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
SCOTT M. PEARSON and ROBERT H. GARDNER
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.

Interesting article

This is from the automatically-generated Google results in the sidebar of my blog.  Often, the factual, new or interesting native plant content is thin, since it's just a keyword-driven search result.  However, this article http://media-newswire.com/release_1125304.html about Tidestrom's lupin has a good lay description of some detailed modeling.  If you have a scientific bent, then you ought to give it a read.

Deborah Small's ethonobotany calendar

http://deborahsmall.files.wordpress.com/2009/12/ethnobotany-calendar-2010.pdf

Seen on a hike at Scout Camp

I almost hit my head on this pair of nearly perfect Leopard Lily (Lilium pardalinum) growing high out of a moist bank near the trail.


Deep Creek swimming hole. Sweet!!!



- Posted at great expense from my iPhone

Water reflections

Back in the day, a typical way of powering equipment was to have a central engine that drove a belt. The belt was then attached as needed to different pieces of equipment. In the 1850s era town of Columbia I saw this drive mechanism, which appears to be an of the sort I've just described, no doubt used in some sort of gold mining operation.



The interesting thing about the engine is that it's powered by water.



The resource that was formerly used as fuel for the gold rush is now considered part of the wealth of California.

Despite an increase in our water savvy, we still like our lawn. Here's a photo of the entry into Laetitia Winery, with the irrigated lawn bright green against the unirrigated background. To their credit, Laetitia has incorporated native plants in their (long and irrigated) driveway border planting, but I have come to expect a little more from our wineries in terms of water usage.


- Posted at great expense from my iPhone

Hike in San Luis Obispo's coastal hills

Just over the hills from Avila Beach is the trailhead of a hike I've done once before.

There's plenty of Mimulus. Some fading to brown:


And some still fresh:


And Poison Oak, already turning red in places:



The lupine has reached and passed it's peak. This is one of the few flowers left:



Lupine seed pods go suddenly from a normal pod shape as they ripen to a helix-like shape that explosively releases and scatters seed. This is known as explosive dehiscence. Poppies do it too.

Lupine seed ripening:


Lupine seed ripened and scattered:



The plant community is coastal woodland on the inland side of the hill with manzanita growing in exposed areas where it can get sun and California Live Oak elsewhere.







There's a flowering plant that I couldn't identify:



Here's the leaves of my mystery plant:




And there's hummingbird sage:



And there's a great view from the top




- Posted at great expense from my iPhone

Ubiquitous tiny yellow meadow flower

Perhaps it's too small to be found in most popular references. This is all over the Sierra right now.






Hypericum doesn't seem right.



I wonder what it is.

- Posted at great expense from my iPhone

Seen around camp

My best guess is Arctostaphylos patula (Greenleaf manzanita).


Iris hartwegii (Hartweg's Iris):


This is smaller than the more widespread variety, Iris missouriensis, and is found in dry pine forests. Colors range around camp, with some paler yellow and white.

Lupinus breweri has a matted, clumping, growth habit.


The flowers look like this:


And this:


- Posted at great expense from my iPhone

Seen on the way to Reservoir Lake

Cool log cabin. There's a number of more modern structures and an extensive packing / camping operation out of here. This is just under 7000 feet.


Kennedy Meadow:


Wyethia mollis (Wooly Mules Ears), just coming into bloom:


Looking back the way we've just come:







Old hardrock mine. It looks collapsed just inside.



Reservoir Lake. It's owned by PG&E, presumably to provide water for hydropower further downstream.



- Posted at great expense from my iPhone

Seen on a hike to Cleo's baths

Lupinus stiversii (Harlequin lupine):




Meadowlands, with a bazillion ladybugs.


Dudleya calcicola (Limestone Dudleya), I think, on a granite outcropping.




Unknown:


Manzanita leaves with parasitic insect action: none, new, and old:


Hiker:


Calochortus venustus (Butterfly Maroppsa Lily), I think. I found only two of these and the other was not yet in bloom. This has three-fold symmetry. I wonder how common that is? Maybe only lillies have it?



Castilleja lemmonii (Meadow Paintbrush) buy it could also be C. applegatei or some other.



Calyptridium umbellatum (Pussypaws): not shown.



The baths:


I went in, but it was so cold that it got painful very rapidly. This was snow melt only an hour or so ago.

- Posted at great expense from my iPhone

Sierra meadow, ~5700 ft

I'm at Lair of the Bear with family. Few wildflowers are to be found due to the recent end of winter. This meadow had one blooming plant that I think is Dodecatheon hendersonii aka Sailor Caps or Mosquito Cap, though I would have called them Shooting Stars.













This is right in the middle of camp. In a few weeks there ought to be some wildflowers.

- Posted at great expense from my iPhone

Snow plant, Sarcodes sanguinea

Snow plants seem one of the first to bloom in the Sierra. They derive energy from soil mycorrhizae, which in turn get their energy from roots and soil decomposition processes. I read some time ago that they are edible, like asparagus, however they are protected and I've never tasted them.

Last year we saw fewer of these and more flowers of other types, indicating a later stage in the bloom cycle. With many trail heads still snowed in this year, peak bloom seems a ways off. Maybe we'll get lucky and see it start to come in.

Here's some babies, I think, about 3" tall at the peak.

A comment from Dylan Eichenberg drew my attention to my misidentification of the picture below.  He rightly points out that it is Pine Drops (Pterospora andromedea).




- Posted at great expense from my iPhone

Bees galore

This one Matilija poppy flower attracted nearly all the bees. There were plenty more to chose from, including at least one with similar open petals. The majority of flowers weren't open quite so much as this folded back, dinner plate-like flower.



- Posted at great expense from my iPhone