3 Your thesis

3.1 Hypotheses and models

Design a chapter that is do-able. In my experience, a plan that is ‘just a bit more’ than the current state-of-the art, will turn into something bigger, and might even turn out to be amazing. A good thesis is a done thesis. Make the hard decisions early: it is less glamorous to design a thesis that is feasible, but it will get you graduated and get you a job.
Getting a chapter finished is a great accomplishment.
If you plan for a career in academia, it can be helpful to work collaboratively.
Make github, google drive, and google docs, to summarize and share your work on a project. Use Github Desktop as a GUI to make using github easier.
Consider Zotero for managing your references. Use the browser plug-in and the add-on for MS Word. Bibtex is another good choice.
Read the literature to formulate your hypotheses. Every thesis is framed within a broader context, for example,

population dynamics in seasonal environments;
population dynamics in stochastic environments;
population dynamics given an earlier age of first reproduction;
pathogen evolution in response to host ecology and immunity;
frameworks to model biological invasions.

There is lots of existing work on these general topics. Read papers from The American Naturalist, Trends in Ecology and Evolution, and Ecology Letters; journals that value generality, until you can describe the state-of-the art facts about a general topic, and explain their relevance for your study question. For example:

Threshold growth quantities, such as R0, are equivalent in seasonal and non-seasonal environments when specific conditions, regarding reproduction and stage-to-stage transitions, are met (Mitchell and Kribs, 2017). While such conditions are met for sea lice, transient dynamics are key to understanding best management practices for sea lice, and so we aim to extend the current theory in this area.

The first sentence describes a specific piece of knowledge about seasonal population dynamics. We show scholarship and build trust with our reviewers by demonstrating our knowledge of Mitchell and Kribs. The second sentence relates this general knowledge to our specific application.

It is good to read about the biology of your study species, but you need to spend at least as much time also reading about general ecological/evolutionary principles.
Also build your knowledge of modelling. You can get ideas for this by knowing the fundamentals well, for example by reading A Biologists Guide to Mathematical Modelling (Otto and Day) and Modeling Infectious Diseases (Keeling and Rohani). Then also tackle the cutting edge by reading articles in the Bulletin of Mathematical Biology, Epidemics, and the Journal of the Royal Society Interface, and also by following up on any citations that take your interest.

3.2 Coding

If you are stuck on coding, perhaps the problem isn’t your coding skills, but that don’t know what you want to code. It may help to write out the steps of your code as pseudo-code.
Most graduate students in my lab are good coders. Talk it through with a labmate. Just saying it out loud can help you realize what you are trying to do isn’t well-defined.
Copy and paste the example from the help file or vignette. Then, step up the complexity of the problem piece-by-piece, checking to see that it still runs after a small round of changes. Continue until you have modified the example code enough to solve your problem.
Find out the line your error is being generated from. Even in MATLAB, where the line of the error is reported, the actual error may have occurred before. You should be able to query the values assigned to quantities after each line is executed to identify the true line of the error.
Take a hypothesis testing, deductive reasoning, approach to debugging. For example, if a function has two arguments, then the error must be in the format/value of one or other argument, or with the function itself: run tests to narrow the possibilities.
Run unit tests: set the mean dispersal distance to zero; do you recover the expected non-spatial population dynamics? Set mortality to zero: does the population grow? Set the birth rate to zero: does the population die out?
Step through your code and query the value of your variables to make sure they are what you think they are.
I don’t want you to be stuck on your code for long. I will help you, but it may take a week or so for me to find a gap in my schedule because this may require me to find a block time. I prefer to code-share with Github.
If you are stuck on your code, the problem may be that you don’t have a good strategy for debugging your code. One way to learn this can be to sit with someone while they debug your code and have them explain what they are thinking as they perform different tests.
I expect you to publish your code alongside your manuscripts and thesis. Archive your code on Figshare, Github, or similar.
The softwares I know(-ish) are MATLAB and R. MATLAB is still popular with mathematical biologists, but it is propretiary and so many of the next generation of mathematical biologists choose open source alternatives. R is very popular with biologists. R’s user community is now so vast that there are packages available to do almost anything. R is free, which isn’t a factor during your graduate studies, but may become a factor at your next place of employment. Although, I don’t code in Python or Julia, you could complete your thesis in these languages if you are comfortable with them/have good reasons to use them. Many members of the lab currently have expertise in macpan2, and you are likely to have accelerated success if you work within this framework and build on this existing knowledge.

3.3 Writing

The more familiar you are with the published literature the better your writing will be, and the better you will be able to formulate hypotheses and explain your ideas.
Writing involves three steps: reading, thinking, and writing. After you read, you need to think about how this new knowledge ties in with your existing knowledge, and with the results you are writing about. If you don’t know what to write, or you don’t like what you’ve written, you may have skipped the thinking step.
Your paper has one main result. You did a lot of work to get to your results, but after doing all the work you need to organize it by prioritizing and de-prioritizing certain elements.
The papers you cite need to fit your story. You probably don’t want to write:

Hurford et al. finds that wolves recolonize slower than expected.

A better sentence is:

Efforts to parameterize and validate reaction-difussion and related spread rate models have generally found that empirical spread rates are slower than the theoretical predictions (Hurford et al.).

This second sentence takes control of the narrative: to tell the story of your results, one important topic you need to discuss is ‘parameterization and validation’. You should arrange your Introduction so that you discuss the topics important to your results. The first example sentence typically appears in an Introduction that is unsure of the general topics that relate to the results (i.e., parameterization and validation). An Introduction written this way lists papers and their main results, and the focus is on citing the papers rather than building a narrative around your results.

Please write in active voice and present tense. For a Methods section it may be okay to write in past tense, but try to keep present tense as much as possible.
Please see How to write a Nature Summary. Writing an abstract this way asks you to think about the broader relevance of your work, and this is often something that doesn’t receive enough attention.
Scientific writing made easy by Turbeck and colleagues is a helpful resource.
Please see Scientific paper outline by Kevin Lafferty. This outline asks the writer to provide paragraphs that show you have summarized the relevant literature on your topic. One component of this is the study system, but this comes after summarizing the literature on the ‘big picture’ question.
Start the outline of your paper by deciding what figures you will include. The writing needs to be concise, and planning this way will help keep a streamlined focus.
Most members of the lab are using overleaf to write their manuscripts and thesis. Latex is stable, and MS Word usually crashes, especially when using equation editor in combination with copy and paste. Some members of the lab that have significant biology components of their thesis will write in Microsoft Word, which is also fine.
Get feedback from me on your writing early and often. This helps you to understand my expectations for your written work. If you are hoping to quickly finish writing your thesis, the timeline is more likely to proceed as you expect if you are familiar with my expectations and feedback on your writing.
Get your peers to read your writing.
How to write a theoretical paper that people will cite has good advice.
Write concisely, and write the paper so that readers will find reading it interesting. Focus on explaining concepts and context; technical details are important, but they may belong in an Appendix. When proof-reading your work, consider whether the meaning of your sentence can be preserved if some words are deleted. For example, ‘the fact that, the earth is a sphere’ can usually be edited down to ‘the earth is a sphere’: generally, ‘the fact that’ seems to add nothing.
Try to avoid complex sentence structures so that your writing is more easily readable. For example, ‘By revisiting our analysis of historical data, we can calculate new quantities’ can have the comma edited out and the sentence can proceed in order making it more readable, if we revise it to ‘We calculated new quantities by revisiting historical data’.
Don’t write things that aren’t true or you aren’t going to back up, for example, ‘Climate change is the biggest problem of our generation’; if this is an ecology paper, you won’t back up that sentence, that sentence belongs in an sociology paper.

3.4 Artificial intelligence

It is well-known that ChatGPT can write essays for undergraduate biology courses and receive good marks, but also that using AI in this way can introduce fake references and have substantial flaws. I have been asked to review work by graduate students that has contained large, substantial flaws because it has been AI-generated. It is fine to use AI to increase your productivity but remember: you control AI, it doesn’t not control you. Neither of us gain anything if you hope to trick me into thinking that you understand what you are doing by producing something superficial with AI that falls apart on careful inspection. Giving me AI-generated work because you would prefer not to admit that you don’t understand just sets your timeline to graduation back as I have to sort through the flawed work. You can use AI successfully in your work, but you do need to have some idea of what is correct and what is wrong, so you can train your AI assistant in the right direction.
A resource on AI in mathematical biology.