Plant growth is a process that is highly relevant in a range of contexts. The ability of an individual plant to grow and achieve a certain size in a given environment is one of the prerequisites to reproduce successfully and achieve the desired yield.

Plant growth is of fundamental importance as it forms the basis of all agricultural productivity. It is therefore not surprising that the processes underlying plant growth are of immense importance to researchers.

These include the biophysical and biochemical limitations on photosynthesis, that respiration should not be wasteful or should be made less ‘wasteful’ in order to have more photosynthates available for growth.

Other researchers would want to work on the efficient uptake or use of nutrients including water or study the molecular mechanisms that determine cell division. The ultimate goal is often to change or affect these processes in a way that will positively shape the growth and productivity of plants.

Plant Environment and Light Intensity

Understanding plant growth becomes even more challenging because of the strong effect of the environment, which may modulate the various components of the growth processes in different, sometimes contrasting ways.

For example, plants grown at high light intensities generally have higher rates of photosynthesis and thereby a higher rate of biomass production per unit leaf area than low‐light grown plants. However, plants grown at high light at the same time have a reduced amount of leaf area per unit plant mass.

At light levels higher than 25 mol m−2 day−1, this may lead to a situation where, for some species, the growth rate is not stimulated anymore although the rate of photosynthesis per unit leaf area is still increasing. Physiological interactions may become even more complex when two or more environmental factors interact.

Quantitative Estimates of Total Plant Mass

Plant growth models as a simplification of complex systems have tremendous value as a way to structure and integrate available knowledge, test hypotheses and come up with quantitative estimates of total plant mass, above‐ground mass and/or yield.

Plant growth models come in a wide variety, ranging from simple formulae that mathematically capture plant size over time with just two or three parameters, up to highly complicated simulation models that evaluate global change effects on the performance of vegetation worldwide.

They apply an array of conceptual approaches and incorporate a range of more‐or‐less detailed physiological processes, mostly centred around the carbon economy of the plant, as this provides the backbone for all growth.

Empirical Models

The simplest models of plant mass or productivity are empirical models, also denoted as statistical models. Empirical models are frequently used in such different fields as agriculture, horticulture and forestry to describe and/or forecast the productivity in monocultures of economically interesting plant species.

In terms of mechanism, they can be considered as a ‘null‐model’, as they do not contain any physiological processes at all, rather, they can be seen as dose response curves (DRCs) which relate biomass or yield observations in a given geographic location or climatic zone to one climatic or edaphic variable of interest.

They can also be extended to include several independent factors. Simple or multiple regression techniques then provide an equation that can be used as a predictor for biomass.

Empirical models are extremely simple yet effective in their ability to predict the productivity of natural and crop stands with one notable exception: they perform badly if they are to predict yield outside the boundaries where data have been collected.

One example where extrapolation may lead to erroneous estimates is the case of temperature.

Generally, crops like rice and maize are relatively cold‐sensitive and grow and produce better at warmer temperatures.

However, this may not be extrapolated to too high night temperatures, as quite some species become sterile under those conditions, with reduced yield.

Photosynthesis – Respiration Model

Mechanisms in Plant Growth and Development

The next level of complexity is formed by models that explicitly simulate photosynthesis and respiration.

Employing the dependencies of photosynthesis for light, CO2 and temperature, as well as the amount of leaf area present for a given plant or canopy, such models calculate the total carbon fixation of a plant or vegetation over a given time step.

Subsequently sugars required for maintenance of respiration are subtracted from the total amount of produced photosynthates, and the remaining sugars are then distributed with some rule over the various vegetative and generative compartments of the plant.

In a final step, these sugars are converted to biomass, after which the whole calculation repeats again for the next reaction.

This process or mechanism is dependent upon:

The amount of N in the leaves available for the photosynthetic machinery.
The extent to which a plant canopy is approached as one big leaf or as different leaf layers.
Water or nutrient availability.
Temperature constraints.

Importance of Growth Mechanism Simulations in Plants

The mechanistic simulation models of plant growth have considerable uses in the study of plants. These include:

To predict the growth rate or productivity of a crop in a variety of climatic conditions.
They also form an indispensable help in management decision making.
To predict growth outside the strict boundaries where conditions for plant performance have been tested experimentally.

Although an exact tolerance limit is generally not stated, crop modellers often seem to accept differences between observed and predicted growth of 10–15% as being reasonably good.

Different wheat models, developed by research groups based on different continents, are generally performing very well at the geographic location they were developed for.

Mechanistic Top‐Down Models

An alternative way to analyze growth is a top‐down approach. Starting with the total biomass of the plant, one can dig down and factorize the underlying parameters and processes into increasingly more detailed components.

This approach is often applied to analyze experimental data in a systematic framework based on carbon‐economy principles.

Aim of such an analysis is to examine which of the underlying processes vary between treatments, genotypes or species and which ones remain relatively constant.

Relative Growth Rate (RGR)

The most basic expression of growth is the so‐called ‘Absolute Growth Rate’ (AGR), which is the change in size of the plant per unit of time. If AGR is constant, plant mass will increase linearly over time.

This variable does not incorporate the changes in size of young plants, as they will often increase biomass in a way that is approximately proportional to the biomass of the plant already present.

The principle of proportional growth is engrained in the concept of ‘Relative Growth Rate’ If RGR would be strictly constant, then plant mass will follow an exponential trajectory over time:

Factorizing RGR in Underlying Components

Following not only the progression in plant mass, but also in leaf area allows RGR to be factorized into two underlying components, one representing the total amount of leaf area per unit plant mass (Leaf Area Ratio; LAR), the other the increase in biomass per unit leaf area [Unit Leaf Rate (ULR); an alternative term is Net Assimilation Rate (NAR).

The power of this simple factorization cannot be overestimated because ULR is often strongly correlated with photosynthesis.

Read Also: Traditional Plant Growth Analysis

Hence, without doing more than weighing plants and measuring leaf area, already a fairly good indication can be obtained whether observed differences in RGR are due to the structural component (LAR) or to the gas exchange, as characterized by the ULR.

This then is achieved without any measurements of photosynthesis or respiration, with all their problems of scaling up from leaf to whole plant and from the short term (with measurements mostly carried out over minutes or, at best, hours) to the full day or growth season.

LAR can be factorised further into two components, the fraction of the total biomass allocated to leaves (Leaf Mass Fraction; LMF) and the amount of leaf area that is realized per unit biomass invested in leaves, which is termed Specific Leaf Area (SLA). RGR, ULR, LAR, SLA and LMF are the classical parameters used in growth analysis.

In summary, although final biomass or yield would be the indicator for how successful a plant integrates the various processes and organs, the main result of such a model would be an improved understanding of the intricate network of physiological and morphological traits and how that is responding when the environment changes.

In this article, we discussed a range of plant growth models with varying physiological detail. This included empirical models, mechanistic bottom‐up models, which often focus only on the carbon‐supply part of growth; and more‐or‐less mechanistic top‐down models factorizing RGR into increasingly smaller subcomponents. On the whole, RGR, ULR, LAR, SLA and LMF are the classical parameters used in growth analysis.