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.

Nutrient limitation, climate, and bison

Relationships between mid- (a, c) and late-summer (b, d) precipitation and bison weights for each year for Konza Prairie (a, b) and Tallgrass Prairie Preserve (c, d). Calf weights and yearling weight gain (YWG) were adjusted for differences in sex ratios to represent the average weight of an average male and average female bison. Midsummer weights were standardized for variation in late-summer precipitation and vice versa.

In RSWP, I write a lot about nutrient limitation of plants. One thing that comes out strongly as we look at how ecosystems function is that nutrient limitation in plants can induce nutrient limitation in herbivores. Especially for nitrogen which animals generally cannot access through other means except by eating plants.

We just had a paper published that illustrates a few important points regarding nutrient limitation in grazers and the distal controls on grazer performance. In the paper, we examined how interannual variation in the timing and magnitude of precipitation affected the weight gain of free-roaming bison. Every year, the bison herds are rounded up, and each individual weighed. Bison weights of calves and animals in their second growing season (yearlings) were analyzed for 14 years for Konza Prairie, Kansas, and 12 years for Tallgrass Prairie Preserve, Oklahoma. The sites are both native grasslands on the drier edge of what is considered humid grasslands. The records of weight gain for wild herbivores are among the longest known—only Marco Festa-Bianchet’s excellent work on mountain goats is comparable.

As we looked at how much weight the animals gained each year, we found was that more rain late in the summer increased the weight gain of the bison. Not much of a surprise there. More rain in August, which is often dry, means more green grass later for the animals, which would allow them to grow more. What was unexpected (to some) was that having more precipitation early in the middle of the growing season (late June, early July) caused animals to gain less weight. Why? Here, it’s not the quantity of food, but its quality. What we found was that having high precipitation in the middle of the growing season also increased flowering (see previous post on flowering). More flowering means more low-quality stems, which lowers the average protein concentrations of the grass, and lowers weight gain. This idea wasn’t entirely unknown—some ranchers say a dry June is money in the bank—but it was the first time quantified scientifically.

Now, it also might be the quality of the leaves that is low in high mid-summer precipitation years (we don’t have data on that), but the data illustrate a few key points. First, in grasslands, quality is as important to consider as quantity when considering grazer performance. As I describe in RSWP, there are glaring examples of this being glossed over (as well as great examples of its consideration). Second, as we think about how grasslands are structured and how they might change, the timing of precipitation can be as important as the amount. Increase or decrease the amount of precipitation by half and bison gain the same weight. Shift it from August to early July and weight plummets.

What we learn from simple observations continues to amaze me. By no means have we plumbed the depths of understanding the complexity of grasslands. Complements to both Konza’s Gene Towne and The Nature Conservancy’s Bob Hamilton for doing such a great job for more than a decade.

Craine JM, Joern A, Towne EG, Hamilton RG. 2009. Consequences of climate variability for the performance of bison in tallgrass prairie. Global Change Biology 15: 772-779.

Grass flowering and climate

25-year record of flowering of Schizachyrium scoparium (open circles uplands, closed circles lowlands).

We’re just about ready to submit a paper that analyzes 25 years of flowering for three grass species at Konza. As far as I know, this is the longest continuous record of flowering effort for grasses (although there always seems to be some European record that dwarfs any North American record). In short, every fall, the number and weight of flowering culms for three species of grass (Andropogon gerardii, Sorghastrum nutans, and Schizachyrium scoparium) are measured in an annually burned watershed. The three species are, more or less, the three dominant grasses at Konza.

When I asked what people expected from the data, there were two main beliefs. First, species were offset in their flowering. It was generally held that some years were good flowering years for Andropogon, others for Sorghastrum. Second, flowering was much greater after a dry year, especially for Sorghastrum. The latter was likely an extension of the Birch effect, which I’ve talked about in previous posts.

In general, we found that a good flowering year for one species was a good flowering year for all species. By no means was there an inverse relationship for flowering between species among years. The differences among species, were interesting though, and reinforced the idea that it is not just the amount of precipitation that falls that is important in grasslands, but the timing of the precipitation. For example, years with greater precipitation early in the growing season benefited Sorghastrum flowering, while greater precipitation late in the growing season benefited Schizachyrium. Why the belief for inverse relationships among species? More than likely its due to their differences in flowering phenology. This year was a good flowering year for all three species, but a person would have sworn it was a good year for Andropogon in mid July, as it is the first to start to flower, while the same person would have sworn it was a good year for Schizachyrium in early late August when it began to flower in earnest.

The offsets in flowering are important components of understanding questions such as species coexistence, but it is the question about antecedent climates that tests our fundamental understanding of how grasslands work. At the heart of the matter is whether conditions during the previous year will generally affect current year’s dynamics. If so, processes like the Birch effect become more central and ecosystems become a lot more complex.

Despite the assurances, over 25 years, there was no effect of previous year’s precipitation. Wet years had a lot of flowering regardless of whether the previous year was dry or wet. Dry years had little flowering, regardless of whether the previous year was dry or wet.

The conclusions seemed pretty straightforward, except for a short paper by Knapp and Hulbert in 1985. They had measured flowering in the same watershed as our dataset a few years before our dataset began. What was interesting was that flowering in 1981 was 6-10 times greater than any year of our 25 year record. 1981 was a sea of grass horse high not because 1981 was especially wet, but because 1980 was especially dry. A month where every day was over 100 degrees Celsius. Cows starving. Lawns dying.

As such, even though Konza had a 25-year record, some events happen rarely, and when they do, they can be spectacular. There are a lot of questions that are raised by the dataset. Was it the Birch effect that caused the immense flowering or reduced competition from plants dying? How dry to soils have to be for how long for N to explode? What really struck me was that no long-term dataset is ever long enough. 25 years of data just wasn’t long enough to capture even a hint of the importance of rare events. Who knows what year 26 will bring? I’m sure a lot of people will be watching a bit more closely.

Transitive limitation and precipitation

Thinking more about N and water, I was looking over the Huxman-Smith et al. 2004 Nature paper. This paper summarizes the sensitivity of ANPP to precipitation. With data from 14 sites, they calculate rainfall use efficiencies across years to see how RUE changes with mean annual precipitation. They find that wetter sites have lower RUE, but all sites converge on a constant RUE. (Above figure is precipitation vs. ANPP (g m-2), each x-axis tick is 500 mm y-1).

The most interesting art of the paper are statements on resource limitation.

Here are some key sentences:

1) the authors predict that “the removal of other resource limitations so that precipitation becomes the primary limiting resource will result in an increase in site-level RUE that approaches RUEmax.”

2) “sites with high production potential in years with greater than average precipitation, soil nitrogen or other limiting resources might transiently limit biological activity.”

3) They also state that “biogeochemical constraints (limitation of activity by resources other than water) can increase with increasing precipitation”.

The approach the authors take to limitation is generally one of serial limitation. First one resource limits, and then another. The authors seem to hold the idea that multiple resources can co-limit ANPP, but they are mute about mechanisms or what the tradeoffs are. There is no evidence they considered substitutability leading to co-limitation, or transitive limitation (water limiting N availability). Looking at statement 3 above, they just as easily could have said that biogeochemical constraints can also decrease with increasing precipitation.

The unstated model they use follows something like this: less rain, greater water stress, less limitation by other resources, less production, greater WUE.

The existence of transitive limitation changes the entire story of ANPP responses to increased precipitation: less rain, less nitrogen mineralized, greater limitation by N, less production.

The relationship between ANPP and precipitation is, here, just a ratio. The important part of research is always to look one level of mechanism below the pattern of interest.

For example, if plant WUE was a key factor in RUE, then wouldn’t sites dominated by C4 vegetation have an inherently higher RUE than sites dominated by C3 vegetation? But, if the observed RUE was driven by N mineralization responses to increased soil moisture, wouldn’t they be the same? Although Cedar Creek (CDR) might show no increase in ANPP with increased precipitation due to strong N limitation, there might be unique patterns of sensitivity of N mineralization to variation in precipitation there. For example, maybe with the sandy soils, soil moisture isn't much greater in a high precipitation year.

At this point, both mechanistic hypotheses should be considered equally (one can’t be favored because it comes first). It’d be interesting to see how much of the patterns could be explained by transitive limitation.

Huxman, T. E., M. D. Smith, P. A. Fay, A. K. Knapp, M. R. Shaw, M. E. Loik, S. D. Smith, D. T. Tissue, J. C. Zak, J. F. Weltzin, W. T. Pockman, O. E. Sala, B. M. Haddad, J. Harte, G. W. Koch, S. Schwinning, E. E. Small, and D. G. Williams. 2004. Convergence across biomes to a common rain-use efficiency. Nature 429:651-654.

Co-limitation by water and nitrogen

Resource limitation is one of the great driving factors that structure ecosystem function and ultimately the evolution of species. Yet, rarely should only one resource be limiting to plants. As I outline in RSWP, co-limitation should be the rule rather than exception. Yet, the paradigm shift in our understanding of limitation is still developing.

One of the most important dual limitations to plants is between water and nitrogen. In many ecosystems, increases in biomass are observed when nitrogen is added as well as water. Yet, why would these two resources co-limit production? For example at Konza Prairie, ANPP frequently responds to water addition and is greater in wetter years. In addition, ANPP increases with N fertilization. Mechanistically, how can this be?

One reason why co-limitation occurs is because of acquisition tradeoffs—allocating resources to acquire one resource does not also lead to the acquisition of the other. Their costs are separate. For example, CO2 and water can co-limit because of their spatial separation in acquisition as well as their direct tradeoff in photosynthesis. Yet, generally the same unit of root can acquire both water and nitrogen as they are coincident in the soil.

Co-limitation can also arise when gain or loss rates from the ecosystem are co-dependent on the resources’ availability, causing the resources to be supplied at the same ratio demanded by plants. For example, N and P will often co-limit production because N is more likely to be lost from the soil when P is limiting. When the ratios of supplies and demand match, increases in productivity occur only when both resources are added, not each individually (see Figure 4.2 in RSWP). Yet, the pattern of co-limitation for water and N just doesn’t support this. Productivity generally responds to the addition of each, not just both. Although N2-fixation might be more likely when soils are wet, which bring supply and demand ratios closer,  N loss can also be greater when soils are wet (dentification, leaching). Plus, N loss is not more likely when soils are dry.

If these two main reasons do not apply, why do N and water frequently co-limit production? The secret might lie in the figure at the top of the post. 35 years ago, researchers incubated a number of soils at a range of soil moistures. They found that N mineralization typically was highest at some high soil moisture. As soil moisture declined, N mineralization declined linearly.

These might be old data, but the consequences are still amazing, even today. For example, if soil moisture declines from 80% water-filled pore space to 70%, which is still a lot of water for any plant, N mineralization would decline by 12%. Add that water back and N mineralization increases. If this is the case, then when it rains or an area is irrigated, N-limited plants would see an increase in productivity without ever being directly limited by water.

There is other evidence that water might not be directly limiting to productivity, but seem to be. For example, there is the curious observation that there is often plenty of water in the soil for seemingly water-limited plants right below their lowest roots. Dave Wedin noticed that in the Sandhills of Nebraska, there is often plenty of water right below the roots of the C4 grasses, which extend only 25 cm deep. Turns out same thing happens in Konza. These plants can easily produce roots deeper than they do, they just don’t. Why? Because all the soil organic matter is in the top of the soil profile. The water below that zone is of no use to the plants. By the time the shallow soils dry out, no N is being mineralized for the deeper water to be useful.

There are a number of other questions that need to be answered about co-limitation between N and water. Certainly soils can dry out to the point where neither water nor N is available to plants. How often does this occur and are there cross-overs where water becomes more limiting than N? Also, if deep water is available to plants, why don’t they lift it up to shallow soils to increase N mineralization?

All good questions, but the key is not necessarily the answer with which we end as much as the question with which we start. And we always have to start with understanding the mechanisms the determine the patterns in which we are interested. In this case, we have to start by testing co-limitation from the beginning and then asking why co-limitation occurs.

Figure from: Stanford, G. and E. Epstein. 1974. Nitrogen mineralization-water relations in soils. Soil Science Society of America Journal 38:103-107.