Not an area of research I'm currently involved in, but some of the indices mentioned in this paper (available via ResearchGate) look useful:

http://onlinelibrary.wiley.com/doi/10.1046/j.1440-1703.2001.00368.x/abstract

I think the concept of 'spatial extinction' as you define it isn't accurate. It is, at least theoretically, possible for alien species to occupy "spots" within a habitat that weren't previously taken by native vegetation. Alternatively, an alien species may replace certain species / vegetation types in some but not all parts of a given habitat, allowing the native vegetation to co-exit locally. Over large periods of time, shifts in dominance have been observed, e.g. Calluna vulgaris and Molinia caerulea on moorlands. To me that is incongruent with the notion of extinction.

http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2664.1999.00435.x/pdf

If we agree that every spot where an exotic plant currently grows, is a spot where a native plant formerly grew, then we can proceed with defining Spatial Extinction.

My perspective on the concept of "Spatial Extinction" is from California where the original native plant understory is 99.99% spatially extinct, and I surveyed western States at http://www.ecoseeds.com/megatransect.html and found spatial extinction everywhere I looked.

Spatial extinction is "the substitution on the spot with an exotic plant now growing where a native plant once grew", but the spatial extinction process starts with the removal of that native plant on that particular spot, by whatever human means achieve that, animal grazing, plows, herbicides, etc.

You can now say that once the native plant is removed from a particular spot of land , that spot is now vulnerable to the process of spatial extinction. Then the final and permanent establishment of spatial extinction is when the exotic plant occupies that spot where a native plant once grew, for eternity, or until the next Ice Age scrapes that weed off?

Hi Craig,

The attached paper by Gilbert and Levine may be helpful - not exactly what you are talking about, but 'extinction debt' (latent local extinction) is a broadly similar concept. I feel like you'd need to distinguish the concept of spatial extinction from the concepts of competitive displacement, range contraction and extinction debt, in order to get tractability.  

All the best,

Joe

"Spatial extinction" suggests a one-way process, but human intervention can be successful in eradicating or reducing an introduced species, allowing the native flora to recover and recapture a site. I will upload a case study describing Bitou Bush control in coastal dune vegetation as an example and there are many more success stories indicating a two-way process, although just as many one-way failures. Perhaps the most apt question then is, why has it been possible to reverse some weed invasions but not others? 

Maybe "spatial displacement" would more accurately describe the process? 

Without human intervention, similar to extinction itself, "Spatial extinction" is a one-way process and its final chapter comes when any dormant native seeds still dormant in the soil underneath the exotic plant growing on that spot, finally die.  

This Spatial extinction process has been going on here in California and the Western States for about 150 years, and in the Mid-west for 200 years, and on the East Coast for 400 years.  When the different plant families of the dormant native seeds in the soil die underneath the exotics each year, that seals the final chapter of Spatial extinction on that spot for the native species that formerly occupied the area.

Of course humans can rescue seeds from relict stands of the natives that are left in the area, eradicate the exotics and replant and reconstruct the original ecosystem.  But on the scale of tens of millions of acres like in California where it has been removed, unless some outside funding like carbon credit taxes are available, then there would be not be possible to reverse the "Spatial extinction" process. 

Your concept is flawed, until you take into account the seed banks.  In Mountain Fynbos and some Lowland Fynbos species, seed banks may persist for 3 fire cycles (45-100 years) under 100% cover alien (pine and wattle) stands.   

It stands to reason that "spatial extinction" in these cases only occurs after 3 generations.  If in the meantime a biocontrol is introduced (see the extensive South African literature), or moves in (e.g. Zulubius on Acacia cyclops), or "evolves" (e.g. switching hosts - examples??) within the 3 generations (or land use management changes) then spatial extinction may be forestalled.

Also spatial extinction is likely to be selective: short-rotation species may for instance be able to survive with the alien (completing their life cycle before a longer-lived species can re-establish full closure following a disturbance), whereas long-lived understorey species may be selected against (and canopy-stored seed bank species extremely strongly selected against - extinction occurring with the death of the last individual plant), but of course, it is the seed bank longevity that determines time to extinction.

For your concept to work you need to generalize it to more than systems of annual or near-annual plants with seed longevity of the same order of magnitude.

Thanks for your reply.

 I am writing from a very unfortunate  California perspective, where 99.99% of the native understory between two meters and 1,000 meters elevation is not physically present on the surface any more, and has been replaced by solid stands of over 1,000 exotic plant species, like the two pictures I show at the beginning of this question.

So at what point do us humans start discussing the final extinction of plant species--when the very last one is dead on the surface and its seeds in the soil are dead also?  

I am suggesting starting a discussion using the term "Spatial Extinction" to indicate that on a square meter by square meter basis, exotic plants are creating a trend towards complete extinction, and perhaps we should take note, say when the exotic plants have caused Spatial Extinction of say 50% or more of the native understory?

Or when 50% of the native understory is Spatially Extinct, and only barren ground exists where they once grew and the exotic plants have not moved in yet.  Worldwide this is a more common case of grazing removing the native understory, and the barrens do not have exotic plants filling in the empty niche yet. 

I call those area have Spatial Extinction without exotics replacing them as being  vulnerable to exotic plant occupancy in the future.  If you look at any spot on the planet through http://www.confluence.org photos, you see the native plant under stories are in tatters planet-wide. 

Then we could have more time to reverse the Spatial Extinction trend if we wanted to, but if we wait to have the discussions until things get as bad as in California, when 99.99% is gone, it makes it fantasically more expensive to reverse a trend like that when it has gone so close to final extinction. 

For example my test plot to reverse Spatial Extinction on a 10 meter by 15 meter grassland plot in the hills of Palo Alto, California, is probably going to cost US$100,000 by the time I have the 30-40 species back in place, that made up that native understory as a functioning ecosystem, at http://www.ecoseeds.com/arastradero.html.

Or a 14 year-project costing US$225,000 per acre, at http://www.ecoseeds.com/road.test.html  and only getting a single grass species re-established, out of the 30-40 grass and wildflower species you really need to make things right again, like what it originally existed at http://www.ecoseeds.com/wild.html.