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PubMed2004

Effects of genetic drift on variance components under a general model of epistasis.

We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.

Analysis of Variance↗
PubMedDate not supplied

Strong founder effect in Drosophila pseudoobscura colonizing New Zealand from North America.

The North American native species Drosophila pseudoobscura was first identified in New Zealand in the last few decades. Here, we have studied the genetic consequences of its spread across the Pacific Ocean. Using 10 microsatellites that are highly variable in North American populations, we found that the New Zealand population has substantially fewer alleles, a much lower average heterozygosity, and significantly different allele frequencies at these loci. We have discussed the relative sensitivity of these parameters for detecting the founding event. X-linked loci were more strongly differentiated between continents than autosomal loci, as reflected by larger changes in allele frequencies and greater reductions in numbers of alleles and average heterozygosity. The severity of the genetic diversity loss supports a scenario of a few D. pseudoobscura females being introduced to New Zealand from North America.

Alleles↗
PubMed1980

Analyzing gene-frequency data when the effective population size is finite.

The statistical methods used by SCHAFFER, YARDLEY and ANDERSON (1977) and by GIBSON et al. (1979) to analyze the variation in allele frequencies in two common types of experimental procedure, where the effective population size is finite, are extended to a more general situation involving a greater range of experiments. The analysis developed is more sensitive in detecting changes in allele frequency due to both fluctuating and balancing selection, as well as to directional selection. The error involved in many studies due to ignoring the effective population size structure would appear to be large. The range of hypothesis that can be considered may be increased as well. Finally, the method of determining bounds for the effective population size, when a particular genetic model is known to hold for a data set, is also outlined.

Alleles↗
PubMed1973

Patterns of gene variation in central and marginal populations of Drosophila robusta.

The central and marginal populations of D. robusta differ greatly in the level of inversion polymorphism; the marginal populations are monomorphic or nearly so and the central populations are highly polymorphic. This paper presents the frequencies of alleles at forty gene loci in various populations of D. robusta, studied by electrophoresis of proteins and enzymes. Population samples were obtained from eight widely separated populations of D. robusta which included the central, the extreme marginal and the intervening populations between the center and the margins. We find that the proportion of polymorphic loci and average heterozygosity per individual is slightly higher in the marginal populations than the central populations. In D. robusta on an average, 39% of the loci are polymorphic and the average proportion of loci heterozygous per individual is 11%. A breakdown of loci in three categories, viz, hydrolytic enzymes and some other enzymes, larval proteins and glycolytic and Kreb's cycle enzymes, shows that in all populations the level of polymorphism is highest in the hydrolytic enzymes, intermediate in larval proteins and least in the glycolytic and Kreb's cycle enzymes. On the average, the proportion of loci heterozygous per individual for three groups of loci is: hydrolytic enzymes and others (.164), larval proteins (.115) and glycolytic and Kreb's cycle enzymes (.037). We also observe that in all populations the level of polymorphism on the X chromosome is far less than the expected 38%; in salivary gland cells the euchromatic length of the X chromosome is 38% of the entire genome. Lower levels of polymorphism for the X chromosome loci are explained due to low probability of balanced polymorphisms for the X-linked loci since the conditions for establishment of balanced polymorphism for X-linked loci are more restrictive than for the autosomal loci.-The polymorphic loci can be grouped according to pattern of allele frequencies in different populations as follows: (1) The allele frequencies are similar in all populations at the XDH, Pep-1 and Hex-1 loci. (2) The alleles at the Est-1, Est-2, Amy loci and the AP-4(1.0) and the LAP-1(.90) alleles show north south clinal change in frequency. (3) There is north south and east west differentiation at the Pt-5, Pt-8 and Pt-9 loci and the allele AP-4(.81). (4) Polymorphism at loci such as Fum, B.Ox, Hex-8, Pep-2 and Pep-3 are restricted to only one or two of the populations. (5) Allele frequencies at the MDH and ODH loci fluctuate between populations. (6) Allele frequencies at many polymorphic loci such as Est-1, Est-2, LAP-1, AP-4, Pt-5, Pt-8, Pt-9, Pt-16, MDH, Fum change clinally within a gene arrangement. The pattern of gene variation in D. robusta is very complex and cannot be easily explained due to migration of neutral alleles between once-isolated populations or to semi-isolation of neutral alleles. The observations of the pattern of allele variation in different populations, high levels of polymorphism in the marginal populations which have small population size and low levels of polymorphism of the X chromosome loci all support the argument in favor of balancing selection as the main mechanism for the maintenance of these polymorphisms. Environmental factors must play a role in the maintenance of a great deal of these polymorphisms, since we observe clinal allele frequency changes even within a given inversion type.

Acid Phosphatase↗
PubMedDate not supplied

Lactate dehydrogenase: a polymorphism of Anoplarchus purpurescens: geographic variation in central California.

Previous studies on the muscle lactate dehydrogenase polymorphism of the stichaeid fish Anoplarchus purpurescens in Puget Sound have demonstrated the existence of a clinal pattern of allele frequency. The LDH-A' allele was observed to increase toward the south, with several environmental factors showing correlation with this change in allele frequency. Populations from California were sampled in the present study to determine whether or not gene frequencies along an independent transect near the southern end of the species distribution are consistent with the interpretation that the geographic patterns reflect the influence of environmental factors. In California, the LDH-A' allele decreases in frequency to the south. This observation necessitates the reevaluation of possible environmental influences on the LDH polymorphism. Only one of several proposed hypotheses is completely consistent with the geographic patterns observed along both the Washington and California transects. However, the genetic differentiation along the California coast cannot be unequivically ascribed to the influence of environmental factors; current morphological data indicate the possibility of historical influences on the population genetic structure of California A. purpurescens.

Animals↗
PubMedDate not supplied

The mode of evolution of molecular markers in populations of house mice under artificial selection for locomotor behavior.

A complete understanding of the mode of evolution of molecular markers is important for making inferences about different population genetic parameters, especially because a number of studies have reported patterns of allelic variation at molecular markers that are not in agreement with neutral evolutionary expectations. In the present study, house mice (Mus domesticus) from the fourteenth generation of a selection experiment for increased voluntary wheel-running activity were used to test how selection on a complex behavior affects the distribution of allelic variation by examining patterns of variation at six microsatellite and four allozyme loci. This population had a hierarchical structure that allowed for simultaneous testing of the effects of selection and genetic drift on the distribution of allelic variation by comparing observed patterns of allele frequencies and estimates of genetic divergence at multiple hierarchical levels to expectations under models of neutral evolution. The levels of genetic divergence among replicate lines and between selection groups, estimated from microsatellite data or pooled microsatellite and allozyme data, were not significantly different from expectations under neutral evolution. Furthermore, the pattern of change of allele frequencies between the base population and generation 14 was largely in agreement with expectations under neutral evolution (although the PGM locus exhibited a pattern of change within populations that was difficult to explain under neutral evolution). Overall the results generally provide support for the neutral evolution of molecular markers.

Animals↗
PubMed1993

Major histocompatibility complex class IV restriction fragment length polymorphism markers in replicated meat-type chicken lines divergently selected for high or low early immune response.

Information on MHC may improve the efficiency of selection for immunological traits via the application of marker assisted selection or by selecting directly for a specific restriction fragment length polymorphism (RFLP) band or MHC haplotype. An experimental procedure is presented here for identifying MHC genes that are related to early immune response. A Class IV cDNA clone was used to probe Southern blots of erythrocyte genomic DNA from chickens. Chickens were taken from the second (S2) and third (S3) generations of replicated lines divergently selected for high antibody response (HC1, HC2) or low antibody response (LC1, LC2) to Escherichia coli vaccination at 10 days of age. These selection criteria have been found to be associated with other immunological parameters. The hypothesis that these selected lines differ in their MHC loci was evaluated by comparing the frequencies of MHC RFLP markers (single RFLP bands) and haplotypes (patterns of RFLP bands). The significant differences between LC and HC in the frequency of many MHC RFLP bands and of five MHC haplotypes indicate that early antibody production is influenced by MHC genes. The reliability of the association between the selection and frequency differences was tested and proven in most cases by analysis of the replicated lines. These differences in RFLP markers represent a change in allelic frequencies in MHC genes, probably due to selection. The results imply a connection between the Class IV genes and early antibody production, and they show the potential of prospective breeding not only by immunological phenotype but also by genotype (i.e., using RFLP markers of the MHC).

Animals↗
PubMed1998

Distribution of allelic forms of erythrocyte H1 histones in Japanese quail populations divergently selected for amount of weight loss after transient starvation.

Three polymorphic subtypes of erythrocyte histone H1 (H1.a, H1.b, and H1.z) were analyzed using a sodium dodecyl sulfate polyacrylamide gel in quail populations divergently selected for a high (line 1) or low (line 2) reduction in body mass following temporary food withdrawal. Both H1.b and H1.z histone alleles were found to be differently distributed in these populations during the selection period. The frequency of b1 in line 2 was approximately 1.9-2.8 times lower than in line 1 and approached the values in line 1 when the selection was suspended. Similarly, the frequency of allele z2 at locus H1.z increased significantly (about 1.6-2.3 times) in line 2 during selection and returned to the initial values when selection was stopped. On the other hand, allele a0 at locus H1.a was kept at relatively low levels (usually below 0.05) in both lines during selection. At that time its level was approximately three to four times lower than in a random mating control population. When selection was suspended, the frequency of a0 in line 1 increased significantly, approaching the values in the control line, and remained essentially unchanged in line 2. Thus, all three polymorphic histone H1 loci in quail responded through changes in allele frequencies to the breeding selection, which was directed at the amount of body weight loss upon transient starvation. It seems that either H1 histone locus could be linked to loci controlling the rate of body weight reduction following starvation or weight loss during fasting might be influenced by a panel of H1 histone alleles that can contribute to functional differences in avian chromatin.

Alleles↗
PubMed2000

Empirical Bayes procedure for estimating genetic distance between populations and effective population size.

We developed an empirical Bayes procedure to estimate genetic distances between populations using allele frequencies. This procedure makes it possible to describe the skewness of the genetic distance while taking full account of the uncertainty of the sample allele frequencies. Dirichlet priors of the allele frequencies are specified, and the posterior distributions of the various composite parameters are obtained by Monte Carlo simulation. To avoid overdependence on subjective priors, we adopt a hierarchical model and estimate hyperparameters by maximizing the joint marginal-likelihood function. Taking advantage of the empirical Bayesian procedure, we extend the method to estimate the effective population size using temporal changes in allele frequencies. The method is applied to data sets on red sea bream, herring, northern pike, and ayu broodstock. It is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis. The joint marginal-likelihood function also estimates the rate of gene flow into island populations.

Algorithms↗
PubMed2025

Genome-wide Parallelism Underlies Rapid Freshwater Adaptation Fueled by Standing Genetic Variation in a Wild Fish.

A fundamental focus of ecological and evolutionary biology is determining how natural populations adapt to environmental changes. Rapid parallel phenotypic evolution can be leveraged to uncover the genetics of adaptation. Using population genomic approaches, we investigated the genetic architecture underlying rapid parallel freshwater adaptation of Neosalanx brevirostris by comparing four freshwater-resident populations with their common ancestral anadromous population. We demonstrated that the rapid parallel adaptation to freshwater followed a complex polygenic architecture and was characterized by genomic-level parallelism, which proceeded predominantly through repeated selection on the preexisting standing genetic variations. Frequencies of the genome-wide adaptive standing variations were moderate in the ancestral anadromous population, which had pre-adapted to fluctuating salinities. Relatively large allele frequency shifts were observed at some adaptive single-nucleotide polymorphisms (SNPs) during parallel adaptation to freshwater environments, with a large fraction of freshwater-favored alleles being fixed or nearly fixed. These adaptive SNPs were involved in multiple biological functions associated with osmoregulation, immunoregulation, locomotion, metabolism, etc., which were highly consistent with the polygenic architecture of adaptive divergence between the two ecotypes involving multiple complex physiological and behavioral traits. This work provides insight into the mechanisms by which natural populations rapidly evolve to changes in the environment and highlights the importance of standing genetic variation for the evolutionary potential of populations facing global environmental changes.

Animals↗
PubMed2003

Dynamics of molecular markers linked to the resistance loci in a mosquito-Plasmodium system.

Models on the evolution of resistance to parasitism generally assume fitness tradeoffs between the costs of being parasitized and the costs associated with resistance. This study tested this assumption using the yellow fever mosquito Aedes aegypti and malaria parasite Plasmodium gallinaceum system. Experimental mosquito populations were created by mixing susceptible and resistant strains in equal proportions, and then the dynamics of markers linked to loci for Plasmodium resistance and other unlinked neutral markers were determined over 12 generations. We found that when the mixed population was maintained under parasite-free conditions, the frequencies of alleles specific to the susceptible strain at markers closely linked to the loci for resistance (QTL markers) as well as other unlinked markers increased significantly in the first generation and then fluctuated around equilibrium frequencies for all six markers. However, when the mixed population was exposed to an infected blood meal every generation, allele frequencies at the QTL markers for resistance were not significantly changed. Small population size caused significant random fluctuations of allele frequencies at all marker loci. Consistent allele frequency changes in the QTL markers and other unlinked markers suggest that the reduced fitness in the resistant population has a genome-wide effect on the genetic makeup of the mixed population. Continuous exposure to parasites promoted the maintenance of alleles from the resistant Moyo-R strain in the mixed population. The results are discussed in relation to the proposed malaria control strategy through genetic disruption of vector competence.

Aedes↗
PubMed2002

Perspective: Here's to Fisher, additive genetic variance, and the fundamental theorem of natural selection.

Fisher's fundamental theorem of natural selection, that the rate of change of fitness is given by the additive genetic variance of fitness, has generated much discussion since its appearance in 1930. Fisher tried to capture in the formula the change in population fitness attributable to changes of allele frequencies, when all else is not included. Lessard's formulation comes closest to Fisher's intention, as well as this can be judged. Additional terms can be added to account for other changes. The "theorem" as stated by Fisher is not exact, and therefore not a theorem, but it does encapsulate a great deal of evolutionary meaning in a simple statement. I also discuss the effectiveness of reproductive-value weighting and the theorem in integrated form. Finally, an optimum principle, analogous to least action and Hamilton's principle in physics, is discussed.

Gene Frequency↗
PubMed2001

Distinguishing two types of gray mullet, Mugil cephalus L. (Mugiliformes: Mugilidae), by using glucose-6-phosphate isomerase (GPI) allozymes with special reference to enzyme activities.

The resident and migratory types of gray mullet, Mugil cephalus, on the coast of Taiwan can not be separated morphologically. Allozyme analysis was applied to estimate genetic variation between the two types of gray mullet and to test whether they belong to different populations. After starch gel electrophoresis, different allelic frequency spectra of glucose-6-phosphate isomerase-A (GPI-A) between stocks was observed. The resident stock contained Gpi-A(135) and Gpi-A(100), whereas the migratory type contained Gpi-A(100) only. In addition, GPI activities of locus A showed two distinct profiles between the two alleles. The results broadly revealed that Gpi-A allelic frequency was not regulated by temperature changes even after 6 months of thermal acclimation. This suggests that natural selection may play a role in shaping the allelic frequency change during the migratory journey. These findings suggest that the Gpi-A allelic difference can be used for population discrimination.

Acclimatization↗
PubMed2001

Analysis of haemochromatosis gene mutations in a population from the Mediterranean Basin.

BACKGROUND/AIMS: The C282Y mutation in the haemochromatosis gene (HFE) located on chromosome 6 has been identified as the main genetic basis of hereditary haemochromatosis (HH). Two more mutations of that gene, H63D and S65C, appear to be associated with milder forms of HH. A high allele frequency for C282Y and H63D mutations was reported in populations from North Europe, while incomplete information is available for individuals from the Mediterranean Basin where C282Y homozygotes comprise a smaller percentage of HH cases. In this study we investigated the allele frequency of HFE mutations and the association between HFE mutations and cases of HH in a population from the South of Italy (Sicily and Calabria). In addition, we evaluated a possible association between HFE mutations and either chronic liver disease or type II diabetes. PATIENTS AND METHODS: Three hundred and twenty-seven individuals (654 chromosomes) were tested for C282Y, H63D and S65C mutations of the HFE gene by restriction fragment length polymorphism. Four had HH, 23 had hepatocellular carcinoma, 100 had chronic liver disease, 100 had type II diabetes, and 100 were healthy controls. RESULTS: Both C282Y and S65C mutations were each detected in one of the 654 chromosomes analysed (allele frequency=0.15%), while H63D change was found in 122 chromosomes (allele frequency=18.6%) and was equally distributed in all the categories examined. One healthy individual had compound heterozygosity for C282Y and H63D mutations. The frequency of C282Y in this Southern Italian sample was the lowest yet reported for a population of European origin. None of the four HH patients was either homozygous or heterozygous for C282Y. CONCLUSIONS: In Mediterranean populations from Southern Italy the C282Y mutation occurs sporadically and HFE polymorphisms seem to have little diagnostic relevance.

Chromosomes, Human, Pair 6↗
PubMed2000

Dieldrin resistance in Lucilia cuprina (the australian sheep blowfly): chance, selection and response.

Discrete-generation population cages of Lucilia cuprina were initiated with dieldrin-resistant allele (Rdl ) frequencies of 1 or 5% and maintained for 17 generations on media with concentrations of dieldrin in the range 0-0.006% (w/v). The probability of the initial establishment of the Rdl allele in a population was consistently greater at the 5% frequency and dependent on the concentration of dieldrin in the medium for both starting frequencies. Once the resistant allele was established responses to selection were concentration-dependent. It was concluded that in the absence of dieldrin the susceptible allele was selectively favoured, at 0. 00005% (w/v) concentration selection and random genetic drift influenced changes in allele frequency and at concentrations above this the Rdl allele was at a selective advantage. Fixation of Rdl occurred at the higher concentrations. The influence of random genetic drift and selection on the genetic response during the evolution of insecticide resistance is discussed.

Alleles↗
PubMed1986

[Evolution of the dominance of rec-loci. A mathematical model].

The possibility of evolutionary explanation of dominance relations for alleles in selective-neutral rec-loci was explored by means of numerical experiments. It was shown that selection for two-loci fitness system causing the secondary (induced) selection for the rec-system, results in changing the allele frequency of the second-level modificator gene controlling the dominance relations in the rec-locus. The dominance of rec-allele, providing the favourable for the given conditions level of crossing-over between selected fitness loci, is established, due to these changes. It was found that the neutral dominance modificator can influence the dynamics of the whole system.

Animals↗
PubMed2001

The frequency of founder mutations in the BRCA1, BRCA2, and APC genes in Australian Ashkenazi Jews: implications for the generality of U.S. population data.

BACKGROUND: Several studies have shown that Ashkenazi Jews in the United States and Israel have a high prevalence of the founder mutations BRCA1 185delAG, BRCA1 5382insC, BRCA2 6174delT, and APC I1307K at frequencies of 1.0--1.1%, 0.2--0.3%, 0.6--1.4%, and 6.1--7.0%, respectively. The objective of this study was to compare the prevalence of these alleles in the Australian Jewish population with that of U.S. Jews. Australian Jews have a different history of migration, with less opportunity for changes in allele frequency due to conversion or intermarriage with non-Jewish Australians. The results obtained therefore can be used to assess whether U.S. data can be generalized to other Jewish populations. SUBJECTS AND METHODS. Subject samples were ascertained through a screening program for Tay-Sachs disease as part of a community-based screening program in New South Wales and Victoria. DNA extracted from 1200 deidentified blood samples was tested using amplification refractory mutation system polymerase chain reaction. RESULTS: The allele frequencies found were as follows: BRCA1 185delAG 1.25% (95% confidence interval [CI], 0.62--1.88%), BRCA1 5382insC 0.25% (95% CI, 0--0.53%), BRCA2 6174delT 1.08% (95% CI, 0.50--1.67%), and APC I1307K 8.67% (95% CI, 7.07--10.26%). The prevalence of breast carcinoma predisposition alleles therefore is greater than 2.5% in Australian Ashkenazim. CONCLUSIONS: There were no significant differences between the allele frequencies in Australian Ashkenazim and those identified in other studies with similar ascertainment strategies, despite the different migration patterns of Australian Jews. This suggests the broad applicability of the U.S. and Israeli data, not only to Australian Ashkenazim, but also to Ashkenazi communities throughout the world.

Adult↗
PubMed1983

Accuracy of estimated phylogenetic trees from molecular data. II. Gene frequency data.

The accuracies and efficiencies of three different methods of making phylogenetic trees from gene frequency data were examined by using computer simulation. The methods examined are UPGMA, Farris' (1972) method, and Tateno et al.'s (1982) modified Farris method. In the computer simulation eight species (or populations) were assumed to evolve according to a given model tree, and the evolutionary changes of allele frequencies were followed by using the infinite-allele model. At the end of the simulated evolution five genetic distance measures (Nei's standard and minimum distances, Rogers' distance, Cavalli-Sforza's f theta, and the modified Cavalli-Sforza distance) were computed for all pairs of species, and the distance matrix obtained for each distance measure was used for reconstructing a phylogenetic tree. The phylogenetic tree obtained was then compared with the model tree. The results obtained indicate that in all tree-making methods examined the accuracies of both the topology and branch lengths of a reconstructed tree (rooted tree) are very low when the number of loci used is less than 20 but gradually increase with increasing number of loci. When the expected number of gene substitutions (M) for the shortest branch is 0.1 or more per locus and 30 or more loci are used, the topological error as measured by the distortion index (dT) is not great, but the probability of obtaining the correct topology (P) is less than 0.5 even with 60 loci. When M is as small as 0.004, P is substantially lower. In obtaining a good topology (small dT and high P) UPGMA and the modified Farris method generally show a better performance than the Farris method. The poor performance of the Farris method is observed even when Rogers' distance which obeys the triangle inequality is used. The main reason for this seems to be that the Farris method often gives overestimates of branch lengths. For estimating the expected branch lengths of the true tree UPGMA shows the best performance. For this purpose Nei's standard distance gives a better result than the others because of its linear relationship with the number of gene substitutions. Rogers' or Cavalli-Sforza's distance gives a phylogenetic tree in which the parts near the root are condensed and the other parts are elongated. It is recommended that more than 30 loci, including both polymorphic and monomorphic loci, be used for making phylogenetic trees. The conclusions from this study seem to apply also to data on nucleotide differences obtained by the restriction enzyme techniques.

Algorithms↗