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Hi, for single species what is envisaged for evolutionary dynamics and stochasticity (last year as an intro to ODEs I taught them about noisy exponential growth, which becomes exactly exponential in large N limit — I have slides for this). Similarly, there is Evolutionary dynamics in the ecology sections, so what do you have in mind and how do we keep it consistent with what I'll be adding/teaching for basic pop gen? It's possible this is already what you thinking, but would be nice to talk at the end about eco-evolutionary feedbacks to tie in both themes together. |
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I have written out a list of topics that I currently cover (attached Some stuff would cover species interactions and spatial structure. Perhaps one thing to consider is to be flexible about the split single species-species interactions. Interactions build normally quite naturally from single species descriptions (eg the LV interaction model as a generalisation of the logistic model). Much of the exercises I have used are based around the use of XPP/AUTO. If we stop using that we need to think what/if/how we can replace that with Python based exercises, Perhaps the Python implementation of AUTO works I have never used it, and in my experiences, it is the front end that normally causes issues. WIll it be worth it? My guess is probably not. But ditching it will affect a lot of the structure of the latter end of the teaching where some of it uses quite advanced analysis that will not be easy to code up in Python. Also, a lot of the teaching is based on the visualisation that is possible in this programme. Replacing that will not be all that simple and require quite a bit of work. |
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Just a thought. If Bhavin picks up the first week and can make a start on single populations, leading onto evolutionary dynamics. Week two can then continue on the evolutionary path. In week 3 we then follow up with more complex interactions between different populations. That would mean a lot of the current structure, at least for now can carry over and we can then continue to integrate it into this framework. One aspect that is perhaps most difficult to fit in naturally is matrix algebra, eigenvalues etc. I don;t know to what degree this is needed for single populations. Would imagine one would need it for evolution/selection. I will certainly need it for the species interactions |
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Hi All, sorry got a bit snowed just before Christmas and didn't act on any of this! @vaajansen I don't think I am teaching any of the first week — @mhasoba do let me know if you do. But I've attached all my Maths2Biology teaching from last year, including a ppt file called 1DExponentialGrowth.pptx .. ok won't let me as too large! I've attached the ppt file only! |
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Hello folks, I am populating the schedule for the 3 weeks of the E&E Modelling Module here @yanzhu624 and @Lakezh , please have a look at next week's schedule (we can make tweaks till tomorrow). @BhavKhatri and @tinyuhui, please add your (+Austin's) week's (of 20th) schedule to the same sheet using the next week's data / entries as an example. Your last year's schedule is here. Please add in lecture or practical titles, so that I can make suggestions for how to best fit them into the new structure above. @vaajansen, can you please remind me which days you cannot make in the week of the 27th? I will populate the timetable sheet accordingly. Basically you will pick up where I leave off, and will not need to add anything to your previous lectures (except perhaps moving away from xppaut - TBD) - @yanzhu624 , any update on the xppaut front? (See discussion thread above) |
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Hi Samraat
Can schedule also go on github please? Still struggling to access sharept
I am free for all of the week of 27th apart from Wednesday from midday. I am hosting a seminar speaker, it would help if I could leave a little earlier, say 11 or so
After this discussion I want to rework the first lecture (single population models) to connect better to what Bhavin has done. I think a fun thing to do is to link discrete and continuous models better. I think that can be done using a generation approach and this could make an interesting contribution to the text book part. @bhavin, I have an idea what you will cover but can you give me an outline? I
Exercises/practical work is going to be a problem. They were almost all centred around XPPAUTO. Even if this can be done within python, I have no idea how to operate this or how the front end works and will need serious help with this: I will not be able to do this on my own in the next week. Perhaps a better alternative is to rework it all into programming sort of problems, but it will be a considerable effort to develop that, and I wonder about the pedagogic effectiveness of it all (it will take the focus away from understanding the underlying logical structure and become a programming/debugging/outputting stuff on a screen exercise). Part of the issue that I fear we will run into, is that to get output that makes sense, you need to have a got front end way to plot things. This is what well-developed programmes give you in their front end. Not using that means you have to do all of this by hand, which is cumbersome and only partially relevant. And even if take this approach, it cannot be done in a week.
What sort of other exercises do you set them in the other part of the course?
Best
Vincent
From: mhasoba ***@***.***>
Sent: Wednesday, January 8, 2025 6:03 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Hello folks,
I am populating the schedule for the 3 weeks of the E&E Modelling Module here<https://imperiallondon.sharepoint.com/:x:/r/sites/CMEEMasters2024-25-LB-Teaching/Shared%20Documents/Teaching/LIFE70064_Mathematical_Modelling_in_Ecology_and_Evolution.xlsx?d=w8266f1b4d2a447568a19c82aa9412202&csf=1&web=1&e=XcAYPs>
@yanzhu624<https://github.com/yanzhu624> and @yanzhu624<https://github.com/yanzhu624>, please have a look at next week's schedule (we can make tweaks till tomorrow).
@BhavKhatri<https://github.com/BhavKhatri> and @tinyuhui<https://github.com/tinyuhui>, please add your (+Austin's) week's (of 20th<https://imperiallondon.sharepoint.com/:x:/r/sites/CMEEMasters2024-25-LB/Shared%20Documents/General/LP_timetable_CMEE.xlsx?d=w87ab16e8d9b84f3e9a10545b0d623d9e&csf=1&web=1&e=Dxshmn>) schedule to the same sheet using the next week's data / entries as an example. Your last year's schedule is here<https://imperiallondon.sharepoint.com/:f:/r/sites/CMEEMasters2024-25-LB-Teaching/Shared%20Documents/Teaching?csf=1&web=1&e=EDQUMV>. Please add in lecture or practical titles, so that I can make suggestions for how to best fit them into the new structure above.
@vaajansen<https://github.com/vaajansen>, can you please remind me which days you cannot make in the week of the 27th? I will populate the timetable sheet accordingly. Basically you will pick up where I leave off, and will not need to add anything to your previous lectures (except perhaps moving away from xppaut - TBD) - @yanzhu624<https://github.com/yanzhu624> , any update on the xppaut front? (See discussion thread above)
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Hi Bhavin
Just spoke to Samraat. Have an idea how to proceed and tie it all together. Will write it down (hopefully before Monday) and post
I was wondering to what detail you will cover exponential and logistic growth, but after having spoken to Samraat I think the overlap is fairly limited, and where it exist useful
V
From: Bhavin Khatri ***@***.***>
Sent: Thursday, January 9, 2025 1:51 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Hi Vincent, not very clear what you want me to cover on 27th or what outline you would like to see - just to be clear I'm not teaching any of the intro stuff next week. A brief description of the things I am teaching in the Evolution week (20th on) are now updated on the spreadsheet for the timetable.
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I had a chat with Samraat and the overall advice was to keep the bulk of my lectures as was. I will add some new stuff, but will hang on to what was there. Based on that I wrote out a summary of the week (apart from Wednesday which Samraat and Yan will cover). Is attached I alos went through the practical material. Some of it can be salvaged by asking students to implement it in Python (or whatever language they have been using to code up ODE models). Also attached. (green: can be modified. red: probably not feasible, orange: perhaps). Yan, have a look. I will need help with this, I don't use python or R Some stuff I have taken out to free up the wednesday. I have taken out apparent competition (not a great loss probably, a bit niche) but also the stuff I did on chaos in the logistic map because Samraat is covering that. There was some interesting biological examples as well as an really nice exercise showing the limits to predictability (still in attached practicals file). Is easy to code up, in case you want to use it elsewhere. What i have added is the idea of linking discrete and continuous first order models using a generation expansion. That links fitness, reproduction number and multiplier together and is a nice connection. One thing that really needs to be amended is in the current notebook explanation of growth the idea of parent to offspring ratio should be replaced by the number of offspring per parent. Much more intuitive and links all this stuff nicely together Looking at the other outlines of what has been proposed: there is a degree of overlap, but I hope it will reinforce rather than put students off. If you think too much, let me know. |
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@BhavKhatri , I am only seeing 3 / 5 days currently populated in the Week 2 schedule - I assume its work in progress? |
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Hi Bhavin
I will write something out in the next few days to clarify
But basically it is the argument that links the condition for growth in the continuous model b-d>1 to the discrete condition b/d>1 in a way that it generalises to Leslie matrices. It is also the argument underlying the use of fitness as expected the number of offspring and R0, the reproductive number in epidemiology. The latter is done through a next generation matrix. That is the same idea. It brings it all under one umbrella
V
From: Bhavin Khatri ***@***.***>
Sent: Saturday, January 18, 2025 12:57 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Hi @vaajansen<https://github.com/vaajansen> , just looking at this again as I'm about to teach evolutionary modelling. Can you clarify this paragraph:
"What i have added is the idea of linking discrete and continuous first order models using a generation expansion. That links fitness, reproduction number and multiplier together and is a nice connection. One thing that really needs to be amended is in the current notebook explanation of growth the idea of parent to offspring ratio should be replaced by the number of offspring per parent. Much more intuitive and links all this stuff nicely together"
Since I'm going to do through going from discrete to continuous in the context of simple models of (frequency independent) selection, but not clear what you mean by generation expansion? Would be good if we were consistent, and just want to make sure we don't confuse the students!
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I will try to get something on paper before that, but just do what you normally do, it will tie in
The only thing not to use is the parent to offspring ratio, instead use number of offspring per parent
Sorry, yes, should be b-d>0 which in a generational approach corresponds to b/d>1 (no of offspring per parent exceeds 1)
From: Bhavin Khatri ***@***.***>
Sent: Saturday, January 18, 2025 4:09 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Ok.. but my teaching starts at 10am Mon! (I assume b-d>1 is a typo!).
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Hi Bhavin
This is still a work in progress but here is a first attempt at writing down the lecture material for one of my lectures on Monday 27 where I link continuous time and discrete time models. I hope It makes the reasoning clear
Sorry, in haste but thought you could do with it now
Good luck tomorrow
Vincent
From: Bhavin Khatri ***@***.***>
Sent: Saturday, January 18, 2025 4:09 PM
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Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Ok.. but my teaching starts at 10am Mon! (I assume b-d>1 is a typo!).
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Yes I did! Sorry
From: Bhavin Khatri ***@***.***>
Sent: Sunday, January 19, 2025 1:39 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Hi @vaajansen<https://github.com/vaajansen> thanks- did you mean to post an attachment?
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the attachment to the emails don't seem to make it here. Trying again now as a direct post |
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Cheers Bhavin
I tried to make clear that the two approaches give different results, but will sharpen that and your comments are very useful for that
There is pros and cons for both. The interpolation that you apply has the issue that it has no clear biological interpretation (you are filling in the dynamics between time points where you have not specified what the biology does, so it all fits, but you lose the meaning). The generation expansion preserves the meaning (you start the full continuous description) but completely changes the meaning of time and that is difficult to get your head around but is incredibly powerful in interpreting the results. Both are valid measures for fitness or growth so it is not one against the other, they serve different means
As I wrote this I was tempted to do the master equation and show how the individual discreteness in a full stochastic model can lead to the exponential model, but as we don't really deal with stochasticity I thought it was a bit too much for this course. It would be neat to do the whole thing starting from scratch all the way up, but my fear is that we will lose as good as all students on the way
Good luck with the teaching
Vincent
From: Bhavin Khatri ***@***.***>
Sent: Sunday, January 19, 2025 5:58 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Ok! Briefly read this.. first I thought you were writing down a Master eqn.. but you're not. Looks very neat, but I think you/we need to be careful, since I make connection between Wrightian and Mathusian fitness with relation f = ln(w) - I think the maths 4 biology appendix also does the same for exponential growth for continuous growth rate v and discrete time R (v = ln(R)) - and (having given it literally only a few moments thought) I'm not sure how this fits into the picture you've just described in your note of R=b/d (I think they are subtly different is the answer, since one is a truly discrete time process N_{i+1} = RN_i and v = ln(R) is a literal interpolation for dN/dt= vN, and what you have is actually still a continuous time process - I think you need to make that clear, since in your note you say let's go to discrete time- but you are tracking age cohorts)
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HI Bhavin
Good suggestion, it indeed isn't time.
Will do, and that was exactly the plan
Good luck with the teaching this week
Vincent
From: Bhavin Khatri ***@***.***>
Sent: Monday, January 20, 2025 2:18 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Yep agree! I think this is very nice, but regarding "completely changing the meaning of time" - I would avoid the confusion by not calling this time but generation class/cohort and just say individuals from different generation classes can overlap at a given time, which is clearly the case - but there is clearly an approximate ordering of generation class/cohort with time. Then I imagine this naturally leads onto talking about age structure in a population. What might be nice if you plotted n0(t), n1(t), ... nk(t) vs time, which should show peaked functions, whose peaks arise at successively later times, but there is overlap of the tails.
I think I tried rudimentary Master eqns in the first couple of years I taught Maths 4 Biology and it was a bit of a stretch!!
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Hi
I thought we were moving towards we would rewrite them away from XPPAUT but I would need help with this. Still waiting for input from Yhan that end. I can't do this myself. Also not sure what format you are looking for or what is useful/meaningful to do
Time is drawing very short now
Vincent
From: mhasoba ***@***.***>
Sent: Thursday, January 23, 2025 11:30 AM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
@vaajansen<https://github.com/vaajansen> , any further thoughts on modifying your practicals? Are you planning to sticj with XPPAUT for this year?
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In the document I circulated a couple of weeks ago I flagged up specific examples, the detail is all there, but I would need help in getting that into python and in a way that fits in with the rest of the coursework. The challenge is to turn them into something that is useful and instructive for them to do
But if we stick to XPP for this year that will certainly facilitate the teaching. Ok, let's do that
V
From: mhasoba ***@***.***>
Sent: Thursday, January 23, 2025 2:28 PM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
We would need specific examples from you with solutions that could be implemented in Python.
Yeah, this year let's stick with xppaut...
TBD in next iteration!
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Hi Samraat
That is great! Thank you!
I am trying to link my lecture to stuff that has appeared on the MQB page, but it is all taking time. I am rewriting sections because of this and need to add materials, I am in middle of it all. Lectures will be in powerpoint, but can be converted into pdf if you want (normally rather horrid end result)
I am currently working on text for your book. I have done it in Latex so I can concentrate on content but should be easy to convert. It is not finished yet, but I have the latest effort attached. It needs an excursion into structured models. This has eaten up most time, I am afraid
I will work on the powerpoints and practical descriptions and send them, but it will be over the weekend
V
From: mhasoba ***@***.***>
Sent: Friday, January 24, 2025 11:01 AM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT] Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
In that case, I will share the same instructions<content/lectures/EcolMod_VJ> as last year - I have checked and it all works as before in the UNIX terminal. Please share this year's lectures / practicals as soon as they are ready.
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Reminder to @mhasoba to include a section on models vs laws vs theories vs paradigms in the intro Chapter of E&E modelling section |
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Not sure what this is for, but I quite liked this paper
Lawton, J. H. 1999. Are there general laws in ecology? Oikos 84:177-192.
It might help to keep that section short
Getting pressure on my time in Jan. would be nice if we could decide on some structure
V
From: mhasoba ***@***.***>
Sent: 09 October 2025 09:17
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
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Reminder to @mhasoba<https://github.com/mhasoba> to include a section on models vs laws vs theories vs paradigms in the intro Chapter of E&E modelling section
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I am on campus everyday, I just noticed, happy to pop into Silwood. Can do everyday, but Thursday is the one where it is not so easy, leaves Mo after 4, Tue after 4, Wed after 3, Fri after 5. If need be can bring time forward by a half an hour by coming be car. Actually, mornings of Thursday, Fri also possible
Any good?
Vincent
From: mhasoba ***@***.***>
Sent: 22 October 2025 18:41
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
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Just finishing up my 4-week Bootcamp teaching - how about we meet next week?
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Hows tomorrow?
…On Wed, 22 Oct 2025, 22:23 Vincent Jansen, ***@***.***> wrote:
I am on campus everyday, I just noticed, happy to pop into Silwood. Can do
everyday, but Thursday is the one where it is not so easy, leaves Mo after
4, Tue after 4, Wed after 3, Fri after 5. If need be can bring time forward
by a half an hour by coming be car. Actually, mornings of Thursday, Fri
also possible
Any good?
Vincent
From: mhasoba ***@***.***>
Sent: 22 October 2025 18:41
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's
Ecological and Evolutionary modelling section (Discussion #145)
This email originated from outside Royal Holloway. Be cautious using
links, attachments and QR codes.
Just finishing up my 4-week Bootcamp teaching - how about we meet next
week?
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Reply to this email directly, view it on GitHub<
#145 (reply in thread)>,
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Ok if it's in the morning
From: mhasoba ***@***.***>
Sent: Thursday, October 23, 2025 8:19 AM
To: MulQuaBio/MQB ***@***.***>
Cc: Jansen, Vincent ***@***.***>; Mention ***@***.***>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
This email originated from outside Royal Holloway. Be cautious using links, attachments and QR codes.
Hows tomorrow?
On Wed, 22 Oct 2025, 22:23 Vincent Jansen, ***@***.***<mailto:***@***.***>> wrote:
I am on campus everyday, I just noticed, happy to pop into Silwood. Can do
everyday, but Thursday is the one where it is not so easy, leaves Mo after
4, Tue after 4, Wed after 3, Fri after 5. If need be can bring time forward
by a half an hour by coming be car. Actually, mornings of Thursday, Fri
also possible
Any good?
Vincent
From: mhasoba ***@***.***<mailto:***@***.***>>
Sent: 22 October 2025 18:41
To: MulQuaBio/MQB ***@***.***<mailto:***@***.***>>
Cc: Jansen, Vincent ***@***.***<mailto:***@***.***>>; Mention ***@***.***<mailto:***@***.***>>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's
Ecological and Evolutionary modelling section (Discussion #145)
This email originated from outside Royal Holloway. Be cautious using
links, attachments and QR codes.
Just finishing up my 4-week Bootcamp teaching - how about we meet next
week?
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#145 (reply in thread)>,
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Assume it is Fri Morning. What time?
Vincent
From: Jansen, Vincent
Sent: Thursday, October 23, 2025 10:15 AM
To: 'MulQuaBio/MQB' ***@***.***>
Subject: RE: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
Ok if it's in the morning
From: mhasoba ***@***.******@***.***>>
Sent: Thursday, October 23, 2025 8:19 AM
To: MulQuaBio/MQB ***@***.******@***.***>>
Cc: Jansen, Vincent ***@***.******@***.***>>; Mention ***@***.******@***.***>>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's Ecological and Evolutionary modelling section (Discussion #145)
This email originated from outside Royal Holloway. Be cautious using links, attachments and QR codes.
Hows tomorrow?
On Wed, 22 Oct 2025, 22:23 Vincent Jansen, ***@***.***<mailto:***@***.***>> wrote:
I am on campus everyday, I just noticed, happy to pop into Silwood. Can do
everyday, but Thursday is the one where it is not so easy, leaves Mo after
4, Tue after 4, Wed after 3, Fri after 5. If need be can bring time forward
by a half an hour by coming be car. Actually, mornings of Thursday, Fri
also possible
Any good?
Vincent
From: mhasoba ***@***.***<mailto:***@***.***>>
Sent: 22 October 2025 18:41
To: MulQuaBio/MQB ***@***.***<mailto:***@***.***>>
Cc: Jansen, Vincent ***@***.***<mailto:***@***.***>>; Mention ***@***.***<mailto:***@***.***>>
Subject: [EXT]Re: [MulQuaBio/MQB] Proposed structure of new MQB's
Ecological and Evolutionary modelling section (Discussion #145)
This email originated from outside Royal Holloway. Be cautious using
links, attachments and QR codes.
Just finishing up my 4-week Bootcamp teaching - how about we meet next
week?
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@BhavKhatri , @jrosindell, @yanzhu624, @tinyuhui , and @vaajansen, here is the proposed structure for a new set of materials under MQB to teach Ecological and Evolutionary theory and modelling (Please comment / suggest changes).
Introduction
The metabolic basis of everything
Single populations
Species Interactions
Spatial structure
Communities, Food-webs and Ecosystems
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