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Elizabeth S. Allman, John A. Rhodes - Mathematical models in biology_ solution manual
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Elizabeth S. Allman, John A. Rhodes - Mathematical models in biology_ solution manual
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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
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