Modeling competition for water: calling the race

Sensitivity of water uptake to changes in parameters for crops grown with weeds or weed-free. Parameters in the lower right are a lot more important when competing against weeds than when weed-free.

When competition is a race from the start line--like with crops--the best strategy is to run fast.

Dunbabin 2007 modeled this by simulating the growth of plants with 3-d models of root systems in order to examine sensitivity of uptake of water, nitrogen, and phosphorus to variation in key root parameters.

Looking at what parameters are important when crops are competing against weeds, here's what Dunbabin says about that:

"the ability to quickly (growth rate) and effectively occupy (rooting density) the soil volume during crop establishment, may be important for denying weeds water and nutrients, thereby conferring competitive ability"

When there is no competition between crops and weeds, effective exploration is important:

"The ranking of P uptake efficiency as important for the acquisition of mobile nitrate and water
resources by weed-free crops...suggests that foraging for the least mobile, and often most limiting nutrient, may provide the best strategy for acquiring all soil resources (Robinson, 1996a)."

Here, the modeled plants are growing in relatively low-P soils, so to acquire the most water, you have to have a big plant. Having a strategy for effective acquisition of P becomes the most important parameters there.

One parameter not important regardless of whether there is competition or not? Potential transpiration rate.

Water is a mobile resource, but roots still have to wait for water to move to them.

Considering that nitrogen uptake kinetics aren't important for nitrogen competition, and mass flow is slower than diffusion, this makes sense.

It is important to note that the arena of competition is important here. The plants were started from seed (I think) and allowed to grow for 12 weeks, simulating a quick crop rotation.

The question here is what aspects of roots become important when competition is not a 12-week race? What becomes important when perennials occupy the same space for years? And if nutrients aren't limiting? Then what?

What does the optimal root system look like for plants growing in the absence of interspecific competition when water is limiting, but nutrients aren't?

A few thick roots?

Many thin roots?

Unknown.

Exploring competition for water

From Lobet et al. 2014

It is true that drought kills plants. 

Drought lowers soil moisture. Low soil moisture kills plants. Therefore, drought kills plants. 

Yet, the rate at which drought lowers soil moisture is dependent on the plants that are present in soil. 

Plants lower soil moisture. Low soil moisture kills plants. Therefore, drought kills plants. 

Therefore, it is also true to say that plants kill plants. 

And when plants kill plants by using resources, that's resource competition. 

There has been a lot of great work over the past decade examining the mechanisms of how drought kills plants. 

But not so much on how plants kill plants when water is limiting. 

About a decade ago I was curious about some of the mechanisms of how plants compete for nutrients.

To explore this, I put together a model...actually I asked Trevor to put together a model...to simulate the movement and uptake of nutrients in soils.

This model was parameterized at a fine scale and could simulate the supply, movement, and uptake of nutrients in soils. 

It was able to show patterns of nutrient distribution in soils like this.. 

2 cm x 2 cm cross section of soil with all roots orthogonal to the plane. Red indicates high nutrient concentrations in soil solution. Blue is low.

With the model, I was able to show that plants acquired nutrients in proportion to the fraction of all the root length they had in a given volume of soil. Plants had a lot more roots than they needed to take up nutrients...if there was no competition. Once more than one plant had roots in a given volume of soil, a race set in.

As a result, plants can have 1000 times more roots that is optimal for maximizing growth.

That all pertained to nutrients though.

I'm curious about how competition for water works.

For example, does competition for water favor plants with high root length density? Would this also lead to a race like nutrients.

For competitive purposes, is there any benefit to being able to sustain a low minimum water potential? Under what conditions, if any, does drought tolerance affect competitive outcomes?

I'm also curious about the interactions between nutrients and water. Does increasing transpiration rate help with nutrient competition? Do dry soils exacerbate nutrient limitation?

But first, I need to adjust the model to handle water.

That means making soil moisture dynamic, parameterizing water fluxes between pixels and into roots.

The hardest part of all of this is figuring out how to parameterize water uptake by a  given root. There is no simple Michaelis-Menten equation here. Roots are a 1000 connected little straws

Still, I've been impressed by some of the developments in root modeling over the past few years.

I can expand on that later.

Unreinforcing insularity: burning and soil moisture

I had a conversation with a prominent cattle rancher in town the other day. I asked him if he had followed any of the news on the recent research out of K-State on the timing of burning.

He said he had.

I asked him what he thought of it.

He said in his gravelly voice, "I think it's a bunch of bullshit."

When I asked him why, he said that if you burn early, everyone knows that the soils will dry out. With less litter, there will be more evaporation and less rainfall will enter the ground because more will run off. You are going to get less productivity.

He didn't know that I had helped write the paper, which was just fine. I got more honest answers than I would have otherwise.

I explained to him that having litter on the ground often reduces how much rain enters the ground--canopy interception creates a dispersed puddle that can evaporate before wetting the soil.

I also explained that there was never any strong evidence that soil moisture was lower when you burned early.

The only data on that are from 50 years ago and were never done in a manner that was scientifically rigorous enough to be definitive.

The data were taken with neutron probes, which is a fine technique, but there was confoundment between treatments and sites.

When you look at the data, the data suggest that early-burned grasslands have less soil moisture than late-burned watersheds.

But, a couple things are suspect with the data.

First, over the winter, soils should recharge so that they are wet throughout the soil profile regardless of the treatment. But, December and January soil moistures are already an inch lower in the early burns.

This is more likely due to that site just happening to be able to hold less water.

Second, if litter is important for holding soil moisture in, unburned soils should be wettest. They are the driest.

Third, the rate of decline of soil moisture during the growing season for the different treatments are almost exactly the same. When does the differential drying occur? This likely means they are using soil water at the same rate.

Fourth, let's say that data are correct and there is an inch less of water in the top five feet of soil.

How much of an effect would that have on production?

A general rainfall use efficiency is about 0.3 g m-2 mm-1 or 75 lbs/acre/inch.

What was the "effect" in the experiment of a having 1 inch less of soil moisture in the soil profile?

Typical rainfall use efficiencies would predict a reduction of productivity of 7-8 g m-2 or 75 lbs/acre.

What was seen? A reduction in productivity of over 1000 lbs/acre (100 g m-2).

Original data use to support idea that early-spring burning reduces productivity. Here, OU is ordinary uplands, which is probably the most relevant. Note the ~25% lower productivity in the pasture that was subjected to early-spring burning. Early-spring burning was March 20. Mid-spring April 10. Late spring was May 1.  

That's over an order of magnitude too much.

In all, that's really the only data out there that is used to support greater drying in early-burned grasslands.

It's unrealistic.

The rancher's response to these highlights?

Something to the effect of "Regardless of what the data say, I trust what other ranchers say they've seen."

Even though none of those ranchers would have ever seen a grassland that was burned in the fall for 20 years straight...

Insularity can be hard to break...

Multivariate statistics...what to use.

Path diagram to figuring out what type of multivariate statistics to use.

Dave Wedin use to joke that the Joe Craine way of analyzing the data is to take it all and put it into a PCA and see what you get. 

There's some truth to that. PCA has served me well. And almost every time I get forced to use a different multivariate analysis, PCA seems to give me similar results. 

For example, in the last burning paper a reviewer insisted we use NMDS for our plant cover data rather than PCA. Correlation coefficient between NMDS and PCA Axes 1-3: 0.93, 0.89, 0.71. Same story from each.

Still, it's good to know what other options there are out there. 

I've been looking at bacterial data with Noah and found the Ramette 2007 paper on multivariate analyses in microbial ecology. Noah uses Principal Coordinates Analysis and I was trying to remember the difference between PCA and PCoA.

It's a good user guide to multivariate statistics in general.

One thing that was interesting was a multivariate analysis of the different types of multivariate statistics different disciplines use. 

Ramette, A. 2007. Multivariate analyses in microbial ecology. FEMS Microbiology Ecology 62:142-160.

Quick hit on male bison weights

Display of bison weights from Konza over time. The upper bound of the data envelope shows the weight dynamics of the largest males.

We didn't EID tag any of the large males at Konza, but the raw data lets us infer a bit about what is going on with their weights.

When the big males get on the scale they rarely have any other individuals with them and they move slow across, so we can get a pretty accurate weight.

If you look at all the data, you can see a clear pattern with the upper bound of the dataset. These are the big males.

Since early April, it looks like the big males gained about 200 kg.

In early July, the upper bound was 920 kg. That's over 2000 lbs.

For reference, during the fall roundup we once had an animal hit 930 kg. After that, top weights were no more than 850 kg (1870 lbs).

Since early July, it looks the biggest males have lost about 100 kg**.

That's a tremendous amount of weight to lose in just a month.

**Note that it could be that the biggest males decided to not walk over the scale during the past month. But, right now all the males and females are together, so if the females have been walking over it, so have the males.

That degree of weight loss is plausible. July and August are the rut, and that's when the bulls are going to be eating the least and "exercising" the most.

Where this becomes interesting is starting to understand the continental scale patterns and thinking about how climate change will affect grazers.

We know that cool, northern grasslands produce bigger bison than warmer, southern grasslands. At least in the fall.

One hypothesis is that the fall weights might be higher for bison in the north, but mid-summer weights are the same. In southern grasslands, forage quality drops enough such that the southern animals lose weight while the northern animals maintain it.

Alternatively, the northern animals might be even bigger midsummer.

In a few weeks, I'll head up to South Dakota to install a walk over scale there.

By this time next year, we just might have the answer.

More forensics on burning

There still is debate smoldering over the timing of burning on grasslands here in the Flint Hills.

Much of the debate stems from research conducted here in Kansas over 50 years ago.

A little more forensics is illuminating.

The key evidence to suggest that burning should be done in late spring is from the weight gain of cattle in an experiment that burned pastures at different times: early-, mid-, and late-spring with an unburned contrast, too. In the experiment, each month, the cattle would be taken off pasture and weighed to examine monthly weight gain. The experiment was carried out from 1950-1966.

In the first reporting of the results from the experiment (Anderson et al. 1970), the authors showed no significant difference in monthly weight gain for cattle placed on pastures with early- and late-spring burns.

Their conclusion was a lot more certain than their data.

“Mid- and late-spring burning produced more weight gain on steers than nonburning. Late-spring burning also increased steer gains over early-spring burning. The weight gain obtained with early-spring burning was essentially equal to that obtained with nonburning.”

So, although there were never any significant differences in weight gain, the conclusions were that there were.

It is possible that when you add up all the monthly gains for a year, you get significant increases in weight gain. As far as I can tell, that was never tested.

When the data were summarized in a later publication, the monthly weight gains are compiled into a 5-month weight gain. But there are no error bars. No tests of significance.

Often, these results have been reported as stating that burning in late spring leads to 32 pounds greater weight gain over a 5 month period (May – September). I’m not sure where that number comes from because the graph only shows 26 pounds difference. Yet, most of the cattle in the Flint Hills are only left out on pasture for 3 months. May, June, and July. If you go back to the 1970 paper, over the 3-month May-July period, differences in weight gain were measured at just 9 pounds.

9 pounds is still 9 pounds, though. Yet, is it? There is no evidence to show that the 9 pounds, no less 26 pounds, is actually significant. That means 9 pounds might be 0 pounds.

There are other parts of the research that are curious. For example, if you look at the productivity data, burning just 42 d earlier results in a 25% reduction in grass productivity. In contrast, 20 years of data at Konza shows no significant reduction in grass productivity. What would cause such a marked reduction in productivity? In the past, it was suspected that soils dried out a lot faster without any cover, but there is actually little evidence to support this.

Could it have been differences in forage quality? Again, no data were ever taken on forage quality for pastures burned at different times.

Also, the average date of burn for the late-season burn was May 1. The stocking date for all the animals? May 1. How that actually happened, I have no idea.

So what might be going on here?

One limitation of the work is that there was no spatial replication for the experiment. Each pasture had a different treatment. There was only one pasture for each treatment. Treatments were not rotated among pastures. Replication came from measuring the same pasture year after year.

In scientific terms, that means site differences and treatment differences were confounded. In lay terms, we have no way to know whether any differences in weight gain were because of the pasture that happened to be picked for the early-season burn happened to have worse forage than the late-season pastures.

This is exactly why scientists replicate.

Still, replication at this scale is certainly hard. We only have so much land to work with. You do the best you can.

Yet, is it impossible to do? No. Can it still be done? Yes.

Scientists could easily work with ranchers to use their operations as experiments. Different ranchers could burn at different times and they could record their animals weight gains. That’s a whole lot better than extrapolating from a few hundred acres at one spot to a much broader area.

In all, was the past work suggestive that late-spring burning was optimal. Certainly. But there are too many questions about the certainty of the results and their broader relevance.

At this point, the most conservative, commutative interpretation of all the data is that there are no significant effects of early-season burning on weight gain.

Interpreted within the context of the experimental design and more recent data, it is hard to be convinced of the necessity to burn in late April in the Flint Hills.