Interactions between Abiotic Environmental Conditions and Resources

Review:

Crop yield is a function of resource use. In general, resource-use efficiencies are the products of resource uptake (capture) and resource utilization (biomass or yield produced per unit of resource captured) (Janssen, 1998).

Y/S = U/S (resource uptake) × Y/U (resource utilization efficiency)

Y/U is the physiological RUE; U/S is the ecological RUE.

Improving Y/U is often the goal of biotechnology.

U/S for a particular resource depends on the levels of other resources and on environmental conditions. Therefore we expect that plant growth or crop yield will depend on the interactions among resources and environmental conditions, as well as on the supplies of those resources.

Factors that influence crop yield are of several types and include:

• Environmental conditions, not under grower control: temperature, wind, seasonality, topography, length of growing season, relative humidity; soil type, soil depth, SOM, soil pH; pest, weed and pathogen populations (in part).
• Environmental conditions under partial grower control: pest, weed, and pathogen populations; SOM; soil structure; soil pH.
• Resources not under grower control: light, CO2, water (precipitation), nutrients released by mineralization.
• Resources under grower control: nutrients (from fertilizer), water (from irrigation).
• Crop varieties.
• Management: land preparation, choice of cropping system; choice of cultivars; date of planting; plant population; timing of nutrient input; timing of pest, weed and pathogen control; date of harvest; management of residues.
• Infrastructural or institutional factors: access to credit, suitable varieties, extension services, inputs, markets.

What is the combined effect of two or more resources, environmental factors, or management practices on crop yield? Do these factors act independently, or is there some sort of synergistic or antagonistic responses when these factors vary? Is their combined effect different from what we might expect considering each factor separately?

How do we investigate such complexity?

Types of Interactions

1. Law of the Minimum

The publication of Justus Liebig's Organic Chemistry and its Application to Agriculture and Physiology in 1840 marked the beginning of agricultural science (Foth & Ellis, 1988).

Liebig proposed that crop growth was limited by whichever nutrient was present in the lowest amount relative to its demand. = "Law of the Minimum"

[Ironically: Liebig had a "disdain" for field experiments and experimenters, who "assailed Liebig's assertion that plants obtained their nitrogen from atmospheric ammonia. Liebig responded with equal vigour, but with less constraint by the facts." (Evans, 1998, p. 98)]

2. Percentage Sufficiency (= multiplicative interaction)

Proposed by Mitscherlich in 1909, who argued that the yield potential of two limiting factors was determined by the product of the yield potential of each factor acting independently.

This gives rise to multiplicative models: eg. Y = f(N) × f(P) × f(water) × f(light).

Examples:

• Park Nobel's Environmental Productivity Index:

EPI = Water Index x Temperature Index x PAR Index

• Wallace & Wallace (1993) "Multiple Action Yield Fraction":

Relative Yield = Product[F_i] = F₁ × F₂ × F₃ × F₄ × ... × F_i

They reviewed several empirical studies; and claimed this model provided the best fit.

Relative yield in this case is the ratio of actual yield to a theoretical maximum. According to Wallace & Wallace:

if theoretical maximum = 1.0,

record yields for most crops = 0.6;

best-grower yields = 0.4;

average yields = 0.2-0.25.

Although this analysis suggests that there is considerable room to improve yields, the very nature of a multiplicative model suggests that yields much lower than maximum are to be expected.

For example:

• if 10 resources or factors are limiting yield and each is at 80% of its maximum value, then the expected value for relative yield is: RY = (0.8)¹⁰ = 0.11.
• Likewise, for 10 factors at 90% of their maximum value: RY = (0.9)¹⁰ = 0.35;
• for 10 factors at 95% of their maximum value: RY = (0.95)¹⁰ = 0.60;
• or for 20 factors at 95% of their maximum value: RY = (0.95)²⁰ = 0.36.

A resource that limits growth in a Liebig-type manner (the only limiting resource) is often referred to as the limiting resource; when resources limit growth in a multiplicative manner each resource is usually referred to as a limiting resource. I tend to use the term limiting resource to refer to any resource whose addition results in an increase in crop growth or yield.

3. Synergistic Interaction

A synergistic response occurs when the response to both factors is greater than that expected from each factor acting independently. Prasad & Power (1997) give the following example of a synergistic interaction:

	Response to:			Estimated contribution of:
Crop	N (kg ha-1)	P (kg ha-1)	N + P (kg ha-1)	N (%)	P (%)	Interaction (%)
Sorghum	110	490	1570	7	31	62
Finger millet	390	170	1300	30	13	57

Why aren't synergistic interactions more commonly observed? Ecosystem responses (e.g., yield) involve complex processes; if more than one process controls the rate of a response, and each process is controlled by a different limiting factor, then supplying both limiting factors to the system should give a synergistic response.

Distinguishing Types of Interactions

The problem of distinguishing different types of interactions can be formally solved using a simple statistical model. For example, with two factors the model is:

Y = B₀ + B₁X₁ + B₂X₂ + B_1,2X₁X₂ + error

A statistical analysis (such as analysis of variance-ANOVA) would test for the significance of the various coefficients B_i. For instance, if B₁ is significantly different from 0, that means that resource or factor X₁ does affect the yield, Y. The following table then permits us to precisely define how two variable are interacting '+' means the coefficient is positive and statistically significant; '0' means the coefficient is not statistically significant; and '-' means the coefficient is negative and statistically significant:

B1	B2	B1,2	Nature of Interaction
+	0	0	X1 is limiting (no response to X2)
0	+	0	X2 is limiting (no response to X1)
+	+	0	X1 and X2 effects are additive
0	0	+	X1 and X2 effects are multiplicative
+	+	+	X1 and X2 effects are synergistic
+	+	-	X1 and X2 are antagonistic

Approaches to Studying Complexity

I. Experimental

Factorial experiments can be analyzed as discussed above. In practice, these experiments are very limited in the number of factors that can be included (4 is probably the upper limit).

Experiments are widely regarded as "good science" but they have severe shortcomings in ecology, namely that they are:

• Artificial (simplified conditions may not reflect "real world situations")
• Strongly context specific (i.e., difficult to extrapolate)

A more important critique of experiments is that they may not address processes that in fact control much of the agroecosystem function. "Many ecologists ... focus on their small scale questions amenable to experimental tests and remain oblivious to the larger scale processes which may largely account for the patterns they study." (Dayton and Tegner, 1984, cited in Schneider, 1994).

II. Modeling

An alternative to experimentation is modeling. Scientists use models all of the time, of various types (Reynolds et al., 1993):

• conceptual-including flow diagrams, mass balance equations, etc. that provide a qualitative picture of a process or system.
• empirical-an equation developed from data describing the relationship between variables

Empirical models are based on statistical formulations. For example, an empirical model relating yield to nitrogen fertilization, based on the outcome of a field experiment, might be:

Y = 2330 + 10.6 (N-rate) - 0.12 (N-rate)²

• phenomenological-common, to describe a process. E.g. dN/dt = rN(1-N/K) the model for logistic population growth. Physiological processes are usually described by phenomenological models.

Phenomenological models "describe the behavior of a system ... without decomposition into lower-level subsystems." (Reynolds et al., 1993)

• simulation--attempt to describe how a system functions

These are also referred to as mechanistic models sensu Reynolds et al. (1993), and may consist of both empirical and phenomenological equations; i.e., the processes in simulation models are usually phenomenological models; the equations that relate parameters to environmental conditions are often empirical models.

Reynolds et al. (1993) argue that equations describing the processes be based at the level of the biological hierarchy [see introduction] only 1-2 levels below that addressed by the model-they such not be excessively reductionist.

Simulation modeling combines a conceptual flow diagram with equations describing each flow. The components of such models include (after Jorgensen, 1986):

• Forcing functions or external variables (that is, environmental conditions such as temperature, precipitation)
• State variables (components, such as pools in a nutrient cycling model)
• Processes (flows), represented by equations- either empirical or phenomenological models
• Parameters. Obtained by experimentation, literature, or estimating (guessing!) Resource-use efficiencies might be examples of parameters in a crop growth model.
• Universal constants.

Model construction involves:

• Define the problem and the appropriate spatial and temporal scope
• Develop a conceptual model (a diagram or flow chart, in ecology, based on knowledge of natural history of the system); Can include feedbacks, conditional responses
• Write equations to describe the processes
• Estimate unknown parameters
• Calibrate the model [test output to see if it is realistic]
• Revise the model
• Validate the model [test model predictions with independent data]
• Revise the model again (if needed)
• Test hypotheses, that is, perform "what-if" experiments.

Examples of modeling in ecology include models of nutrient cycling (for example EPIC, CENTURY) and food webs, Crop Growth Models (for example, SOYGRO), or the Club of Rome (Meadows et al., 1992, Beyond the Limits) ambitious World3 model of world population growth, food production, economic development, and natural resource utilization.

The latter model has 225 variables, but has been criticized as being too simplistic and pessimistic. Meadows et al. (1992) stated that "The purpose-the only purpose-of World3 is to understand the possible modes of approach of the human economy to the carrying capacity of the planet."

It is in the hypothesis-testing stage that the investigator can better study the interaction of many different resources and environmental conditions, by setting up a variety of scenarios, each differing in one (or more) factors.

Example: Brown and Rosenberg (1997)

Model Used: EPIC

Variables Examined: Temperture, precipitation, solar radiation, vapor pressure, CO2, stomatal resistence, LAI

Number of Combinations Modeled: 34

Crops Examined: Missouri corn, Iowa corn, Nebraska irrigated corn, Iowa soybean, Nebraska sorghum, Kansas wheat

Sample of Results:

Crop	Scenario 26: Temperature-Increase Precipitation-Increase Solar Radiation-Decrease Vapor Pressure-Increase CO2-550 ppm Stomatal Resistance-Increase	Scenario 24: Temperature-Increase Precipitation-Decrease Solar Radiation-Increase Vapor Pressure-Decrease CO2-550 ppm Stomatal Resistance-Increase
	Percent Change in Yields
Missouri corn Iowa corn Nebraska corn Iowa soybean Nebraska sorghum Kansas wheat	-5 15 -13 0 36 10	-2 -9 -5 -4 -24 0

In this model, an important effect of increased temperature was accelerated phenological development, which shortened the time to harvest, lowered yields, and decreased water-use efficiency.

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20 February 2003