Population genetic structure of Nantucket pine tip moth

Summary Variation at polymorphic isozyme loci was analyzed in Nantucket pine tip moth (NPTM) populations from 5 geographic locations. At the North Carolina location, populations representing 3 generations at 3 local sites were also studied. Four of the loci investigated (LAP, MDH, -GPDH and AK), although variable, had few alleles per locus (3–5) and few differences among populations in allele frequencies. At each locus, all populations had the same allele at a high frequency.At the PGM locus, fifteen alleles were identified and allelic frequencies varied among populations. At least eight alleles were present within a population and, in most populations, two or more alleles had high frequencies that differed among populations. An excess of homozygotes over Hardy-Weinberg expectations was found for 7 out of the 10 populations studied, indicating the probable existence of some form of inbreeding structure or populational subdivision within sampled stands.Joint consideration of the results observed for PGM and the other four loci is counterindicative of neutrality at all loci and strongly indicative of genetic differentiation among locally disjunct populations.Published as Paper No. 6751 of the Journal Series of the North Carolina Agricultural Research Service     

Allozyme polymorphism of Mdh and α-Gpdh in Ixodes ricinus populations: comparison of borreliae-infected and uninfected ticks

Ixodes ricinus Linnaeus (Acari: Ixodidae) ticks are vectors of numerous infectious diseases in humans and animals. The allozyme variability of MDH and α-Gpdh was detected by native polyacrylamide gel electrophoresis in I. ricinus natural populations in three localities in Serbia. Four alleles of Mdh locus (MDH 1, MDH 2, MDH 3 and MDH X) and four alleles of α-Gpdh locus (VS, S, F and VF) were detected. Interpopulation differences in Mdh and α-Gpdh allele frequencies were statistically insignificant. Significant difference in α-Gpdh allele frequencies between males and females was recorded in the largest sample only. Differences in allele frequencies, detected between borreliae-infected and uninfected I. ricinus ticks, were close to the level of statistical significance, especially for α-Gpdh locus. Clear significant difference appeared in females when sexes were tested separatelly (P = 0.037). It is interesting that genotypes containing rarer alleles (MDH 1 and S) were infected in higher proportion in comparison to other genotypes. Our results point towards a possible role of Mdh and α-Gpdh loci in I. ricinus ticks in the determination of energy requirements for host seeking. Sex differences in α-Gpdh allele frequencies suggest that selective pressure, concerning efficiency of reserve materials utilisation, points to α-Gpdh rather than to Mdh locus.     

Genetics and polymorphism of a duplicated malate dehydrogenase (MDH) locus in the grasshopperOxya japonica japonica (Orthoptera:Acrididae:Oxyinae)

A biochemical genetic study of the enzyme malate dehydrogenase (MDH) was conducted in the grasshopperOxya j. japonica. Analysis of MDH electrophoretic variation in this species of grasshopper shows that one of the two autosomal loci for MDH in grasshoppers, the Mdh-2 locus, controlling the anodal set of MDH isozymes, is duplicated. Results of breeding studies confirm this and the observed polymorphism at theMdh-2 locus in the two populations ofOxya j. japonica studied can be attributed to three forms of linked alleles at the duplicated locus in equilibrium in both populations. In this respect, all individuals of this species possess heterozygous allelic combinations at the duplicatedMdh-2 locus, which may account for the spread of the duplicated locus in the populations of this species of grasshopper.This research was supported by a grant (Vote F) from the University of Malaya, Kuala Lumpur.     

GENETIC CONSEQUENCES OF AUTOPOLYPLOIDY IN TOLMIEA (SAXIFRAGACEAE)

Although there is an extensive literature on the genetic attributes of allopolyploids, very little information is available regarding the genetic consequences of autopolyploidy in natural populations. We therefore addressed the major predicted genetic consequences of autopolyploidy using diploid and tetraploid populations of Tolmiea menziesii. Individual autotetraploid plants frequently maintain three or four alleles at single loci: 39% of the 678 tetraploid plants exhibited three or four alleles for at least one locus. Heterozygosity was also significantly higher in autotetraploid populations than in diploid populations: H_° = 0.070 and 0.237 in diploid and tetraploid Tolmiea, respectively. Most of the genetic diversity in T. menziesii is maintained within populations (ratio of gene diversity within populations to mean total genetic diversity = 0.636). The total genetic diversity due to differentiation between the two cytotypes is only 0.055. Such a low degree of differentiation between cytotypes would be expected between a diploid and its autotetraploid derivative. Most diploid and all tetraploid populations examined are in genetic equilibrium. Diploid and tetraploid Tolmiea share three or four alleles at six of eight polymorphic loci. This suggests that either autotetraploid Tolmiea was formed via crossing of genetically different diploids (perhaps via a triploid intermediate) or autopolyploidy occurred more than once in separate individual plants, followed by later crossing of autotetraploids.     

Phenotypic polymorphism and allele differentiation of isozymes in fodder beet,multigerm sugar beet and monogerm sugar beet

Summary Thirteen enzymes (MDH, SDH, LAP, PGM, PX, IDH, GPI, 6PGD, APH, GOT, GDH, ME and SOD) of 3 cultivated beet (B. vulgaris L.) gene pools, comprising 12 accessions of fodder beet, 11 of old multigerm sugar beet and 10 of modern monogerm sugar beet, were investigated using horizontal starch gel electrophoresis. Eleven accessions of primitive or wild B. vulgaris were also included for the comparison of isozymes. Variation in isozyme phenotypes was investigated to detect diversity in the three cultivated forms of beet. Phenotypic variation was observed in all except ME and SOD, which were monomorphic. A high degree of phenotypic polymorphism (Pj) was found in GDH, PGM, IDH, APH and MDH. Differences in phenotypic polymorphism in MDH, GPI and PX were recognized between fodder beet and both sugar beet groups. Average polymorphism for 13 enzymes in both sugar beets was significantly higher than that in fodder beet. For 13 enzymes, the existence of high isozyme diversity in both sugar beet gene pools was revealed. Allele frequencies in 13 alleles of five enzyme-coding loci, Lap, Px-1, Aph-1, Got-2 and Gdh-2, were investigated. New alleles, Px-1 ¹ and Got-2 ¹, were found in fodder beet accessions. No significant differences of average allele frequencies of five loci between fodder beet and both sugar beets were recognized. Several unique alleles and different isozyme phenotypes were observed in the accessions of B. vulgaris ssp. macrocarpa and ssp. adanensis. Future utilization of cultivated beet gene pools for sugar beet breeding is discussed from the viewpoint of genetic resources.     

Allozyme variation within and among populations of onion (Allium cepa L.) from West Africa

Local germplasm of onion (Allium cepa L.) in West Africa is threatened by extinction. Sixteen populations of onion collected in five countries in West Africa were investigated for isozyme polymorphism using four polymorphic enzyme systems (ADH, MDH, 6-PGDH and PGI) among nine enzyme systems assayed. This is the first report on the genetic diversity of local landraces of onion. The inheritance of two dimeric enzyme systems PGI and MDH was demonstrated using F₂ progeny arrays. The PGI system revealed a single locus with three alleles, and the MDH system revealed three loci with four alleles. Four polymorphic systems revealed nine alleles (adh-a1 and a2, mdh-c1 and c2, 6-pgdh-a1 and a2, and pgi-a1, a2 and a3) in the 16 local populations observed. The mean number of alleles per polymorphic locus was 2.25, and 67% of the alleles were present in all populations. Allele 6-pgdh-a2 was present in only two landraces (from Niger and Nigeria); it is considered to be a rare allele (frequency approximately 2%). Among the 16 populations, within-population diversity was greater (90%) than between-population diversity (10%). Genetic distance analyses showed an aggregate of all populations except for two, which originated from Nigeria, an English-speaking country. Received: 24 August 1995 / Accepted: 26 February 2001     

ASSOCIATION BETWEEN QUANTITATIVE TRAITS AND ALLOZYME HETEROZYGOSITY IN A TETRASOMIC SPECIES: DACTYLIS GLOMERATA

Tetraploid individuals of orchardgrass (Dactylis glomerata L. subsp. hispanica Roth.) sampled from a natural population were used to evaluate the correlation between both single and multilocus heterozygosity at 7 enzyme loci, and several quantitative traits (plant size at time of collection, leaf weight, and panicle number in experimental trials). Four hundred and forty-eight plants were studied at the 7 loci and 288 of these individuals were scored for an additional eighth locus. Five genotype classes (monogenic, simplex, and duplex digenic, trigenic, and tetragenic) were distinguished according to their heterozygosity level. Multilocus heterozygosity showed a significant positive correlation with both leaf and panicle yield in experimental conditions, but not with original plant size, which was found to be markedly influenced by environmental microheterogeneity. Multilocus heterozygosity, estimated from both the number of heterozygous loci and the number of distinct alleles per locus, had a significant influence on plant performance. Individual locus effects were positive and significant at two loci (GOT1 and PX1). Panicle number increased regularly with heterozygosity level (from monogenics to tetragenics) at the GOT1 locus, as did leaf weight and panicle number at the PX1 locus. Such variation would be predicted by overdominance at these loci or at linked loci. Significant relationships between leaf yield and heterozygosity level at the GOT1 locus distinguished the homozygotes from the heterozygotes (of any class) and was thus more consistent with inbreeding effects. No significant differences were observed among the five genotype classes for any quantitative trait at the six remaining loci. At both the GOT1 and PX1 loci, heterozygosity had a significant independent effect on leaf weight and panicle number even when the correlation between these traits was removed by analysis of covariance.     

Electrophoretic detection of enzyme variation among Japanese red-coloured spider mites of the genus Tetranychus (Acari: Tetranychidae)

The genetic variation in phosphoglucoisomerase (PGI) and malate dehydrogenase (MDH) was studied in red-pigmented Japanese spider mites of the genus Tetranychus by means of poly-acrylamide gel electrophoresis. The analysis revealed (1) that Tetranychus kanzawai possesses five and three alleles for PGI and MDH, respectively and that PGI allele frequencies clearly differ between the Hokkaido and the Honshu populations (2) that Tetranychus urticae and Tetranychus pueraricola, two closely related species, have different alleles for PGI and (3) that two populations of Tetranychus piercei, a species which had only been found on the islands of Okinawa, were obtained from Honshu and that the PGI locus is fixed for different alleles in the two populations. The two enzyme systems are apparently useful not only for discrimination of spider mite species but also for the detection of intraspecific variation. © Rapid Science Ltd. 1998     

Patterns and levels of genetic differentiation in North American populations of the Alaskan wheatgrass complex

Levels and distribution of genetic variation were assessed using six allozymes in 27 populations of Alaskan wheatgrass (Elymus alaskanus) from different locations in Canada, USA, Greenland and Russia to obtain information on the genetic structure of these populations. The enzyme systems were ACO, DIA, GPI, MDH, PGM and SKD. Allozyme variation at the species level was high, with 64.3% (Ps) of the loci being polymorphic, an average number of alleles per locus of 1.9 (As), and an average genetic diversity of 0.17 (Hes). Differentiation was found in the populations studied, with the following findings: (1) statistically significant differences were found in allele frequencies among populations for every polymorphic locus (P < 0.001); (2) 63% of the total allozyme variation at polymorphic loci was partitioned among populations (GST = 0.63); (3) relatively low mean genetic distances between the populations were obtained (mean D = 0.029); (4) the genetic structure of Russian populations are clearly distinct from the other populations, the cluster and principal component analyses revealed the same genetic patterns of relationships among populations. This study also indicates that E. alaskanus contains different levels of allozyme variation in its populations. Furthermore, some banding patterns at the loci Aco-1, Aco-2, Gpi-2, Mdh-1, Skd-1, Skd-2 can be used as markers to identify individual populations.     

Electrophoretic variability in natural populations of Drosophila melanogaster and Drosophila simulans

Genetic variation at 59 gene loci coding for enzymes (50) and larval proteins (9) has been studied in sympatric populations of Drosophila melanogaster and D. simulans from insular and continental origin. The average number of alleles per locus, the mean proportion of polymorphic loci and the mean heterozygosity are similar both within and between species. There are however some significant differences between D. simulans populations in the genotypic frequencies for four polymorphic loci.     

Allozyme polymorphism and phylogenetic relationships in Apis mellifera subspecies selectively reared in Poland and Bulgaria

The genetic variability of honey bee populations of three subspecies selectively reared in Poland (A. m. carnica and A. m. caucasica) and Bulgaria (A. m. macedonica-type rodopica) was studied using isoenzyme analysis of six enzyme systems (MDH-1, ME, EST-3, ALP, PGM and HK) corresponding to 6 loci. All loci were found to be polymorphic in the studied populations. Three alleles were detected at each locus: MHD-1 (MDH65, MDH80 and MDH100), Me (ME90, ME100 and ME106), EST-3 (EST94, EST100 and EST118), ALP (ALP80 ALP90 and ALP100), PGM (PGM80, PGM100 and PGM114) and HK (HK87, HK100 and HK110). The observed and expected heterozygosities (Ho and He) ranged from 0.196 (A. m. macedonica SM) to 0.265 (A. m. carnica MV) and from 0.224 (A. m. macedonica SM) to 0.273 (A. m. carnica GR), respectively. Allele frequencies of all loci were used to estimate Nei's (1972) genetic distance, which was found to range from 0.003 (between A. m. macedonica TR and SM and between A. m. carnica GR and MV populations) to 0.057 (between A. m. macedonica SM and A. m. caucasica populations). The estimated mean F(ST) value from allozyme data was 0.0364. A UPGMA dendrogram was obtained by genetic distance matrix methods; A. m. macedonica (type rodopica), A. m. carnica and A. m. caucasica populations represented different clades.     

Preliminary data on the genetic differentiation of Mytilus desolationis Lamy 1936 and Aulacomya ater regia Powell 1957 (Bivalvia,mytilidae) in the Kerguelen Islands (Terres Australes et Antarctiques Françaises)

Summary Mussel populations in the Kerguelen Islands constitute an excellent model in which to study genetic differentiation, because of the exceptional geographic position of the islands with consequent very low external gene flow, the variety of biotopes that they occupy and their abundance there. Enzyme polymorphism and the electrophoretic variability of some loci have been studied in four populations of Mytilus desolationis Lamy 1936 and in four other populations of Aulacomya ater regia Powell 1957. In both species 67% of the loci were polymorphic. The electrophoretic variability of ACP-2, LAP-1, LAP-2, PGI and PGM in M. desolationis populations, and of ACP-2, LAP-1, LAP-2 and MDH in A. ater regia populations was analyzed by correspondence analysis. For M. desolationis the four populations studied were found to be heterogeneous; four loci contribute clearly to this differentiation. The populations from sheltered and exposed areas were distinguishable on the basis of the allelic frequencies of LAP-1 and LAP-2. The allelic frequencies of PGI and PGM allow further differentiation of the populations. For A. ater regia the four populations studied were distinguishable on the basis of the allele frequencies of ACP-2 and LAP-1 and the differences could not actually be related to their environmental conditions.     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

Genetic structure of two Turkish brown trout populations

The genetic structure of two brown trout Salmo trutta populations living in Lake Abant in Bolu and Üzüm River in Antalya was determined by examining 15 enzyme coding loci ( AAT, ADH, LDH, MDH, MEP, GPI, PGM and SOD ) using starch gel electrophoresis. Population specific mobilities were observed for the fixed alleles of LDH-B2, mMEP-2 and SOD-1 loci. Polymorphisms in sAA T-4, GPI-B2 loci were observed within the populations. Average heterozygosity of Abant and Antalya populations was 0.0358 and 0.0224 respectively. For LDH-C which is the post glaciation marker locus, the ancestral allele * 105 was found to be fixed in both of the populations. Nei's genetic distance between the two populations was 0.2507 which is the level of genetic distance often found between different species. This difference seems to be due to the presence of unique alleles in the LDH-B2, mMEP-2 and SOD-1 loci of the Abant population, indicating that the conservation of the Abant population and its heterozygosity is of prime importance.     

Isozyme gene markers in Vicia faba L.

Summary This study was conducted to assess the genetic basis of the variability observed for the glutamate oxaloacetate transaminase (GOT), Superoxide dismutase (SOD), esterase (EST), and malate dehydrogenase (MDH) isozyme systems in different open-pollinated Vicia faba varieties. Individual plants showing contrasting zymogram patterns were simultaneously selfed and cross-combined. Crossing was unsuccessful in producing progeny, and only selfed progenies were suitable for genetical analysis of isozyme variability. Three zones of GOT activity were made visible. The isozyme of GOT-2 and GOT-3 zones were dimeric and under the control of three alleles at the Got-2 locus and two alleles at the Got-3 locus, respectively. The isozymes of the GOT-1 zone did not show any variability. Three zones of SOD isozyme activity were made visible. The isozymes occurring in the SOD-1 (chloroplastic isozyme form) and SOD-2 (cytosol isozyme form) zones were dimeric and under the control of two alleles at the Sod-1 and Sod-2 loci. The isozyme visualized in the SOD-3 zone (mitochondrial isozyme form) were tetrameric and under the control of two alleles at the Sod-3 locus. Apparently the isozymes made visible in the most anodal esterase zones EST-1, EST-2, and EST-3 were monomeric, and the occurrence of two alleles at each of two different loci explained the variability observed in the EST-2 and EST-3 zones. For MDH, only two five-banded zymogram pattern types were found, and every selfed progeny showed only one of the two zymogram type, indicating that each individual possessed fixed alleles at the loci controlling MDH isozyme. Got-2, Got-3, Sod-1, Sod-2, and Sod-3 appear to be five new isozyme gene markers that can be useful in Vicia faba breeding for linkage study, varietal fingerprinting, outcrossing rate estimate, and indirect selection for quantitative characters.     

Genetic variability in European <Emphasis Type="Italic">Leptestheria dahalacensis</Emphasis> (Rüppel, 1837) (Crustacea,Branchiopoda, Spinicaudata)

The genetic variability of the gonochoric Leptestheria dahalacensis (Rüppel, 1837) was studied through the analysis of mitochondrial and nuclear (microsatellite loci) markers in eight Italian and two Central European populations. Mitochondrial data exhibited a low variability, as only six mitotypes were scored: five in Italy and one for both Central European samples, with a very low number of substitutions. All analysed microsatellite loci were variable, with 3–5 alleles per locus and 1–4 alleles per population. All populations were at the Hardy–Weinberg equilibrium, with the exceptions of two samples for locus ldAC-16, due to heterozygote excess, and of four populations for locus ldAC-11, probably linked to the presence of null alleles. A substantial population structuring was found between Central European and Italian samples for both utilized markers. This observation may be explained by isolation by distance and/or recent isolation events. On the other hand, the absence of a clear inter-pond variability in Italian sample comparisons may be ascribed to high dispersal ability in the short range. Handling editor: K. Martens     

Genetic basis of tristyly in tetraploid Oxalis alpina (Oxalidaceae)

The inheritance of style‐morphs was investigated in tetraploid populations of tristylous Oxalis alpina (Oxalidaceae) to determine if alleles controlling style‐morphs are expressed at duplicated loci. In tetraploid populations, a dominant S allele leads to expression of the short‐styled phenotype at the short/non‐short locus and is epistatic to the M allele at the mid/long locus. The M allele results in expression of the mid‐styled phenotype but only if the S allele is absent. Long‐styled morphs are homozygous recessive at the short and mid loci. Test crosses of many tetraploid short‐styled individuals resulted in segregations of short‐, mid‐ and long‐styled individuals which, because of linkage between the short and mid loci, can only occur with polyploidy and expression of alleles at duplicated loci. Segregation patterns from three crosses suggest the possibility of disomic inheritance via preferential pairing of chromosomes in tetraploid populations of O. alpina. Segregation patterns in the progeny of mid‐styled individuals indicated that only a few individuals had more than one copy of the M allele, despite the potential for accumulation of M alleles via self‐fertilization of partially self‐compatible mid‐styled morphs in some populations. © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179 , 308–318.     

Mapping of simple sequence repeat (SSR) DNA markers in diploid and tetraploid alfalfa

Cultivated alfalfa (Medicago sativa) is an autotetraploid. However, all three existing alfalfa genetic maps resulted from crosses of diploid alfalfa. The current study was undertaken to evaluate the use of Simple Sequence Repeat (SSR) DNA markers for mapping in diploid and tetraploid alfalfa. Ten SSR markers were incorporated into an existing F₂ diploid alfalfa RFLP map and also mapped in an F₂ tetraploid population. The tetraploid population had two to four alleles in each of the loci examined. The segregation of these alleles in the tetraploid mapping population generally was clear and easy to interpret. Because of the complexity of tetrasomic linkage analysis and a lack of computer software to accommodate it, linkage relationships at the tetraploid level were determined using a single-dose allele (SDA) analysis, where the presence or absence of each allele was scored independently of the other alleles at the same locus. The SDA diploid map was also constructed to compare mapping using SDA to the standard co-dominant method. Linkage groups were generally conserved among the tetraploid and the two diploid linkage maps, except for segments where severe segregation distortion was present. Segregation distortion, which was present in both tetraploid and diploid populations, probably resulted from inbreeding depression. The ease of analysis together with the abundance of SSR loci in the alfalfa genome indicated that SSR markers should be a useful tool for mapping tetraploid alfalfa. Received: 10 September 1999 / Accepted: 11 November 1999     

Polymorphism of Trinucleotide Repeats at Loci FRAXA and FRAXE in the Population of Tomsk

Polymorphism of CGG and GCC trinucleotide repeats, whose expansions at the FRAXA and FRAXE loci have been identified as causative mutations in two forms of mental retardation, was studied in Slavic population of Tomsk. At the FRAXA locus a total of 31 allelic variants ranging from 8 to 56 copies of CGG repeat with two modal classes of 28–29 and 18–20 repeat units (with the frequencies of 24.6 and 11.5% respectively) were revealed. Compared to other populations, this locus was characterized by unusually high frequency of intermediate alleles with the sizes of more than 40 CGG repeat units (12.4%). Since intermediate repeats of the FRAXAlocus were more prone to instability than normal alleles, it was suggested that Slavic population of Siberia had higher risk of the development of FMR1 dynamic mutations, giving rise to the Martin–Bell syndrome. The FRAXE allele frequency distribution was demonstrated to be normal with 18 allelic variants ranging from 9 to 27 GCC repeat units. In the population of Tomsk this locus had higher than in other populations frequency (26.7%) of short (less than 15 repeat units in size) alleles. In addition, in the Tomsk population both loci were characterized by high level of heterozygosity and low frequencies of modal allele classes. These results can be explained by the high level of outbreeding typical of the population of Siberia.     

Ecogeographical distribution of HMW glutenin alleles in populations of the wild tetraploid wheat Triticum turgidum var. dicoccoides

Summary Polymorphism of high molecular weight (HMW) glutenin subunits in 466 accessions of the wild tetraploid wheat Triticum turgidum var. dicoccoides in Israel was characterized with regard to the ecogeographical distribution of the HMW glutenin alleles, both between and within 22 populations, and along transects in a single population. While some populations were monomorphic for all the HMW glutenin loci, namely, Glu-A1-1, Glu-A1-2, Glu-B1-1 and Glu-B1-2, others contained up to four alleles per locus. Intrapopulation variability could be predicted by the geographical distribution: marginal populations tended to be more uniform than those at the center of distribution. The various HMW glutenin alleles tended to be clustered, both at a regional level and within a single population along transects of collection. It is suggested that this clustering is due to selection pressures acting both at a regional and at a microenvironmental level. This was confirmed by the significant correlations found between the MW of subunits encoded by Glu-A1-1 and the populations' altitude, average temperature and rainfall. The possible selective values of seed storage proteins are discussed.