Notes on methods and potential figures

[gclawson1]

We've decided to move forward with species "likelihood of persistence" as our impact measurement, using the same method described in Duran et al.:

The impact on population persistence of losing a given amount of AOH increases as total AOH decreases, resulting in a concave relationship between remaining AOH and local persistence (Kitzes & Harte, 2014). Although the detailed form of this relationship has yet to be investigated, we followed other studies (Balmford, Green, Onial, Phalan, & Balmford, 2019; Strassburg et al., 2017; Thomas et al., 2004) in converting changes in AOH into changes in population persistence using a power-law function with an exponent <1. Remaining proportions of AOH were used to derive a nonlinear ‘persistence score’, P, which captures the cumulative effect of habitat loss on the likelihood of the species' persistence in the study region.

To calculate the likelihood of persistence (P), hereafter called persistence score:

P = E^z

where E is the remaining proportion of the original AOH, or the original AOH in a cell minus the impacted AOH in a cell, divided by the original AOH in a cell.

E = (AOH_orig - AOH_impacted)/AOH_orig <------ this is right, right?

and z is the extinction coefficient, assumed to be z = 0.25

We used a range of z-values to assess the effects of plausible variation in the extinction coefficient (see Supporting Information Section 3 and Figure S3). Our qualitative conclusions concerning the relative role of human activities on estimated biodiversity impacts were not dependent on the choice of a particular value of z. We therefore adopted a z-value of 0.25 in the main text, based upon its ability to predict proportions of species becoming extinct or threatened as a result of habitat loss (Brooks & Balmford, 1996; Brooks, Pimm, & Oyugi, 1999).

So if a cell has 100km2 of habitat, and 50 km2 of it is impacted, we would see:

P = ((100-50)/100)^0.25 = 0.84089641525 in that cell.

Because saving a raster for each species and scenario is 1) impracticle considering I would have to save millions of rasters, and would take forever, and 2) we don't need that level of detail, I propose we aggregate species into larger functional taxa groups. For now I am going to assume groups to be:

Terrestrial:

• mammals
• birds
• reptiles and amphibians (if we can get this data)

Marine:

• mammals
• birds
• reptiles and amphibians
• invertebrates
• fish

For marine, it could be useful to consider splitting of the "fish" and "invertebrates" categories even more, since these are very large groupings, with a wide diversity of functional groups in them.

Then we can save rasters for number of species in each cell, mean persistence scores, and sd persistence score for each larger taxon group and across all spp for each ingredient, allocation, diet scenarios. This way, instead of saving millions of rasters, we will just have to save ~1000 rasters or so. And will probably end up saving these in csvs, rather than rasters, so I would be saving a lot less than ~1000 files if I figure that out

Once all of this, I'm imagining figures could look something like this (excuse my horrible drawing skills):

• I drew this before I decided on the persistence scores, so the legend for the second figure should be persistence score, rather than what I have written
• Just drawing this out to try to imagine what the end goal could be, I'm sure we'll think of better and more figures

[gclawson1]

We mentioned a possible "hotspot" figure, and I really like this figure from Harfoot et al. : https://www.nature.com/articles/s41559-021-01542-9

Global threat hotspots (90th percentile of risk, the product of the probability of impact and the species richness) for amphibians, birds and mammals for the six principal threats

[cottrellr]

Nice yeah this is a good approach given there will be risk everywhere so the top 10th percentile makes sense.

[gclawson1]

Been doing some exploration of the likelihood of persistence method and our data. I'm seeing that likelihood of persistence is very high in the cases I'm looking at (and I suspect in all cases), because the km2 of impacted AOH in each cell is so low in comparison to the 100 km2 of original habitat in each cell. Here are two examples, one marine and one terrestrial:

Terrestrial example:

• Note the km2 impacted is maxed out around 0.4 km2, while each cell is ~100 km2

Then calculating likelihood of persistence:

Marine example:

And I don't think these numbers will significantly change across species because of how little raw material ingredient harvest there is in comparison to habitat extent. For instance, the total amount of SPC disturbance is ~3000 km2, with the max km2 being ~1.5 km2 in a cell. This means that for any species, the max amount of overlap it could have in a cell is 1.5 km2, while their amount of AOH in a cell is always going to be 100. So for SPC, the minimum likelihood of persistence value for any species would be ((100 - 1.5)/100)^0.25 = 0.99622871975.

If we were looking at total agriculture, this would obviously be very different, but because we are just looking at aquaculture feed agriculture, the actual likelihood of persistence values themselves aren't all that interesting.. But I suppose looking at the hotspots of worst case scenarios (even if the likelihood of persistence is still very high) is still interesting

[cottrellr]

Ok good to see this side by side. I agree, that using total likelihood of persistence is hard to see the differences in (and slightly counter intuitive with the lower value being higher impact).

That said, just using km2 is not meaningful. As your exploring has showed, whether 1km2 or 1000km2 of AOH impacted is important for a species depends on the size of total habitat available.

So my suggestion would be, either using proportion of habitat or likelihood of persistence. With both what we want to show is not what proportion they have left or the total likelihood of persistence given feed production, but what the reduction to that proportion or that likelihood of persistence is because of feed production (i.e. proportion of AOH impacted, or 1-likelihood of persistence). That makes sense?

[gclawson1]

Inverse persistence (1-p) example:

Proportion of AOH impacted example:

[cottrellr]

Cool, maybe we can chat a little today about what to go forward with. Both look good to me, but could also be a question for Biomar, like how they would be interested in reporting biodiversity impact.

[gclawson1]

Agreed, looking forward to chatting later. I put together some slides to get Beth all caught up on everything