Percolation theoretic understanding of landscape ecology

Sometimes I have good ideas.  Less often those ideas are new.  Given my interest in native plants as habitat, about 6 months ago I thought I would try to model wildlife migration on a grid (which would stand in for typical suburban lots) using percolation theory.  However, a quick Google search turns up lots of prior work.  So this is only a potentially good idea that isn't even novel.

The first article that I read was confusing on more than one level.  Give the first page a read (or not) below.  My guess is that you'll quickly get bogged down and skip past it.

Neutral Models: Useful Tools for Understanding Landscape Patterns
8.1 Introduction
A neutral model is a minimum set of rules required to generate pattern in the absence of a particular process (or set of processes) being studied. The results of the neutral model provide a means of testing the effect of the measured process on patterns that are actually observed (Caswell l976). If observed patterns do not differ from the neutral model, then the measured process has not significantly affected the observed pattern. Conversely, when results differ from model predictions in a way that is consistent with a particular process, then strong evidence for the importance of this process has been obtained. Several authors have argued that formulation of a proper neutral model is necessary for hypothesis testing, because data often exhibit nonrandom patterns in the absence of the causal mechanisms of interest (Quinn and Dunham 1983). This approach has been discussed extensively in the field of community ecology (e.g., Conner and Simberloff 1984, 1986; Haefner 1988) as well as other areas of biology (Nitecki and Hoffman 1987).

Neutral models are useful in landscape ecology, a field of ecology that emphasizes the complex relationships between landscape pattern and ecological process (Turner 1989, Gardner and O'tieill1991). Processes, such as disturbance, can produce landscape patterns by changing the abundance and location of habitat patches (Baker 1992). Likewise, patterns have important effects on ecological processes. For example, habitat fragmentation affects metapopulation dynamics (Holt et al. 1995), gene flow (Ballal et a1.1994), and dispersal (Santos and Telleria 1994). The purpose of this chapter is to demonstrate the usefulness of neutral models to landscape ecology by discussing how neutral models (1) assist the investigator in understanding patterns in spatial data and (2) are useful for generating maps for quantifying the effect of landscape pattern on ecological processes.

8.2 A Simple Neutral Model
Neutral models help landscape ecologists understand relationships between measures of spatial pattern and landcover abundance. A simple neutral model designed to explore the effect of changes in the abundance of a habitat on the spatial pattern of landcover (Gardner et al. 1987) was derived from the principles of percolation theory (Stauffer and Aharony 1992).

Was I right?

Even after reading this article several times, I don't have a good plain English understanding of what they are trying to say.  This isn't helped by the fact that I seem to have stumbled upon a small tempest in a teapot regarding the use of a neutral model versus a null model.  In population ecology and related fields, a null model seems to be a migration model fit with constraints measured from data whereas the neutral model attempts a statistically based description that can be scaled to data.  I'm probably wrong, but that's what I'm going with right now.


No new sources

The graphic above was pulled from the Little Hoover Commission (LHC) executive summary and shows that California has less than about 1 MAF water growth COMBINED available from new sources (surface storage, forest management, desalination, cloud seeding, rain dances and prayers) assuming we meet the low estimate in each category. Meeting  the high estimate of increased surface storage has the greatest impact of that bunch, but probably requires significant new infrastructure (dams) which don't seem to have political traction right now and even then could only account for an additional 1M increase. 

On the other hand, of the four top potential water sources, NONE exploit new water.  ALL are savings estimates based on conservation (though they call it efficiency in the case of ag).

Increased agricultural efficiency is the lowest of the top four in terms of savings and seems either hit or miss, with an order of magnitude difference between low and high estimates.  That order of magnitude uncertainty is not something that encourages putting great faith in ag savings.  

Groundwater storage is the next lowest potential payback of the top four.  I believe that they are referring to natural infiltration rather than pumping excess water underground in times of excess.  Interestingly, there's a current groundswell of support among gardeners, city planners, and environmentalists for better groundwater infiltration to prevent storm run off and one can find many examples of urban rain gardens designed to capture, use, and infiltrate rain water rather than sending it to the storm sewer system.  This seems a feasible method to capture more water, since it is already gaining traction, requires no central planning other than infiltration standards, is distributed, can be incrementally implemented, and has other beneficial effects such as improving coastal water quality.  A successful PR campaign might make even more headway here.

The two greatest potential areas of saving, recycled water (so called "toilet to tap" programs) and urban efficiency (low flow toilets, shorter showers, less garden watering, etc) are also both conservation measures. I'm not sure I need to say much about them other than to point at the graph to show how much more potential is there than in any other measure.

The important point here is that we have about 1 MAC more water that is feasible from new sources or better management of existing sources and more than 3.5 MAF available from conservation measures, assuming we meet the minimum in each category.  So excuse the hyperbolic headline trumpeting "no" new sources, it's just that conservation trumps new sources in the two most critical categories of cost and impact.

See On the pulic record blog for more insighful commentary on this topic.

As a point of reference, I think that California's industry and population uses about 9 million acre feet (MAF) of water a year, a number I extrapolated from elsewhere on the web but which could be wrong since I'm was a bit careless. I'm not sure if this includes ag.  In any case, this number is a convenient reference, since 1 MAF is about 10% of 9 MAF and the graphic breaks things down in bite sized 0.5 MAF increments.