Genetic parameters for agronomic characteristics. I. Early and intermediate breeding populations of true potato seed

The original variation in the source population as well as the selection method may influence the genetic variation in further cycles of genetic improvement. Therefore, the objectives of this research were to determine genetic parameters (variance components and heritability) in source and intermediate stages of a true potato seed (TPS) breeding population and to calculate the genetic and phenotypic correlations in this breeding material developed by the Centro Internacional de la Papa (CIP). The intermediate stage was derived from a source population adapted to the warm lowland tropics plus introduction of exotic germplasm from North America and Europe. Non-additive genetic variation was almost nil for plant survival, tuber yield and tuber shape uniformity in both stages of the breeding population and no quantitative genetic variation for uniformity of tuber color was observed in both source and intermediate breeding materials. Heritability was higher in the intermediate stage than in the source population for plant survival (0.86 vs 0.66), tuber yield (0.30 vs 0.14) and tuber shape (0.77 vs 0.51), but it was the reverse for tuber uniformity (0.11 vs 0.72). These results suggest that potato breeders at CIP were able to keep enough genetic variation for most important characteristics for potato production from true seed in their intermediate breeding materials by adding new sources of variation to the original breeding population. Additive genetic and phenotypic correlations were significant and positive between plant vigor after transplanting and tuber yield, and tuber shape and tuber uniformity, which suggest that high yielding offspring result from early vigorous growth, and that tuber uniformity could depend on tuber shape uniformity in this breeding material.     

Early generation selection for agronomic characters in a potato breeding programme

Summary A random sample of seedlings representing high, medium and poor vigour was studied for tuber colour, tuber shape, eye depth, tuber cracking, tuber yield per plant, average tuber weight and number of tubers per plant in four successive generations (F₁, F₁, F₁C₂, and F₁C₃). Based on the performance of vigour groups in various generations and inter-generation correlation coefficients, we propose a procedure for the elimination of unproductive genotypes early in the breeding programme. The data indicates that seedlings of poor vigour can be discarded at the seedling stage prior to transplantation in the field. The rejection of clones on the basis of tuber colour, tuber shape, eye depth and tuber cracking can also be initiated at the seedling stage. For tuber yield and average tuber weight a negative selection (rejection of poor phenotypes) is suggested from the first clonal generation and for number of tubers, from second clonal generation, until statistically sound replicated trials can be conducted for carrying out positive selection.     

Progeny selection for agronomic characters in early generations of a potato breeding programme

 Repeatabilities of progeny means, and the univariate cross prediction method were used to study the effectiveness of progeny selection for agronomically important characters in early generations of potato (Solanum tuberosum L.) breeding. The study was based on 90 progenies (72 crosses+18 selfs) evaluated for three successive generations, i.e. seedling, first clonal and second clonal generations. Repeatabilities of progeny means were measured as correlation coefficients between generations. In the univariate cross prediction method, progeny means and within-progeny standard deviations were used to calculate the proportions of clones exceeding the target values, and correlation coefficients between generations for predicted and observed proportions of clones, were calculated. Population means varied from generation to generation. Correlation coefficients between generations for progeny means for most of the characters were significant, but moderate. These were higher than the correlation coefficients between predicted and observed proportions of clones exceeding the target values. The possibility of using progeny means as a selection parameter to reduce the number of genotypes to be examined in later stages by rejecting the poor crosses in seedling generation is discussed. Received: 8 January 1997/Accepted: 28 February 1997     

Inbreeding and true seed in tetrasomic potato. IV. Synthetic cultivars

A true potato seed (TPS) synthetic cultivar from open pollination may broaden the genetic base in potato. A synthetic cultivar can also reduce the effect of inbreeding and maintain the productivity from generation to generation. Selected tetraploid parental genotypes, based on combining-ability tests, were chosen for isolated polycrosses to obtain tetraploid offspring. A series of experiments were undertaken to investigate the development of these TPS synthetic populations in two Peruvian locations: San Ramon, a rainfed, humid, mid-altitude environment, and La Molina, an arid, coastal environment under irrigation. Natural open-pollinated synthetics or control-mixture synthetics, involving two to six parents, had a similar tuber set but plant survival and tuber weight were higher in control synthetics including two or six parents. The results suggest that two-parent open-pollinated TPS synthetics may be a feasible option by selecting the right parents for the base population. A subsequent experiment showed that four-parent control synthetics (i.e. double crosses) were the best for tuber weight and size, followed by the two-parent control synthetics. Synthetic breeding populations could be shared with other breeders, who in cooperation with their local farmers may select promising genotypes for further cultivar release. Received: 15 December 2000 / Accepted: 4 April 2001     

Cybrids and tetrad sterility for developing true potato seed hybrids

Potato cybrids result from the fusion between cytoplasm and nuclear gene donors. Such genetic materials are an alternative means to broaden the breeding pool by non‐sexual gene transfer. Tetrad pollen sterility provides also another source of male sterility with some potential for true potato seed breeding. The objective of this research was to investigate cybrid‐derived offspring for both agronomic and reproductive characteristics in two contrasting Peruvian locations, and to examine new exotic germplasm for tetrad sterility, with the aim of broadening the breeding pool available at the Centro Internacional de la Papa (CIP). The cybrids were derived from fusions between Y‐245.7, a clone with tetrad sterility, and Atzimba. These cybrids were crossed with selected male parents from the CIP breeding population, and their hybrid offspring were tested in La Molina (coastal desert) and Huancayo (cool highlands). In addition, other clones with tetrad sterility were also crossed with selected testers to determine their breeding value. There were significant differences for tuber yield, style length, and berry number among the hybrid offspring, and the genotype by environment interaction was significant for tuber yield and berry number. The top 25% highest yielding cybrid‐derived offspring across both locations showed the same tuber yield although they were significantly different for some of the reproductive characteristics. With the exception of one cybrid, the others did not exhibit segregation for tetrad sterility in their hybrid offspring, which were male fertile. However, the offspring derived from crosses between other sources of tetrad sterility and the same testers all showed tetrad sterility, and some of them had outstanding tuber yield at La Molina. The lack of segregation for tetrad sterility in these new crosses suggests that the non‐cybrid, male sterile, female parents are triplex or quadriplex for the Tr nuclear locus, which interacts with a sensitive cytoplasm (e.g. Trs from S. verrucosum or S. stoloniferum) to produce tetrad sterility in potato.     

Inbreeding and true seed in tetrasomic potato. II. Selfing and sib-mating in heterogeneous hybrid populations of Solanum tuberosum

 Inbreeding depression may affect the performance of consecutive generations of potatoes propagated by true potato seed (TPS). The effect of inbreeding was established using selfed and sib-mated generations of five TPS families. Correlation coefficients were calculated between the level of inbreeding and different traits. Inbreeding depression was expressed mainly by pollen viability, as measured by its stainability (r=−0.912, P<0.01), and tuber yield (r=−0.837, 0.01<P<0.05). The results also indicated that without unavoidable selection inbreeding depression is expected to be more evident. Furthermore, the TPS families responded quite differently to inbreeding depression. They did not show the same amount of depression for yield as they did for the characters concerning fertility. The high tuber-yielding families displayed a greater inbreeding depression for tuber yield than the lower-yielding families. Received: 10 November 1997 / Accepted: 3 March 1998     

Producing commercially attractive,uniform true potato seed progenies: the influence of breeding scheme and parental genotype

The production of attractive, uniform true potato seed (TPS) progenies was investigated. Four breeding schemes were compared: intercrossing tetraploid cultivars (cv x cv); doubled dihaploids x cultivars (ddh x cv); cultivars x diploid unreduced-gamete producers (cv x FDR) and doubled dihaploids x diploid unreduced-gamete producers (ddh x FDR). Fifty three progenies and five clones were grown in a glasshouse in a randomised complete block design with three replicates of 25 plants per progeny and clone. Each plant's tubers were counted and the colour, shape, quality of skin finish, flesh colour, and commencai attractiveness (which includes yield) recorded. The most uniform progenies were also selected by visual comparison with the clones. For mean attractiveness, differences (P < 0.001) between breeding schemes and between progenies within breeding schemes were detected. The cv x cv and cv x FDR progenies were more attractive than clonal controls. There were significant additive and non-additive effects for attractiveness in all breeding schemes except cv x FDR. There were between-progeny differences (P < 0.001) for uniformity for all characters. Progenies uniform for one character could be variable for other traits. Breeding schemes gave different levels of uniformity (P < 0.001) for all characters except shape and flesh colour, but none gave low levels of variation for all traits. Doubled-dihaploid parents increased the variation in progenies. There were uniformity differences (P < 0.001) between progenies within breeding schemes for all characters. Evidence of additive and nonadditive genetic variation for uniformity in all traits was detected. In each breeding scheme, parents with good general combining ability (GCA) for uniformity in several characters were identified. Visually selected uniform progenies had parents with good GCAs for uniformity in a range of traits and high specific combining abilities (SCAs) for several traits. A desynaptic first-division restitution (FDR) clone and a male-sterile doubled-dihaploid clone had the best GCAs for tuber uniformity in TPS progenies. Achieving multitrait uniformity in TPS is problematic but may be aided by the selection of parents with GCAs for uniformity coupled with progeny testing to allow for non-additive effects.     

Inbreeding and true seed in tetrasomic potato. III. Early selection for seedling vigor in open-pollinated populations

Tuber yield in open-pollinated (OP) offspring of potato cultivars appears to be correlated with the proportion of hybrids within each population. OP true potato seed (TPS) from ten selected clones was tested in an experiment at two Peruvian locations, San Ramón (mid-altitude warm tropics) and Huancayo (highland cool tropics), to investigate the early selection effect on OP populations. Another experiment in La Molina (dry coast) was included to confirm the results from these other two locations. The results clearly showed that plant survival, tuber yield and berry number can be increased by a strong early selection. Likewise, the results suggested that the most-promising OP offspring for TPS production could be derived from tetraploid clones with a high rate of outcrossing. This experiment demonstrates that high tuber yield may be obtained in OP TPS cultivars with little effort, using early selection for seedling vigor in the nursery. Genetic interpretation of this response to early selection indicates that both the intensity of selection and non-additive genetic variation for tuber yield account for these observed gains. Received: 15 December 2000 / Accepted: 4 April 2001     

Quantitative genetic parameters of agronomic and quality traits in a global germplasm collection reveal excellent breeding perspectives for Jatropha curcas L.

Jatropha curcas L. (jatropha) is an undomesticated plant, which has received great attention in recent years for its potential in biofuel production and in greening and rehabilitation of wastelands. Yet the absence of improved cultivars and the lack of agronomic knowledge are limiting factors for successful jatropha cultivation. The objectives of the present study were to investigate the perspectives of a worldwide jatropha breeding program and specifically to (i) estimate variance components and heritabilities for agronomic and quality traits in the early phase of cultivation; (ii) assess phenotypic and genetic correlations among those traits; and (iii) discuss strategies for breeding high yielding jatropha cultivars. Data on various traits was collected from 375 jatropha genotypes, which were tested at seven locations during the first 3 years of growth. The accumulated seed yields and the seed yields per harvest year differed significantly among the testing locations. The estimates of genetic and genotype‐by‐environment interaction variances were significant and estimates of heritabilities were high for all yield parameters. The estimates of genetic correlations indicated a strong association among yield parameters. Oil yield was strongly correlated with seed yield and only weakly with oil content in seeds. The perspectives of a jatropha breeding program are excellent. Improved cultivars, definition of favorable environmental factors and refinement of agronomic management practices are needed to secure sustainable jatropha cultivation.     

Genetic parameters for lameness,mastitis and dagginess in a multi-breed sheep population

The objective of the present study was to quantify the extent of genetic variation in three health-related traits namely dagginess, lameness and mastitis, in an Irish sheep population. Each of the health traits investigated pose substantial welfare implications as well as considerable economic costs to producers. Data were also available on four body-related traits, namely body condition score (BCS), live weight, muscle depth and fat depth. Animals were categorised as lambs (<365 days old) or ewes (⩾365 days old) and were analysed both separately and combined. After edits, 39 315 records from 264 flocks between the years 2009 and 2015 inclusive were analysed. Variance components were estimated using animal linear mixed models. Fixed effects included contemporary group, represented as a three-way interaction between flock, date of inspection and animal type (i.e. lamb, yearling ewe (i.e. females ⩾365 days but <730 days old that have not yet had a recorded lambing) or ewe), animal breed proportion, coefficients of heterosis and recombination, animal gender (lambs only), animal parity (ewes only; lambs were assigned a separate ‘parity’) and the difference in age of the animal from the median of the respective parity/age group. An additive genetic effect and residual effect were both fitted as random terms with maternal genetic and non-genetic components also considered for traits of the lambs. The direct heritability of dagginess was similar across age groups (0.14 to 0.15), whereas the direct heritability of lameness ranged from 0.06 (ewes) to 0.12 (lambs). The direct heritability of mastitis was 0.04. For dagginess, 13% of the phenotypic variation was explained by dam litter, whereas the maternal heritability of dagginess was 0.05. The genetic correlation between ewe and lamb dagginess was 0.38; the correlation between ewe and lamb lameness was close to zero but was associated with a large standard error. Direct genetic correlations were evident between dagginess and BCS in ewes and between lameness and BCS in lambs. The present study has demonstrated that ample genetic variation exists for all three health traits investigated indicating that genetic improvement is indeed possible.     

Genetic diversity in a seed production population vs. natural populations of Sitka Spruce

Isozyme analysis was applied to estimate the level of variation and the genetic structure of a seed-production population (i.e., seed orchard) and 10 range-wide natural populations of Sitka spruce (Picea sitchensis (Bong.) Carr.). Gene diversity and heterozygosity estimates were comparatively high in both the seed orchard and the natural populations studied. The seed orchard population showed a significantly higher number of alleles per locus and percentage of polymorphic loci. Though not significant, mean heterozygosity of the seed orchard was higher than that observed for all natural populations. Genetic distance analysis indicated that the seed-orchard population was genetically similar to three natural populations from which the parent trees were selected. Parent trees sampling breadth has been identified as the major cause for the observed increased level. The impact of recurrent selection and seed orchard biology and management on maintaining the genetic diversity is discussed.     

Discovery of a synaptic mutant in potato haploids and its usefulness for potato breeding

Summary A synaptic mutant was found in haploids (2n=2x=24) extracted from the Mexican potato variety Atzimba (2n=4x=48). The mutant is inherited as a simple Mendelian recessive, designated sy4. Meiotic abnormalities of the mutant during microsporogenesis include: poor synapsis at pachytene; high frequency of univalents at diakinesis; elongated and curved spindles and univalents being scattered over the spindles at metaphase I and anaphase I; abnormal chromosome distribution at anaphase I; and production of sterile pollen, presumably due to unbalanced chromosome complement. The expression of sy4 in megasporogenesis was also detected. The sy4 mutant is very useful for potato breeding when combined with another meiotic mutant, parallel spindles (ps), because haploids homozygous for sy4 and ps produce fertile 2n pollen which transmit almost intact genotypes of the parents to the progenies. Thus, the meiotic mutants provide a powerful breeding method for maximizing heterozygosity and epistasis. They can also provide a very efficient method of transferring diploid germplasm, which has desired characteristics efficiently combined at the 2x level, to tetraploids. Many haploids have been identified with 2n pollen production by ps alone or by sy4 and ps, vigorous growth and good flowering, and a high level of resistance to late blight. The importance of a further search for meiotic mutants and their use for breeding is discussed.     

Inbreeding and true seed in tetrasomic potato. I. Selfing and open pollination in Andean landraces (Solanum tuberosum Gp. Andigena)

 True potato seed (TPS) may be an alternative method of potato production in developing countries. A breeding method for the sexual propagation of this vegetatively propagated crop should consider the development of parental lines and the type of cultivar to be released. Open-pollinated (OP) cultivars seem to be an inexpensive procedure to produce potato from true seed. However, OP progenies are the result of selfing and outcrossing in male-fertile tetraploid potatoes. The aim of the present research was to establish the effect of inbreeding and open pollination in TPS. Ten Andigena clones were used as parental material to derive hybrid (S₀), inbred (S₁ and S₂), and open-pollinated (OP₁ and OP₂) generations. Significant differences among generations were found for pollen production, pollen viability (as determined by its stainability with aceto-carmine glycerol), number of flowers and berries plant^-1, number of seeds berry^-1, weight of 1000 seeds, and tuber yield plant^-1. The parental populations were significantly different for most of the traits, but not for flower production and berry weight. The interaction of population ×generation was significant for pollen and seed production as well as for weight for 1000 seeds. All the traits evaluated except seed weight showed a strong inbreeding depression, while the OP progenies had intermediate values between the S₀ and the S₁. This demonstrates that open pollination in potatoes is not exclusively the product of selfing; it also results from outcrossing. Received: 10 November 1997 / Accepted: 3 March 1998     

AB-QTL analysis in winter wheat: II. Genetic analysis of seedling and field resistance against leaf rust in a wheat advanced backcross population

The present study aimed to localize exotic quantitative trait locus (QTL) alleles for the improvement of leaf rust (P. triticina) resistance in an advanced backcross (AB) population, B22, which is derived from a cross between the winter wheat cultivar Batis (Triticum aestivum) and the synthetic wheat accession Syn022L. The latter was developed from hybridization of T. turgidum ssp. dicoccoides and T. tauschii. Altogether, 250 BC₂F₃ lines of B22 were assessed for seedling resistance against the leaf rust isolate 77WxR under controlled conditions. In addition, field resistance against leaf rust was evaluated by assessing symptom severity under natural infestation across multiple environments. Simultaneously, population B22 was genotyped with a total of 97 SSR markers, distributed over the wheat A, B and D genomes. The phenotype and genotype data were subjected to QTL analysis by applying a 3-factorial mixed model analysis of variance including the marker genotype as a fixed effect and the environments, the lines and the marker by environment interactions as random effects. The QTL analysis revealed six putative QTLs for seedling resistance and seven for field resistance. For seedling resistance, the effects of exotic QTL alleles improved resistance at all detected loci. The maximum decrease of disease symptoms (−46.3%) was associated with marker locus Xbarc149 on chromosome 1D. For field resistance, two loci had stable main effects across environments and five loci exhibited marker by environment interaction effects. The strongest effects were detected at marker locus Xbarc149 on chromosome 1D, at which the exotic allele decreased seedling symptoms by 46.3% and field symptoms by 43.6%, respectively. Some of the detected QTLs co-localized with known resistance genes, while others appear to be as novel resistance loci. Our findings indicate, that the exotic wheat accession Syn022L may be useful for the improvement of leaf rust resistance in cultivated wheat.     

Genetic parameters for growth, reproductive and maternal traits in a multibreed meat sheep population

The genetic parameters for growth, reproductive and maternal traits in a multibreed meat sheep population were estimated by applying the Average Information Restricted Maximum Likelihood method to an animal model. Data from a flock supported by the Programa de Melhoramento Genético de Caprinos e Ovinos de Corte (GENECOC) were used. The traits studied included birth weight (BW), weaning weight (WW), slaughter weight (SW), yearling weight (YW), weight gain from birth to weaning (GBW), weight gain from weaning to slaughter (GWS), weight gain from weaning to yearling (GWY), age at first lambing (AFL), lambing interval (LI), gestation length (GL), lambing date (LD - number of days between the start of breeding season and lambing), litter weight at birth (LWB) and litter weight at weaning (LWW). The direct heritabilities were 0.35, 0.81, 0.65, 0.49, 0.20, 0.15 and 0.39 for BW, WW, SW, YW, GBW, GWS and GWY, respectively, and 0.04, 0.06, 0.10, 0.05, 0.15 and 0.11 for AFL, LI, GL, LD, LWB and LWW, respectively. Positive genetic correlations were observed among body weights. In contrast, there was a negative genetic correlation between GBW and GWS (-0.49) and GBW and GWY (-0.56). Positive genetic correlations were observed between AFL and LI, LI and GL, and LWB and LWW. These results indicate a strong maternal influence in this herd and the presence of sufficient genetic variation to allow mass selection for growth traits. Additive effects were of little importance for reproductive traits, and other strategies are necessary to improve the performance of these animals.     

Field performance of Solanum sisymbriifolium, a trap crop for potato cyst nematodes. II. Root characteristics

Hatching of potato cyst nematodes is induced by root exudates of Solanaceae, such as Solanum sisymbriifolium, and is therefore related to root length distribution of this crop. A mathematical model was derived to relate the hatching potential to root length density (RLD). A series of field experiments was carried out to study actual root length distribution of S. sisymbriifolium in relation to shoot properties and to provide input into the model. Using a modified Poisson distribution formula for the three‐dimensional distribution of roots in a volume of soil, the relation between the zone of influence of hatching agents and the RLD could be derived. On this basis, the minimal RLD was estimated, which is needed to expose 75%, 90% or 95% of cysts to root exudates, as a function of the length of the zone of influence of hatching agents on cysts. The logarithm of the total root length showed a linear relation with the logarithms of above‐ground biomass and with leaf area index. Root diameter distribution was the same for all crops examined and independent of soil depth. Fine roots (<0.4 mm in diameter) constituted around 50% of total root length. Using a zone of influence of 1.00, 0.75 and 0.50 cm around the centre of each root, a minimal RLD for sufficient soil exploration (75%) was estimated. Depth at which that minimal RLD was exceeded was linearly related to total root length (km m^?2) and to above‐ground crop biomass, enabling estimations being made of the potential hatching efficacy as related to measurable properties of S. sisymbriifolium crops. The proposed approach to derive potential hatching effects from crop properties needs further validation; particularly, the distance of influence of root exudates is a critical factor.     

不同生育时期遮光对马铃薯光合特性和产量的影响

为了研究不同生育时期遮光对马铃薯光合特性和产量的影响,明确马铃薯不同生育时期对弱光的耐受性,对2个马铃薯品种(‘冀张薯12号'和‘冀张薯8号')进行了4个生育时期(苗期、苗期至现蕾期、现蕾期至开花初期、开花初期至收获期)和3个遮光度(不遮光对照、20%遮光率和50%遮光率)的处理试验。结果表明: 与不遮光处理相比,20%遮光率下,2个品种马铃薯苗期SPAD值显著降低,苗期至现蕾期、现蕾期至开花初期SPAD值无显著变化,开花初期遮光15 d可使SPAD值呈一定程度增加;50%遮光率下,2个品种马铃薯SPAD值变化趋势与前者相同,除开花初期增幅加大外,其他生育时期变化幅度接近。各时期遮光对马铃薯叶片气孔导度(g_s)影响不大,除50%遮光率下‘冀张薯8号'叶片g_s在开花初期较对照显著降低43.9%外,其他处理的g_s与对照均无显著差异。遮光后叶片胞间CO₂浓度(C_i)呈增加趋势,苗期、苗期至现蕾期50%遮光可使C_i显著增加,其余各时期的C_i无显著变化。4个时期遮光处理的叶片净光合速率(P_n)均降低,2个品种马铃薯叶片P_n在50%遮光处理下的降幅均大于20%遮光处理,‘冀张薯12号'除在苗期遮光处理的叶片P_n降幅大于‘冀张薯8号'外,其余时期的降幅均小于‘冀张薯8号'。4个时期遮光使马铃薯产量均降低,且50%遮光处理降幅大于20%遮光处理。‘冀张薯12号'在苗期不耐弱光,其余时期的耐弱光能力优于‘冀张薯8号'。综合分析表明,耐弱光能力强的品种遮光处理后,叶片P_n和g_s降幅小、C_i增幅小,产量降幅也小。     

Analysis of QTLs for yield components, agronomic traits, and disease resistance in an advanced backcross population of spring barley.

Hordeum vulgare subsp. spontaneum, the wild progenitor of barley, is a potential source of useful genetic variation for barley breeding programs. The objective of this study was to map quantitative trait loci (QTLs) in an advanced backcross population of barley. A total of 207 BC3 lines were developed using the 2-rowed German spring cultivar Hordeum vulgare subsp. vulgare 'Brenda' as a recurrent parent and the H. vulgare subsp. spontaneum accession HS584 as a donor parent. The lines were genotyped by 108 simple-sequence repeat (SSR) markers and evaluated in field tests for the measurement of grain yield and its components, such as ear length, spikelet number per spike, grain number per spike, spike number, and 1000-grain mass, as well as heading date and plant height. A total of 100 QTLs were detected. Ten QTLs with increasing effects were found for ear length, spikelet number, and grain number per spike. Three QTLs contributed by HS584 were found to significantly decrease days to heading across all years at 2 locations. In addition, 2 QTLs from HS584 on chromosomes 2H and 3H were associated with resistance to leaf rust. Based on genotypic data obtained from this population, 55 introgression lines carrying 1 or 2 donor segments were selected to develop a set of doubled-haploid lines, which will be used to reconfirm and investigate the effects of 100 QTLs for future genetic studies.     

On the construction of the population projection matrix for a population grouped in unequal stages.

It is shown how it is possible to construct a projection matrix for a population grouped in unequal stages directly from a known projection matrix for the population grouped in equal age intervals.