Field Notes Journal Entry
What the Models Have Become
A reflective assessment of the seasonal modelling work so far — where the models succeed, where they struggle, and what they may actually be becoming
The seasonal modelling work began in a fairly modest way.
At first, the goal was simply to explore whether a small ordinary differential equation solver could reproduce the broad seasonal shapes seen in wildlife records.
The models were intentionally simple.
The hope was that simplicity would make experimentation easier:
- Small equations
- Understandable parameters
- Visible behaviour
- Fast iteration
At the time, it was not entirely clear how far that approach would go.
A few weeks later, three working model families now exist:
- Seasonal presence models
- Winter visitor models
- Resident detectability models
All three are capable of reproducing recognisable seasonal behaviour across a growing set of species.
The obvious question now is:
“What exactly has this work become?”
This post is an attempt to answer that honestly — including both the strengths and the limitations.
More Than Curve Fitting
One of the most important changes has been conceptual rather than technical.
Early versions of the models were largely concerned with shape:
- Can a curve rise and fall in roughly the right place?
- Can it reproduce a seasonal peak?
- Can it mimic broad timing?
That alone can be useful, but it risks becoming little more than mathematical tracing.
Gradually, however, the models - particularly the resident species model - began to shift towards something more interesting.
Parameters started to represent recognisable ecological ideas:
- Delayed summer suppression
- Persistence of detectability
- Seasonal carry-over
- Post-peak decline
- Autumn arrival forcing
- Winter persistence
At that point, the models stopped feeling like arbitrary curve generators.
Instead, they became small mechanistic hypotheses.
The question changed from:
“Can this equation reproduce the shape?”
to:
“What process might produce this shape?”
That transition matters.
The Importance of Interpretability
One deliberate decision throughout the work has been to avoid turning the models into opaque optimisation systems.
The models remain intentionally inspectable.
Most parameters still have names that can be understood directly:
- Growth rate
- Decay rate
- Seasonal peak
- Suppression timing
- Forcing width
This simplicity is a major strength of the project.
A more complex system might produce tighter fits, but at the cost of clarity.
Here, it is usually possible to look at a parameter set and understand the ecological story it is trying to tell.
That interpretability has become increasingly valuable as the models have evolved.
In many cases, the most useful outcome is not the fit itself, but the explanation suggested by the fit.
Why the Three-Model Structure Matters
One of the more important developments was the decision to separate the modelling work into three distinct behavioural families:
- Seasonal species
- Winter visitors
- Resident species
Initially, it was tempting to imagine a single general model that could handle everything.
In practice, that quickly became awkward.
The ecological structure of these groups is genuinely different.
A swift and a robin are not variations of the same seasonal process.
Nor is a winter visitor simply a summer visitor shifted around the calendar.
Each group has its own dynamics:
- Appearance
- Persistence
- Suppression
- Decline
- Recovery
Splitting the system into separate model families made the models both simpler and more expressive.
Rather than forcing one equation to do everything poorly, each model could focus on a smaller and more coherent ecological problem.
The Resident Detectability Model
Of the three current approaches, the resident detectability model has probably become the most interesting.
Earlier versions behaved too symmetrically.
Species increased and declined too smoothly, producing curves that looked mathematically tidy but ecologically artificial.
The addition of the following changed it considerably:
- Persistence
- Delayed suppression
- Asymmetric seasonal decay
- Carry-over behaviour
The resulting curves now show something closer to seasonal inertia.
Detectability can remain elevated after peak breeding activity has passed, before collapsing more rapidly later in the year.
This behaviour feels substantially more alive than the earlier versions.
Importantly, it also reflects something that appears repeatedly in the observed data: seasonal change is often asymmetric.
Spring build-up and late-summer decline are not mirror images of one another.
The Strength of Simplicity
One of the most encouraging outcomes has been that relatively small equations can reproduce a surprisingly large amount of observed behaviour.
The solver itself remains deliberately lightweight.
This has proven useful.
The models are:
- Easy to modify
- Quick to experiment with
- Relatively easy to understand
- Capable of rapid iteration
That flexibility has allowed the work to evolve quickly.
More importantly, it has kept the modelling process exploratory rather than rigid, and there is still room to ask:
- What happens if persistence increases?
- What happens if suppression is delayed?
- What happens if decline sharpens after the peak?
Those questions remain approachable because the system itself remains approachable.
What the Models Still Are
At the same time, it is important not to overstate what has been achieved.
These are still toy mechanistic models.
They are not full ecological system simulations.
At present:
- Environmental drivers are mostly implicit
- Weather is absent
- Species interactions are absent
- Stochastic behaviour is limited
- Observation bias is simplified
- Spatial effects are absent
The models primarily describe seasonal phenomenology, the changing shape of detectability or presence through the year.
That is still useful, but it is a much narrower problem than modelling an ecosystem itself.
The Risk of Increasing Complexity
As the models improve, another risk begins to appear.
Additional parameters almost always improve fit quality but every added mechanism introduces new problems:
- Parameter degeneracy
- Over-fitting
- Reduced interpretability
- Unstable optimisation
- Multiple equally plausible solutions
This may become one of the most important balancing points in future development, as there is a danger that complexity could slowly erode the very qualities that currently make the models useful.
At present, the models occupy a productive middle ground, being simple enough to understand but expressive enough to capture recognisable ecological structure.
Preserving that balance will matter.
The Role of Failure
One of the more surprising outcomes has been that model failure is often as informative as model success.
Some species fit extremely well.
Others resist simplification entirely.
In several cases, the mismatches appear to reveal genuine ecological structure:
- Multiple behavioural phases
- Abrupt transitions
- Irregular seasonal behaviour
- Overlapping processes
These failures are valuable because they identify where the assumptions of the model stop matching the biology.
That is often more interesting than a perfect fit.
A species that cannot be reduced to a smooth seasonal process may be telling a more complicated ecological story.
A Different Kind of Field Notes
Perhaps the most unexpected aspect of the project is how naturally it has started to connect back to the wider Field Notes work.
The modelling is no longer separate from the observations. Instead, the two increasingly inform one another, with long-term records suggesting seasonal structure and the models attempt to describe that structure mechanistically.
The mismatches then suggest where the observations may contain additional ecological complexity.
This creates a feedback loop between:
- Observation
- Interpretation
- Modelling
- Further observation
That feels increasingly close to the real purpose of the work.
Where Things Stand
At this point, the project feels less like a collection of equations and more like a small experimental framework for exploring seasonal ecological behaviour.
It is still simple.
It is still incomplete.
It remains very much exploratory.
However, the models now appear capable of expressing something genuinely useful; small, interpretable hypotheses about how seasonal detectability behaves through time.
That alone feels like meaningful progress.
For now, perhaps the most honest summary is this:
The models are still simple — but they are beginning to say interesting things
Tool
ODE Solver
A simple tool for exploring time-based models
The seasonal presence and detectability models were developed using a small, general-purpose ordinary differential equation solver, designed for experimentation and visualisation.
It allows simple systems to be defined and explored over time, making it possible to test how patterns might arise from underlying processes.
The application, the models, and instructions on how to run them are provided in the GitHub repository.