Countdown #4—competition and supply preemption

Dave Tilman’s great advance for understanding competition over 30 years ago was to introduce the idea that competitive outcomes were determined by resource reduction. Phytoplankton that could lower the concentration of a limiting nutrient to the lowest level would become competitively superior. When applied to plants in soil, the concentration reduction hypothesis assumed that soil solutions were well-mixed and it was the average soil solution concentration that determined the rate at which a plant grew. As such, lowering the average soil solution concentration of a limiting nutrient was the key to displacing other species.

Leaving aside the assumptions of the nature of the nutrient supply, for plants in soil, resource reduction is still the mechanism for competitive displacement. Yet, it’s not concentration reduction, but supply preemption that determines competitive superiority. When nutrients are limiting, a plant competes for a limiting nutrient supply by attempting to preempt the nutrient supply from other plants. Due to the relatively slow diffusion of nutrients in soil, as roots acquire nutrients from the soil solution, nutrient supplies are partitioned among plants based on the relative amount of root length they hold in a particular soil volume. The key to acquiring the majority of a given nutrient supply is root length dominance, which reduces the availability of nutrients to others.

Although the magnitude of this conceptual shift is open, supply preemption is the proper application of resource reduction to plants growing in soil. What about other resources? As I discuss in RSWP, supply preemption is the best concept for understanding light competition, too. Water is notoriously pulsed in availability, but supply preemption rules here, too. Just a bit different than nutrients that are supplied evenly over time.

Competition research can be summarized as “who wins and why?” The secret to competing for resources is to get them before your neighbors do. Took about 30 years to nail down how that works on land, and it'll probably take another few decades likely to nail down the details.

Countdown to Publication: #5—Co-limitation in a Post-Liebigian world

With RSWP scheduled for publication in less than a month (at least that is what Amazon tells me), I thought it would be interesting to highlight some of what I think are the key advances of the book. A self-promoter might call this “Countdown to a New Paradigm”, I’ll just call it Countdown to Publication, I guess. [As an aside, if you ever want to promote your career, start an intellectual battle with someone on a different continent and agree not to attempt to resolve your differences. It works great every time.] I do think #5 represents a new paradigm. Not a paradigm I should be credited with, but a fundamental change in how we think of resource limitation.

The Law of the Minimum that describes the basic ecological concept of limitation was established at a time when little was known about nutrient cycling and was not applied initially to limitation by light. The three parts of Liebig’s Law of the Minimum are

1) Growth is limited by the resource that is supplied at the lowest rate relative to the demands of the plant.
2) Growth is proportional to the rate of supply of the most limiting resource.
3) Growth cannot be increased by increasing the supply of a non-limiting nutrient.

In the Liebigian world of limitation, generally only one nutrient could be limiting at a time. In a post-Liebigian world, it is likely that there is co-limitation to growth among different resources, not just serial limitation. Co-limitation is more likely to occur than would be predicted from Liebig’s Law of the Minimum because a) nutrients supplied in excess are more likely to be lost, b) species differ in the stoichiometry of demands for optimal growth, c) plants can store resources to balance temporally variable rates of supply, and d) plants can increase the availability of the most limiting resource. If there are tradeoffs in acquisition between different allocation strategies, whether for increasing supplies or acquiring a greater fraction of a given supply, co-limitation is likely to occur. Nutrients and light. Water and CO2. Nitrogen and phosphorus. I expand on this in the book, but these co-limitations fundamentally alter our approach to understand everything from global change to evolution.

The existence of co-limitation is not that novel, nor even the suggestion that it should be common. Yet, the consequences of this focus are reach far. Resource co-limitation in the post-Liebig world does not only manifest itself in responses in productivity to the addition of two resources with no increases if only one resource is added. Due to allocational tradeoffs, plants can be co-limited by multiple resources and respond to individual resources independently. Also, the only way to understand why one resource is limiting is by understanding which resource is co-limiting with it.

When resources are co-limiting, costs for different allocation strategies or the production of different structures should be evaluated with a dual-currency model. Evaluating costs with just one resource ignores the often great cost of the second resource. There is no money in ecology—it’s a bartering world with a few key staples.

Lastly, natural selection favors plants that adjust their allocation strategies such that multiple resources are co-limiting. As such, plants are also selected to balance their resource use efficiencies to match resource supply ratios. For example, plants that grow with high relative limitation of nitrogen should have higher ratios of nutrient to light use efficiencies than plants that grow in environments with greater relative limitation by light. Resource limitation provides a fundamental constraint on efficiency of resource use that makes the world predictable.

Colimitation indices

Resource limitation is a fundamental structuring force in ecosystems. I've written a lot about how we need better ways to analyze the simple factorial experiments that are used to determine limitation.  Boiling down patterns of limitation to a single number or two is going to be a big help understanding broader patterns of limitation. Below, I introduce a colimitation index, that separates out some key patterns. 

Let’s start with a basic limitation experiment. 4 treatments: Control (0), +N, +P, +NP.

B₀ is biomass of controls

B_N is biomass with +N

B_P is biomass with +P

B_NP is biomass with +N+P

To make matters simple, let’s assume that there is no effect of P added alone and that the biomass of plants with N and P added is greater than unfertilized biomass.

With this, we’re trying to separate three cases.

1) Classic co-limitation (co-limitation by supply) where there is no direct effect of N (or a relatively small one).

2) Primary limitation by N and secondary limitation by P

3) Single resource limitation where there is an N effect, but no effect of P on N-fertilized plants.

There are two ways to calculate a co-limitation index (CI) based on absolute or relative changes in biomass.

First we can compare the absolute changes in biomass relative to controls and compare the N effect to the NP effect. If we calculate the co-limitation index as

(BN-B0)-(BNP-B0)/2

then a plant that had a CI > 0 would be primarily limited by N and secondarily by P. A CI <>

The interpretation of the pattern would be that soils with low P availability are co-limited by N and P. As P availability increases plants are more likely to be primarily limited by N and secondarily limited by P.

That’s a pretty clean story, but the problem with this approach is that you cannot separate if a plant is secondarily limited by P or just limited by N.

To get around this we can calculate a co-limitation index as:

(BN-B0)/(BNP-B0)

With this index, 0≤CI<0.5><1> 

Here are the patterns for the 100 soils data:

Pretty much the same story. Plants start out co-limited by N and P at low P availability. Then as P availability increases P limitation becomes more secondary until ~30 ppm available P at which we’re into strict single limitation by N. The problem with this approach is that the relative index is sensitive to BNP. For the graph at left I had to exclude two points that had |CI|>10.  

With these approaches statistical significance relative to threshold values, e.g. CI = 0 for the first index, are possible. I’m not sure how to extract them from JMP yet.

Note with a factorial resource addition experiment there are something like 9 different basic responses when you include inhibition and responses by individual resources. There will be no way to boil, but we might be able to get the most important patterns down to 2.

 

Arbuscular mycorrhizal fungi and nitrogen acquisition

How plants acquire nitrogen is one of the fundamental questions in understanding plant adaptations to low nutrient availability. For many years, plants were understood to associate with mycorrhizal fungi in order to acquire P. Later it was understood that some types of mycorrhizal fungi (ectomycorrhizal and ericoid) acquired organic N and transferred that to the host plant. Yet, for many years it was unknown whether arbuscular mycorrhizal fungi were important in the N nutrition of plants.

Leigh, Hodge, and Fitter (2009) take a big step in showing that arbuscular mycorrhizal fungi acquire N from the soil and transfer the N to plants. Building on earlier work by Hodge, the authors grew Plantago lanceolata in microcosms with two compartments. In some, plant roots had access to the second compartment which contained 13C and 15N enriched shoots. In others, only arbuscular mycorrhizal fungi could access the compartment. The authors show that the arbuscular mycorrhizal access inorganic N derived from the shoot material and transfer a large fraction of it to the plants. In one case, ~20% of the plant’s N came from the AM fungi.

In showing the ability of AM to acquire N and transfer large amounts of it to the plant, the study is an important one. The degree to which this potential is ecologically important remains to be seen. In this study, the AM fungi had access to a large, N-rich patch that the roots did not. In nature, it doesn't seem too often that an N-starved plant find's itself on the other side of a goretex barrier from a rotting carcass. Yet, if there ever is a race for a patch, can AM fungi find it before roots? Do they proliferate and therefore compete better than roots? Can they access small, rich patches that roots cannot? The experiment by Leigh, Hodge, and Fitter is an important step in our understanding. The next experiment might be the really important step.

Leigh, Hodge, and Fitter. 2009. “Arbuscular mycorrhizal fungi can transfer substantial amounts of nitrogen to their host plant from organic material” New Phytologist, 181: 199-207.

How to analyze limitation experiments

Figure 4.2 from RSWP

Resource limitation in plants can only truly be assessed with resource addition experiments. Many other correlates with resource limitation have been proposed, but to tell for sure, you have to add the resource in question. Although resource addition can persist in some cases even after the addition of the resource, this is the best approach. 

In RSWP, I discuss how the patterns of responses to resource addition can be used to help constrain the mechanisms by which the resources limit plants. The case in point was “co-limitation”, generally defined where more than one resource limits plant production. Yet, there can be many patterns to co-limitation (see above figure). For example, plants can be co-limited by two resources if the two resources are supplied in the exact ratio they are demanded by plants. Alternatively, plants can be co-limited by two resources if there are trade-offs in allocation to acquire the two resources. For example, plants might need to acquire both water deep in the soil and N shallow in the soil, but the same unit of biomass cannot be allocated to acquire both. Serial limitation exists when resource A limits biomass first and after limitation by A is relieved, resource B limits biomass.

There is a lot to learn from past and future resource addition experiments by beginning to analyze the patterns of limitation. Yet, one thing I hadn’t developed was how one does this statistically.

Most resource addition experiments are analyzed with a two-way ANOVA, which compares the marginal changes in biomass with resource addition relative to the biomass of plants without resources added. If one of these marginal changes is significant, then the limitation is considered “single-resource” limitation. If both are significant, there is co-limitation. If only the interaction term is significant (no response to either resource A or B, but A and B together), then again there is co-limitation.

The problem with this approach is when you have a significant effect of one resource and a positive interaction term. Addition of resource A increases biomass by a certain amount, addition of both A and B increase biomass by even more. A significant main effect of one resource and a positive interaction term could signify either serial limitation or co-limitation by supply. If the main effect of resource A is small, then the patterns imply co-limitation by supply. If the main effect of resource A is large relative to the interaction, then there is serial limitation.

To differentiate these two cases with an ANOVA, one would have to set an arbitrary cut-off for what a “small” significant main effect. For example, if biomass increases less than 15% with resource A addition then the statistically significant main effect is not biologically significant and we can assume co-limitation by supply.

This approach is tenable, but arbitrary. A better way to analyze resource addition experiments is by comparing levels. Not ANOVA’s, but Tukey’s tests that determine with categories are significantly different. This approach is functionally the same as ANOVA in many ways, but allows one to separate the two types of co-limitation. All one has to do is calculate the average of biomass with no additional resources added and biomass with both resources added. Then one compares the amount of biomass with one resource added to the average of control and 2-resources. If it’s less, co-limitation by supply. If it’s more, serial limitation. Determining whether the levels are significantly more or less than the average requires combining errors, which is simple to do, although it remains to be seen how many experiments have enough power to separate the cases.

The centrifugal force of scientific progress

Scientific progress is often portrayed as a march through time. This analogy is a helpful one, except for one key point. Marches are linear. With marches, as we answer questions, we move forward to answer new questions. The size of the frontier of ignorance is invariant.

More than a march, scientific progress is a centrifugal force. For every question we answer, multiple questions are generated. The size of the frontier of ignorance is ever expanding. This isn't just Einstein's "The more I learn, the more I realize I don't know". It's more like, "the more I learn, the more I need to learn." 

For ecology, the centrifugal forces are even more acute. There aren't that many more ecologists than there were a few decades ago, but the number of questions that have been generated by the past 30 years of research, not to mention the ever increasing centrality of ecology to societal well-being, dilutes our power to answer questions. That said, it takes a long time to answer any one ecological question. And ecological knowledge is not necessarily globally applicable. Ecological questions have to be tested multiple times for generality.

The number of questions ecology has had to incorporate into its discipline is immense. If the number of ecologists stays constant, the speed at which we answer questions also stays constant, but the number of questions that we are asked to answer increases, which questions are left behind? 

The answer is not the less relevant ones, but probably the recalcitrant fundamental ones. Case in point, Grime's Plant Strategies and Vegetation texts (1979 or 2001) has few peers in the literature. The degree of integration among topics and depth of scholarship is admirable. Yet, outside of the CSR triangle, few of the ideas in the book seem to have been recognized in the literature. And the number of independent researchers that have tested CSR probably can be counted on one hand. Tilman's R* theories suffer a similar fate. R* has never been tested in terrestrial ecosystems outside the state of Minnesota. 

These are two of the most important theories in plant ecology. The number of citations they have generated are rarely equalled, but they haven't given rise to research proportional to their importance. And it's not because Grime or Tilman answered their questions so completely. So many of the questions that were generated in the early 1980's still lay as unanswered now as then. 

There are two reactions to centrifugal forces. The first is to ride the force and keep asking questions at the frontiers. The second is to resist the force to maintain position. Many of the recent developments in ecology are incredibly exciting and deserve a central place within the discipline: urban ecology, invasion biology, conservation ecology, ecogenomics, and climate change research for example. But as we expand to fill these areas, we have to look back and ask how well we have answered the questions we are leaving behind, and whether our ability to answer questions on the frontier will be hindered by leaving the questions that make up the core of our discipline. If we do not work to increase the number of ecologists, or the speed at which we answer questions, than hard choices will continue to have to be made on which questions go unanswered.

The importance of surveys: a case study with plant 15N

Needles of Abies lasiocarpa, a specimen of which was found to have the lowest recorded foliar del15N of wild plants on the planet. (Image from USDA)

Both experimental and natural gradients are important ecological tools for understanding . The pendulum of relative importance has always been in motion on these and it is probably safe to say that there is more funding for experiments than surveying gradients. There are certainly some questions that can only be answered with experiments (e.g. effects of elevated CO2 on plants), while gradients are uniquely poised to shed light on other questions, such as long-term soil development. 

Just like experiments are sophisticated tools, so are surveys. Do them well, and understanding can come quickly. Do them poorly, and knowledge generation can stall. Case in point, I've been working for some time on understanding global patterns of plant natural abundance nitrogen isotopes. As I've mentioned before, these isotopes have the potential to provide powerful insight into the workings of the N cycle. When ecologists first began to examine patterns of plant 15N in the early 1980's, there weren't obvious differences among types of plants as there were with 13C and C3 and C4 plants, for example. The one thing that stood out was that N2-fixing plants (e.g. legumes) often had signatures that were similar to the atmosphere (del15N of 0). With this observation, the next 15 years or so was dominated by trying to interpret plant 15N signatures with respect to fixation, with little success. Missing during this time were all the environmental correlates and other species differences that might shed light on dominant processes constraining plant 15N. 

Fast forward to the present, and the battle is still being waged to narrow ecological interpretations of plant 15N. We're still working on getting published a synthesis of 10,000 foliar 15N samples. One thing that is interesting about the data are the extremes. The lowest recorded foliar del 15N is -14.4 from an Abies lasiocarpa at Lyman Glacier in Washington state (Hobbie et al. 2005) . The highest recorded 15N is 17.2 from a Cassia in Thailand (Yoneyama et al. 1990). If we take these two endpoints of ecological gradients, the basic patterns of controls on plant 15N are clear. The Abies is ectomycorrhizal, has foliar N concentration of 12 mg g-1 and is from a cold ecosystem. The Cassia is from an arbuscular plant (in Fabaceae, but found to be non-fixing based on infection) with a foliar N concentration of 33 mg g-1 and from a hot ecosystem. These contrasts (mycorrhizal type, mean annual temperature, and foliar N concentrations) encapsulate the majority of contrasts we see in our larger dataset. 

I feel like with the foliar 15N data, we weren't patient enough in seeking out extremes. And it's set us back 20 years in understanding the N cycle. Before we got locked into fixation, there should have been a number of surveys of plant 15N. Sample a number of taxa across the globe until the extremes and patterns become available. The 10,000 data points that we have only represent about $100,000 worth of analyses.

When we become interested in a pattern or process, good surveys are critical. Do them wrong, and the development of knowledge becomes stunted. And not just for isotopes. There are a number of other ecological patterns and processes that could benefit from better surveys such as soil microbial communities, root anatomy, plant phenology. If we think of these surveys as antiquated natural history, they are unlikely to be done well in a timely manner. But, if we think of them as sampling a diversity of natural experiments, maybe they'll be seen as worth the investment.