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7. The simplest type of inheritance occurs when a trait is governed by a pair of genes, each of which may be of two types, say G and g. An individual may have a GG combination, or Gg (which is the same as gG), or gg. Often, the GG and Gg genotypes are indistinguishable in appearance, in which case we say that the G gene dominates the g gene. An individual is called dominant if they have GG genes, a hybrid if they have Gg genes, and recessive if they have gg. Consider a process of continued matings. We start with an individual whose genotype is known, and mate it with a hybrid. An offpsring is chosen at random and is mated with a hybrid. This process is repeated through a number of generations. The genotype of the chosen offpsring in successive generations can be represented by a Markov chain. The states are indicated by GG, Gg, and gg respectively. The stochastic matrix is: P = GG Gg 99 GG Gg 99 [0.5 0.25 0] 0.5 0.5 0.5 0 0.25 0.5 a) Suppose the process is started with a hybrid bred to a hybrid. What is the probability of each outcome (dominant, hybrid, recessive) after one iteration? (b) What is the probability of each outcome after two iterations? (c) What is the steady-state vector for this Markov chain?

7. The simplest type of inheritance occurs when a trait is governed by a pair of genes, each of which may be of two types, say G and g. An individual may have a GG combination, or Gg (which is the same as gG), or gg. Often, the GG and Gg genotypes are indistinguishable in appearance, in which case we say that the G gene dominates the g gene. An individual is called dominant if they have GG genes, a hybrid if they have Gg genes, and recessive if they have gg. Consider a process of continued matings. We start with an individual whose genotype is known, and mate it with a hybrid. An offpsring is chosen at random and is mated with a hybrid. This process is repeated through a number of generations. The genotype of the chosen offpsring in successive generations can be represented by a Markov chain. The states are indicated by GG, Gg, and gg respectively. The stochastic matrix is: P = GG Gg 99 GG Gg 99 [0.5 0.25 0] 0.5 0.5 0.5 0 0.25 0.5 a) Suppose the process is started with a hybrid bred to a hybrid. What is the probability of each outcome (dominant, hybrid, recessive) after one iteration? (b) What is the probability of each outcome after two iterations? (c) What is the steady-state vector for this Markov chain?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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7. The simplest type of inheritance occurs when a trait is governed by a pair of genes, each of which may be of two types, say G and g. An individual may have a GG combination, or Gg (which is the same as gG), or gg. Often, the GG and Gg genotypes are indistinguishable in appearance, in which case we say that the G gene dominates the g gene. An individual is called dominant if they have GG genes, a hybrid if they have Gg genes, and recessive if they have gg. Consider a process of continued matings. We start with an individual whose genotype is known, and mate it with a hybrid. An offpsring is chosen at random and is mated with a hybrid. This process is repeated through a number of generations. The genotype of the chosen offpsring in successive generations can be represented by a Markov chain. The states are indicated by GG, Gg, and gg respectively. The stochastic matrix is: P = GG Gg 99 GG Gg 99 [0.5 0.25 0] 0.5 0.5 0.5 0 0.25 0.5 a) Suppose the process is started with a hybrid bred to a hybrid. What is the probability of each outcome (dominant, hybrid, recessive) after one iteration? (b) What is the probability of each outcome after two iterations? (c) What is the steady-state vector for this Markov chain?
Transcribed Image Text:7. The simplest type of inheritance occurs when a trait is governed by a pair of genes, each of which may be of two types, say G and g. An individual may have a GG combination, or Gg (which is the same as gG), or gg. Often, the GG and Gg genotypes are indistinguishable in appearance, in which case we say that the G gene dominates the g gene. An individual is called dominant if they have GG genes, a hybrid if they have Gg genes, and recessive if they have gg. Consider a process of continued matings. We start with an individual whose genotype is known, and mate it with a hybrid. An offpsring is chosen at random and is mated with a hybrid. This process is repeated through a number of generations. The genotype of the chosen offpsring in successive generations can be represented by a Markov chain. The states are indicated by GG, Gg, and gg respectively. The stochastic matrix is: P = GG Gg 99 GG Gg 99 [0.5 0.25 0] 0.5 0.5 0.5 0 0.25 0.5 a) Suppose the process is started with a hybrid bred to a hybrid. What is the probability of each outcome (dominant, hybrid, recessive) after one iteration? (b) What is the probability of each outcome after two iterations? (c) What is the steady-state vector for this Markov chain?
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