# PopulationCurve

> PopulationCurve draws population growth on axes of time against population, from 0 to years in duration seconds from delay, a dot at the head of each…

Page: https://fframes-kit.pages.dev/docs/biology/population-curve/
Cargo feature: `biology` (`fframes-kit = { version = "..", features = ["biology"] }`)

`PopulationCurve` draws population growth on axes of time against population, from 0 to
`years` in `duration` seconds from `delay`, a dot at the head of each curve. Its `model` is
one of three:

- **`PopulationModel::Logistic`:** growth from `n0` at rate `r` levels off at the dashed
  carrying capacity `k`. With `compare` the exponential curve with the same start and rate is
  drawn faded beside it, until it leaves the top.
- **`PopulationModel::Exponential`:** the same growth with no limit.
- **`PopulationModel::PredatorPrey`:** Lotka-Volterra, with prey and predators rising and
  falling in turn. `PopulationModel::PREDATOR_PREY` cycles about every six time units.

A legend names each curve in its colour from `colors`. `series(count)` gives the values the
curves draw. Gallery scenes: `PopulationCurve` (logistic) and `PredatorPrey`.

Gallery clip of `PopulationCurve`: https://fframes-kit.pages.dev/media/scenes/PopulationCurve-82bb16a3.mp4

Gallery clip of `PredatorPrey`: https://fframes-kit.pages.dev/media/scenes/PredatorPrey-7b6221dc.mp4

```rust
use fframes_kit::prelude::*;

let logistic = PopulationCurve { k: 500.0, n0: 5.0, ..PopulationCurve::default() };
let n = &logistic.series(100)[0];
assert!((n[100] - 500.0).abs() < 5.0); // levelled off at K

fn cycles<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    ui.show(PopulationCurve {
        model: PopulationModel::PREDATOR_PREY,
        years: 20.0,
        ..ui.defaults()
    })
}
```

## API

Components are plain structs. Set the fields you need and fill the rest with `..ui.defaults()`: the defaults below come from the current theme (`theme.` values are fields of `Theme`).

### PopulationCurve

| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `model` | `PopulationModel` | `PopulationModel::Logistic` | Which curves: `Logistic`, `Exponential` or `PredatorPrey`. |
| `r` | `f64` | `0.8` | Growth rate per year (per unit of the time axis). |
| `k` | `f64` | `1000.0` | Carrying capacity, the population a logistic curve levels off at; it also sets the height of the vertical axis. |
| `n0` | `f64` | `10.0` | Starting population at time 0. |
| `years` | `f64` | `15.0` | Length of the time axis; the curves run from 0 to `years`. |
| `compare` | `bool` | `true` | Draws the faded exponential curve beside a logistic one when `true`. |
| `delay` | `f32` | `0.0` | Seconds after the container's start before the curves begin to draw. |
| `duration` | `f32` | `5.0` | Seconds the curves take to draw from 0 to `years`. |
| `center` | `(f64, f64)` | `(-0.8, -0.3)` | The middle of the axes, in units of `ui.space`. |
| `x_length` | `f64` | `8.5` | Width of the axes, in units of `ui.space`. |
| `y_length` | `f64` | `5.2` | Height of the axes, in units of `ui.space`. |
| `colors` | `[Color; 2]` | `[Color::hex("#69db7c"), Color::hex("#ff8787")]` | Colours of the first and the second curve; a faded comparison curve uses the second. |
| `axis_color` | `Color` | `theme.colors.muted` | Colour of the axes. |
| `label_style` | `TextStyle` | `label_style` | The font of the axis labels, numbers and legend: family, size in pixels and weight. |
| `text_color` | `Color` | `theme.colors.text` | Colour of the legend and the carrying-capacity label. |
| `enter` | `Option<FadeIn>` | `None` | Fade in at the start; `None` for none. |
| `exit` | `Option<FadeOut>` | `None` | Fade out before the end; `None` for none. |

Methods:

- `fn series(&self, count: usize) -> Vec<Vec<f64>>`: The populations at `count + 1` evenly spaced times from 0 to `years`: one series, or prey and then predators.

Feature `biology` · [Source](https://github.com/khanhthanhdev/fframes-kit/blob/main/fframes-kit/src/kits/biology/population.rs#L73)