ST2302 Stochastic population models/MA8002 - Applied Biomodellling for PhD Students, spring 2020


May 24: No aids are permitted during the exam.

May 18: About the oral exam: Chapter 5 is included as self study so you should look at it before the exam too although the emphasis will be on chapters 1-4. And, yes, ST2302 is graded as usual (whereas students from biology taking it as the phd-course MA8002 only get pass or not).

During the exam, I will show a pdf with some written questions, topics and equations and then we will ask you about these topics. This can include questions about definitions, questions about the interpretation and meaning of particular results in the textbooks, and giving some explanation of how some of the results in the textbook are derived.

If you need write something such as an equation and show us during the exam you can do this (provided you have a camera on your pc) but we aim at asking questions that can be answered just by talking.

March 16: I posted a mini project that you can work on in the next few weeks. Also fill in which dates are possible for the oral exam below (we will most likely carry out the exam via Skype). I'm available on email, Skype (jtufto) and Skype for business if you have questions.

Jan. 15: Lectures are on Mondays 12:15-14:00 in F4 and Tuesdays 8:15-10:00 in R40 starting in week 4 (First lecture monday, January 20).

Jan. 14: We need to find suitable times for the lectures (and I'll need to find a better room than e304) so please fill in your available time points at this link.

General information

Lecturer: Jarle Tufto

The course textbook is available here.

The syllabus is as follows: Chapters 1-5.

References to much of the primary literature can be found in Lande, Engen & Sæther (2003) but this book has much less detailed mathematical derivations so is probably harder to read. Some of the material on diffusion processes is based on Karlin and Taylor, 1981, ch. 15. You may be able to find a pdf version online.

Engen, Lande, Sæther & Dobson 2009 covers much of the same material on reproductive value dynamics as Ch. 4. Age-structured models more generally is covered in much greater detail in Caswell's book on Matrix population models

We also offer an advanced phd-course on stochastic differential equation.


There will be an oral exam (about 45 mins per student). Date sometime between Mai 4 and June 6 to be decided. Please fill in possible dates in this spreadsheet. We will do the exam via zoom.

Friday May 8 Zoom link
10:00 Martha Thorstensen
11:00 Jannik Mähn
Wednesday May 27 Zoom link
10:00 Kenneth Aase
12:00 Astrid Raunsgard
13:00 Clara Esther Constance Panchaud

If anyone else plan to take the exam or want a different date, you can still fill in or update possible dates in the above spreadsheet. A zoom link will be posted here before the exam.

Mini project


Jan. 20: Ch. 1.1-1.4

Jan. 21: Ch. 1.5-1.7

Jan. 27: Ch. 1.7-1.8 (except 1.8.1).

Jan. 28: Ch. 1.9 (Exercise 10 and 16)

Feb. 3: Ch. 2.1-2.5

Feb. 4: Ch. 2.5-2.7.2

Feb. 10: Ch. 2.8 (Exercise 13), Ch. 3.1-3.5

Feb. 11: 3.5-3.7

Feb. 17: 3.8.1-3.8.3 (Exercise 9)

Feb. 18: 3.8.4-3.9

Feb. 24: 3.10-3.11.

Feb. 25: 3.12, 3.13-14, 3.15.

March 2: Ch. 4.1-4.3.1 (Exercise 2, 4)

March 3: Ch. 4.3.2-

March 9: Ch. 4.3.2-4.3.4, 4.3.6

March 10: "Estimation" section in Engen et. al. 2009 (see above link) Ch. 4.3.7

Ch. 5: Instead of lectures I suggest that you do the above mini project:

Suggested exercises

There will not be arranged ordinary exercise hours, but there are several excersies in the compendium you are encouraged to try to solve.

Exercises of "suitable" difficulty - Chapter 1: 1,2,5,6,7,12-18. Some suggested solutions

And from Chapter 2: 7,8,9,10.

And from Chapter 3: 1-7, 12, 13, 14, 20, 21. Suggested solutions to Chapter 2 and 3

From Chapter 4: 1, (2, 3, 4, 5), 10, 16, 17.

From Ch. 5: 2,5,7,8,9,16,17,18,19 (lots of calculations), 20

More solutions from Chapter 1 to Chapter 5 here.

2020-05-24, Jarle Tufto