A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067.

Planets with radii between that of the Earth and Neptune (hereafter referred to as 'sub-Neptunes') are found in close-in orbits around more than half of all Sun-like stars1,2. However, their composition, formation and evolution remain poorly understood3. The study of multiplanetary systems offers an opportunity to investigate the outcomes of planet formation and evolution while controlling for initial conditions and environment. Those in resonance (with their orbital periods related by a ratio of small integers) are particularly valuable because they imply a system architecture practically unchanged since its birth. Here we present the observations of six transiting planets around the bright nearby star HD 110067. We find that the planets follow a chain of resonant orbits. A dynamical study of the innermost planet triplet allowed the prediction and later confirmation of the orbits of the rest of the planets in the system. The six planets are found to be sub-Neptunes with radii ranging from 1.94R⊕ to 2.85R⊕. Three of the planets have measured masses, yielding low bulk densities that suggest the presence of large hydrogen-dominated atmospheres.

Direct and maternal genetic differences between lines of mice selected for body weight and litter size: traits of dams.

Genetic differences in performance of dams were estimated by linear contrasts using means of two selected lines of mice and reciprocal F1's, F2's and backcrosses. The lines were selected for increased 6-wk body weight (W) or increased litter size (L). Genetic differences estimated were direct average (gD), direct heterosis (hD), maternal average (gM), progeny average (gP), and progeny heterosis (hP). For dam weight and feed consumption from 12 to 21 d postpartum (pp), gD was the largest genetic difference and favored line W. For litter size, litter weight at birth, litter efficiency (litter weight gain/dam feed consumption) from birth to 12 d pp and within litter mortality from 1 to 21 d pp, gD favored L and, except for hD in litter efficiency, was the most important genetic difference for these traits. Direct heterosis was the only significant difference for litter weight at 21 d pp, litter efficiency from 12 to 21 d pp and within litter mortality at parturition. The gM were larger in W than in L for dam weight and feed consumption, and for litter size and weight at birth, but they were usually of smaller magnitude than gD. The gP were significant only in litter traits measured before 12 d pp and favored W. For no trait measured was hP of consequence. Line differences in dam and litter weight accounted for genetic differences in dam feed consumption. Genetic differences in litter size at birth were not due to line differences in dam weight. The lower mortality within litters nursed by crossbred dams was responsible for hD on litter weight and litter efficiency. Within but not among lines, higher mortality rates were associated with larger litters.

Postpartum performance in a diallel cross among lines of mice selected for litter size and body weight.

Postpartum dam performance was studied in a complete diallel design involving five lines of mice. The selection criterion in each line was: large litter size at birth (L+); large 6-wk body weight (W+); an index for large litter size and small 6-wk body weight (L+W-); the complementary index (L-W+) and random (K). Females from the five lines and 20 reciprocal F1 crosses were mated to sires of a randomly selected control line (CC). Correlated responses in average direct genetic and average maternal genetic effects for dam body weight and litter size at parturition persisted throughout lactation, indicating important pleiotropic effects. Major correlated responses occurred for litter weight, feed intake and litter feed efficiency, primarily due to average direct genetic effects. Using general combining ability and net line effects as criteria for choosing among lines, L+ had a distinct advantage if the objective was to increase litter size in a crossing program. If the objective was to maximize litter weaning weight, then W+ would be favored for net line effects, while L+ and W+ would be about equivalent for general combining ability. None of the lines had an advantage for litter feed efficiency. Direct heterosis for dam weight at 12 and 21 d of lactation averaged 2.7 and 1.9%, while for litter size the respective averages were 7.4 and 7.3%. The W+ X L+W- cross exhibited overdominance for litter size. Direct heterosis was moderate for feed intake and litter weight, but was negligible for litter feed efficiency because of the mathematical relationship among the three traits. Maternal heterosis for preweaning progeny growth was suppressed because of heterosis for litter size in the dam. Grand-maternal effects on growth of the young were small and would not be an important consideration in choosing among these lines in a crossbreeding program.

Reproductive performance in a diallel cross among lines of mice selected for litter size and body weight.

Genetic factors affecting female reproductive performance in lines of mice with a known history of selection were estimated from a 5 X 5 diallel cross. Lines were selected as follows: large litter size at birth (L+); large 6-wk body weight (W+); an index for large litter size and small 6-wk body weight (L+W-); the complementary index (L-W+) and randomly (K). Partitioning of direct and correlated responses for litter size, 6-wk body weight and related traits into average direct genetic (li) and average maternal genetic (mi) effects indicated that the magnitude of differences in li exceeded those in mi. Lines having positive responses in li were W+ greater than L+ greater than L-W+ for dam body weight, L+ greater than L+W- greater than W+ for litter size and L+ greater than (W+, L+W-) for litter birth weight, whereas L-W+ responded negatively for litter size. A positive association was found between mi for litter size and dam body weight, W+ and L-W+ being high and L+ and L+W- low for both traits. Female infertility and time from male exposure to parturition had relatively small correlated responses. Line rankings in general combining ability (gi) and net line effects were similar for the respective traits. Depending upon the line and trait involved, the relative contribution of average direct genetic and line direct heterotic (hi) effects to general combining ability [gi = (1/2) li + hi] varied. Line heterosis refers to average heterosis in crosses involving that line. Direct heterosis ( hij ) for each trait differed considerably among crosses. The three crosses showing the highest hij for litter size at birth, W+ X L-W+ (1.78), L+ X W+ (1.28) and L-W+ X L+W- (1.22), possibly had loci contributing directional dominance to litter size with frequencies of parental lines deviating in opposite directions relative to mean gene frequency. The correlation between absolute difference in parental line means and hij for litter size was not significant, suggesting that the magnitudes of absolute differences in parental means were not reliable predictors of divergence in gene frequency. Crossbred performance increased linearly with midparent values for litter size at birth (b = .88 +/- .09, R2 = .92) and dam parturition body weight (b = 1.13 +/- .04, R2 = .99), the latter trait showing an increase (P less than .01) in heterosis as midparent values increased.

Genetic interpretation and analysis of diallel crosses with animals.

A genetic framework was developed for the interpretation of statistical parameters estimated from a diallel experiment among a fixed set of lines. These included average direct genetic, average maternal genetic, general combining ability, reciprocal, and line and specific direct and maternal heterotic effects. The genetic model is based on direct and maternal additive and dominance genetic effects as would be expected in animal species. The model assumes that dominance is the underlying basis of heterosis. As an example, litter size at birth was analyzed from a 5 × 5 diallel cross with mice.

Correlated responses in growth and body composition of replicated single-trait and index selected lines of mice.

Correlated responses in growth, body composition and efficiency were evaluated in lines of mice selected in the following ways: W(+)T i (o) , increased six-week body weight (WT6); W ° T i (+) , increased six-week tail length (TL6); W(+)T i (-) , increased WT6 and decreased TL6; W(-)T i (+) , decreased WT6 and increased TL6; M16, increased three-to six-week postweaning gain (PWG). Each of the first four selection treatments had two replicate lines (i = 1, 2) selected for 13 generations and the fifth treatment had one line selected for 30 generations. All lines were derived from a randombred ICR albino population which served as a control. Additional traits studied were three-week body weight and tail length, postweaning gain in tail length, percent body composition (ash, fat, moisture and protein) at six weeks of age, and three-to six-week feed consumption (CONS) and efficiency (EFF = PWG/CONS). Efficiency of body constituent gains (ash, fat, protein and caloric value) were determined by dividing each constituent by CONS. Relative to selection treatments, replicate variation in the array of traits was small and was primarily attributable to the effects of genetic drift; more frequent significant replicate differences among traits in W(+)T(-) were associated with a replicate difference in cumulative selection differentials. Selection for different criteria involving WT6 and TL6 did not change the allometric relationship between tail length and body weight in the three-to six-week age interval. The significant divergence between W(+)T ° and W °T(+) and between W(+)T(-) and W(-)T(+) was as expected for WT6 and TL6. Significant asymmetry of selection response between W(+)T(-) and W(-)T(+) for WT6 and TL6 was attributed to maternal effects. In agreement with theory, antagonistic index selection generally yielded smaller genetic responses than single trait selection. Positive correlated responses in CONS and EFF were found for M16 and W(+)T °. Significant correlated changes in CONS (positive in W °T(+) and negative in W(-)T(+)) were not accompanied by a significant change in EFF. In contrast, W(+)T(-) evinced an increased EFF and no change in CONS. Percent fat increased significantly in W(+)T ° and M16. For W(+)T(o), W(+)T(-) and M16, an increased energetic, fat and ash efficiency was observed, whereas M16 exhibited a positive increment in protein efficiency as well. Among selection treatment means, there were high positive correlations between WT6 and fat weight, protein weight, percent fat, CONS and EFF and a high negative correlation between WT6 and percent protein.