Field Notes Journal Entry
Where the Models Work, and Where They Don’t
Reviewing how well the seasonal models reproduce observed patterns, and what their limitations reveal
In the previous post, three simple models were introduced to describe seasonal patterns:
- Resident detectability
- Seasonal presence
- Winter presence
Each was designed to reproduce a different kind of ecological signal.
The next step has been to fit these models across a working set of species, and to compare the simulated curves with the observed data.
What follows is not a formal evaluation. Instead, it is a first pass: a simple assessment of where the models work, and where they begin to struggle.
A First Pass Assessment
Across the working set, most species fall into one of three outcomes:
- Good fit – the model closely matches the observed pattern
- Acceptable fit – the overall shape is right, but details are smoothed or damped
- No match – the model fails to capture the structure of the data
This is not a strict classification. It is simply a way of describing how well the simulated curves align with what is observed.
Even at this stage, a clear pattern begins to emerge.
Where the Models Work Well
Many species are well described by the models.
Seasonal species such as swift and chiffchaff produce clean, single peaks that align closely with the simulated curves. The timing, shape, and duration of the season are all captured with little adjustment.
Similarly, a number of resident species show smooth, continuous variation through the year. In these cases, the model reproduces:
- Higher detectability in winter and early spring
- Lower detectability in mid-summer
- A gradual return towards winter
For these species, the assumptions of the model match the underlying pattern.
The result is not just a good fit, but a useful one: a simple curve that reflects the main seasonal behaviour.
Acceptable Fits and the Role of Smoothing
A larger group of species fall into an “acceptable” category.
Here, the model captures the overall shape, but tends to smooth the details. This shows up in consistent ways:
- Peaks are slightly lower than observed
- Declines after the peak are more gradual
- Late-season “tails” are a little too strong
This behaviour is not surprising. The models are deliberately simple, and the fitting process favours smooth, stable curves.
In many cases, this smoothing may even be helpful. Observed data can be irregular, influenced by weather, sampling effort, or short-term events. The model can reveal the underlying seasonal signal by removing some of that noise.
For species such as buttercup or red campion, the result feels reasonable: the model does not match every detail, but it tells the right seasonal story.
Double Peaks and Blended Signals
Some species show more complex patterns, particularly those with two phases in the year.
Examples include:
- Plants with flowering and fruiting periods
- Butterflies with multiple broods
In these cases, the observed data may show two peaks. The model, however, produces a single smooth curve between them.
This is not strictly incorrect, but it does hide structure. What appears as one broad season may in fact be composed of two distinct ecological phases.
For now, these are treated as acceptable fits, but they highlight a limitation of the current approach.
Where the Models Begin to Struggle
A smaller number of species do not fit well.
In some cases, the model is simply under strain. The general pattern is present, but important features are misplaced or oversimplified. This often appears as:
- Misalignment in the timing of peaks
- Loss of smaller secondary features
- Overly smooth transitions where sharper changes occur
Goldfinch is an example of this. The model captures the idea of year-round presence, but misses the detail of how activity changes through the seasons.
Model Mismatch and Ecological Complexity
A few species fall into a different category altogether.
Here, the problem is not parameter choice, but model structure.
Species such as jay or magpie show patterns that are not well described by a single smooth seasonal curve. Instead, their records suggest distinct behavioural phases:
- Periods of high visibility
- Periods of low detectability
- Sudden increases linked to specific seasonal behaviours
These produce patterns with sharp transitions and uneven structure, which the model cannot reproduce.
In these cases, the mismatch is informative. It suggests that the species is not governed by a single seasonal process, but by a combination of behaviours that vary through the year.
What This Reveals
Taken together, the results are encouraging.
Most species are reasonably well described by simple models. This suggests that a large part of seasonal variation can be understood in terms of:
- Timing of presence
- Strength of seasonal activity
- Gradual changes in detectability
At the same time, the mismatches are equally valuable.
They highlight where additional complexity exists:
- Multiple seasonal phases
- Abrupt behavioural shifts
- Changes in detectability that are not smooth
Rather than being failures, these cases point to where the underlying ecology is more complex than the model assumes.
A Useful Balance
The aim of this work has not been to produce perfect fits.
Instead, it has been to find a balance:
- Models that are simple enough to interpret
- Yet flexible enough to reproduce real patterns
In most cases, that balance holds.
Where it does not, the differences themselves become useful. They draw attention to species whose behaviour cannot be reduced to a single seasonal curve.
Next Steps
This first pass provides a starting point.
The next steps are likely to include:
- Refining the models where small improvements are possible
- Identifying groups of species that share similar limitations
- Deciding where additional complexity is justified
More importantly, the results can now begin to feed back into the Field Notes pages.
Each species can carry not just a description of its seasonal pattern, but also an indication of how well that pattern can be explained by a simple model.
For now, the conclusion is straightforward:
Simple models go a long way — but where they fall short, they often reveal something interesting about the species itself
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.