Butterfly Pattern Research Articles

Geometry, number theory, and the butterfly spectrum of two-dimensional Bloch electrons.

We take a deeper dive into the geometry and the number theory that underlay the butterfly graphs of the Harper and the generalized Harper models of Bloch electrons in a magnetic field. The root of the number theoretical characteristics of the fractal spectrum is traced to a close relationship between the Farey tree-the hierarchical tree that generates all rationals and the Wannier diagram-a graph that labels all the gaps of the butterfly graph. The resulting Farey-Wannier hierarchical lattice of trapezoids provides a geometrical representation of the nested pattern of butterflies in the butterfly graph. Some features of the energy spectrum, such as absence of some of the Wannier trajectories in the butterfly graph falling outside the number theoretical framework, can be stated as a simple rule of minimal violation of mirror symmetry. In a generalized Harper model, number theoretical framework prevails with the Farey-Wannier hierarchical lattice regrouping to form some hexagonal cells creating different species of butterflies.

Mathematical modeling of the eyespots in butterfly wings

Butterfly wing color patterns are a representative model system for studying biological pattern formation, due to their two-dimensional simple structural and high inter- and intra-specific variabilities. Moreover, butterfly color patterns have demonstrated roles in mate choice, thermoregulation, and predator avoidance via disruptive coloration, attack deflection, aposematism, mimicry, and masquerade. Because of the importance of color patterns to many aspects of butterfly biology and their apparent tractability for study, color patterns have been the subjects of many attempts to model their development. Early attempts focused on generalized mechanisms of pattern formation such as reaction-diffusion, diffusion gradient, lateral inhibition, and threshold responses, without reference to any specific gene products. As candidate genes with expression patterns that resembled incipient color patterns were identified, genetic regulatory networks were proposed for color pattern formation based on gene functions inferred from other insects with wings, such as Drosophila. Particularly detailed networks incorporating the gene products, Distal-less (Dll), Engrailed (En), Hedgehog (Hh), Cubitus interruptus (Ci), Transforming growth factor-β (TGF-β), and Wingless (Wg), have been proposed for butterfly border ocelli (eyespots) which helps the investigation of the formation of these patterns. Thus, in this work, we develop a mathematical model including the gene products En, Hh, Ci, TGF-β, and Wg to mimic and investigate the eyespot formation in butterflies. Our simulations show that the level of En has peaks in the inner and outer rings and the level of Ci has peaks in the inner and middle rings. The interactions among these peaks activate cells to produce white, black, and yellow pigments in the inner, middle, and outer rings, respectively, which captures the eyespot pattern of wild type Bicyclus anynana butterflies. Additionally, our simulations suggest that lack of En generates a single black spot and lack of Hh or Ci generates a single white spot, and a deficiency of TGF-β or Wg will cause the loss of the outer yellow ring. These deficient patterns are similar to those observed in the eyespots of Vanessa atalanta, Vanessa altissima, and Chlosyne nycteis. Thus, our model also provides a hypothesis to explain the mechanism of generating the deficient patterns in these species.

Do sub-groups of butterflies display different elevational distribution patterns in the Eastern Himalaya, India?

Understanding the pattern of biodiversity along environmental gradients helps in identifying diversity hotspot areas that can be prioritized for conservation. While the elevational distribution of several taxa has been studied, responses of the sub-groups within a taxon to elevation and its associated factors are not properly understood. Here we study species richness and butterfly density along an elevation gradient in Sikkim, Eastern Himalaya, India and explore the underlying causes of the patterns. We sampled butterflies using a fixed-width point count method in 16 elevational bands (150–200 m intervals), between a range of 300 and 3300 m a.s.l. We categorized butterflies into various sub-groups based on family, range size, biogeographic affinity, and host-plant specialization. We recorded 3603 individuals and 253 species of butterflies after the completion of 1860 point counts. Overall, species richness in the majority of the sub-groups (except for Riodinidae and Palearctic species) declines with elevation, as does the density of almost all the sub-groups. From a selection of environmental factors, annual actual evapotranspiration has the strongest effect on the species richness pattern of butterflies as well as on the density of the overall butterfly community, especially the Lycaenidae family. The richness and density of butterfly groups display varied responses to the richness and density of trees and shrubs. The conducive climatic conditions and diverse habitats in the lower valleys of the Eastern Himalaya support a high diversity of butterflies (with majority of small range species) and thus warrants conservation attention.

High-Quality Genome Assembly and Comprehensive Transcriptome of the Painted Lady Butterfly Vanessa cardui.

The painted lady butterfly, Vanessa cardui, has the longest migration routes, the widest hostplant diversity, and one of the most complex wing patterns of any insect. Due to minimal culturing requirements, easily characterized wing pattern elements, and technical feasibility of CRISPR/Cas9 genome editing, V. cardui is emerging as a functional genomics model for diverse research programs. Here, we report a high-quality, annotated genome assembly of the V. cardui genome, generated using 84× coverage of PacBio long-read data, which we assembled into 205 contigs with a total length of 425.4 Mb (N50 = 10.3 Mb). The genome was very complete (single-copy complete Benchmarking Universal Single-Copy Orthologs [BUSCO] 97%), with contigs assembled into presumptive chromosomes using synteny analyses. Our annotation used embryonic, larval, and pupal transcriptomes, and 20 transcriptomes across five different wing developmental stages. Gene annotations showed a high level of accuracy and completeness, with 14,437 predicted protein-coding genes. This annotated genome assembly constitutes an important resource for diverse functional genomic studies ranging from the developmental genetic basis of butterfly color pattern, to coevolution with diverse hostplants.

Image-Based Automated Species Identification: Can Virtual Data Augmentation Overcome Problems of Insufficient Sampling?

Automated species identification and delimitation is challenging, particularly in rare and thus often scarcely sampled species, which do not allow sufficient discrimination of infraspecific versus interspecific variation. Typical problems arising from either low or exaggerated interspecific morphological differentiation are best met by automated methods of machine learning that learn efficient and effective species identification from training samples. However, limited infraspecific sampling remains a key challenge also in machine learning. In this study, we assessed whether a data augmentation approach may help to overcome the problem of scarce training data in automated visual species identification. The stepwise augmentation of data comprised image rotation as well as visual and virtual augmentation. The visual data augmentation applies classic approaches of data augmentation and generation of artificial images using a generative adversarial networks approach. Descriptive feature vectors are derived from bottleneck features of a VGG-16 convolutional neural network that are then stepwise reduced in dimensionality using Global Average Pooling and principal component analysis to prevent overfitting. Finally, data augmentation employs synthetic additional sampling in feature space by an oversampling algorithm in vector space. Applied on four different image data sets, which include scarab beetle genitalia (Pleophylla, Schizonycha) as well as wing patterns of bees (Osmia) and cattleheart butterflies (Parides), our augmentation approach outperformed a deep learning baseline approach by means of resulting identification accuracy with nonaugmented data as well as a traditional 2D morphometric approach (Procrustes analysis of scarab beetle genitalia). [Deep learning; image-based species identification; generative adversarial networks; limited infraspecific sampling; synthetic oversampling.].

Elevational and seasonal patterns of butterflies and hawkmoths in plant-pollinator networks in tropical rainforests of Mount Cameroon

Butterflies and moths are conspicuous flower visitors but their role in plant-pollinator interactions has rarely been quantified, especially in tropical rainforests. Moreover, we have virtually no knowledge of environmental factors affecting the role of lepidopterans in pollination networks. We videorecorded flower-visiting butterflies and hawkmoths on 212 plant species (> 26,000 recorded hrs) along the complete elevational gradient of rainforests on Mount Cameroon in dry and wet seasons. Altogether, we recorded 734 flower visits by 80 butterfly and 27 hawkmoth species, representing only ~ 4% of all flower visits. Although lepidopterans visited flowers of only a third of the plant species, they appeared to be key visitors for several plants. Lepidopterans visited flowers most frequently at mid-elevations and dry season, mirroring their local elevational patterns of diversity. Characteristics of interaction networks showed no apparent elevational or seasonal patterns, probably because of the high specialisation of all networks. Significant non-linear changes of proboscis and forewing lengths were found along elevation. A positive relationship between the lengths of proboscis of hesperiid butterflies and tube of visited flowers was detected. Differences in floral preferences were found between sphingids and butterflies, revealing the importance of nectar production, floral size and shape for sphingids, and floral colour for butterflies. The revealed trait-matching and floral preferences confirmed their potential to drive floral evolution in tropical ecosystems.

Differential Diagnosis of Corpus Callosum Lesions: Beyond the Typical Butterfly Pattern.

Corpus callosum lesions have a wide range of causes, and integration of key imaging findings with the patient’s clinical history helps narrow the differential diagnosis and direct treatment.

Metapopulation Patterns of Iberian Butterflies Revealed by Fuzzy Logic.

Simple SummaryWe tested the usefulness of new analytical tools such as fuzzy set theory to reveal the hidden internal complexity of the geographic distribution of species. Fuzzy set theory replaces the crisp notion of presence/absence of a species, typical of species distribution atlases, with the fuzzy notion of favorability for the species occurrence. Species distribution ranges are then revealed as more complex than recorded presences suggest, and metapopulation theory, which predicts fragmented favorable patches with connectivity among them, can be operationally analyzed. We identified the favorable patches for 222 butterfly species in the Iberian Peninsula using high values of favorability. We calculated the cost of reaching any part of the territory from a favorable patch using low values of favorability and distance and computed the inverse as connectivity. Some of the favorable territories can be vacant patches but also belong to the metapopulation structure, as they may be recolonized. This information is relevant for territory management and biodiversity conservation, serving to justify the protection of new areas or the modification of contours of reserves based on the role they play for the populations of interest.Metapopulation theory considers that the populations of many species are fragmented into patches connected by the migration of individuals through an interterritorial matrix. We applied fuzzy set theory and environmental favorability (F) functions to reveal the metapopulational structure of the 222 butterfly species in the Iberian Peninsula. We used the sets of contiguous grid cells with high favorability (F ≥ 0.8), to identify the favorable patches for each species. We superimposed the known occurrence data to reveal the occupied and empty favorable patches, as unoccupied patches are functional in a metapopulation dynamics analysis. We analyzed the connectivity between patches of each metapopulation by focusing on the territory of intermediate and low favorability for the species (F < 0.8). The friction that each cell opposes to the passage of individuals was computed as 1-F. We used the r.cost function of QGIS to calculate the cost of reaching each cell from a favorable patch. The inverse of the cost was computed as connectivity. Only 126 species can be considered to have a metapopulation structure. These metapopulation structures are part of the dark biodiversity of butterflies because their identification is not evident from the observation of the occurrence data but was revealed using favorability functions.

Fulgide Derivative-Based Solid-State Reversible Fluorescent Switches for Advanced Optical Memory

Fulgide Derivative-Based Solid-State Reversible Fluorescent Switches for Advanced Optical Memory

The Effects of GC-Biased Gene Conversion on Patterns of Genetic Diversity among and across Butterfly Genomes.

Recombination reshuffles the alleles of a population through crossover and gene conversion. These mechanisms have considerable consequences on the evolution and maintenance of genetic diversity. Crossover, for example, can increase genetic diversity by breaking the linkage between selected and nearby neutral variants. Bias in favor of G or C alleles during gene conversion may instead promote the fixation of one allele over the other, thus decreasing diversity. Mutation bias from G or C to A and T opposes GC-biased gene conversion (gBGC). Less recognized is that these two processes may—when balanced—promote genetic diversity. Here, we investigate how gBGC and mutation bias shape genetic diversity patterns in wood white butterflies (Leptidea sp.). This constitutes the first in-depth investigation of gBGC in butterflies. Using 60 resequenced genomes from six populations of three species, we find substantial variation in the strength of gBGC across lineages. When modeling the balance of gBGC and mutation bias and comparing analytical results with empirical data, we reject gBGC as the main determinant of genetic diversity in these butterfly species. As alternatives, we consider linked selection and GC content. We find evidence that high values of both reduce diversity. We also show that the joint effects of gBGC and mutation bias can give rise to a diversity pattern which resembles the signature of linked selection. Consequently, gBGC should be considered when interpreting the effects of linked selection on levels of genetic diversity.

Spatial phylogenetics of butterflies in relation to environmental drivers and angiosperm diversity across North America

SummaryBroad-scale, quantitative assessments of insect biodiversity and the factors shaping it remain particularly poorly explored. Here we undertook a spatial phylogenetic analysis of North American butterflies to test whether climate stability and temperature gradients have shaped their diversity and endemism. We also performed the first quantitative comparisons of spatial phylogenetic patterns between butterflies and flowering plants. We expected concordance between the two groups based on shared historical environmental drivers and presumed strong butterfly-host plant specializations. We instead found that biodiversity patterns in butterflies are strikingly different from flowering plants, especially warm deserts. In particular, butterflies show different patterns of phylogenetic clustering compared with flowering plants, suggesting differences in habitat conservation between the two groups. These results suggest that shared biogeographic histories and trophic associations do not necessarily assure similar diversity outcomes. The work has applied value in conservation planning, documenting warm deserts as a North American butterfly biodiversity hotspot.

Assemblages and seasonal patterns in butterflies across different ecosystems in a sub-tropical zone of Jammu Shiwaliks, Jammu and Kashmir, India

The present study was aimed to understand the community structure and functionality of butterflies in three different sub-tropical ecosystems concerning the habitat types and seasonality. We sampled the butterflies for their abundance, diversity and host plant specificity from 21 linear transects placed in a stratified random manner in heterogeneous mosaic landscapes, urban green spaces and natural forests from April to December 2018. Overall, 6384 individuals of 118 butterfly species in 81 genera, six families and 20 subfamilies were observed. Our results indicated that the land cover type and the seasonal variability had a pronounced influence on the species richness, abundance, diversity and similarity across different sites with significantly higher values recorded for mosaic landscapes during the wet season. In contrast, the urban built-up site was more speciose with higher abundance than natural forests. Each system harboured unique species assemblages with high similarity among the sites as well as seasons. Presence of protected and habitat exclusive species substantiate a high conservation value of these habitats especially the urban green spaces, and thus, calls for effective management strategies for the conservation and proliferation of butterflies in sub-tropical areas of Jammu region.

The Fractal Geometry of the Nymphalid Groundplan: Self-Similar Configuration of Color Pattern Symmetry Systems in Butterfly Wings.

Simple SummaryHighly diverse color patterns of butterfly wings can be explained as modifications of an archetypical color pattern of nymphalid butterflies called the nymphalid groundplan. The nymphalid groundplan contains three major symmetry systems and a discal symmetry system, but their relationships have been elusive. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species color-pattern comparisons of the hindwings in nymphalid butterflies. It was shown that all symmetry systems can be expressed as various structures, suggesting the equivalence (homology) of these systems in developmental potential. In some cases, the discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, indicating a unified supersymmetry system covering the entire wing. These results suggest that butterfly color patterns are hierarchically constructed; one system is nested within another system, which is a self-similar relationship that achieves the fractal geometry. This self-similarity is likely mediated by the serial induction of organizers during development, and a possible mechanism is proposed for symmetry breaking of the system morphology, which contributes to the diversity of butterfly wing color patterns.The nymphalid groundplan is an archetypical color pattern of nymphalid butterflies involving three major symmetry systems and a discal symmetry system, which share the basic morphogenesis unit. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species comparisons of nymphalid hindwings. Based on findings in Neope and Symbrenthia, all three major symmetry systems can be expressed as bands, spots, or eyespot-like structures, suggesting equivalence (homology) of these systems in developmental potential. The discal symmetry system can also be expressed as various structures. The discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, based mainly on findings in Agrias, indicating a unified supersymmetry system covering the entire wing. The border symmetry system can occupy the central part of the wing when the central symmetry system is compromised, as seen in Callicore. These results suggest that butterfly color patterns are hierarchically constructed in a self-similar fashion, as the fractal geometry of the nymphalid groundplan. This self-similarity is likely mediated by the serial induction of organizers, and symmetry breaking of the system morphology may be generated by the collision of opposing signals during development.

Magneto-sensitive photonic crystal ink for quick printing of smart devices with structural colors.

In this paper, we report a facile strategy to combine magneto-responsive photonic crystal (MRPC) inkwith 3D printing technology. The building blocks of MRPC are based on Fe3O4 magnetic nanoparticle clusters (MNCs) with uniform and tunable size. The MNC dispersion is able to change its photonic band gap from red to blue as the external magnetic field strength is increased. The magneto-responsive photonic crystal ink can be readily obtained by taking advantage of an ethylene glycol (EG)-in-oil emulsion with a reinforced silicone rubber prepolymer as the outer phase. Using the well-designed formula, the MNC dispersion can be well-preserved inside the emulsion droplets of the ink, maintaining its original contactless magnetic field response. As a proof of concept, custom quick response code and butterfly patterns were successfully printed and showed vivid and tunable color as a function of the external magnetic field strength with good repeatability.

A Depth-First Iterative Algorithm for the Conjugate Pair Fast Fourier Transform

The Split-Radix Fast Fourier Transform has the same low arithmetic complexity as the related Conjugate Pair Fast Fourier Transform. Both transforms have an irregular datapath structure which is straightforwardly expressed only in recursive forms. Furthermore, the conjugate pair variant has a complicated input indexing pattern which requires existing iterative implementations to rely on precomputed tables. It however allows optimization of the memory bandwidth as it requires a single twiddle factor load per radix-4 butterfly. In existing algorithms, this comes at the cost of using additional precomputed tables or performing recursive function calls. In this paper we present two novel approaches that handle both the butterfly scheduling and the input index generation of the Conjugate Pair Fast Fourier Transform. The proposed algorithm is cache-friendly because it is depth-first, non-recursive and does not rely on precomputed index tables. In order to achieve this, we relate the butterfly execution pattern of the Split-Radix and Conjugate Pair FFTs to the binary carry sequence. Based on this finding, we describe how common integer arithmetic and bitwise operations can be used to perform input reordering and depth-first traversal of the transform datapath with O(1) space complexity.

Movements and occurrence in two closely related fritillary species

Mobility may affect species' distribution patterns in heterogeneous landscapes, and it might impact fitness by influencing mating success, predation avoidance, and foraging success. Here, we studied causes and consequences of mobility patterns in butterflies: Argynnis adippe, a specialist constrained to warm microhabitats within woodland landscapes, and A. aglaja, a relative generalist that also inhabits grasslands, and tolerates lower temperatures. We explored associations of movement and occurrence patterns, population size and density, niche breadth, wing size, and different types of behaviour prior to capture by conducting a mark‐release‐recapture study on the Swedish island Öland. We marked 1 935 A. aglaja and 123 A. adippe and achieved recapture rates of 9.5% (A. aglaja), and 8.9% (A. adippe). Estimated population densities were 5 066 and 814 individuals per km2, for A. aglaja and A. adippe, respectively. Argynnis aglaja was less likely to perform long‐distance flights according to estimated dispersal kernels, hinting at negative density‐dependent dispersal in these species. Although we detected the longest flight distances ever in these species in MRR studies (11.9 km for A. aglaja and 3.7 km for A. adippe), most butterflies were recaptured within 200 meters (60–80%). Low recapture rates along with low estimated residence times and the potential for long movement might indicate that many individuals left the study area, and that the species form open populations, stretching over large areas. Despite significant differences in wing size and behaviour types, mean observed flight distances were similar in these species.

Multimodal Imaging in a Long-standing Case of Pattern Dystrophy

Purpose: The aim of this study is to report the case of a patient diagnosed with butterfly pattern dystrophy (BPD), which during yearly follow-up visits developed a concomitant pachychoroidal neovasculopathy (PNV). Methods: Case report focusing on the role multimodal imaging in patients with pattern dystrophies (PDs) Case report: We describe a case of a 52-year-old woman,which was initially diagnosed with BPD by fundus examination, fundus autofluorescence and optical coherence tomofraphy findings. Interestingly, during yearly follow-up visits, the presence of a thickened choroid bilaterally associated with the onset of concomitant choroidal neovascularizations (CNVs) in the right eye was made possibile by adopting multimodal imaging, in particular optical coherence tomography angiography. Fluorescein angiography and indocyanine green angiography findings helped us to make the diagnosis of PNV. Conclusion: We described for the first time a case of PD, which after several years progressed to PNV. Hence, we deem that multimodal imaging and in particular optical coherence tomography angiography represent an important diagnostic tool in the management of PDs.

Miocene Diversification and High-Altitude Adaptation of Parnassius Butterflies (Lepidoptera: Papilionidae) in Qinghai-Tibet Plateau Revealed by Large-Scale Transcriptomic Data.

Simple SummaryParnassius butterflies have contributed to fundamental studies in biogeography, insect–plant interactions, and other fields of conservation biology and ecology. However, the early evolutionary pattern and molecular adaptation mechanism of this alpine butterfly group to high altitudes in Qinghai–Tibet Plateau are poorly understood up to now. In this study, we report for the first time, a relatively large-scale transcriptomic dataset of eight Parnassius species and their two closely related papilionid species, a dated phylogeny based on hundreds of gene sequences, and potential genetic mechanisms underlying the high-altitude adaptation by investigating changes in evolutionary rates and positively selected genes. Overall, our findings indicate that the transcriptome data sets reported here can provide some new insights into the spatiotemporally evolutionary pattern and high altitude adaptation of Parnassius butterflies from the extrinsic and intrinsic view, and will support further expressional and functional studies that will help interested researchers to address evolution, biodiversity and conservation questions concerning Parnassius and other butterfly species.The early evolutionary pattern and molecular adaptation mechanism of alpine Parnassius butterflies to high altitudes in Qinghai–Tibet Plateau are poorly understood up to now, due to difficulties in sampling, limited sequence data, and time calibration issues. Here, we present large-scale transcriptomic datasets of eight representative Parnassius species to reveal the phylogenetic timescale and potential genetic basis for high-altitude adaptation with multiple analytic strategies using 476 orthologous genes. Our phylogenetic results strongly supported that the subgenus Parnassius formed a well-resolved basal clade, and the subgenera Tadumia and Kailasius were closely related in the phylogenetic trees. In addition, molecular dating analyses showed that the Parnassius began to diverge at about 13.0 to 14.3 million years ago (middle Miocene), correlated with their hostplant’s spatiotemporal distributions, as well as geological and palaeoenvironmental changes of the Qinghai–Tibet Plateau. Moreover, the accelerated evolutionary rate, candidate positively selected genes and their potentially functional changes were detected, probably contributed to the high-altitude adaptation of Parnassius species. Overall, our study provided some new insights into the spatiotemporally evolutionary pattern and high altitude adaptation of Parnassius butterflies from the extrinsic and intrinsic view, which will help to address evolution, biodiversity, and conservation questions concerning Parnassius and other butterfly species.

Butterfly diversity of Chennai, Kancheepuram, Chengalpet and Thiruvallur districts in Tamil Nadu, India

A long term butterfly study was conducted from January 2014 to March 2020 at 17 locations with varied habitats namely Tropical Dry Evergreen forests, Grasslands, Scrubland, Wetland and Community park covering four districts namely Chennai, Kancheepuram, Chengalpet and Thiruvallur of Tamil Nadu, India. A total of 128 species from the Chennai district, 114 species from the Chengalpet district, 67 species from Thiruvallur district, and 66 species from Kancheepuram district were recorded. The habitat of Tropical dry Evergreen Forest habitat recorded the highest butterfly number with 118 species. The sighting of the Red-spot Jezebel (Deliasdes combesi) was the most significant record from this study. The butterfly diversity in the month of November was seen to be the highest. We also assessed the relative abundance and species distribution patterns of butterflies in the study area.

Updates and Advances in the Management of Lateral Meniscal Radial Tears: A Critical Analysis Review.

Because of their increased mobility, lack of resistance to hoop stresses, and decreased blood supply, radial tears of the lateral meniscus are more troublesome to heal than vertical longitudinal tears. Given the success of meniscal root repairs, radial tears of the lateral meniscal body should be given strong consideration for repair because of a more reproducible ability to heal such lesions in young, active patients. Technique options that should be considered for the less common anterior radial tears of the lateral meniscus include outside-in repair, self-capturing suture-passing devices, and orthobiologic treatments to stimulate healing. Although a variety of suture techniques, including the double horizontal mattress and horizontal butterfly patterns, have demonstrated improvements in patient outcomes, evidence is still limited with regard to the ideal suture pattern for radial tears.