Developmental plasticity and variability in the formation of egg-spots,a pigmentation ornament in the cichlid Astatotilapia calliptera

Vertebrate pigmentation patterns are highly diverse, yet we have a limited understanding of how evolutionary changes to genetic, cellular, and developmental mechanisms generate variation. To address this, we examine the formation of a sexually-selected male ornament exhibiting inter- and intraspecific variation, the egg-spot pattern, consisting of circular yellow-orange markings on the male anal fins of haplochromine cichlid fishes. We focus on Astatotilapia calliptera, the ancestor-type species of the Malawi cichlid adaptive radiation of over 850 species. We identify a key role for iridophores in initializing egg-spot aggregations composed of iridophore-xanthophore associations. Despite adult sexual dimorphism, aggregations initially form in both males and females, with development only diverging between the sexes at later stages. Unexpectedly, we found that the timing of egg-spot initialization is plastic. The earlier individuals are socially isolated, the earlier the aggregations form, with iridophores being the cell type that responds to changes to the social environment. Furthermore, we observe apparent competitive interactions between adjacent egg-spot aggregations, which strongly suggests that egg-spot patterning results mostly from cell-autonomous cellular interactions. Together, these results demonstrate that A. calliptera egg-spot development is an exciting model for investigating pigment pattern formation at the cellular level in a system with developmental plasticity, sexual dimorphism, and intraspecific variation. As A. calliptera represents the ancestral bauplan for egg-spots, these findings provide a baseline for informed comparisons across the incredibly diverse Malawi cichlid radiation.     

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.     

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction–diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace–Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.     

Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments

In many semi-arid environments, vegetation is self-organised into spatial patterns. The most striking examples of this are on gentle slopes, where striped patterns are typical, running parallel to the contours. Previously, Klausmeier [1999. Regular and irregular patterns in semiarid vegetation. Science 284, 1826-1828.] has proposed a model for vegetation stripes based on competition for water. Here, we present a detailed study of the patterned solutions in the full nonlinear model, using numerical bifurcation analysis of both the pattern odes and the model pdes. We show that patterns exist for a wide range of rainfall levels, and in particular for much lower rainfall than have been considered by previous authors. Moreover, we show that for many rainfall levels, patterns with a variety of different wavelengths are stable, with mode selection dependent on initial conditions. This raises the possibility of hysteresis, and in numerical solutions of the model we show that pattern selection depends on rainfall history in a relatively simple way.     

Symmetries,non-Euclidean metrics,and patterns in a Swift–Hohenberg model of the visual cortex

The aim of this work is to investigate the effect of the shift-twist symmetry on pattern formation processes in the visual cortex. First, we describe a generic set of Riemannian metrics of the feature space of orientation preference that obeys properties of the shift-twist, translation, and reflection symmetries. Second, these metrics are embedded in a modified Swift-Hohenberg model. As a result we get a pattern formation process that resembles the pattern formation process in the visual cortex. We focus on the final stable patterns that are regular and periodic. In a third step we analyze the influences on pattern formation using weakly nonlinear theory and mode analysis. We compare the results of the present approach with earlier models.     

SEXUAL SELECTION ON BODY SIZE AND SHAPE IN THE WESTERN HARVESTER ANT,POGONOMYRMEX OCCIDENTALIS CRESSON

Mating in social insects has generally been studied in relation to reproductive allocation and relatedness. Despite the tremendous morphological diversity in social insects, little is known about how individual morphology affects mating success. We examined the correlation of male size and shape with mating success in the western harvester ant, Pogonomyrmex occidentalis. Larger males had significantly higher mating success in two independent collections of males at mating aggregations. We also detected significant linear and nonlinear selection on aspects of male shape that were consistent across years. These shape components are independent of size, suggesting that male mating success is a complex function of size and shape. Successful males had elongate thoraxes and short mandibles relative to males collected at random at the lek. Overall, mated males also had longer postpetioles relative to body size, but there was also evidence of nonlinear selection on relative postpetiole length in both years. We found no evidence of assortative mating based on size or multivariate shape measures in either year, but in one year we found weak assortative mating based on some univariate traits.     

Spatial Ecological Hierarchies: Coexistence on Heterogeneous Landscapes via Scale Niche Diversification

Spatially heterogeneous environments are generally characterized by nested landscape patterns with resource aggregations on several scales. Empirical studies indicate that such nested landscape patterns impose selection constraints on the perceptive scales of animals, but the underlying selection mechanisms are unclear. We investigated the selection dynamics of perceptive scale within a spatial resource utilization model, where the environment is characterized by its resource distribution and species differ in their perceptive scales and resource preemption capabilities. Using three model landscapes with various resource distributions, we found that the optimal perceptive scale is determined by scale-specific attributes of the landscape pattern and that the number of coexisting species increases with the number of characteristic scales. Based on the results of this model, we argue that resource aggregations on different scales act as distinct resources and that animal species of particular perceptive scales are superior in utilizing resource aggregations of comparable spatial extent. Due to the allometric relationship between body size and perceptive scale, such fitness difference might result in discontinuous body mass distributions.     

Stripes,spots, or reversed spots in two-dimensional Turing systems

Two-dimensional Turing models can generate stationary striped patterns or spotted patterns, and are used to explain the body pattern formation of animals. We studied the effects of the choice of reaction terms on pattern selection, i.e., which pattern is likely to be formed. We examined in detail a model with linear reaction terms and additional constraint terms that confine two variables within a finite range. In the one-dimensional model, a periodic stationary pattern can be formed only when the activator level is constrained both from below and from above. In the two-dimensional model, the relative distance of the equilibrium level of the activator between the upper and lower limitations determines the pattern selection. Striped patterns are produced when the equilibrium is equally distant from the upper and the lower limitations, but spotted patterns are produced when the equilibrium is clearly closer to one than to the other of two limitations. We then examined models with nonlinear reaction terms, including both activator-inhibitor and activator-depletion substrate type models; we attempted to explain the pattern selection of these nonlinear models based on the results of linear models with constraints. The distribution of the activator level is skewed positively and negatively for spotted patterns and reversed spotted patterns, respectively. In contrast, the skew of the distribution of the activator level was close to zero in the case of striped patterns. This observation provides a heuristic argument of how the location of the equilibrium between the constraints leads to pattern selection.     

A Nonlocal Continuum Model for Biological Aggregation

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact support and steep edges that correspond to localized biological aggregations, or clumps. These steady-state clumps are reached through a dynamic coarsening process. In the limit of large population size, the clumps approach a constant density swarm with abrupt edges. We use energy arguments to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit. The energy result holds in higher dimensions as well, and is demonstrated via numerical simulations in two dimensions.     

Impacts of fish aggregation devices on size structures of skipjack tuna Katsuwonus pelamis

Tuna purse seine fisheries target fish aggregated in schools, including free schools that are formed naturally based on fish biology and aggregations associated with natural and/or artificial drifting objects. Using data collected from skipjack tuna (Katsuwonus pelamis) fisheries, we evaluated differences in size structures between drifting-floating-object-associated schools and unassociated schools. We developed a generalized linear model to remove impacts of environmental variables on skipjack size composition. This study indicates that the drifting-floating-object-associated schools tended to have significantly wider size ranges than the unassociated schools. This suggests that unassociated schools were likely formed based on similarity in sizes among individuals within a school while drifting-floating-object-associated schools were probably composed of individuals of large size ranges and their formation was not based on the “size selection” rule. We concluded that the unassociated schools and the drifting-floating-object-associated schools were formed through different mechanisms, and drifting floating objects could aggregate unassociated schools of different size structures. Thus, a large scale of deployment of man-made floating objects might disrupt the spatial aggregation pattern of fish that otherwise tended to school based on their sizes in the absence of floating objects.     

Contrasting abundance and contribution of clonal proliferation to the population structure of the corkscrew sea anemone Bartholomea annulata in the tropical Western Atlantic

Clonal propagation is an important life history trait for many sessile organisms, and often leads to the formation of monoclonal aggregations. In the marine environment, sea anemones have been model species for testing theory regarding the evolution of sex and understanding the contribution of sexual versus asexual reproduction to the population structure in facultatively clonal animals. However, little attention has been paid to tropical actiniarians. The corkscrew anemone Bartholomea annulata is common in tropical marine habitats in the western Atlantic and Caribbean; it forms small aggregations (2–4 anemones) on coral reefs and larger aggregations (>10 anemones) in mangrove habitats. We used field surveys and molecular analyses to investigate patterns of distribution, abundance, and genetic structure of aggregations formed by B. annulata on a reef in the US Virgin Islands and in a unique mangrove habitat in the Florida Keys. Abundance was greatest at the abandoned rock quarry mangrove habitat in the Florida Keys, where anemones formed continuously distributed aggregations carpeting the exposed limestone walls. Genetic diversity assessed via intersimple sequence repeats (ISSRs) and six microsatellite loci revealed that asexual reproduction plays only a minor role in the formation of both small and large anemone aggregations. Specifically, ISSR analyses showed that only ~10% of anemone aggregations were clonal in the US Virgin Islands, while microsatellite genotyping identified clonality in only 1 of 35 aggregations. In the Florida Keys, only four clonal genotypes were recovered within aggregations, but eight clones, representing 33% of the total surveyed population, had individuals in multiple aggregations. Thus, population structure of B. annulata appears to rely primarily on sexual reproduction, although asexual reproduction may play a nontrivial role in some environments. Mechanisms that drive the formation of genotypically diverse aggregations remain unknown, but may include attraction toward conspecifics, shared use of preferred habitats, or the local retention of larvae in partially enclosed habitats.     

The social elite: Habitat heterogeneity,complexity and quality in granite inselbergs influence patterns of aggregation in Egernia striolata (Lygosominae: Scincidae)

Habitat heterogeneity, structural complexity and habitat quality are key features of the environment that drive species' distribution and patterns of biological organization. Traditionally, pattern‐based studies have focused on faunal responses to biological systems. However, the influence of non‐biological environments such as insular rock outcrops on patterns of vertebrate distribution is conceivably as important, but has received less attention. Granite inselbergs are a naturally heterogeneous and spatially‐limited habitat. As such, they provide an opportunity for investigating whether environmental attributes influence social behaviour in animals that use these kinds of habitat, particularly lizards that are well adapted to saxicoline environments. We applied ecological theory to investigate the influence of habitat heterogeneity, structural complexity and habitat quality on patterns of home‐site occupancy in the crevice skink Egernia striolata (Lygosominea: Scincidae) from insular granite outcrops located within fragmented agricultural landscapes. We compared home‐site occupancy among solitary juveniles, solitary adults and lizard aggregations. We found significant differences in home‐site occupancy between aggregations and solitary lizard outcrop attributes measured at multiple spatial scales. The probability of a home‐site being occupied by an aggregation increased where large rock masses were present, on northern aspects near the core of the outcrop and in structurally variegated landscapes. Significantly more aggregations occupied home‐sites surrounded by high boulder cover and crevice microhabitat. We provide evidence that geophysical attributes of granite inselbergs and landscape context can influence patterns of lizard aggregation. Thus, we clearly document the environmental correlations of variability in sociality among subpopulations of Egernia striolata.     

An investigation of a nonlocal hyperbolic model for self-organization of biological groups

In this article, we introduce and study a new nonlocal hyperbolic model for the formation and movement of animal aggregations. We assume that the nonlocal attractive, repulsive, and alignment interactions between individuals can influence both the speed and the turning rates of group members. We use analytical and numerical techniques to investigate the effect of these nonlocal interactions on the long-time behavior of the patterns exhibited by the model. We establish the local existence and uniqueness and show that the nonlinear hyperbolic system does not develop shock solutions (gradient blow-up). Depending on the relative magnitudes of attraction and repulsion, we show that the solutions of the model either exist globally in time or may exhibit finite-time amplitude blow-up. We illustrate numerically the various patterns displayed by the model: dispersive aggregations, finite-size groups and blow-up patterns, the latter corresponding to aggregations which may collapse to a point. The transition from finite-size to blow-up patterns is governed by the magnitude of the social interactions and the random turning rates. The presence of these types of patterns and the absence of shocks are consequences of the biologically relevant assumptions regarding the form of the speed and the turning rate functions, as well as of the kernels describing the social interactions.     

Effects of spatial pattern and relatedness in an experimental plant community

Many plant species show limited dispersal resulting in spatial and genetic substructures within populations. Consequently, neighbours are often related between each other, resulting in sibling competition. Using seed families of the annuals Capsella bursa-pastoris and Stachys annua we investigated effects of spatial pattern (i.e. random versus aggregated) on total and individual performance at the level of species and seed families under field conditions. At the level of species, we expected that inferior competitors increase, while superior competitors decrease their performance within neighbourhoods of conspecifics. Thus, we expected a species by spatial pattern interaction. Sibling competition, however, might reduce the performance of competitors, when genetically related, rather than non-related individuals are competing. Therefore, aggregations at the level of seed families could decrease the performance of competitors. Alternatively, if the opposite outcome would be observed, kin selection might be hypothesized to have occurred in the past. Because heavy seeds are expected to disperse less than light seeds, we further hypothesized that kin selection might be more likely to occur in superior competitors with heavy, locally dispersed seeds (e.g. Stachys) compared to inferior competitors with light, more distantly dispersed seeds (e.g. Capsella). We found a significant species by spatial pattern interaction. Indeed, the inferior competitor, Capsella, showed increased reproductive biomass production in aggregated compared to random patterns. Whereas, the performance of the superior competitor, Stachys, was to some extent decreased by intraspecific aggregation. Although statistically not significant, effects of intrafamily aggregations tended to be rather negative in Capsella but positive in Stachys. Our results confirmed that spatial patterns affect growth and reproduction of plant species promoting coexistence in plant communities. Although, we could not provide strong evidence for sibling competition or kin selection, our results suggested that competition among relatives was more severe for Capsella (lighter seeds) compared to Stachys (heavier seeds).     

Do male moor frogs (Rana arvalis) lek with kin?

Many amphibian species are known to form leks during breeding season, yet it has seldom been tested which evolutionary forces are likely to act on lek formation in this taxon. We tested the kin selection hypothesis for lek formation by using eight variable microsatellite loci to compare the genetic relationship of 203 males in seven Rana arvalis leks. The results indicate that moor frog males do not lek with kin: their relatedness within leks was not higher than expected by chance. Furthermore, spatially distinct leks within same water bodies could not be distinguished from each other as separate units. These results are not expected if kin selection underlie lek formation. On the basis of these results and general knowledge of anuran breeding biology, we suggest that lek formation in explosively breeding amphibians might have evolved by female choice for breeding aggregations, combined with female choice of habitat. Future work should aim at predicting aggregations based on rules of phonotaxis over different spatial scales, and empirical work should document visitation rates not only for leks of a specific size, but also for different travel distances that visiting females may have had to cover.     

Combining allele frequency and tree‐based approaches improves phylogeographic inference from natural history collections

Model selection approaches in phylogeography have allowed researchers to evaluate the support for competing demographic histories, which provides a mode of inference and a measure of uncertainty in understanding climatic and spatial influences on intraspecific diversity. Here, to rank all models in the comparison set and determine what proportion of the total support the top‐ranked model garners, we conduct model selection using two analytical approaches—allele frequency‐based, implemented in fastsimcoal2 , and gene tree‐based, implemented in phrapl . We then expand this model selection framework by including an assessment of absolute fit of the models to the data. For this, we utilize DNA isolated from existing natural history collections that span the distribution of red alder (Alnus rubra) in the Pacific Northwest of North America to generate genomic data for the evaluation of 13 demographic scenarios. The quality of DNA recovered from herbarium specimen leaf tissue was assessed for its utility and effectiveness in demographic model selection, specifically in the two approaches mentioned. We present strong support for the use of herbarium tissue in the generation of genomic DNA, albeit with the inclusion of additional quality control checks prior to library preparation and analyses with multiple approaches that incorporate various data. Analyses with allele frequency spectra and gene trees predominantly support A. rubra having experienced an ancient vicariance event with intermittent and frequent gene flow between the disjunct populations. Additionally, the data consistently fit the most frequently selected model, corroborating the model selection techniques. Finally, these results suggest that the A. rubra disjunct populations do not represent separate species.     

Nonlinear selection and the evolution of variances and covariances for continuous characters in an anole

The pattern of genetic variances and covariances among characters, summarized in the additive genetic variance‐covariance matrix, G , determines how a population will respond to linear natural selection. However, G itself also evolves in response to selection. In particular, we expect that, over time, G will evolve correspondence with the pattern of multivariate nonlinear natural selection. In this study, we substitute the phenotypic variance‐covariance matrix ( P ) for G to determine if the pattern of multivariate nonlinear selection in a natural population of Anolis cristatellus, an arboreal lizard from Puerto Rico, has influenced the evolution of genetic variances and covariances in this species. Although results varied among our estimates of P and fitness, and among our analytic techniques, we find significant evidence for congruence between nonlinear selection and P , suggesting that natural selection may have influenced the evolution of genetic constraint in this species.     

Pattern Formation by Competition: A Biological Example

We present a simple model based on a reaction-diffusion equation to explain pattern formation in a multicellular bacterium (Streptomyces). We assume competition for resources as the basic mechanism that leads to pattern formation; in particular we are able to reproduce the spatial pattern formed by bacterial aerial mycelium in the case of growth in minimal (low resources) and maximal (large resources) culture media.     

Distribution Pattern of Far Eastern Sea Cucumber Apostichopus japonicus in Busse Lagoon (Southern Sakhalin)

We analyzed the distribution pattern and size structure in aggregations of the far eastern sea cucumber (trepang), Apostichopus japonicus in Busse Lagoon (Southern Sakhalin). Trepang populations, which differ in their size composition and population density, have been grouped by their spatial differentiation. It has been shown that in the absence of solid substrates in the lagoon, the animals gather on substrates such as the alga Ahnfeltia tobuchiensis and on clusters of the oyster Crassostrea gigas. It is found that on the southeastern part of the lagoon, trepang makes up an extensive aggregation confined to the bed of Ahnfeltia; the distribution of the holothurians mostly has a random pattern. In the northwestern part of the lagoon, trepang makes up aggregations on oyster and algal beds; the distribution of these aggregations shows a random pattern.     

Pattern formation in reaction-diffusion models with nonuniform domain growth

Recent examples of biological pattern formation where a pattern changes qualitatively as the underlying domain grows have given rise to renewed interest in the reaction-diffusion (Turing) model for pattern formation. Several authors have now reported studies showing that with the addition of domain growth the Turing model can generate sequences of patterns consistent with experimental observations. These studies demonstrate the tendency for the symmetrical splitting or insertion of concentration peaks in response to domain growth. This process has also been suggested as a mechanism for reliable pattern selection. However, thus far authors have only considered the restricted case where growth is uniform throughout the domain. In this paper we generalize our recent results for reaction-diffusion pattern formation on growing domains to consider the effects of spatially nonuniform growth. The purpose is twofold: firstly to demonstrate that the addition of weak spatial heterogeneity does not significantly alter pattern selection from the uniform case, but secondly that sufficiently strong nonuniformity, for example where only a restricted part of the domain is growing, can give rise to sequences of patterns not seen for the uniform case, giving a further mechanism for controlling pattern selection. A framework for modelling is presented in which domain expansion and boundary (apical) growth are unified in a consistent manner. The results have implications for all reaction-diffusion type models subject to underlying domain growth.