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Modelling primary production

BRIEN E. NORTON *

(*) Brien E. Norton: Assistant Director, US/IBP Desert Biome Programme, Ecology Center, Utah State University, U.S.A.


Introduction
Special problems in desert research and modelling
Modelling primary production


SUMMARY

Arid land ecosystems present some special problems for modellers: 1) precipitation and primary production can vary substantially from one year to the next; 2) the dispersion of perennial plants confers a spatial heterogeneity on many environmental variables. There are two basic approaches to modelling primary production. The first begins with generation of assimilated carbon and proceeds to allocate this material to other organs which then undergo respiration. Due to our limited understanding of translocation and root respiration, this approach has limited practical value for long-term simulations of community production. The second approach calculates biomass change consumption by herbivores and litter fall. It is derived from easily obtained data and is more accurate over a long period. It is also more easily adapted to treat plant succession.

Introduction

A model can be as simple as a regression equation relating production and precipitation, or as complex as a collection of equations with which the flow of carbon through various compartments of an ecosystem can be tracked. In the latter case computers are necessary to handle all the calculations and bookkeeping involved to simulate, for example, annual community production from a daily time-step, and the model is accordingly programmed for computer execution. Such computerized models of ecosystems or parts of ecosystems, are being developed by the desert research programme of the US/IBP. Data to build the models have been generated in the four North American desert types, which vary substantially from one another. The cool sagebrush desert of America's Great Basin receives its precipitation mostly from winter snow and experiences a predominant spring growing season. The Mohave Desert is the driest (mean precipitation of 110 mm), but like the sagebrush type its rainfall comes in winter, and spring temperature is an important regulator of growth. The Sonoran Desert, with its characteristic succulent flora, exhibits a bimodal rainfall pattern of spring and late summer. Precipitation extends from summer into winter in the Chihuahuan Desert type, with a dry spring.

Each type is distinguished by its own flora, community structure, and pattern of production, but none of these deserts is heavily utilised by livestock like the North African regions, and none is so similar in floristics and climate that it could be used as an analogue of the Sahel. It would therefore be unwise to apply our understanding of American deserts directly to the Sahel. However, there may be a number of parallels in the ecology of the two systems, and something may be learned from our attempts to model a desert ecosystem.

Special problems in desert research and modelling

Climatologists have documented the general fact that as mean annual precipitation decreases, the coefficient of variation rises. This is true of a large region but even more so for a localised area reflecting the uneven geographic and temporal distribution of precipitation from one km² to the next. This variability poses problems for predicting climate conditions on the one hand and primary production on the other. Figure 1 demonstrates this phenomenon with contrasting precipitation and productivity measures for two consecutive years in the Mohave Desert. The primary production was measured over an area of 0.46 km². The eight months of precipitation represent the period of effective rainfall preceding production assessment. The most striking feature of this figure is not the nearly sevenfold increase in total primary production, but the 210-fold increase in the productivity of annual species. The wetter year saw a 20 % increase in the ephemeral flora, and a different set of genera assumed dominance of the ephemeral community. The opportunistic nature of productivity of ephemerals is common to most deserts (the undisturbed sagebrush desert being an exception), and is made possible by the low ground cover of perennial species - only 20 % for the Mohave site discussed above.

The low ground cover values for perennials and the associated clumped pattern of dispersion create two generalised microenvironments: the local environment of the perennial plant canopy, and the harsher environment of the exposed interspaces. This strong development of spatial heterogeneity in the vegetation imposes a family of similar distribution on related biotic and abiotic variables.

- Litter accumulates and aeolian deposits form beneath the shrub canopies, which elevates the soil profile with a horizon richer in nutrients and organic matter than the interspace soil.

- Infiltration of rainfall is higher beneath perennial plant canopies due to interception and stem flow, the presence of surface litter and debris, and the more permeable surface soil horizon.

- The loss of water through evapotranspiratory processes is higher below perennial plants as soils dry out, which may eventually lead to less soil moisture stress in the interspaces where less water originally infiltrated.

- In North American deserts where algal crusts fix nitrogen, the fixation rate is reduced beneath shrub canopies by volatile inhibitors in plant litter, while the loss of nitrogen by volatilization is enhanced in the canopy zone.

- Seed densities are often higher in the canopy zone, and as a result these areas are subject to intensive foraging by g rodents that sort through the top few cm of the soil horizon.

- In drier-than-average years, annual plant species favour the canopy habitat and their pattern of dispersion parallels the perennial plant distribution. Beneath large shrubs, shade-tolerant ephemerals are dispersed in relation to aspect and distance from the trunk. This particular pattern can cause corresponding variation in nitrogen content of surface soil and mulch, which decreases with increasing distance from the base of the large shrub.

- The cycling of nutrients, especially nitrogen and phosphorus, occurs in localised islands oriented to the distribution of perennial species. In mature communities this phenomenon will create higher levels of nutrients throughout the soil profile beneath the perennial plants.

- Root biomass is also more dense beneath perennials, and there is a correspondingly greater density of soil arthropods and nematodes in the canopy zone soils.

- The more moderate habitat beneath a perennial plant will often favor the establishment of other perennial species. The classic example of this is the saguaro cactus of Arizona, which only regenerates within the protection of other perennial plants.

Figure 1 - Production des plantes annuelles et des plantes vivaces pendant deux années successives.

This inherent heterogeneity of the system is particularly vexing to modelling activities. It could mean more than a mere duplication of effort, when one considers the many interactions that occur between the canopy and interspace zones. The majority of these interactions are in the soil subsystem, and are associated with the growth, decay and uptake behaviour of the roots. Unfortunately, the dynamics of roots and their rhizospheral organisms are the least understood of any division of desert ecology. So far, the IBP desert programme has not grappled with the problems of modelling a horizontally heterogeneous system.

Modelling primary production

The level of complexity of a model of primary production is generally constrained by a) our under standing of the biology and/or ecology of the community in question, and b) the availability of suitable data with which to develop the quantitative relationships that comprise the model. It is this second condition that has polarised plant growth modelling into two approaches: one that begins with net carbon fixation via photosynthesis, and one that "black-boxes" carbon movement into and within the plant and simply deals with changes in biomass. The first approach is often called "mechanistic", the second is frequently referred to as "empirical". For convenience, I will adopt this nomenclatural convention, even though both approaches in fact have a strong empirical basis.

The "Mechanistic" Approach

The first step in a mechanistic model is to calculate net photosynthate (or net carbon input) produced from CO2 in the photosynthetic process. A number of ecophysiologists working all over the world have studied this process in some detail, and there is a substantial body of experimental data on which to base the relationships between net carbon input and temperature, soil or plant water potential, light photoperiod, atmospheric water vapour pressure, and phenological status of the species under study. In the model these relationships might be expressed in the manner shown in Figure 2, and for a particular species whose gas exchange behaviour is well known it is a straighforward matter to construct a model which will predict net carbon fixation rate with considerable accuracy (Figure 3).

As shown in Figure 4, which diagrams the structure of a mechanistic model of primary production, the second step represents the process of translocation and requires the transference of some of the photosynthate out of the leaf compartment and into the other organs of the plant. Subsequently the amount of carbon lost from these organs via respiration must be calculated. The consequent net allocation constitutes the carbon added to each organ for the time-step employed, and this value must then he converted to carbohydrate and augmented by mineral elements in order to express the increments in terms of biomass. Unfortunately, our understanding of the biology of translocation into, and respiration of, non-photosynthetic organs, especially roots, is deficient when we need to state these rates quantitatively with respect to environmental variables and phenological status. We also need to know more about the turnover rates for roots of arid land species, and the amounts and distribution of living roots in the soil profile. It is also necessary in some models of this kind to distribute carbon increments to tissue types such as structural material, reserve carbon compounds and protein carbon, which is another area of speculation for most arid land species. Despite these difficulties, it is possible to develop reasonable output from a mechanistic model (Figure 5), but only for limited periods of usually less than one year.

A further area of difficulty when constructing a carbon flow, mechanistic mode] is accounting for the influence of herbivores, particularly arthropods and plant parasitic nematodes, on the processes involved. With a knowledge of species present and their population levels, one can estimate metabolic demand and intake requirements, and if information on dietary habits were also available, the amount of plant material consumed by such herbivores could be calculated and the appropriate deductions made on a species/organ basis. But the impact of this herbivore on allocation of photosynthate and respiratory rates may confer a greater importance than the amounts removed would imply. The physiology of laboratory plants is therefore probably quite different from that of field specimens, and if laboratory data are employed in model-building the simulations are likely to misrepresent the field experience.

This paper presents a rather pessimistic view of the progress of mechanistic modelling, which is largely due to the limitations of available data. The modeller can turn to the research scientist and say: "Give us more data". The scientist should reply: "What data do you need, and what data are most important?" This hypothetical exchange introduces a helpful contribution modelling can make to research, even though model simulations may be falling far short of satisfying the field researcher.

A model simulation run can in a sense be viewed as a test of a hypothesis as shown in the following example. Mechanistic modelling at this stage requires some guesswork in calculating translocation and respiration of non-photosynthetic organs. The beginning (assimilation of net carbon) and end-point (biomass increments) can be determined with reasonable accuracy. For the intervening steps the modeller can test a variety of likely relationships by substituting sets of different equations or by adjusting parameters. He can also vary specific variables (such as temperature and stem respiration rate), evaluate them in terms of deviation of outputs from the expected values, and thereby determine which are most critical to the successful operation of the model. This latter exercise, "sensitivity analysis", should indicate to the research scientist which avenues of physiological enquiry will be most productive for further study. A team of modellers and scientists working together should be able to specify and define research objectives and rate their priorities. For the particular example given, it is apparent that the use of labelled carbon, which is traced into plant organs and residual concentrations periodically measured, presents the most fruitful line of research.

Figure 2a- Variation saisonnière de la température optimale de la photosynthèse due a l'acclimatation (2 a) et assujettissement a la lumière du taux de fixation de carbone net pendant le jour (2b).

Figure 2 b - Variation saisonnière de la température optimale de la photosynthèse due a l'acclimatation (2 a) et assujettissement a la lumière du taux de fixation de carbone net pendant le jour (2b).

The "Empirical" Approach

Given the extent of research in gas exchange studies, the mechanistic approach is forced to consider the fate of photosynthate, and therein lies its handicap. In order to side-step such problems of translocation and respiration, the empirical approach models biomass change as measured in the field by simple harvest techniques. The growth relationship here is expressed as:

Biomass (organ or whole plant) = f (moisture, temperature, standing crop, phonological state) for a given species on a given site with its characteristic soil and topographic features. This change may be modified by:

Biomass2 (organ or whole plant) + f (herbivore consumption, death of plant part[s]).

The data base necessary to develop a model of this kind is a meteorological record, the composition by species and biomass of the plant community, utilization by herbivores, and the rate of litter production or conversion to standing dead material. Unlike the mechanistic model, which probably requires a time-step of at the most one week, the empirical model can simulate satisfactorily with a time-step of one year.

An example of an empirical model is one developed by Dr. Don Wilkin from data collected by the U.S. Forest Service on an Experiment Station in southwestern Utah. The vegetation is a salt desert shrub community dominated by Ceratoides, Atriplex, and several perennial grasses. Sheep were grazed during the winter on 100-ha paddocks at different stocking intensities for a period of 40 years. Grazing pressure was maintained as plant production varied by adjusting stocking rate from year to year. Primary production was measured in October before grazing as current year's growth, and percent utilization was estimated for each species at the end of the grazing period. The objective of the model is to simulate primary production after a period of several decades of sheep grazing. The following discussion deals only with primary production; the model also calculates utilization.

Figure 3 - Le cycle quotidien de la photosynthèse nette de Hammada scoparia le 10 juin 1971. Le temps est exprimé en dizièmes d'heure, la photosynthèse nette en grammes de poids sec par heure; x = valeur prévue o = valeur mesurée (avec l'autorisation de E.-D. Schultze et O. L. Lange).

The initial problem was to handle the tremendous variability in growth that occurs from year to year. By conducting a series of correlations it was possible to calculate the highest positive and negative correlation coefficients relating primary production of each species to periods of rainfall. Every combination of strings of monthly precipitation was tested from 1 month at a time up through 24 successive months within the 24-month period prior to measurement of plant growth. The results are summarized in Tables 1 and 2. Similar correlation coefficients could be developed for mean monthly temperatures.

Using the climate record on the site arid the annual production estimates for each year, influence of weather variability was quantified by developing regression equations which calculate the factor by which growth of a species in any particular year deviated from the mean.

Adjustment factor (weather) = b0 + b1 (Aug.-Sept.) + b2 (June-July) +..., etc.

The monthly periods in this equation are the totals of rainfall. An adjustment factor of 1.5 would mean that for the precipitation values used in the equation, plant growth was 50 % higher than average.

Figure 4 - Schéma de circulation pour un modèle de plante.

Figure 5 - Production simulée de carbone dans les organes des espèces éphémères. Unités variables en ordonnée.

Figure 6 - Rendement d'Atriplex confertifolia en herbage, valeurs simulées et valeurs effectivement mesurées

By dividing actual production values by this factor, "normal" growth is calculated - i.e. the growth that would have occurred following an "average" 24-month period. In the operation of the complete model, which also calculates utilization of forage by sheep, the simulation begins with input data listing productivity by plant species, which are immediately converted to "normalised" values. It then determines fractional utilization of each species (not discussed here) and calculates productivity from year to year under "normalised" climatic conditions. At the prescribed end of the simulation, the normal production values are restored to a real situation by multiplying by the adjustment factor (using given monthly precipitation and temperature data). A test of the model against field measurements is shown in Figure 6. These field measurements are from paddocks near those that contributed to the development of the equations used in the model. The model produces reasonable output for sites similar to the one on which the model was based. For application to a somewhat different site the parameters in the equations would have to be reexamined.

With modifications, an empirical model like the one discussed above could attempt simulations of plant succession in addition to community production.

Table 1 - Species-specific patterns of precipitation correlating most positively with the growth of range plant species

Plant Species

Period of Precipitation*

Corr. Coeff.

Atriplex confertifolia

Oct(yr-1) thru Jun(yr)

.93

Eurotia lanata

Aug(yr-1) thru Aug(yr)

.89

Artemisia spinescens

Jun(yr) thru Sept(yr)

.69

Chrysothamnus spp.

Nov(yr-1) thru Dec(yr-1)

.85

Ephedra nevadensis

Apr(yr-1)

.54

Other shrubs

Nov(yr-2)

.89

Hilaria jamesii

May(yr) thru Jul(yr)

.66

Oryzopsis hymenoides

May(yr-1) thru Jul(yr)

.91

Sporobolus spp.

Jun(yr-1) thru Jul(yr)

.93

Other grasses

May(yr-1) thru Aug(yr)

.79

Salsola kali

Jul(yr) thru Aug(yr)

.67

Sphaeralcea grossulariaefolia

Oct(yr-2) thru Aug(yr)

.89

Other fortes

Apr(yr)

.86

* Growth was measured in October of each year on a desert range in southern Utah: "yr" refers to the year in which the growth was measured.

Table 2 - Species-specific patterns of precipitation correlating most negatively with the growth of range plant species

Plant Species

Period of Precipitation*

Corr. Coeff.

Atriplex confertifolia

Jan(yr) thru Feb(yr)

-.62

Eurotia lanata

Jan(yr) thru Feb(yr)

-.37

Artemisia spinescens

Oct(yr-2)

-.62

Chrysothamnus spp.

Feb(yr)

-.56

Ephedra nevadensis

Feb(yr)

-.64

Other shrubs

Jul(yr-1) thru Aug(yr-1)

-.31

Hilaria jamesii

Oct(yr-2) thru Nov(yr-2)

-.67

Oryzopsis hymenoides

Nov(yr-2) thru Mar(yr-1)

-.47

Sporobolus spp.

Jan(yr) thru Feb(yr)

-.57

Other grasses

Feb(yr-1)

-.40

Salsola kali

Oct(yr-2)

-.62

Sphaeralcea grossulariaefolia

Feb(yr-1)

-.34

Other fortes

Jun(yr-1)

-.45

* Growth was measured in October of each year on a desert range in southern Utah: "yr" refers to the year in which the growth was measured.


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