Homework Help is Here – Start Your Trial Now!
Math
Statistics
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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 8EA
See similar textbooks
icon
Related questions
Question
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?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
SEE MORE TEXTBOOKS