ECOLOGY 231/POPULATION BIOLOGY 231

Quantitative Methods in Population Biology

Fall 2015

 


A tentative course schedule is below. Recommended eadings are in "Population Biology" by Hastings, on reserve.  The book "Mathematical Models in Biology" by Edelstein-Keshet  will also be on reserve for the course.  I will also try and get out via e-mail notes for some of the lectures (perhaps scanned versions or perhaps retyped versions).   Grading will be based on homework assignments (70%) and a take home final (30%). The lecture schedule is tentative because my goal here is to teach and not to lecture.   Class is 1:40-3:00 P.M. in 1020 Wickson.

Below the syllabus is a description of various tools for computing numerical solutions.  I will do in class demos with some of them, in particular xpp. 

Instructor: Alan Hastings, 3136AWickson 2-8116 email:amhastings@ucdavis.edu


ASSIGNMENTS

These will be sent via e-mail using the class e-mail list.

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SYLLABUS

DATE

TOPIC

READING IN EDELSTEIN-KESHET

READING IN HASTINGS

9/24

introduction, model formulation

pages 3-11

Pages 1-5

9/29

qualitative behavior of difference equations using linear algebra-part 1

pages 12-21

 

Pages 9-38

 

10/1

qualitative behavior of difference equations using linear algebra-part 2

10/6

Complex eigenvalues, steady states, stability of difference equations<

Pages 22-25, 39-44

Pages 41-60

10/8

more on steady states and stability of difference equations

pages 55-60

Pages 181-188

10/13

chaos and all that

pages 46-55

Pages 96-101

10/15

Nicholson-Bailey dynamics

10/20

model formulation and dimensional analysis

pages 113-128

Pages 81-87

10/22

steady states and stability of differential equations

pp. 128-145

Pages 87-92;119-128

10/27

linearization and linear systems for differential equations

10/29

linear systems of differential equations and stability criteria

11/3

phase plane methods

pages 164-186

Pages 129-180; 189-200

for both lectures

11/5

qualitative behavior of differential equations

pages 186-199

11/10

review of functions of several variables & the diffusion equation

pp. 385-395

11/12

the diffusion equation-part 2

pages 406-410, 437- 441,447-452

11/17

Diffusion equations-part 3

11/19

Diffusion equations-part 4

11/24

TBA

12/1

TBA

 

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Books on reserve in Shields library for the course

 

The books by Hastings and by Edelstein-Keshet and Murray’s book on mathematical biology, and Kot’s book will be on reserve for the course, as well as a couple of others.  


 

 

Solving ODE's and other dynamical systems numerically is an important first step, especailly for nonlinear systems.
This table is a summary of easily available solutions.

 

 

 

Program

   COST

Handles ODES

progamming needed

installation

 graphics

handles PDE's

includes continuation package and bifruaction diagrams

other

xxp-auto

free

Y

very minimal

easy except on windows, possible on windows

yes

no

yes

runs on ipad and iphone, very good tutorials and texts

R and desolve

free

Y

moderate

moderate

yes

yes

no

very good tutorials and texts

matlab and matcont

$ + free

Y

very minimal

moderate

yes

no

yes

good tutorials

mathematica

$$$

Y

very minimal

easy

yes

yes

no

symbolic as well

do it yourself

free

Y

lots

depends

depends

yes

no