In shorthorn cattle, coat colors are governed by a codominant pair of alleles R and W. The homozygous genotype RR produces red, the other homozygote produces white and the heterozygote produces roan ( a mixture of red and white). The presence of horns is produced by the homozygous recessive genotype pp and the polled condition by its dominant allele P.
If roan cows heterozygous for the horned gene are mated to a horned, roan bull, what phenotype ratio is expected in the offspring?

The phenotypic ratio of the cattle offsprings is as follows:

Red polled = 1/8

Red horned = 1/8

White polled = 1/8

White horned = 1/8

Roan polled = 2/8

Roan horned = 2/8

Explanation:

This is a cross involving two genes; one coding for coat color and the other for horn in cattle. The alleles of the first gene (Red, R and White, W) are codominant i.e. will both be expressed in a heterozygous state (Roan, RW). The polled allele (P) is dominant over the horned allele (p) in the second gene.

According to the question, a roan cow that is heterozygous for the horned gene will have genotype, RWPp while a roan bull that is horned will have genotype, RWpp. Hence, in a cross between these two cattles, each parent will undergo meiosis to produce the following possible gamete combinations;

RWPp- RP, Rp, WP, Wp

RWpp- Rp, Rp, Wp, Wp

These gametes used in a punnet square (see attachment) will produce 16 possible offsprings with 6 distinct phenotypes. The phenotypes are:

Red polled (RRPp or RRPP) = 2/16 or 1/8

Red horned (RRpp) = 2/16 or 1/8

White polled (WWPP or WWPp) = 2/16 or 1/8

White horned (WWpp) = 2/16 or 1/8

Roan polled (RWPP or RWPp) = 4/16 or 2/8

Roan horned (RWpp) = 4/16 or 2/8

Mantle convection  is the slow  creepingmotion of earth's solid silicate  mantle  caused by  convection  currents carrying  heat from the interior  to the planet's surface.[1][2]  the earth's surface  lithosphere, which rides atop the  asthenosphere  (the two components of the  upper mantle), is divided into a number of  plates  that are continuously being created and consumed at their opposite  plate boundaries. accretion occurs as mantle is added to the growing edges of a plate, associated with  seafloor spreading. this hot added material cools down by  conduction  and  convection  of heat. at the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of  subduction  usually at an  ocean trench.[3]this subducted material sinks through the earth's interior. some subducted material appears to reach the lower mantle,[4]  while in other regions, this material is impeded from sinking further, possibly due to a phase transition from  spinel  to  silicate perovskiteand  magnesiowustite, an  endothermic reaction.[5]the subducted oceanic crust triggers  volcanism, although the basic mechanisms are varied. volcanism may occur due to processes that add buoyancy to partially melted mantle causing an upward flow due to a decrease in density of the partial melt.secondary forms of convection that may result in surface volcanism are postulated to occur as a consequence of intraplate extension[6]  and  mantle plumes.[7]it is because the mantle can convect that the  tectonic plates  are able to move around the earth's surface.[8]mantle convection seems to have been much more active during the  hadean  period, resulting in gravitational sorting of heavier molten  iron, and  nickel  elements and  sulphides  in the core, and lighter  silicate minerals  in the  mantle.