Exam (elaborations)
Elizabeth S. Allman, John A. Rhodes - Mathematical models in biology_ solution manual
- Course
- Institution
Elizabeth S. Allman, John A. Rhodes - Mathematical models in biology_ solution manual
[Show more]
Content preview
Solutiony Manualfor y
Mathematical Models in y y
Biology:An Introduction
y y y
Elizabeth S. y
y AllmanJohn A. y y
Rhodes
y
Cambridge University Press, 2003
y y y
·
c y 2003, yyElizabeth y S. yyAllman yyand yyJohn yyA. y Rhodes
, Preface
Despite your ybest yefforts, ythere yis ylittle ychance ythat ythese ysolutions yare yerror-free.
yPlease y let y us y know y of y any y mistakes y you y find, y so y that y we y can y correct y them.
Special ythanks yto ythe ypublic ylibraries yof yBerlin, yMaryland; yColumbia, yNorth
yCarolina; yand yClarksville, yVirginia yfor ytheir y hospitality, y and y to y the
y governments yand yprivate ybenefactors ythat yfund ythem. yThey yallowed ythese
ysolutions yto ybe ywritten yunder y more y pleasant y conditions y than y we y expect y most
y students y will y experience.
Elizabeth yAllman
eallman@maine.edu
John
yRhodesyjrhodes@bates.edu
yAssateague yIsland, y Maryland
yCape y Hatteras, y North
y CarolinayBuggs y Island y Lake,
y Virginia
ii
, Contents
Preface ii
Chapter y 1. Dynamic y Modeling y with y Difference y Equations 5
1.1. The y Malthusian y Model 5
1.2. Nonlinear y Models 8
1.3. Analyzing y Nonlinear y Models 10
1.4. Variations y on y the y Logistic y Model 12
1.5. Comments y on y Discrete y and y Continuous y Models 13
Chapter y 2. Linear y Models y of y Structured y Populations 14
2.1. Linear y Models y and y Matrix y Algebra 14
2.2. Projection y Matrices y for y Structured y Models 16
2.3. Eigenvectors y and y Eigenvalues 17
2.4. Computing y Eigenvectors y and y Eigenvalues 19
Chapter y 3. Nonlinear y Models y of y Interactions 21
3.1. A y Simple y Predator–Prey y Model 21
3.2. Equilibria y of y Multipopulation y Models 22
3.3. Linearization y and y Stability 24
3.4. Positive y and y Negative y Interactions 25
Chapter y 4. Modeling y Molecular y Evolution 27
4.2. An y Introduction y to y Probability 27
4.3. Conditional y Probabilities 28
4.4. Matrix y Models y of y Base y Substitution 30
4.5. Phylogenetic y Distances 34
Chapter y 5. Constructing y Phylogenetic y Trees 40
5.1. Phylogenetic y Trees 40
5.2. Tree y Construction: y yDistance y Methods y – y Basics 42
5.3. Tree y Construction: y Distance y Methods y – y Neighbor y Joining 46
5.4. Tree y Construction: y yMaximum y Parsimony 49
5.6. Applications y and y Further y Reading 51
Chapter y 6. Genetics 55
6.1. Mendelian y Genetics 55
6.2. Probability y Distributions y in y Genetics 57
6.3. Linkage 62
6.4. Gene y Frequency y in y Populations 66
iii
, CONTENTS iv
Chapter y 7. Infectious y Disease y Modeling 70
7.1. Elementary y Epidemic y Models 70
7.2. Threshold y Values y and y Critical y Parameters 71
7.3. Variations y on y a y Theme 73
7.4. Multiple y Populations y and y Differentiated y Infectivity 75
Chapter y 8. Curve y Fitting y and y Biological y Modeling 77
8.1. Fitting y Curves y to y Data 77
8.2. The y Method y of y Least y Squares 78
8.3. Polynomial y Curve y Fitting 79
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Ascorers. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $15.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
64438 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now