identify nonobvious constraints on the organization and phylogenetic distribution of evolved patterns that can be explained developmentally, thereby revealing how development may have shaped pattern evolution.

Results

Independent Evolutionary Origins Have Given Rise to Diverse Rodent Patterns.

A systematic study of pattern evolution has not been carried out in rodents. Thus, we first performed a broad survey of museum specimens (Methods) to establish a catalog of rodent patterns and reconstruct their evolutionary diversification. We find that while the dorsal pelage of most rodents is uniformly brown or gray in color, patterns occur in over a 100 species, belonging to 24 genera (5% of all genera; Fig. 1B). Incidences of pattern are widespread across the rodent phylogeny (Fig. 1B) but are concentrated in the family Sciuridae (which contains squirrels, prairie dogs, and chipmunks), and the subfamily Murinae (which contains Old World mice and rats). Together, these two clades contain most genera (19 out of 24) in which patterns evolved.

We next used stochastic character mapping to infer evolutionary gains and losses of patterns in Murinae and Sciuridae (SI Appendix, Fig. S1). We find that patterns evolved multiple times independently, ~7 times in Murinae and at least 10 times in Sciuridae (SI Appendix, Fig. S1). Losses of patterns are much rarer than gains, but have also occurred, for example in the ground squirrel Xerus rutilus, the only unstriped member of its genus (SI Appendix, Fig. S1). There is no evidence that lineages in which patterns evolved diversified at a different rate than lineages without patterns (SI Appendix, Fig. S2).

Repeated origins of patterns provide the opportunity to probe the ecological forces that drove their evolution (SI Appendix, Figs. S3–S5). We find that diurnality is a driver of pattern evolution in both Murinae (SI Appendix, Fig. S3; $P < 0.001$   ) and Sciuridae (SI Appendix, Fig. S4, $P = 0.08$   ). Moreover, among diurnal Sciuridae, we find that patterns have evolved at the highest rate in species that spend most of their time on the ground, rather than in trees (SI Appendix, Fig. S5, $P = 0.06$ ), as suggested by earlier comparative work (23). Together, these results are consistent with the conventional wisdom that rodent stripes evolved as anti-predator camouflage: Such camouflage would indeed be most beneficial in species that are active during the day in relatively open habitats.

Some features of the evolved patterns are broadly conserved: Most patterns consist of longitudinal, symmetrically arranged stripes, with darker and lighter colors alternating (between stripes and their background or between stripes of different colors). However, stripes vary across species in their number, relative positioning along the dorsoventral axis, and color relative to the background (i.e., dark, light, or a combination of both; in the latter case, dark and light stripes typically appear side-by-side) (Fig. 1C). Additionally, a few species have evolved patterns with longitudinally arranged spots in addition to (or instead of) stripes. While patterns are diverse across species, there is little variability in pattern organization across individuals within a species, except for patterns that contain spots: Spots tend to become more disorganized—and therefore more variable—toward the edges of the pattern.

Surprisingly, there is no immediately obvious order to the phylogenetic distribution of evolved patterns (Fig. 1C). Closely related species may have substantially different patterns: For example, within the genus Lemniscomys of grass mice, patterns range from a single stripe to an elaborate pattern of alternating dark and light stripes. At the same time, phylogenetically distant species have convergently evolved similar or identical patterns. For example, a single dark mid-dorsal stripe has evolved five times, a single pair of lateral light stripes has evolved three times, and R. pumilio and the bush squirrel Paraxerus boehmi have independently converged on the same pattern of a pair of light stripes, each flanked by two dark stripes (Fig. 1C). These observations that closely related species may have distinct patterns while distantly related species may have similar or identical patterns are corroborated by formal tests of phylogenetic signal: We fail to detect statistically significant phylogenetic signal in the total number of stripes ( $K=0.26$ , $P=0.42$ ), number of dark stripes ( $K=0.21$ , $P=0.69$ ), and number of light stripes ( $K=0.33$ , $P=0.15$ ) across independently evolved patterns.

Taken together, these results indicate that rodent patterns have independently evolved multiple times, driven by ecological pressures that presumably include predation. While patterns that have independently evolved share common features, they are diverse in terms of the number, color, and positioning of pattern elements. However, at first sight, this diversity appears to be phylogenetically unconstrained.

A Biologically Informed Model Produces Diverse Rodent-like Stripe Patterns.

The observed pattern diversity raises several interesting questions: How did so many patterns evolve, even in closely related species? How can we reconcile diversity across species with lack of variability within species? Is any pattern possible, or are there limits on the scope of evolvable patterns? And finally, are stripe patterns truly evolving “at random,” as the lack of phylogenetic signal seems to suggest, or are some aspects of pattern organization phylogenetically constrained? To explore these questions, we must consider the developmental processes underlying pattern formation.

In R. pumilio, pattern development can be understood conceptually as partially arising from a self-organizing reaction–diffusion mechanism that acts downstream of a dorsoventral morphogen gradient (22). While little is known about the developmental mechanisms of stripe formation in other species, three pieces of evidence suggest that similar developmental mechanisms could be at work across rodents. First, as we have shown above, evolved patterns share several similar features, and in some cases, independent origins have even convergently given rise to identical patterns. Second, it is known theoretically that the mechanism by which stripes form in R. pumilio—coupling reaction–diffusion to upstream morphogen gradients—can give rise to a variety of stable stripe patterns (24–26). Third, to the extent that stripe development has been studied in other striped rodents, molecular mechanisms seem to be conserved: For instance, the genes that regulate melanocyte differentiation during pattern implementation in R. pumilio do so in the Eastern chipmunk Tamias striatus as well (27).

To test whether pattern formation could indeed be achieved by similar mechanisms across rodents, we adapted a developmental model previously built for R. pumilio (22) (Fig. 2A; see Methods for details). This model is based on the Gierer–Meinhardt model, a classical reaction–diffusion model of local activation coupled to lateral inhibition that has a long history in theoretical studies of pattern formation (28, 29). Drawing on what is known from R. pumilio, in our model reaction–diffusion is guided by dorsoventral morphogen gradients that can act to position and orient pattern elements. We hypothesized that variation in the shapes of these gradients could underlie differences in pattern organization across species. Therefore, we explored a range of simple morphogen gradients (Methods).

Fig. 2.

A biologically informed model produces diverse rodent-like stripe patterns. (A) In the model, patterns self-organize by a reaction–diffusion mechanism, guided by variable upstream morphogen gradients. Dorsoventral morphogen gradients $\mu \left(x\right)$ and $\nu \left(x\right)$ are established by diffusion of a morphogen that is produced locally and degrades linearly. Morphogens may be produced either medially, giving rise to a hump-shaped gradient (like $\mu$ in the example shown), or laterally, giving rise to a valley-shaped gradient (like $\nu$ in the example shown). Morphogen kinetic parameters are the production rates $\sigma$ , degradation rates $k$ , and diffusion constants $D$ . After the morphogen gradients have been established, the pattern self-organizes via reaction–diffusion of an activator $u$ and inhibitor $v$ (Methods). The pre-established morphogen gradients modulate the organization of the final pattern by setting the degradation rates $\mu$ and $\nu$ of the activator and inhibitor, respectively. (B), Patterns generated with random morphogen gradients. Each data point represents one of $n=1,000$ patterns. Pattern variability is quantified as the average distance between the pattern and replicate instances of the pattern; pattern complexity is quantified as the average distance between the pattern and random translations of the pattern over a small distance. Colors indicate qualitatively different kinds of patterns.

To qualitatively determine the different kinds of patterns that our general developmental model can produce, we generated patterns for randomly sampled morphogen gradients. We find that the model can generate a wide variety of patterns consisting of spots, stripes (and/or thick bands), or a combination of spots and stripes (Fig. 2B). Stripes are always oriented longitudinally, perpendicular to the gradients. Patterns that only contain stripes (and no spots) turn out to be highly reproducible, meaning that the same pattern organization is obtained in replicate simulations. Thus, morphogen gradients are able to turn an otherwise random pattern (SI Appendix, Fig. S7A) into reproducible patterns of longitudinally oriented stripes.

In summary, we built on previous molecular and modeling work in R. pumilio to develop a general model for rodent pattern formation in which patterns self-organize downstream of variable dorsoventral morphogen gradients. We find that the model is able to generate stripe patterns that, like rodent patterns, consist of highly reproducible longitudinal stripes. Moreover, the fact that we only observe such reproducibility for stripe patterns (and not for patterns with spots) provides a potential explanation for the observation that the only evolved patterns that show individual variability are those that contain spots.

Development Explains Which Pattern Organizations Are Possible.

Having established that the model can indeed generate rodent-like patterns, we next asked to what extent it can recapitulate evolved pattern diversity. Because most evolved patterns consist solely of stripes and there are too few patterns with spots to make evolutionary inferences, we chose to focus only on stripe patterns. Nevertheless, the model can also recapitulate evolved patterns with spots, like those of Lemniscomys and Ictidomys (Fig. 1C). The only evolved pattern that does not appear to be reproducible with our model is the one observed in the 13-lined ground squirrel Ictidomys tridecemlineatus (Fig. 1A), which has periodic alternations of stripes and stripes broken into spots.

To assess the range of stripe patterns that the model can generate, we selected all stripe patterns (i.e., those lacking spots or thick bands) from a large set of 50,000 randomly generated patterns (Fig. 3A). We observe a close resemblance between model-generated stripe patterns and evolved patterns. In particular, the model can recapitulate all evolved patterns with stripes of a single color (dark or light). The model can also recapitulate the evolved patterns with stripes of both colors, although for those patterns, it is limited to explaining the formation of stripes one color at a time (Fig. 3A)—stripe development is currently insufficiently understood to inform a realistic model that would simultaneously account for the formation of both dark and light stripes. For evolved patterns with both colors, we therefore separately compare the dark and light stripes to model-generated outputs.

Fig. 3.

Development explains which pattern organizations are possible. (A) Comparison of model-generated and evolved patterns. In total, $n=3,945$   model-generated stripe patterns (out of a total of 50,000 simulations) are arranged vertically, together with representative examples of evolved patterns with the same organization (in either the dark or the light stripes). Model-generated patterns are represented as dark stripes on a lighter background, but could equivalently have been represented as light stripes on a darker background. (B–D) Comparisons of relative stripe positioning between model-generated and evolved patterns with 3 stripes (B), 4 stripes (C), and 5 stripes (D). In C and D, only symmetric patterns are considered. Histograms show relative stripe positioning for model-generated patterns, quantified as the ratio between the first interstripe distance $d_1$   and the second interstripe distance $d_2$   . Data points indicate relative stripe positioning for evolved patterns of different species, with the error bars indicating the SD across individual specimens. Colors correspond to stripe color (dark or light). Data points are plotted at different heights for visual clarity only. Species included: Li = Lariscus insignis, Ht = Hybomys trivirgatus, Ft = Funambulus tristriatus, Tr = Tamiops rodolphii, Tm = Tamiops macclellandii, Ta = Tamias amoenus, Rp = Rhabdomys pumilio, Pb = Paraxerus boehmi, Mb = Menetes berdmorei, Cl = Callospermophilus lateralis, Fi = Funisciurus isabella, Ts = Tamias striatus, and Fp = Funambulus palmarum.

The model suggests that stripe number is developmentally unconstrained: In model-generated patterns, any number of stripes from 1 to 7 is possible (Fig. 3A). The upper limit of 7 reflects the chosen size of the domain for pattern formation; any number of regularly spaced stripes can be generated on an appropriately sized domain. Among rodents, different species have evolved patterns with any number of stripes from 1 to 6, as well as patterns comprised of many stripes (>10) that cover the whole dorsum. Our model shows that this variation can indeed theoretically be generated from a single developmental process, by appropriate adjustments in the morphogen gradients underlying pattern formation.

While the model predicts any number of stripes to be possible, stripe positioning appears to be constrained: Some stripe positionings were never observed across the large number of simulations, suggesting that they are either impossible or at least very unlikely to be produced with the developmental process under consideration. For example, in model-generated 2-stripe patterns, the two stripes are either positioned medially, close to the midline (Fig. 3A, pattern 2a), or almost completely laterally (Fig. 3A, pattern 2b), but never in between.

To investigate whether constraints on stripe positioning predicted by the model also apply to evolved patterns, we calculated relative interstripe distances, a nondimensional quantity that can be directly compared between model-generated and evolved patterns (provided there are at least 3 stripes). For 3-stripe patterns, we find that the model simply predicts symmetry across the midline (in other words, we did not find any asymmetric patterns among model-generated 3-stripe patterns), and indeed, all the evolved 3-stripe patterns are symmetric (Fig. 3B). For 4-stripe patterns, the model again predicts symmetry, but not just any symmetric pattern is possible: In model-generated patterns, stripes are either roughly equally spaced (Fig. 3A, pattern 4a) or form two pairs of lateral stripes (Fig. 3A, pattern 4b). However, the model failed to generate a hypothetical pattern 4c consisting of a pair of medial stripes together with a lateral stripe on each side (Fig. 3C). In evolved 4-stripe patterns, relative stripe positioning indeed falls within what the model suggests is possible: Both model-generated patterns 4a and pattern 4b have evolved multiple times, but pattern 4c has not (Fig. 3C). Finally, evolved patterns with 5 stripes adhere to the model prediction that stripes should be roughly equally spaced (Fig. 3D). In summary, the model identifies constraints on relative stripe positioning that are confirmed empirically.

To ensure that the identified constraints on pattern organization are not sensitive to the details of the model, we repeated our analysis with an alternative reaction–diffusion mechanism. Specifically, we replaced the Gierer–Meinhardt model by the Gray–Scott model, a reaction–diffusion model for a specific autocatalytic chemical reaction (30, 31) (SI Appendix, Fig. S6A; Methods). The alternative model identifies the same constraints on pattern organization as the original model (SI Appendix, Fig. S6 B and C), confirming the robustness of our results and suggesting that the essential underlying developmental feature is the combination of morphogen gradients with some reaction–diffusion mechanism that is sensitive to these gradients. While the alternative model produces the same patterns as the original model, the frequencies of individual patterns differ: More elaborate patterns with many stripes appear more frequently, whereas patterns with fewer stripes appear less frequently (compare Fig. 3A to SI Appendix, Fig. S6C). Thus, how often a certain pattern is generated is sensitive to the details of the underlying model and should not be interpreted as meaning that it is easier or harder to obtain.

Together, these results indicate that our developmental model is flexible enough to generate patterns with any number of stripes but that the relative positioning of these stripes is constrained. Importantly, even though the model was informed by knowledge about pattern development from only a single species, the patterns that have evolved across species adhere to its predictions. This result lends additional credibility to the idea that diverse rodents use similar developmental mechanisms to generate patterns and suggests that these mechanisms may have constrained what patterns can and cannot evolve.

Development Shapes How Patterns Diversify Over Evolutionary Time.

If development has restricted the range of patterns that can evolve, it may also have shaped how evolution has explored the space of possible patterns. From the perspective of the model, pattern evolution unfolds in a five-dimensional developmental space of possible morphogen gradients (it takes 5 parameters to specify the morphogen gradients; Methods). The geometry of this developmental space determines the paths that pattern evolution can take, at least when we assume that mutations represent small steps in developmental space. We used multidimensional scaling (MDS)—a dimension reduction technique similar to principal component analysis (Methods)—to obtain the two-dimensional representation of developmental space that best preserves the developmental distances between different patterns (Fig. 4A). Patterns tend to be closer together in this 2-dimensional representation if the underlying morphogen gradients are more similar.

Fig. 4.

Development shapes how patterns diversify over evolutionary time. (A) Two-dimensional representation of developmental space obtained using multidimensional scaling (MDS). Each point represents one stripe pattern generated by the model; patterns are plotted closer to each other if the underlying morphogen gradients are more similar. Colors indicate stripe number. Insets indicate the mean location of the data points representing patterns with the same organization. (B and C) Small developmental changes can explain evolutionary changes between 1 and 3 stripes in Hybomys (B) and between 3 and 5 stripes in Funambulus (C). For each comparison, two instantiations of the pattern are chosen that are close to each other in developmental space. (D) Estimates of phylogenetic signal [Blomberg’s $K$ statistic (32)]. Bars indicate SDs across possible phylogenies. Phylogenetic signal in MDS2 values assigned to dark stripes is statistically different from 0. (E) The MDS2 axis separates more medial patterns (lower MDS2) from more lateral patterns (higher MDS2), and phylogenetic signal in MDS2 assigned to dark stripes can therefore be interpreted as the positioning of dark stripes being phylogenetically constrained. This phylogenetic constraint is visualized on the phylogeny of Fig. 1C by painting the patterns depending on the positioning of their dark stripes (i.e., assigned MDS2 value) and painting the tree with a maximum likelihood ancestral reconstruction of MDS2 evolution.

Starting from a pattern without any stripes (0), we infer that it is easiest to evolve a single, mid-dorsal stripe (1) or a single pair of lateral stripes (2b), since these patterns are closest to pattern 0 in developmental space (Fig. 4A). Interestingly, these two patterns are the ones that have independently evolved most often, with pattern 1 evolving five times and pattern 2b evolving three times (Fig. 1C). These simple patterns may in turn represent evolutionary intermediates toward more elaborate patterns that are located farther away in developmental space (Fig. 4A). In genera in which both simple and more elaborate patterns have evolved, we would therefore predict that the simple pattern evolved first and the more elaborate pattern is derived from it.

Our analysis reveals that some changes in pattern organization may have been achieved by surprisingly subtle developmental changes. For example, slightly altering the shape of the morphogen gradients is sufficient to recover the evolutionary changes in stripe number that have occurred in the genera Hybomys (Fig. 4B) and Funambulus (Fig. 4C). On the other hand, other changes in pattern organization are predicted to be more difficult. In particular, the model suggests that it is relevant to distinguish between patterns in which the stripes are located medially (1, 2a, 3, 4a, 5) and patterns in which stripes are located laterally (2b, 4b): These classes of patterns separate on the second axis (MDS2) of developmental space (Fig. 4A) because the underlying morphogen gradients are essentially each other’s mirror image (SI Appendix, Fig. S7). To test the prediction that changing stripe location between medial and lateral is developmentally and hence evolutionarily difficult, we used the model to quantify stripe positioning in evolved patterns. Specifically, we assigned to evolved patterns the MDS2 value corresponding to their pattern organization—thus organizing patterns from more medial to more lateral along a single, developmentally informative axis (Fig. 4E). Using this quantification, we detect statistically significant phylogenetic signal in the positioning of dark stripes, meaning that evolved patterns tend to cluster together phylogenetically depending on whether their dark stripes are located more medially or more laterally (Fig. 4 D and E). Thus, developmental constraints on changes in pattern organization may help to explain the phylogenetic distribution of evolved patterns.

We conclude that, in addition to constraining what patterns can evolve, development may have shaped the paths that evolution can take as it explores the space of possible patterns. Specifically, while patterns initially appeared to have evolved in a phylogenetically unconstrained way, there are in fact phylogenetic constraints on pattern diversification that can, at least in theory, be explained developmentally.

Discussion

In this work, we have built a biologically informed developmental model of pattern formation and used it to interrogate pattern diversification in rodents. Drawing from an empirical understanding of pattern development in R. pumilio, the model combines two classical principles of pattern formation: positional information and reaction–diffusion (13, 26, 33–36). Together, these two principles explain how rodent patterns can be diverse across species, yet reproducible within species. Positional information—in the form of pre-established morphogen gradients that guide pattern formation—allows the model to recapitulate the high interindividual reproducibility that sets rodents apart from mammals with more variable stripe patterns, such as zebras and tigers. At the same time, reaction–diffusion unlocks the power of self-organization, thereby allowing patterns to diversify evolutionarily through changes in developmental parameters.

Along with explaining how development has facilitated diversification, the model also suggested that development has constrained diversification, in ways we were able to verify empirically. First, the model suggests that development imposes a constraint on stripe positioning that can explain why certain hypothetical stripe patterns have failed to evolve. Second, the model suggests that it is developmentally difficult to change stripe position between medial and lateral, a theoretical finding that helps explain the phylogenetic distribution of evolved patterns. Thus, development may have limited both the scope of evolvable patterns and the changes in pattern organization that are possible.

While our findings on the role of development in shaping pattern evolution are supported by both theory and empirical data, they remain tentative in light of the fact that pattern development has only been studied at the molecular level in R. pumilio. Nevertheless, our results bolster the assumption that other rodents use conceptually similar mechanisms: After all, it was not a priori obvious that a single developmental process could indeed recapitulate all observed stripe patterns and help interpret their evolution. Our results therefore suggest that the toolkit for rodent pattern development may have arisen early in evolution and be broadly conserved, thereby facilitating the repeated evolution of patterns in lineages where an ecological opportunity arose—such as in grassland mice that adapted to a diurnal lifestyle.

If rodents are equipped with a developmental toolkit that is flexible enough to generate multiple patterns, how can we understand the specific patterns that evolved in individual lineages? The ecological forces driving pattern evolution likely played a critical role, by selecting for patterns that are well-suited for particular environments. For example, some environments may have selected for cryptic patterns with many stripes, like the pattern of Lemniscomys, which “elegantly blends the mice with the color of their grassland habitat” (37). Other environments may have instead favored patterns with disruptive coloration, like the alternating black-and-white stripes of T. macclellandii, which “serve as camouflage when the squirrels are on the bark of a tree; when frightened they often spread themselves out against the bark to heighten the effect” (38). Besides ecological forces, however, our work highlights a potential twofold role for development in shaping the patterns of individual species. First, ancestral developmental constraints may have biased lineages toward particular patterns (e.g., ones with lateral or medial stripes). Second, development may have facilitated subtle changes in pattern organization among closely related species that seem difficult to resolve ecologically, such as between 1 and 3 stripes in Hybomys mice. Rather than reflecting adaptations to different environments, such differences may have simply resulted from selectively neutral changes that were easily accessible developmentally. Our findings therefore help illuminate the role of development in pattern evolution at the level of individual lineages, although ultimately more empirical work is needed to explain the evolution of specific patterns.

More broadly, our work highlights an exciting frontier for pattern formation models, which historically have been used mainly to explain how particular patterns are generated developmentally (36, 39–52). Here, we have shown how these models can also be leveraged to explore pattern evolution, by generalizing and abstracting developmental findings from a species where development has been studied at the molecular level and then using the resulting model as a guide to interrogate the observed pattern diversity. As developmental data on pattern formation become increasingly available across diverse taxa (13, 53–56), this general approach holds the potential to help uncover what new developmental insights reveal about the evolution of pattern diversity.

Methods

Data Collection.

To catalog patterns, we examined the rodent collection of the American Museum of Natural History in New York City in December 2021. We visually inspected the dorsal pelage of all preserved rodent skins and photographed representative specimens for all species where patterns (in the form of stripes or spots) were visible. We decided to focus on Murinae and Sciuridae because instances of pattern evolution are concentrated in these two clades (Fig. 1). We extensively searched the published literature for descriptions of patterns in Murinae and Sciuridae, finding two additional genera in which patterns evolved in the process: Arvicanthis (57) and Atlantoxerus (58). Our final dataset contained 90 species with patterns (SI Appendix, Table S3), belonging to 12 Sciuridae genera and 7 Murinae genera.

Reconstruction of Pattern Evolution.

We used published phylogenetic trees to reconstruct pattern evolution. We selected a recent all-mammal phylogeny (VertLife project) because it has good coverage for the relevant taxa and because it provides sets of plausible trees rather than a single consensus tree, thereby allowing us to account for phylogenetic uncertainty (59). We reconstructed evolutionary histories for the presence/absence of patterns by fitting a simple Mk model of discrete character evolution (60) to our data. This model assumes that changes in character state (from presence to absence of patterns or from absence to presence of patterns) happen at a rate $r$ that is constant through time and across the different branches of the phylogeny. We used a Bayesian method [implemented in phytools version 1.2 (61)] to estimate the value of $r$ , using a gamma prior with $\beta =1$ centered at the maximum likelihood estimate for $r$ . For each of 100 possible phylogenies, we sampled 100 possible values of $r$ from the posterior. We then created a set of 1,000 stochastic character maps using phytools’ make.simmap function (62), where for each character map, we randomly sampled one of the 100 trees and one of the 100 rate estimates for that particular tree. This set of 1,000 character maps thus accounts for uncertainty in phylogeny, rate of evolution, and timing of evolutionary events (SI Appendix, Fig. S1). We used this set of character maps for inferring gains and losses of patterns; for visualization, we used the visualization-only consensus tree of ref. 59.

Correlates of Pattern Evolution.

Speciation and extinction.

To test whether species with patterns diversify at a different rate than species without patterns, we fit a Binary State Speciation and Extinction (BiSSE) model (63), implemented in the R package diversitree, version 0.9 (64). We used an ANOVA to compare our full model (in which speciation and extinction rates are allowed to depend on the presence or absence of patterns) to a null model (in which speciation and extinction rates are not allowed to depend on the presence or absence of patterns) (SI Appendix, Fig. S2). We calculated a P-value by averaging the P-values obtained for each of the 100 possible phylogenies.

Diel activity.

To test for correlations between pattern evolution and diel activity, we collected data on diel activity in Sciuridae and Murinae from the published literature. Diel activity data for Sciuridae species were readily available from a recent study (65), while diel activity data for Murinae species (many of which have not been studied extensively) had to be compiled from a variety of sources (SI Appendix, Tables S1 and S2). Taken together, we were able to find data for 106 species of Murinae (19% of species represented in our phylogeny, covering 81% of genera) and 161 species of Sciuridae (56% of species represented in our phylogeny, covering 91% of genera). We classified species as either “Diurnal” or “Nocturnal,” also classifying as Diurnal species that were described as active during both night and day. Species that were described as “cathemeral” or “crepuscular” or species for which existing evidence was conflicting were left out of the analysis. We used Pagel’s method (66) [implemented in phytools (61)] to test for association between evolution of pattern and diel activity, using likelihood ratio tests (SI Appendix, Figs. S3 and S4). We calculated P-values and Akaike information criteria (AICs) by averaging P-values and AICs obtained for each of the 100 possible phylogenies.

Locomotion mode.

To test whether differences in habitat could help explain pattern evolution in Sciuridae, we collected data on locomotion mode for Sciuridae species from a recent study (67). This study classified Sciuridae species as gliding (flying squirrels), arboreal (species that spend most of their time in trees), terrestrial (species that spend most of their time on the ground), or intermediate (between arboreal and terrestrial) and provided data for 182 species of Sciuridae (62% of species represented in our phylogeny, covering 97% of genera). To test for association between evolution of pattern and locomotion mode, we fit an Mk model of discrete character evolution to our data, allowing for the rate of pattern evolution to vary depending on locomotion mode. Using a likelihood ratio test, we compared this model to a null model in which the rate of pattern evolution does not depend on locomotion mode (SI Appendix, Fig. S5). We calculated a P-value by averaging the P-values obtained for each of the 100 possible phylogenies.

Cataloging Pattern Organization.

To investigate differences in pattern organization, we focused on three key features of the observed patterns: The number of longitudinal stripes, their relative positioning along the dorsoventral axis, and their color (lighter or darker than the background). Together, these features capture the most salient differences between species. We deliberately ignored more nuanced pattern features, including stripe width, stripe length (some stripes do not run all the way from the head to the tail), and more subtle color variation (e.g., some stripes are more pronounced than others).

To classify the different evolved patterns, we visually identified stripes (which in some cases may be broken into spots, as in Lemniscomys striatus or Ictidomys mexicanus) and classified them as either darker or lighter than the background pelage, using the animal’s head as a reference for the background. In most cases, classifying patterns was straightforward thanks to the high reproducibility of the pattern across individuals. In a small number of cases, however, variation between specimens made describing patterns more challenging. In such cases, we cross-referenced our photographs with published species descriptions (37, 38, 58, 68–75) and opted for the most complete possible description of the stripe pattern possible, thus also including stripes that were only clearly visible in a subset of specimens.

We next created a comprehensive catalog of pattern diversity based on our pattern classifications and our reconstruction of pattern evolution. Specifically, in each of the 17 clades in which patterns evolved independently (SI Appendix, Fig. S1), we selected representative species for each of the unique patterns that had evolved in that clade (SI Appendix, Supplementary Methods). Altogether, the resulting catalog contained 29 species across Murinae and Sciuridae (SI Appendix, Table S3).

Phylogenetic Signal in Stripe Number.

We used our pattern catalog to calculate phylogenetic signal in total stripe number, number of dark stripes, and number of light stripes. In calculating phylogenetic signal, we ignored within-clade phylogenetic relationships, because those are sensitive to the representative species chosen and often poorly resolved. Ignoring within-clade phylogenetic relationships was accomplished by collapsing clades with multiple representative species to a star phylogeny (Fig. 1C). As a result, our estimates of phylogenetic signal give a sense of phylogenetic correlations across independent pattern origins. We used Blomberg’s $K$ (32), implemented in phytools (61), as a measure of phylogenetic signal. Our estimate of phylogenetic signal is the average of the estimates obtained for each of the 100 possible phylogenies. We tested for significant phylogenetic signal ( $K$ different from 0) using the randomization test implemented in phytools.

Modeling Pattern Formation.

To model pattern formation, we adapted a model used previously to study pattern formation in R. pumilio (22). Our model describes the reaction–diffusion dynamics of an activator $u$ and an inhibitor $v$ (Fig. 2A) on the domain $\left[-1,1\right]\times [-1,1]$ with periodic boundary conditions, using the following equations:

$$\begin{array}{c}\frac{\partial u}{\partial t}=f\left(u,v\right)-\mu \left(x\right)·u+D_u·\frac{{\partial }^{2}u}{\partial x^2}, \frac{\partial v}{\partial t}=g\left(u,v\right)-\nu \left(x\right)·v+D_v·\frac{{\partial }^{2}v}{\partial x^2}.\hfill \end{array}$$

The functional forms for $f$   and $g$   are taken as in the Gierer–Meinhardt model for local activation and lateral inhibition (28, 29), with saturation in the activation term, that is, $\begin{array}{c}f\left(u,v\right)=\frac{k{u}^2}{\left(\gamma +v\right)\left(1+u^2/K^2\right)} \mathrm{a}\mathrm{n}\mathrm{d} g\left(u,v\right)=k{u}^2.\hfill \end{array}$

The reaction–diffusion dynamics are modulated by the pre-established morphogen gradients. These morphogen gradients could potentially affect any of the kinetic parameters of the reaction–diffusion model. Previous work suggested that the choice is somewhat arbitrary as the model produces similar results irrespective of which parameter is affected (22). We experimented with modulating the decay rates $\mu$ and $\nu$ of the activator and inhibitor, respectively, and indeed found that the model produces similar patterns irrespective of whether only $\mu$ , only $\nu$ , or both $\mu$ and $\nu$ are modulated. We opted for the most general, two-gradient version of the model in which both $\mu$ and $\nu$ can be independently modulated by morphogen gradients, because this version was able to generate diverse patterns without the need for fine-tuning of the remaining kinetic parameters. Nevertheless, all the patterns that are produced by the two-gradient model can also be recapitulated by a carefully chosen one-gradient model, so none of the patterns we describe strictly require two morphogens for their formation.

For simulations, we fixed all parameters other than $\mu$ and $\nu$ to be $D_u=0.006912$ , $D_v=0.6912$ , $k=10$ , $K=16$ , and $\gamma =0.001$ . For $\mu$ and $\nu$ , we allowed gradients taking values in $\left[{\mu }_{\min },{\mu }_{\max }\right]=\left[5,20\right]$ and $\left[{\nu }_{\min },{\nu }_{\max }\right]=[5,80]$ . This combination of parameters was found to produce patterns with a characteristic length scale similar to that of evolved patterns (SI Appendix, Fig. S7A). The chosen parameters are such that spatial patterns can already form in the absence of any gradient. In particular, for fixed $\mu$ and $\nu$ , the spatially homogeneous steady state of the model is unstable for intermediate values of $\mu /\nu$ (in contrast, if $\mu \gg \nu$ or $\nu \gg \mu$ , then the spatially homogeneous steady state becomes stable), leading to the formation of patterns consisting of spots or labyrinthine stripes (SI Appendix, Fig. S7A). However, the spatial patterns that form for fixed $\mu$ and $\nu$ lack a reproducible organization or orientation.

For simulations, we used the chebfun library in Matlab (76) to numerically determine steady state patterns. Simulations were initialized from homogeneous initial conditions $(u=2$ , $v=2$ ) with some random noise added and run up to $t=5$ (with time steps $dt=0.01$ ). We evaluated the steady state pattern on a $125\times 125$ grid, thus representing each pattern by a $125\times 125$ array of intensity values.

Modeling Morphogen Gradient Establishment.

Pattern self-organization takes place downstream of the establishment of two morphogen gradients $\mu =\mu (x)$   and $\nu =\nu (x)$   . While morphogen gradients can be generated in a variety of ways (77, 78), for simplicity, we consider morphogen gradients that can be realized by the diffusion of a morphogen that is produced locally and degrades linearly (Fig. 2A). This simple mechanism allows for substantial flexibility in the shape of the gradients (e.g., they can be hump-shaped, for a medially produced morphogen, or valley-shaped, for a laterally produced morphogen) but requires no positional information to establish the gradients beyond an initial differentiation of the skin into a more medial and a more lateral region.

We assume that the morphogens are produced at a constant rate $\sigma (x)$ , diffuses with diffusion constant $D$ , and decays linearly at rate $k$ , so that the morphogen concentration $c(x)$ , $x\in \left[-1,1\right]$ satisfies

$$\frac{\partial c}{\partial t}=D·\frac{{\partial }^{2}c}{\partial x^2}+\sigma \left(x\right)-k·c\left(x\right).$$

For a medially produced morphogen, we set $\sigma \left(x\right)=\sigma$ in some domain $x\in [-h,h]$ and $\sigma \left(x\right)=0$ for other $x$ . Assuming zero-flux boundary conditions ( $\frac{\partial c}{\partial x}=0$ for $x=\pm 1$ ; the same solution is obtained with periodic boundary conditions), the resulting diffusion equation has a unique steady-state solution $c(x)$ . Setting $\lambda =\sqrt{D/k}$ , the solution is given by

$$\begin{array}{c}c\left(x\right)=\left\{\begin{array}{c}\frac{\sigma }{k}-\frac{\sigma }{k}·\frac{\sinh \left(\frac{1-h}{\lambda }\right)}{\sinh \left(\frac{1}{\lambda }\right)}·\cosh \left(\frac{x}{\lambda }\right) \mathrm{for} \left|\mathrm{x}\right|\le \mathrm{h},\hfill \\ \frac{\sigma }{k}·\coth \left(\frac{1}{\lambda }\right)·\sinh \left(\frac{h}{\lambda }\right)·\cosh \left(\frac{x}{\lambda }\right)-\frac{\sigma }{k}·\sinh \left(\frac{h}{\lambda }\right)·\sinh \left(\frac{\left|x\right|}{\lambda }\right) \mathrm{for} \left|\mathrm{x}\right|>\mathrm{h}.\end{array}\right.\hfill \end{array}$$

For a laterally produced morphogen, we similarly set $\sigma \left(x\right)=0$ for $x\in [-h,h]$ and $\sigma \left(x\right)=\sigma$ for other $x$ , and the diffusion equation can be solved analogously.

It turns out that the resulting family of possible morphogen gradients can be parametrized by the values of $c(0)$ , $c(1)$ , and $h$ : For each choice of $c(0)$ , $c(1)$ , and $h$ , there is a unique corresponding morphogen gradient. If $c\left(0\right)>c(1)$ , then this gradient is obtained by the diffusion of a morphogen that is produced medially and diffuses laterally; if conversely $c\left(1\right)>c(0)$ , then this gradient is obtained by the diffusion of a morphogen that is produced laterally and diffuses medially.

In the simulations, two morphogen gradients are established that determine the decay rates $\mu =\mu (x)$ and $\nu =\nu (x)$ of the reaction–diffusion model. To ensure both morphogen gradients can be established starting from a single initial differentiation event, the value of $h$ must be the same for $\mu$ and $\nu$ ; therefore, there are five free parameters: $\mu (0)$ , $\mu \left(1\right)$ , $\nu \left(0\right)$ , $\nu \left(1\right)$ , and $h$ . To obtain random morphogen gradients, we sample these parameters uniformly and independently from their respective domains $\left[{\mu }_{\min },{\mu }_{\max }\right]=\left[5,20\right]$ (for $\mu (0)$ and $\mu (1)$ ), $\left[{\nu }_{\min },{\nu }_{\max }\right]=[5,80]$ (for $\nu (0)$ and $\nu (1)$ ), and $[0.05,0.95]$ (for $h$).

Analysis of Model-Generated Patterns.

We identified pattern elements in model-generated patterns based on the mean and SD of activator intensity. For each $x$-coordinate, we calculated the mean and SD intensity across $y$-coordinates, averaging the results for three replicate instances of the pattern. We used the calculated means and SDs to identify three types of pattern elements: stripes, bands, and areas with spots. Stripes are defined as small groups (4–16% of $x$-coordinates) of consecutive $x$-coordinates with high mean intensity and low SD in intensity (SD < 1.5, mean > 3). Bands are defined as larger groups (at least 16% of $x$-coordinates) of consecutive $x$-coordinates with high mean intensity and low SD in intensity (SD < 1.5, mean > 3). Areas with spots are defined as any group (at least 4% of $x$-coordinates) of consecutive $x$ coordinates with sufficiently high SD in intensity (SD > 1.5). We classified patterns based on the pattern elements they contain: patterns with spots but no stripes or bands formed the category “Spots,” patterns with spots and stripes or bands formed the category “Stripes and spots,” and patterns with stripes or bands but no spots formed the category “Stripes and bands.” In this way, each pattern was assigned a category, except for a small minority (<1%) of patterns not containing any pattern elements.

To define pattern variability and pattern complexity, the metrics used in Fig. 2B, we first define the distance $D(u,u\text{'})$ between patterns $u$ and $u\text{'}$ as:

$$D\left(u,u\text{'}\right)=\sqrt{{\displaystyle \sum _x}{\displaystyle \sum _y}{\left(u(x,y)-u\text{'}(\mathrm{x},\mathrm{y})\right)}^2,}$$

where the sum runs over all 125 horizontal coordinates $x$ and vertical coordinates $y$ . Pattern variability is the quadratic-mean distance between three replicate instances $u_1$ , $u_2$ , $u_3$ of the same pattern:

$$\begin{array}{c}\mathrm{Pattern} \mathrm{variability}=\sqrt{\frac{D{(u_{\mathrm{1}},u_{\mathrm{2}})}^{\mathrm{2}}\mathit{+}D{(u_{\mathrm{2}},u_{\mathrm{3}})}^{\mathrm{2}}\mathit{+}D{(u_{\mathrm{3}},u_{\mathrm{1}})}^{\mathrm{2}}}{\mathrm{3}}}.\hfill \end{array}$$

We calculate pattern complexity as the average distance between a pattern $u$ and translations of the pattern over a small distance:

$$\begin{array}{c}\mathrm{Pattern} \mathrm{complexity}=\frac{1}{9}{\displaystyle \sum _{\mathrm{\Delta }x\in \{2,4,8\}}}{\displaystyle \sum _{\mathrm{\Delta }y\in \{2,4,8\}}}D(u,T_{(\mathrm{\Delta }x,\mathrm{\Delta }y)}\left(u\right)),\hfill \end{array}$$

where $T_{(x_0,y_0)}$ denotes translation by the vector $\left(x_0,y_0\right)$.

For our analysis of stripe patterns (Figs. 3 and 4), we selected all patterns that contained no bands or spots. This includes both patterns without any pattern elements, as well as patterns in the category Stripes and bands that do not contain bands. We classified the resulting patterns based on the number of stripes. Patterns with 2 stripes were further classified as 2a ( $w\le 0.48$ ) or 2b ( $w>0.48$ ) depending on the total width $w$ of the pattern (relative to the width of the domain for pattern formation). Patterns with 4 stripes were classified as 4a ( $w\le 0.8$ ) or 4b ( $w>0.8$).

We calculated the developmental distance between patterns generated by morphogen gradients ${\left(\mu ,\nu \right)}_1$ and ${\left(\mu ,\nu \right)}_2$ as:

$$\begin{array}{c}\mathrm{Developmental}\mathrm{distance}={\displaystyle \sum _{\mathrm{x}}}\sqrt{{\left(\frac{{\mu }_1\left(\mathrm{x}\right)-{\mu }_2\left(\mathrm{x}\right)}{{\mu }_{\max }-{\mu }_{\min }}\right)}^2+{\left(\frac{{\nu }_1\left(\mathrm{x}\right)-{\nu }_2\left(\mathrm{x}\right)}{{\nu }_{\max }-{\nu }_{\min }}\right)}^2}.\hfill \end{array}$$

We used multidimensional scaling (MDS) implemented in R (cmdscale with $k=2$ ) to generate the low-dimensional representation of developmental space (Fig. 4A). An MDS finds the low-dimensional representation that best preserves distances between points in a high-dimensional space. In our case, the correlation coefficient between actual distances in the five-dimensional developmental space and distances in the two-dimensional MDS space is $r=0.86$ . An MDS is mathematically equivalent to a principal coordinate analysis (PCoA) and conceptually similar to a principal component analysis (PCA), but in contrast to a PCA, the MDS prioritizes preservation of distances rather than maximizing the amount of explained variance.

Alternative Pattern Formation Model.

To establish the robustness of our results, we also performed simulations using a variant of the Gray–Scott model (30, 31), an alternative reaction–diffusion model for which $f\left(u,v\right)=b{u}^{2}v$ and $g\left(u,v\right)=a-b{u}^{2}v$ (SI Appendix, Fig. S6). The values of the parameters we used are $a=30$ , $b=30$ , $D_u=0.02$ , $D_v=0.2$ , ${\mu }_{\min }=20$ , ${\mu }_{\max }=30$ , ${\nu }_{\min }=1$ , and ${\nu }_{\max }=20$ . We analyzed the results of this model completely analogously to those obtained with our main model.

Stripe Distance Measurements.

To obtain the measurements on stripe positioning shown in Fig. 3, we again made use of the collections of the American Museum of Natural History. We selected at least 5 specimens of each representative species with 3, 4, or 5 dark or light stripes and made caliper measurements of interstripe distances at three positions along the antero-posterior axis. For a few species, we measured less than five specimens because no more were available, or fewer than three positions because the full pattern was restricted to a very narrow part of the dorsum. Relative interstripe distances were first calculated for each position and then averaged across positions.

Phylogenetic Signal in Pattern Organization.

Our model allowed us to quantify pattern organization in a developmentally informative way, making use of the axes MDS1 and MDS2. MDS1 correlates with stripe number (with high MDS1 values corresponding to low stripe number), whereas MDS2 is informative of stripe positioning (with high MDS2 values corresponding to more laterally positioned stripes). We assigned MDS values to evolved patterns by taking the average MDS coordinates of the corresponding model-generated patterns (selecting pattern 7 for evolved patterns where the whole dorsum is covered with stripes) (SI Appendix, Table S3). In doing so, we obtained four variables (MDS1 and MDS2 for dark and light stripes) that we used to test for phylogenetic signal, again using the phylogeny of Fig. 1C (Fig. 4D). Our procedure for calculating and statistically testing phylogenetic signal in pattern organization was completely analogous to the procedure for calculating phylogenetic signal in stripe number, as described above.

For one of the four variables, MDS2 values assigned to dark stripes (reflecting dark stripe positioning), significant phylogenetic signal was detected. To visualize the potential evolutionary constraint in dark stripe positioning, we performed maximum likelihood ancestral reconstruction of MDS2 values using the fastAnc function in phytools (61), as shown in Fig. 4E.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Photos of museum specimens, stripe distance measurements, and code used for pattern formation simulations are available at https://dx.doi.org/10.6084/m9.figshare.c.6854727 (79). Data on diel activity is available in the SI Appendix.