Branch: filling in time series gaps in beaver expansion

[goldma99]

Problem

I only have three snapshots of beaver expansion: 2012, 2017, 2021. I want to know exactly where those beavers were at each year in between.

Potential solutions

• "Mosaic of evidence": imputing beaver expansion
  • First, use ecologist's knowledge about how beavers tend to expand to impute beaver presence in the inter-survey years.
  • Second, adjust "ecology" estimate by ground-truth reports
    • In there years before an area was ecology-estimated to have a beaver, were there 1) requests for beaver control; 2) insurance claims made; 3) applications to Rural Payments support schemes that referenced beavers; 4) iNaturalist sightings? These are lower bounds on beaver presence.
    • If so, adjust the ecology estimate so that the first year of those ground-truth reports become the year when beavers arrived in that location.

Data

• [ ] iNaturalist
• [ ] NFU Mutual, other insurance providers
• [ ] Rural Payments (flood bank or basic payments scheme)
• [ ] NatureScot requests for beaver control

[goldma99]

The description above has it the wrong way around.

• First, estimate the rate of expansion from the observed data (distance/time)
• Next, compare the implied rate of expansion to rates from the literature. Adjust up or down.

[goldma99]

• [ ] How does NatureScot estimate total population from the survey data? This is really important, because if I want to estimate the variations in TE along the extensive margin of beaver habitation, I need to be able to convert observations into population.
• [x] Following Barták et al.'s weighted graph approach, first step needs to be attaching beaver observations to their nearest graph edge (ie, river segment).
• [x] Why are there so many more observations in 2017 than 2012?

[goldma99]

Using known factors (from the ecology literature) that influence beaver movement--as well as road and terrain layers from OS, project movement of individual-equivalent "beavers" over time, given their 2012 starting point.

This is inspired by particle dispersion path modeling like HYSPLIT.

Select the hyperparameters which minimize the 2017 and 2020 errors (relative to the true beaver locations and concentrations in those subsequent years). This might be easiest to do at a small grid-cell level.

So basically saying, if a beaver is in grid cell $i$ in year $t$, with a vector of local characteristics $\Theta$ and a matrix $M$ of the characteristics of the surrounding grid cells $j$, and a vector of preferences $\psi$ (e.g., how much beavers don't like to cross roads, or how willing they are to go up-river, etc.), assign probabilities $p_{j, t+1}$ to each of the surrounding cells.

[goldma99]

What do I need to know:

• [ ] factors that impede/discourage beaver movement (e.g., major roads)
• [ ] replacement/reproduction rate
• [ ] factors that attract beavers (e.g., slowly running water)
• [ ] factors that speed up or slow down beaver dispersal (e.g., temperature)