Advanced backcross QTL analysis of a hard winter wheat × synthetic wheat population

Advanced backcross quantitative trait locus (AB-QTL) analysis was used to identify QTLs for yield and yield components in a backcross population developed from a cross between hard red winter wheat (Triticum aestivum L.) variety Karl 92 and the synthetic wheat line TA 4152-4. Phenotypic data were collected for agronomic traits including heading date, plant height, kernels per spike, kernel weight, tiller number, biomass, harvest index, test weight, grain yield, protein content, and kernel hardness on 190 BC₂F_2:4 lines grown in three replications in two Kansas environments. Severity of wheat soilborne mosaic virus (WSBMV) reaction was evaluated at one location. The population was genotyped using 151 microsatellite markers. Of the ten putative QTLs identified, seven were located on homoeologous group 2 and group 3 chromosomes. The favorable allele was contributed by cultivated parent Karl 92 at seven QTLs including a major one for WSBMV resistance, and by the synthetic parent at three QTLs: for grain hardness, kernels per spike, and tiller number. Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture.     

QTL mapping of resistance to Sclerotinia midstalk rot in RIL of sunflower population NDBLOSsel × CM625

Midstalk rot caused by Sclerotinia sclerotiorum is an important disease of sunflower in its main areas of cultivation. The objectives of this study were to (1) verify quantitative trait loci (QTL) for midstalk-rot resistance found in F₃ families of the NDBLOS_sel × CM625 population in recombinant inbred lines (RIL) derived from the same cross; (2) re-estimate their position and genetic effects; (3) draw inferences about the predictive quality of QTL for midstalk-rot resistance identified in the F₃ families as compared to those in the RIL. Phenotypic data for three resistance (leaf lesion, stem lesion, and speed of fungal growth) and two morphological traits (leaf length and leaf length with petiole) were obtained from 317 RIL following artificial infection in field experiments across two environments. For genotyping the 248 RIL, we selected 41 simple sequence repeat (SSR) markers based on their association with QTL for Sclerotinia midstalk-rot resistance in an earlier study. The resistance traits showed intermediate to high heritabilities and were significantly correlated with each other Genotypic correlations between F₃ families and the RIL were highly significant and ranged between 0.50 for leaf length and 0.64 for stem lesion. For stem lesion, two genomic regions on linkage group (LG) 8 and LG16 explaining 26.5% of the genotypic variance for Sclerotinia midstalk-rot resistance were consistent across generations. For this trait, the genotypic correlation between the observed performance and its prediction based on QTL positions and effects in F₃ families was surprisingly high The genetic effects and predictive quality of these two QTL are promising for application in marker-assisted selection to Sclerotinia midstalk-rot resistance.     

QTL mapping of powdery mildew resistance in WI 2757 cucumber (Cucumis sativus L.)

Powdery mildew (PM) is a very important disease of cucumber (Cucumis sativus L.). Resistant cultivars have been deployed in production for a long time, but the genetic mechanisms of PM resistance in cucumber are not well understood. A 3-year QTL mapping study of PM resistance was conducted with 132 F_2:3 families derived from two cucumber inbred lines WI 2757 (resistant) and True Lemon (susceptible). A genetic map covering 610.4 cM in seven linkage groups was developed with 240 SSR marker loci. Multiple QTL mapping analysis of molecular marker data and disease index of the hypocotyl, cotyledon and true leaf for responses to PM inoculation identified six genomic regions in four chromosomes harboring QTL for PM resistance in WI 2757. Among the six QTL, pm1.1 and pm1.2 in chromosome 1 conferred leaf resistance. Minor QTL pm3.1 (chromosome 3) and pm4.1 (chromosome 4) contributed to disease susceptibility. The two major QTL, pm5.1 and pm5.2 were located in an interval of ~40 cM in chromosome 5 with each explaining 21.0–74.5 % phenotypic variations. Data presented herein support two recessively inherited, linked major QTL in chromosome 5 plus minor QTL in other chromosomes that control the PM resistance in WI 2757. The QTL pm5.2 for hypocotyl resistance plays the most important role in host resistance. Multiple observations in the same year revealed the importance of scoring time in the detection of PM resistance QTL. Results of this study provided new insights into phenotypic and genetic mechanisms of powdery mildew resistance in cucumber.     

QTL in mega-environments: II. Agronomic trait QTL co-localized with seed yield QTL detected in a population derived from a cross of high-yielding adapted × high-yielding exotic soybean lines

Seed yield mega-environment-universal and specific QTL (QTL_U and QTL_SP, respectively) linked to Satt100, Satt130, Satt162, Satt194, Satt259 Satt277 and Sat_126, have been identified in a population derived from a cross between a Chinese and a Canadian soybean [Glycine max (L.) Merrill] elite line. The variation observed in yield could be the consequence of the variation of agronomic traits. Yield-component traits have been reported in the literature, but a better understanding of their impact at the molecular level is still lacking. Therefore, the objectives of this study were to identify traits correlated with yield and to determine if the yield QTL_U and QTL_SP were co-localized with QTL_U and QTL_SP associated with an agronomic trait. A recombinant inbred line (RIL) population was developed from a cross between a high-yielding adapted Canadian and a high-yielding exotic Chinese soybean elite line. The RIL were evaluated in multiple environments in China and Canada during the period from 2004 to 2006. Four yield QTL_U, tagged by markers Satt100, Satt277, Satt162 and Sat_126, were co-localized with a QTL associated with an agronomic trait, behaving as either QTL_U or QTL_SP for the agronomic trait. For example, the yield QTL_U, tagged by marker Satt100 was associated also with 100 seed weight, pods per plant, pods per node, plant height, R1, R5, R8, oil content and protein content in all Canadian environments, but only with pods per plant, pods per node, plant height, R1, R5, R8 and oil content in two or more Chinese environments. No agronomic traits QTL were co-localized with the yield QTL_U tagged by the marker Satt139 or the yield QTL_SP tagged by Satt259, suggesting a physiological basis of the yield in these QTL. The results suggest that a successful introgression of crop productivity alleles from plant introductions into an adapted germplasm could be facilitated by the use of both the QTL_U and QTL_SP because each type of QTL contributed either directly or indirectly through yield-component traits to seed yield of RILs.     

QTL analyses of fiber components and crude protein in an annual × perennial ryegrass interspecific hybrid population

Annual (Lolium multiflorum Lam.) and perennial (Lolium perenne L.) ryegrasses are two important forage and turfgrass species. Improving the digestibility of forage by decreasing fiber content is a major goal in forage crop breeding programs. An annual × perennial ryegrass interspecific hybrid population was used to map quantitative trait loci (QTLs) for fiber components, neutral detergent fiber (NDF), acid detergent fiber (ADF), and acid detergent lignin (ADL), and crude protein (CP). Samples were harvested three times in August and September 2003 and August 2004, respectively. Simple interval mapping was used to detect QTLs from both the male and female parental maps previously developed for the population. Fiber components were all correlated positively with each other and were negatively correlated with CP. The largest correlations were between NDF and ADF with r = 0.86, 0.72, and 0.82 for each of the three harvests. All four traits showed intermediate broad-sense heritability values ranging from 0.35 to 0.72. A total of 63 QTLs were detected for the four traits measured over the three harvests from both the female and male maps. Coincident QTLs were detected on linkage groups (LGs) 2, 6, and 7 for NDF, LGs 1, 2, and 7 for ADF, LGs 6 and 7 for ADL, and LG 2 for CP, respectively. Coincident QTLs were also detected on LGs 2, 6, and 7 for NDF and ADF, providing evidence of the genetic basis of the observed high level of phenotypic correlation. The QTLs on LGs 2, 6, and possibly 7 for fiber components were co-located on the same LG as several lignin biosynthetic genes from perennial ryegrass.     

Identification of QTLs with additive,epistatic and QTL × development interaction effects for seed dormancy in rice

Seed dormancy (SD) is an important agronomic trait affecting crop yield and quality. In this study, one rice population of recombinant inbred lines (RILs) was used to determine the genetic characteristics of SD at the early (4 weeks after heading), middle (5 weeks after heading) and late (6 weeks after heading) development stages. The level of SD decreased with the process of seed development, and the SD was significantly affected by the heading date (HD) and temperature at the early and middle development stages. A total of eight additive quantitative trait loci (QTLs) for SD were identified at three development stages, and more QTLs were expressed at the early and late development stages. Among them, four, one and three additive QTLs were identified at the early, middle and late development stages, respectively. Epistatic QTLs and QTL-by-development interactions were detected by the joint analysis of multi-development phenotypic values, and one additive and two epistatic QTLs were identified. The phenotypic variation of SD explained by each additive, epistatic QTL and QTL × development interaction ranged from 8.0 to 13.5 %, 0.7 to 3.9 % and 1.3 to 2.8 %, respectively. One major QTL qSD7.1 for SD was tightly linked to the major QTL qHD7.4 for HD, which might be applied to reveal the relationship of SD and HD. By comparing chromosomal positions of these additive QTLs with those previously identified, five additive QTLs qSD1.1, qSD2.1, qSD2.2, qSD4.1 and qSD4.2 might represent novel genes. The best three cross combinations for the development of RIL populations were predicted to improve SD. The selected RILs and the identified QTLs might be applicable to improve the rice pre-harvest sprouting tolerance by the marker-assisted selection approach.     

Use of trial clustering to study QTL × environment effects for grain yield and related traits in maize

A population of 300 F_3:4 lines derived from the cross between maize inbred lines F2 and F252 was evaluated for testcross value in a large range of environmental conditions (11 different locations in 2 years: 1995 and 1996) in order to study (1) the magnitude of genotype × environment and (2) the stability of quantitative trait loci (QTL) effects. Several agronomic traits were measured: dry grain yield (DGY), kernel weight, average number of kernels per plant, silking date (SD) and grain moisture at harvest. A large genotype × environment interaction was found, particularly for DGY. A hierarchical classification of trials and an additive main effects and multiplicative interaction (AMMI) model were carried out. Both methods led to the conclusion that trials could be partitioned into three groups consistent with (1) the year of experiment and (2) the water availability (irrigated vs non-irrigated) for the trials sown in 1995. QTL detection was carried out for all the traits in the different groups of trials. Between 9 and 15 QTL were detected for each trait. QTL × group and QTL × trial effects were tested and proved significant for a large proportion of QTL. QTL detection was also performed on coordinates on the first two principal components (PC) of the AMMI model. PC QTL were generally detected in areas where QTL × group and QTL × trial interactions were significant. A region located on chromosome 8 near an SD QTL seemed to play a key role in DGY stability. Our results confirm the key role of water availability and flowering earliness on grain yield stability in maize.     

Genetic variability and QTL mapping of freezing tolerance and related traits in Medicago truncatula

Freezing is a major environmental limitation to crop productivity for a number of species including legumes. We investigated the genetic determinism of freezing tolerance in the model legume Medicago truncatula Gaertn (M. truncatula). After having observed a large variation for freezing tolerance among 15 M. truncatula accessions, the progeny of a F6 recombinant inbred line population, derived from a cross between two accessions, was acclimated to low above-freezing temperatures and assessed for: (a) number of leaves (NOL), leaf area (LA), chlorophyll content index (CCI), shoot and root dry weights (SDW and RDW) at the end of the acclimation period and (b) visual freezing damage (FD) during the freezing treatment and 2 weeks after regrowth and foliar electrolyte leakage (EL) 2 weeks after regrowth. Consistent QTL positions with additive effects for FD were found on LG1, LG4 and LG6, the latter being the most explanatory (R ² ≈ 40 %). QTL for NOL, QTL for EL, NOL and RDW, and QTL for EL and CCI colocalized with FD QTL on LG1, LG4 and LG6, respectively. Favorable alleles for these additive effects were brought by the same parent suggesting that this accession contributes to superior freezing tolerance by affecting plants’ capacity to maintain growth at low above-freezing temperatures. No epistatic effects were found between FD QTL, but for each of the studied traits, 3–6 epistatic effects were detected between loci not detected directly as QTL. These results open the way to the assessment of syntenic relationships between QTL for frost tolerance in M. truncatula and cultivated legume species.     

QTL analyses of drought tolerance and growth for a Salix dasyclados × Salix viminalis hybrid in contrasting water regimes

Quantitative trait loci (QTL) for growth traits and water-use efficiency have been identified in two water regimes (normal and drought-treated) and for a treatment index. A tetraploid hybrid F₂ population originating from a cross between a Salix dasyclados clone (SW901290) and a Salix viminalis clone (Jorunn) was used in the study. The growth response of each individual including both above and below ground dry-matter production (i.e. shoot length, shoot diameter, aboveground and root dry weight, internode length, root dry weight/total dry weight, relative growth rate and leaf nitrogen content) was analysed in a replicated block experiment with two water treatments. A composite interval mapping approach was used to estimate number of QTL, the magnitude of the QTL and their position on genetic linkage maps. QTL specific for each treatment and for the treatment index were found, but QTL common across the treatments and the treatment index were also detected. Each QTL explained from 8% to 29% of the phenotypic variation, depending on trait and treatment. Clusters of QTL for different traits were mapped close to each other at several linkage groups, indicating either a common genetic base or tightly linked QTL. Common QTL identified between treatments and treatment index in the complex trait dry weight can be useful tools in the breeding and selection for drought stress tolerance in Salix.     

QTL in mega-environments: I. Universal and specific seed yield QTL detected in a population derived from a cross of high-yielding adapted × high-yielding exotic soybean lines

Modern soybean [(Glycine max (L.) Merrill] breeding programs rely primarily on the use of elite × elite line crosses to develop high-yielding cultivars. Favorable alleles for traits of interest have been found in exotic germplasm but the successful introduction of such alleles has been hampered by the lack of adaptation of the exotic parent to local mega-environment and difficulties in identifying superior progeny from elite × exotic crosses. The objective of this study was to use a population derived from a cross between an adapted and an exotic elite line to understand the genetic causes underlying adaptation to two mega-environments (China and Canada). A cross between a high-yielding Canadian cultivar ‘OAC Millennium’ and an elite Chinese cultivar ‘Heinong 38’ was performed to develop a recombinant inbred line (RIL) population. The RIL population was evaluated in China and Canada in multiple environments from 2004 to 2006. Significant variation for seed yield was observed among the RILs in both the Chinese and Canadian environment. Individual RILs performed differently between the Chinese and Canadian environments suggesting differential adaptation to intercontinental mega-environments. Seven seed yield quantitative trait loci (QTL) were identified of which five were mega-environment universal QTL (linked to markers Satt100, Satt162, Satt277, Sat_126, and the interval of Satt139-Sat_042) and two were mega-environment-specific QTL (at marker intervals, Satt194-SOYGPA and Satt259-Satt576). Seed yield QTL located near Satt277 has been confirmed and new QTL have been identified explaining between 9 and 37% of the phenotypic variation in seed yield. The QTL located near Satt100 explained the greatest amount of variation ranging from 18 to 37% per environment. Broad sense heritability ranged from 89 to 64% among environments. Epistatic effects have been identified in both mega-environments with pairs of markers explaining between 9 and 14% of the phenotypic variation in seed yield. An improved understanding of the type of QTL action as either universal or mega-environment-specific QTL as well as their interaction may facilitate the development of strategies to introgress specific high-yielding alleles from Chinese to North American germplasm and vice versa to sustain efforts in breeding of high-yielding soybean cultivars.     

QTL analysis of the spring wheat “Chapio” identifies stable stripe rust resistance despite inter-continental genotype × environment interactions

Chapio is a spring wheat developed by CIMMYT in Mexico by a breeding program that focused on multigenic resistances to leaf rust and stripe rust. A population consisting of 277 recombinant inbred lines (RILs) was developed by crossing Chapio with Avocet. The RILs were genotyped with DArT markers (137 randomly selected RILs) and bulked segregant analysis conducted to supplement the map with informative SSR markers. The final map consisted of 264 markers. Phenotyping against stripe rust was conducted for three seasons in Toluca, Mexico and at three sites over two seasons (total of four environments) in Sichuan Province, China. Significant loci across the two inter-continental regions included Lr34/Yr18 on 7DS, Sr2/Yr30 on 3BS, and a QTL on 3D. There were significant genotype × environment interactions with resistance gene Yr31 on 2BS being effective in most of the Toluca environments; however, a late incursion of a virulent pathotype in 2009 rendered this gene ineffective. This locus also had no effect in China. Conversely, a 5BL locus was only effective in the Chinese environments. There were also complex additive interactions. In the Mexican environments, Yr31 suppressed the additive effect of Yr30 and the 3D locus, but not of Lr34/Yr18, while in China, the 3D and 5BL loci were generally not additive with each other, but were additive when combined with other loci. These results indicate the importance of maintaining diverse, multi-genic resistances as Chapio had stable inter-continental resistance despite the fact that there were QTLs that were not effective in either one or the other region.     

Conditions for Global Dynamic Stability of a Class of Resource-Bounded Model Ecosystems

This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are ‘resource bounded’ in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The systems we consider generalize classical multi-species Lotka–Volterra systems, the behaviour of which is characterized by properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized by a single matrix, but rather a family of matrices. We develop a set of ‘explicit conditions’ on the basis of a notion of ‘uniform diagonal dominance’ for such a family of matrices, that allows us to extract a set of sufficient conditions for global asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed.     

Mapping of QTL for resistance to the Mediterranean corn borer attack using the intermated B73 × Mo17 (IBM) population of maize

The Mediterranean corn borer or pink stem borer (MCB, Sesamia nonagrioides Lefebvre) causes important yield losses as a consequence of stalk tunneling and direct kernel damage. B73 and Mo17 are the source of the most commercial valuable maize inbred lines in temperate zones, while the intermated B73 × Mo17 (IBM) population is an invaluable source for QTL identification. However, no or few experiments have been carried out to detect QTL for corn borer resistance in the B73 × Mo17 population. The objective of this work was to locate QTL for resistance to stem tunneling and kernel damage by MCB in the IBM population. We detected a QTL for kernel damage at bin 8.05, although the effect was small and two QTL for stalk tunneling at bins 1.06 and 9.04 in which the additive effects were 4 cm, approximately. The two QTL detected for MCB resistance were close to other QTL consistently found for European corn borer (ECB, Ostrinia nubilalis Hübner) resistance, indicating mechanisms of resistance common to both pests or gene clusters controlling resistance to different plagues. The precise mapping achieved with the IBM population will facilitate the QTL pyramiding and the positional cloning of the detected QTL.     

QTL mapping of stripe,leaf and stem rust resistance genes in a Kariega × Avocet S doubled haploid wheat population

Adult plant resistance to stripe (yellow) rust in the wheat cultivar Kariega has previously been ascribed to a major quantitative trait locus (QTL) on each of chromosomes 2B and 7D, along with a number of minor QTL. We have extended both the size of the cv. Kariega × cv. Avocet S mapping population, and the marker coverage within it, by assembling a set of Diversity Array Technology (DArT) markers. This has allowed for the analysis of the genetic basis of the adult plant and seedling resistances to stripe, leaf and stem rust present in the two mapping population parents. The stripe rust reactions of the segregating material were assessed in both field (three scoring dates) and greenhouse experiments. The chromosome 2B QTL became more important than the Lr34/Yr18 complex on chromosome 7D as the plants aged. As the infection progressed, the two QTL explained an increasing proportion of the variance for percentage leaf area infected. The cv. Kariega allele at the minor chromosome 4A QTL had a consistent effect on the severity of stripe rust infection and the overall plant reaction at the earlier scoring dates, but lost importance as the disease progressed. Several rust resistances were detected using an improved greenhouse-based test.     

QTL for fibre-related traits in grain × sweet sorghum as a tool for the enhancement of sorghum as a biomass crop

Compared to maize and temperate grasses, sorghum has received less attention in terms of improving cell wall components. The objectives of this study were to identify quantitative trait loci (QTL) with main effects, epistatic and pleiotropic effects along with QTL × environment (QE) interactions controlling fibre-related traits in sorghum. Neutral detergent fibre (NDF), acid detergent fibre (ADF), acid detergent lignin (ADL), cellulose, hemicellulose, fresh leaf mass, stripped stalk mass, dry stalk mass, fresh biomass and dry biomass were analysed from a population of 188 grain × sweet sorghum recombinant inbred lines. A genetic map consisting of 157 DNA markers was constructed, and QTL were detected using composite interval mapping (CIM). CIM detected more than 5 additive QTL per trait explaining 7.1–24.7% of the phenotypic variation. Abundant co-localization of these QTL was observed across all chromosomes, and the highest cluster was identified on chromosome 6. Searching for candidate genes using the confidence interval of our QTL clusters reveals that these clusters might comprise a set of genes that are tightly linked. Some QTL showed multiple effects; however, the allele for each trait was favouring the parent with the increasing effect. QE interactions were observed for QTL showing multiple effects. Additive × additive interaction was observed for 7 out of 10 traits, indicating the importance of epistatic analysis. However, the phenotypic variation explained by digenic interactions was lower compared to the individual QTL. Our results indicate that various genetic components contribute to fibre-related traits and should be considered during the enhancement of sorghum for lignocellulosic biomass.     

QTL mapping for grain filling rate and yield-related traits in RILs of the Chinese winter wheat population Heshangmai × Yu8679

A set of 142 winter wheat recombinant inbred lines (RILs) deriving from the cross Heshangmai x Yu8679 were tried in four ecological environments during the seasons 2006 and 2007. Nine agronomic traits comprising mean grain filling rate (GFR(mean)), maximum grain filling rate (GFR(max)), grain filling duration (GFD), grain number per ear (GNE), grain weight per ear (GWE), flowering time (FT), maturation time (MT), plant height (PHT) and thousand grain weight (TGW) were evaluated in Beijing (2006 and 2007), Chengdu (2007) and Hefei (2007). A genetic map comprising 173 SSR markers and two EST markers was generated. Based on the genetic map and phenotypic data, quantitative trait loci (QTL) were mapped for these agronomic traits. A total of 99 putative QTLs were identified for the nine traits over four environments except GFD, PHT and MT, measured in two environments (BJ07 and CD07), respectively. Of the QTL detected, 17 for GFR(mean), 16 for GFR(max), 21 for TGW and 10 for GWE involving the chromosomes 1A, 1B, 2A, 2D, 3A, 3B, 3D, 4A, 4D, 5A, 5B, 6D and 7D were identified. Moreover, 13 genomic regions showing pleiotropic effects were detected in chromosomes 1A, 1B, 1D, 2A, 2B, 2D, 3A, 3B, 4B, 4D, 5B, 6D and 7D; these QTL revealing pleiotropic effects may be informative for a better understanding of the genetic basis of grain filling rate and other yield-related traits, and represent potential targets for multi-trait marker aided selection in wheat.     

Heading date QTL in a spring × winter barley cross evaluated in Mediterranean environments

Heading date is a key trait for the adaptation of barley to Mediterranean environments. We studied the genetic control of flowering time under Northern Spanish (Mediterranean) conditions using a new population derived from the spring/winter cross Beka/Mogador. A set of 120 doubled haploid lines was evaluated in the field, and under controlled temperature and photoperiod conditions. Genotyping was carried out with 215 markers (RFLP, STS, RAPD, AFLP, SSR), including markers for vernalization candidate genes, HvBM5 (Vrn-H1), HvZCCT (Vrn-H2), and HvT SNP22 (Ppd-H1). Four major QTL, and the interactions between them, accounted for most of the variation in both field (71–92%) and greenhouse trials (55–86%). These were coincident with the location of the major genes for response to vernalization and short photoperiod (Ppd-H2 on chromosome 1H). A major QTL, near the centromere of chromosome 2H was the most important under autumn sowing conditions. Although it is detected under all conditions, its action seems not independent from environmental cues. An epistatic interaction involving the two vernalization genes was detected when the plants were grown without vernalization and under long photoperiod. The simultaneous presence of the winter Mogador allele at the two loci produced a marked delay in heading date, beyond a mere additive effect. This interaction, combined with the effect of the gene responsive to short photoperiod, Ppd-H2, was found responsible of the phenomenon known as short-day vernalization, present in some of the lines of the population. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Environmental Fluctuations and Level of Density-Compensation Strongly Affects the Probability of Fixation and Fixation Times

The probability of, and time to, fixation of a mutation in a population has traditionally been studied by the classic Wright–Fisher model where population size is constant. Recent theoretical expansions have covered fluctuating populations in various ways but have not incorporated models of how the environment fluctuates in combination with different levels of density-compensation affecting fecundity. We tested the hypothesis that the probability of, and time to, fixation of neutral, advantageous and deleterious mutations is dependent on how the environment fluctuates over time, and on the level of density-compensation. We found that fixation probabilities and times were dependent on the pattern of autocorrelation of carrying capacity over time and interacted with density-compensation. The pattern found was most pronounced at small population sizes. The patterns differed greatly depending on whether the mutation was neutral, advantageous, or disadvantageous. The results indicate that the degree of mismatch between carrying capacity and population size is a key factor, rather than population size per se, and that effective population sizes can be very low also when the census population size is far above the carrying capacity. This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations.