Mechanical Transgressive Segregation and the Rapid Origin of Trophic Novelty

Functional trait plasticity diverges between sexes in African cichlids: A contribution toward ecological sexual dimorphism?

Phenotypic plasticity enables development to produce multiple phenotypes in response to environmental conditions. Plasticity driven variation has been suggested to play a key role in adaptive divergence, and plasticity itself can evolve. However, the interaction of plasticity with the multiple levels involved with adaptive divergence is less understood. For example, sexual dimorphism can contribute adaptive variation through ecological sexual dimorphism (ESD), but the contribution of plasticity to this phenomenon is unknown. Therefore, to determine the potential contribution of plasticity to ESD, we used the adaptive radiation of Malawi cichlids. Two mouthbrooding species (Labeotropheus fuelleborni and Tropheops "Red Cheek") with differences in foraging tactics underwent foraging experiments using benthic and limnetic treatments while accounting for sex. Plasticity in craniofacial shape and three functionally important traits were measured. Plasticity was shown, but without any sex-based differences in shape. However, for mechanical advantage traits of the mandible sex by diet interactions were found. This suggests that ESD, may be influenced by phenotypic plasticity that diverges between sexes. Given the involvement of the mandible in parental care in cichlids this may indicate that sexual divergence in plasticity may trade-off against maternal care tactics.

The effect of experimental hybridization on cognition and brain anatomy: Limited phenotypic variation and transgression in Poeciliidae

Hybridization can promote phenotypic variation and often produces trait combinations distinct from the parental species. This increase in available variation can lead to the manifestation of functional novelty when new phenotypes bear adaptive value under the environmental conditions in which they occur. Although the role of hybridization as a driver of variation and novelty in traits linked to fitness is well recognized, it remains largely unknown whether hybridization can fuel behavioral novelty by promoting phenotypic variation in brain morphology and/or cognitive traits. To address this question, we investigated the effect of hybridization on brain anatomy, learning ability, and cognitive flexibility in first- and second-generation hybrids of two closely related fish species (Poecilia reticulata and Poecilia wingei). Overall, we found that F1 and F2 hybrids showed intermediate brain morphology and cognitive traits compared to parental groups. Moreover, as phenotypic dispersion and transgression were low for both brain and cognitive traits, we suggest that hybridization is not a strong driver of brain anatomical and cognitive diversification in these Poeciliidae. To determine the generality of this conclusion, hybridization experiments with cognitive tests need to be repeated in other families.

Differences among reciprocal hybrids of Labeotropheus

Current evidence suggests that hybridization played a crucial role in the early evolution and diversification of the species flocks of cichlid fishes in the African Great Lakes. Nonetheless, evidence for hybridization in the extant cichlid fauna is scant, suggesting that hybridization is rare in the modern era, perhaps enforced by natural or sexual selection acting against F1 hybrids. Additionally, most experimental studies of hybridization perform a hybrid cross in one direction, ignoring the reciprocal hybrid. In this study, we perform reciprocal crosses between sympatric congeners from Lake Malaŵi, Labeotropheus fuelleborni and L. trewavasae, in order to compare the body shape and coloration of males of both of these hybrids, as well as to examine how these hybrids fare during both inter- and intrasexual interactions. We found that L. trewavasae-sired hybrid males are intermediate to the parental species both morphologically and chromatically, while the reciprocal L. fuelleborni-sired hybrids are likely transgressive hybrids. Males of these transgressive hybrids also fare poorly during our mate choice experiments. While female L. trewavasae reject them as possible mates, male L. trewavasae do not make a distinction between them and conspecific males. Selection against transgressive F1 hybrids as observed in our crossing experiments may help explain why contemporary hybridization in Lake Malaŵi cichlids appears to be rare.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10750-022-05092-4.

Ecological outcomes of hybridization vary extensively in Catostomus fishes

Hybridization outcomes vary geographically and can depend on the environment. Hybridization can also reshape biotic interactions, leading to ecological shifts. If hybrids function differently ecologically in ways that enhance or reduce fitness, and those ecological roles vary geographically, ecological factors might explain variation in hybridization outcomes. However, relatively few studies have focused on ecological traits of hybrids. We compared the feeding ecology of Catostomus fish species and hybrids by using stable isotopes (δ13 C and δ15 N) as a proxy for diet and habitat use, and compared two native species, an introduced species, and three interspecific hybrid crosses. We included hybrids and parental species from seven rivers where hybridization outcomes vary. Relative isotopic niches of native species varied geographically, but native species did not fully overlap in isotopic space in any river sampled, suggesting little overlap of resource use between historically sympatric species. The introduced species overlapped with one or both native species in every river, suggesting similar resource use and potential competition. Hybrids occupied intermediate, matching, or more transgressive isotopic niches, and varied within and among rivers. Ecological outcomes of hybridization varied across locations, implying that hybridization might have unpredictable, idiosyncratic ecological effects.

Assessing the Levels of Functional Adaptation: Finite Element Analysis Reveals Species, Hybrid, and Sexual Variation in the Biomechanics of African Cichlid Mandibles

To understand how adaptive divergence emerges it is essential to examine the function of phenotypic traits along a continuum. For vertebrates, the mandible provides a key link with foraging and other important activities which has made it highly relevant for investigations of biomechanical change. Variation in mandible shape is known to correspond with ecology but its function is often only investigated between distinct species. However, for such divergence to occur and be maintained selection likely draws from many sources of biomechanical variation. African cichlids represent an exemplar model for understanding how such processes unfold with mandible variation existing between species, sexes, and is likely generated in nature by the potential for hybridization. We explored such mandible variation through a finite element modelling approach and predicted that hybrids and females would have reduced functional capabilities, the former in line with disruptive selection and the latter due to potential trade-offs incurred by maternal mouthbrooding in Malawian haplochromines. We revealed evidence of structural adaptations between Tropheops ‘Red Cheek’ and Labeotrophues fuelleborni that impacted the dispersion of mechanical stress in ways that matched the foraging of these species. Also, hybrids showed higher stresses relative to both species across the mandible. Sexual dimorphism in stress handling was evident despite minor differences in shape with males showing enhanced load resistance. However, in hybrids it appeared that males were disadvantaged relative to females, and displayed asymmetry in load handling. Together, these results show evidence of species and sex based biomechanical variation, that could be targeted by divergent selection.

Of bars and stripes: A Malawi cichlid hybrid cross provides insights into genetic modularity and evolution of modifier loci underlying colour pattern diversification

Understanding the origins of phenotypic diversity among closely related species remains an important largely unsolved question in evolutionary biology. With over 800 species, Lake Malawi haplochromine cichlid fishes are a prominent example of extremely fast evolution of diversity including variation in colouration. Previously, a single major effect gene, agrp2 (asip2b), has been linked to evolutionary losses and gains of horizontal stripe patterns in cichlids, but it remains unknown what causes more fine-scale variation in the number and continuity of the stripes. Also, the genetic basis of the most common colour pattern in African cichlids, vertical bars, and potential interactions between the two colour patterns remain unknown. Based on a hybrid cross of the horizontally striped Lake Malawi cichlid Pseudotropheus cyaneorhabdos and the vertically barred species Chindongo demasoni we investigated the genetic basis of both colour patterns. The distribution of phenotypes in the F₂  generation of the cross indicates that horizontal stripes and vertical bars are independently inherited patterns that are caused by two sets of genetic modules. While horizontal stripes are largely controlled by few major effect loci, vertical bars are a highly polygenic trait. Horizontal stripes show substantial variation in the F₂  generation that, interestingly, resemble naturally occurring phenotypes found in other Lake Malawi cichlid species. Quantitative trait loci (QTL) mapping of this cross reveals known (agrp2) and unknown loci underlying horizontal stripe patterns. These findings provide novel insights into the incremental fine-tuning of an adaptive trait that diversified through the evolution of additional modifier loci.

Rapid generation of ecologically relevant behavioral novelty in experimental cichlid hybrids

The East African cichlid radiations are characterized by repeated and rapid diversification into many distinct species with different ecological specializations and by a history of hybridization events between nonsister species. Such hybridization might provide important fuel for adaptive radiation. Interspecific hybrids can have extreme trait values or novel trait combinations and such transgressive phenotypes may allow some hybrids to explore ecological niches neither of the parental species could tap into. Here, we investigate the potential of second-generation (F2) hybrids between two generalist cichlid species from Lake Malawi to exploit a resource neither parental species is specialized on: feeding by sifting sand. Some of the F2 hybrids phenotypically resembled fish of species that are specialized on sand sifting. We combined experimental behavioral and morphometric approaches to test whether the F2 hybrids are transgressive in both morphology and behavior related to sand sifting. We then performed a quantitative trait loci (QTL) analysis using RADseq markers to investigate the genetic architecture of morphological and behavioral traits. We show that transgression is present in several morphological traits, that novel trait combinations occur, and we observe transgressive trait values in sand sifting behavior in some of the F2 hybrids. Moreover, we find QTLs for morphology and for sand sifting behavior, suggesting the existence of some loci with moderate to large effects. We demonstrate that hybridization has the potential to rapidly generate novel and ecologically relevant phenotypes that may be suited to a niche neither of the parental species occupies. Interspecific hybridization may thereby contribute to the rapid generation of ecological diversity in cichlid radiations.

Hybridization and transgressive exploration of colour pattern and wing morphology in Heliconius butterflies

Hybridization can generate novel phenotypes distinct from those of parental lineages, a phenomenon known as transgressive trait variation. Transgressive phenotypes might negatively or positively affect hybrid fitness, and increase available variation. Closely related species of Heliconius butterflies regularly produce hybrids in nature, and hybridization is thought to play a role in the diversification of novel wing colour patterns despite strong stabilizing selection due to interspecific mimicry. Here, we studied wing phenotypes in first- and second-generation hybrids produced by controlled crosses between either two co-mimetic species of Heliconius or between two nonmimetic species. We quantified wing size, shape and colour pattern variation and asked whether hybrids displayed transgressive wing phenotypes. Discrete traits underlain by major-effect loci, such as the presence or absence of colour patches, generate novel phenotypes. For quantitative traits, such as wing shape or subtle colour pattern characters, hybrids only exceed the parental range in specific dimensions of the morphological space. Overall, our study addresses some of the challenges in defining and measuring phenotypic transgression for multivariate traits and our data suggest that the extent to which transgressive trait variation in hybrids contributes to phenotypic diversity depends on the complexity and the genetic architecture of the traits.

Rapid adaptive evolution of scale-eating kinematics to a novel ecological niche

The origins of novel trophic specialization, in which organisms begin to exploit resources for the first time, may be explained by shifts in behavior such as foraging preferences or feeding kinematics. One way to investigate behavioral mechanisms underlying ecological novelty is by comparing prey capture kinematics among species. We investigated the contribution of kinematics to the origins of a novel ecological niche for scale-eating within a microendemic adaptive radiation of pupfishes on San Salvador Island, Bahamas. We compared prey capture kinematics across three species of pupfish while they consumed shrimp and scales in the lab, and found that scale-eating pupfish exhibited peak gape sizes twice as large as in other species, but also attacked prey with a more obtuse angle between their lower jaw and suspensorium. We then investigated how this variation in feeding kinematics could explain scale-biting performance by measuring bite size (surface area removed) from standardized gelatin cubes. We found that a combination of larger peak gape and more obtuse lower jaw and suspensorium angles resulted in approximately 40% more surface area removed per strike, indicating that scale-eaters may reside on a performance optimum for scale biting. To test whether feeding performance could contribute to reproductive isolation between species, we also measured F1 hybrids and found that their kinematics and performance more closely resembled generalists, suggesting that F1 hybrids may have low fitness in the scale-eating niche. Ultimately, our results suggest that the evolution of strike kinematics in this radiation is an adaptation to the novel niche of scale eating.

Recombining Your Way Out of Trouble: The Genetic Architecture of Hybrid Fitness under Environmental Stress

Hybridization between species can either promote or impede adaptation. But we know very little about the genetic basis of hybrid fitness, especially in nondomesticated organisms, and when populations are facing environmental stress. We made genetically variable F2 hybrid populations from two divergent Saccharomyces yeast species. We exposed populations to ten toxins and sequenced the most resilient hybrids on low coverage using ddRADseq to investigate four aspects of their genomes: 1) hybridity, 2) interspecific heterozygosity, 3) epistasis (positive or negative associations between nonhomologous chromosomes), and 4) ploidy. We used linear mixed-effect models and simulations to measure to which extent hybrid genome composition was contingent on the environment. Genomes grown in different environments varied in every aspect of hybridness measured, revealing strong genotype–environment interactions. We also found selection against heterozygosity or directional selection for one of the parental alleles, with larger fitness of genomes carrying more homozygous allelic combinations in an otherwise hybrid genomic background. In addition, individual chromosomes and chromosomal interactions showed significant species biases and pervasive aneuploidies. Against our expectations, we observed multiple beneficial, opposite-species chromosome associations, confirmed by epistasis- and selection-free computer simulations, which is surprising given the large divergence of parental genomes (∼15%). Together, these results suggest that successful, stress-resilient hybrid genomes can be assembled from the best features of both parents without paying high costs of negative epistasis. This illustrates the importance of measuring genetic trait architecture in an environmental context when determining the evolutionary potential of genetically diverse hybrid populations.

Interspecific hybridization can generate functional novelty in cichlid fish

The role of interspecific hybridization in evolution is still being debated. Interspecific hybridization has been suggested to facilitate the evolution of ecological novelty, and hence the invasion of new niches and adaptive radiation when ecological opportunity is present beyond the parental species niches. On the other hand, hybrids between two ecologically divergent species may perform less well than parental species in their respective niches because hybrids would be intermediate in performance in both niches. The evolutionary consequences of hybridization may hence be context-dependent, depending on whether ecological opportunities, beyond those of the parental species, do or do not exist. Surprisingly, these complementary predictions may never have been tested in the same experiment in animals. To do so, we investigate if hybrids between ecologically distinct cichlid species perform less well than the parental species when feeding on food either parent is adapted to, and if the same hybrids perform better than their parents when feeding on food none of the species are adapted to. We generated two first-generation hybrid crosses between species of African cichlids. In feeding efficiency experiments we measured the performance of hybrids and parental species on food types representing both parental species niches and additional 'novel' niches, not used by either of the parental species but by other species in the African cichlid radiations. We found that hybrids can have higher feeding efficiencies on the 'novel' food types but typically have lower efficiencies on parental food types when compared to parental species. This suggests that hybridization can generate functional variation that can be of ecological relevance allowing the access to resources outside of either parental species niche. Hence, we provide support for the hypothesis of ecological context-dependency of the evolutionary impact of interspecific hybridization.

Evolution of a soft-tissue foraging adaptation in African cichlids: Roles for novelty, convergence, and constraint

Understanding the origins of biodiversity demands consideration of both extrinsic (e.g., ecological opportunity) and intrinsic (e.g., developmental constraint) factors. Here, we use a combination of phylogenetic and genetic tools to address the origin of novelty in African cichlids. In particular, we focus on an extreme hypertrophied snout that is structurally integrated with the upper jaw. We show that this bizarre trait has evolved independently in at least two distinct and ecologically successful cichlid clades. We find that snout dimensions are decoupled both phenotypically and genetically, which has enabled it to evolve independently in multiple directions. Further, patterns of variation among species and within a genetic mapping pedigree suggest that relative to snout length, depth is under greater genetic and/or developmental constraint. Models of evolution suggest that snout shape is under selection for feeding behavior, with snout depth being important for algae scraping and snout length for sand sifting. Indeed, the deep snout of some algivores is achieved via an expansion of the intermaxillary ligament, which is important for jaw stability and may increase feeding performance. Overall, our data imply that the evolution of exaggerated snout depth required overcoming a genetic/developmental constraint, which led to expanded ecological opportunity via foraging adaptation.

Pleiotropic jaw morphology links the evolution of mechanical modularity and functional feeding convergence in Lake Malawi cichlids

Complexity in how mechanistic variation translates into ecological novelty could be critical to organismal diversification. For instance, when multiple distinct morphologies can generate the same mechanical or functional phenotype, this could mitigate trade-offs and/or provide alternative ways to meet the same ecological challenge. To investigate how this type of complexity shapes diversity in a classic adaptive radiation, we tested several evolutionary consequences of the anterior jaw four-bar linkage for Lake Malawi cichlid trophic diversification. Using a novel phylogenetic framework, we demonstrated that different mechanical outputs of the same four jaw elements are evolutionarily associated with both jaw protrusion distance and jaw protrusion angle. However, these two functional aspects of jaw protrusion have evolved independently. Additionally, although four-bar morphology showed little evidence for attraction to optima, there was substantial evidence of adaptive peaks for emergent four-bar linkage mechanics and jaw protrusion abilities among Malawi feeding guilds. Finally, we highlighted a clear case of two cichlid species that have -independently evolved to graze algae in less than 2 Myr and have converged on similar jaw protrusion abilities as well as four-bar linkage mechanics, but have evolved these similarities via non-convergent four-bar morphologies.

Evolutionary diversity as a catalyst for biological discovery

The tremendous diversity of animal behaviors has inspired generations of scientists from an array of biological disciplines. To complement investigations of ecological and evolutionary factors contributing to behavioral evolution, modern sequencing, gene editing, computational and neuroscience tools now provide a means to discover the proximate mechanisms upon which natural selection acts to generate behavioral diversity. Social behaviors are motivated behaviors that can differ tremendously between closely related species, suggesting phylogenetic plasticity in their underlying biological mechanisms. In addition, convergent evolution has repeatedly given rise to similar forms of social behavior and mating systems in distantly related species. Social behavioral divergence and convergence provides an entry point for understanding the neurogenetic mechanisms contributing to behavioral diversity. We argue that the greatest strides in discovering mechanisms contributing to social behavioral diversity will be achieved through integration of interdisciplinary comparative approaches with modern tools in diverse species systems. We review recent advances and future potential for discovering mechanisms underlying social behavioral variation; highlighting patterns of social behavioral evolution, oxytocin and vasopressin neuropeptide systems, genetic/transcriptional "toolkits," modern experimental tools, and alternative species systems, with particular emphasis on Microtine rodents and Lake Malawi cichlid fishes.

Phylogenomics of a putatively convergent novelty: did hypertrophied lips evolve once or repeatedly in Lake Malawi cichlid fishes?

BACKGROUND

Phylogenies provide critical information about convergence during adaptive radiation. To test whether there have been multiple origins of a distinctive trophic phenotype in one of the most rapidly radiating groups known, we used ultra-conserved elements (UCEs) to examine the evolutionary affinities of Lake Malawi cichlids lineages exhibiting greatly hypertrophied lips.

RESULTS

The hypertrophied lip cichlids Cheilochromis euchilus, Eclectochromis ornatus, Placidochromis "Mbenji fatlip", and Placidochromis milomo are all nested within the non-mbuna clade of Malawi cichlids based on both concatenated sequence and single nucleotide polymorphism (SNP) inferred phylogenies. Lichnochromis acuticeps that exhibits slightly hypertrophied lips also appears to have evolutionary affinities to this group. However, Chilotilapia rhoadesii that lacks hypertrophied lips was recovered as nested within the species Cheilochromis euchilus. Species tree reconstructions and analyses of introgression provided largely ambiguous patterns of Malawi cichlid evolution.

CONCLUSIONS

Contrary to mitochondrial DNA phylogenies, bifurcating trees based on our 1024 UCE loci supported close affinities of Lake Malawi lineages with hypertrophied lips. However, incomplete lineage sorting in Malawi tends to render these inferences more tenuous. Phylogenomic analyses will continue to provide powerful inferences about whether phenotypic novelties arose once or multiple times during adaptive radiation.

Selection, hybridization, and the evolution of morphology in the Lake Malaŵi endemic cichlids of the genus Labeotropheus

The cichlid fishes of Lake Malaŵi are the paramount example of adaptive radiation in vertebrates. Evidence of their astounding diversity is perhaps most visible in their adaptations for obtaining food; the genus Labeotropheus, due to their prominent snouts, are an interesting example of an extreme adaptation for feeding. Two different body types are found in this genus: a deep-bodied form (e.g., L. fuelleborni) found most often in turbulent shallow water; and a slender bodied form (e.g., L. trewavasae) found in structurally-complex deep water habitats. Here we test the hypothesis that L. trewavasae should suffer a loss in fitness, measured as growth rate, if raised in turbulence; additionally, we examined growth and morphology of L. fuelleborni and L. fuelleborni x L. trewavasae hybrids under these conditions. We did find the predicted loss of fitness in turbulent-raised L. trewavasae, but found no loss of fitness for L. fuelleborni in either condition; hybrids, due to an unusual morphology, performed better in turbulent as opposed to control conditions. Fitness in turbulent conditions was dependent upon morphology, with deeper bodies and upturned neurocrania allowing a greater growth rate under these conditions. Directional selection on morphology was crucial in the evolution of morphology in the Labeotropheus.

Evolution of skeletal and muscular morphology within the functionally integrated lower jaw adduction system of sculpins and relatives (Cottoidei)

Vertebrate lever mechanics are defined by the morphology of skeletal elements and the properties of their muscular actuators; these metrics characterize functional diversity. The components of lever systems work in coordination ("functional integration") and may show strong covariation across evolutionary history ("evolutionary integration"), both of which have been hypothesized to constrain phenotypic diversity. We quantified evolutionary integration in a functionally integrated system - the lower jaw of sculpins and relatives (Actinopterygii: Cottoidei). Sculpins primarily rely on suction feeding for prey capture, but there is considerable variation in evasiveness of their prey, resulting in variation in anatomy of the lower jaw-closing mechanism. We used functionally-relevant linear measurements to characterize skeletal and muscular components of this system among 25 cottoid species and two outgroup Hexagrammoidei (greenling) species. We quantified evolutionary covariation and correlation of jaw-closing mechanical advantage (i.e., skeletal leverage) and muscle architecture (i.e., gearing) by correlating phylogenetically independent contrasts and fitting phylogenetically corrected generalized least squares models. We found no evidence of evolutionary covariation in muscle architecture and skeletal leverage. While we found a positive evolutionary correlation between out-lever length and adductor muscle fiber length, there was no significant evolutionary correlation between in-lever length and adductor muscle fiber length. We also found a positive evolutionary correlation between in- and out-lever lengths. These results suggest that skeletal morphology and muscle morphology contribute independently to biomechanical diversity among closely related species, indicating the importance of considering both skeletal and muscular variation in studies of ecomorphological diversification.

Identification and validation of FaP1D7, a putative marker associated with the biosynthesis of methyl butanoate in cultivated strawberry (Fragaria x ananassa)

Breeding strawberry (Fragaria x ananassa) with enhanced fruit flavour is one of the top breeding goals of many strawberry-producing countries. Although several genes involved in the biosynthetic pathways of key aroma compounds have been identified, the development and application of molecular markers associated with fruit flavour remain limited. This study aims to identify molecular markers closely linked to genes controlling strawberry aroma. A purpose-built Subtracted Diversity Array (SDA) known as Fragaria Discovery Panel (FDP) was used for marker screening. Polymorphic sequences associated with key aroma compounds were identified from two DNA bulks with extreme phenotypes, established using 50 F₁ progeny plants derived from Juliette X 07-102-41 cross, two strawberry genotypes differing in aroma profile. A total of 49 polymorphic markers for eight key aroma compounds were detected using genotypic data of the extreme DNA bulks and phenotypic data obtained from gas chromatography-mass spectrometry (GC-MS). A similarity search against the physical maps of Fragaria vesca revealed that FaP1D7 is linked to genes potentially involved in the synthesis of methyl butanoate. A C/T SNP was detected within the feature, which could possibly be converted to a molecular tool for rapid screening of the strawberry accessions for their methyl butanoate production capacity.

The Integrated Genomic Architecture and Evolution of Dental Divergence in East African Cichlid Fishes (Haplochromis chilotes x H. nyererei)

The independent evolution of the two toothed jaws of cichlid fishes is thought to have promoted their unparalleled ecological divergence and species richness. However, dental divergence in cichlids could exhibit substantial genetic covariance and this could dictate how traits like tooth numbers evolve in different African Lakes and on their two jaws. To test this hypothesis, we used a hybrid mapping cross of two trophically divergent Lake Victoria species (Haplochromis chilotes × Haplochromis nyererei) to examine genomic regions associated with cichlid tooth diversity. Surprisingly, a similar genomic region was found to be associated with oral jaw tooth numbers in cichlids from both Lake Malawi and Lake Victoria. Likewise, this same genomic location was associated with variation in pharyngeal jaw tooth numbers. Similar relationships between tooth numbers on the two jaws in both our Victoria hybrid population and across the phylogenetic diversity of Malawi cichlids additionally suggests that tooth numbers on the two jaws of haplochromine cichlids might generally coevolve owing to shared genetic underpinnings. Integrated, rather than independent, genomic architectures could be key to the incomparable evolutionary divergence and convergence in cichlid tooth numbers.