identifying population extinctions

[Joachim Mergeay]

Hi genetic indicator group,

In today's discussion, we shortly touched on the subject of identifying how many populations went extinct. 

This is often much harder than it seems, for two reasons: 

As the area of occupancy (AOO) and extent of occurrence (EOO) of a population shrink from a single large continuous metapopulation with diffuse subpopulation boundaries, you go from 1 population to many populations, say 9. 

Populations lost: ZERO. In fact, your ratio is an integer: 9/1: you gained eight populations.

As the decline continues you then go from many isolated populations to again a few isolated populations (say 2). Depending on your point of reference, you can say that you gained many to a few populations. 

Populations lost: it depends on your point of reference. If your reference is the first point in time, it's  zero, you gained 1 population. 

If your reference is however the onset of fragmentation, you have lost 78% of the populations. 

Secondly, consider that historical records of species presence are often more incomplete. We have may have data on the occurrence from early species atlas projects, but not on the absence. So you may have scattered dots on a map (e.g., 10 km x 10 km squares). We can use this to show that a species occurred at some time in a certain area, but not anymore. We lost some of the area of occupancy, but did we also lose a population? Very often, that's hard to establish.

Take as an example the attached cartoon, a grid of 10 x 10 cells, with occupancy indicated by a O.

In the top we have the true distribution and area, at the bottom the observed distribution.  

We go from 1 (large continuous) to 9 (fragmented) to 2 populations. How many populations did we lose? You could say none at all. The population just became much smaller and fragmented into two. We can see that the area of occupancy went from 100 grid cells in 1900 to 8 in 2020. However, we rarely have such detailed data. 

More typically, the occupancy would be like in the bottom: some observations, and no observations where the species was present, by a lack of observation effort/knowledge.

In the 1900 situation, it's hard to see if we had 1 large population or a handful of them.  

At the 1960 situation we see we lost cells relative to 1900, but did we lose a population? 

We can clearly tell that the extent of occurrence declined from 1900 to now, and from 1960 to now. We're unsure of the AOO declined between 1900 and 1960, but it did decline between 1960 and 2020. 

But did we lose a population? If 1960 is your point of reference we did. If we use 1900 we didn't.  

Red lists use AOO and EOO, but not on the time scales I considered here. Red Lists only assess this for the past 3 generations or 10 years (whichever is longest). 

So the question now is: do we also set a baseline somewhere? Do we ask to standardize a methodology to assess extinctions? If we don't, you can cherry pick any way you want, and with the same data claim the number of populations grew by 200% (1900 to 2020) or declined by 80% (1960 to 2020). 

Just some thoughts on issues we encountered for the Belgian assessment. 

Joachim & Luis

[shoban]

Thanks Joachim for iillustrating this in more detail than we had previously considered.  Do you have suggestions for how to deal with this problem, both for the baseline, for the fragmentation, and for the what is a population?

[shoban]

Message from Fumiko... not sure why it deleted:

Hi Joachim ＆ Luis and all,

My other suggestion for the way of modifying  indicator 1 is to make it individual-based;

sum (number of individuals in populations >= 500Ne)/sum (number of individuals in all populations)

The meaning of this indicator is the proportion of individuals that have >=500 effective population size in the population they belong to.

This is a weighted version of indicator 1, where the weights are the population sizes.

In a large continuous population, it could be re-defined as

(number of individuals who have >=500 Ne in their neighborhood)/ (total number of individuals of the species)

The definition clearly solves the two problems we discussed yesterday.

1. For a continuous large population, the latter definition of indicator 1 does not require the difficulty of defining "a population".

2. It reduces the impact of the extinction of local populations on the value of the indicator as far as the extinct population is small.

For example, suppose that there were 4 populations with the sizes of 100, 5900, 7000, and 7000. 

Then the smallest one goes extinct.

The original indicator value changes from 3/4 to 3/3. The difference is 1 - 0.75 = 0.25.

The individual-based indicator value changes from 19900/20000 to 19900/19900. The difference is 1 - 0.975 = 0.005   

This modification seems to be too drastic, but at least for data requirement and easiness of calculation,

it does not require any additional information and is easier to calculate for a large continuous population, 

though it requires defining "neighborhood", which is also required for the original indicator 1 in the process to define "population". 

On the other hand, this definition completely removes the essence of "a genetically distinctive population" from indicator 1.

The original definition of indicator 1 included the concept of  "a genetically distinctive population" through the process of defining populations.

I said the re-defined index is the weighted version by populations sizes,

but from a different view of point, the original indicator is weighted by distinctiveness;

each individual has a different weight in the original indicator, i.e. individuals in a large population have smaller weights, and individuals in a small population have larger weights due to their distinctiveness.

Now the difference between the two indicators is clearer; indicator 1 is a kind of isolation index and indicator 2 is for conserving genetic diversity among distinctive populations.

I do not insist on making this modification, but I hope it will help to understand the nature of the two indicators that are being generated by the current definitions.

[Ishihama Fumiko]

Sean, Thanks for posting it again!

I'm not sure why it was deleted as well.

Fumiko 

2023年3月11日土曜日 7:11:43 UTC+9 shoban:

[Joachim Mergeay]

Hi Sean,

We've been brainstorming about this. 

One way to deal with this is by hierarchically evaluating extinctions/colonizations, and we'll try to provide examples at the next meeting:

1. If you can easily count the number of populations you had before and after: use that. There are instances where this is clear. Mention the time frame over which populations were lost or gained. 

2. If you had a large continuous population and now only fragments: use the change in Area of Occupancy (AOO) before and now. This is a measure that can be positive (increase in area) or negative (decrease in area). This could be done by counting the number of grid cells occupied at each time. Provide the time frame over which this was estimated. 

3. In some cases this isn't possible either. In that case, estimate the change in the Extent of Occurrence. This is much more crude, but it will provide information on dramatic changes. 

All these area indicators are related to population size change (under the assumption of equal density per grid cell), and are thus related to genetic summary statistics: there is a mathematical (non-linear) relationship between the effective number of alleles (or He) and population size, and a (nearly) linear relation between allelic richness and population size (cfr the "mutations-area relation, Exposito-Alonso et al. 2022, or simply the formula (AR) ̂=M/M+M/(M+1)+M/(M+2)+…+M/(M+2N-1) with M=4Nµ)

We are checking to what extent we can apply these alternative change estimates (Delta AOO or Delta EOO) to our data. 

Joachim 

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Joachim Mergeay (he/him)

Research Institute for Nature and Forest - Belgium                                  

Associate Professor KULeuven Ecology Evolution and Biodiversity Conservation

Tel: +32 499 942 942

Meldpunt wolven Vlaamse overheid : wo...@inbo.be

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[Ishihama Fumiko]

Hi Joachim,

It's very interesting that hierarchical evaluation will solve the problem.

Too bad I won't be able to attend the meeting next week to hear the explanation.

(I organize a symposium about genetic diversity evaluation and targets of NBSAPs of Japan for genetic diversity on the day)

By the way, I'm not sure delta AOO and delta EOO are alternatives for which indicators (1 or 2?).

Delta EOO would be an alternative for indicator 2 rather than 1, but AOO seems very different from both two indicators.

From my understanding, the important characteristic of indicator 1 is that it takes spatial subpopulation structure into consideration, but AOO does not.

To consider spatial structure within a continuous large population, some kind of indicators for habitat fragmentation may be useful.

E.g. degree of fragmentation in; https://www.pnas.org/doi/full/10.1073/pnas.1705769114

 

Fumiko

2023年3月14日火曜日 0:06:11 UTC+9 joachim...@inbo.be: