PI curve

The PI (photosynthesis-irradiance) curve is a graphical representation of the empirical relationship between solar irradiance and photosynthesis. A derivation of the Michaelis–Menten curve, it shows the generally positive correlation between light intensity and photosynthetic rate. Plotted along the x-axis is the independent variable, light intensity (irradiance), while the y-axis is reserved for the dependent variable, photosynthetic rate.

Photosynthesis-irradiance curve
P v I curve


The PI curve can be applied to terrestrial and marine reactions but is most commonly used to explain ocean-dwelling phytoplankton’s photosynthetic response to changes in light intensity. Using this tool to approximate biological productivity is important because phytoplankton contribute ~50%[1] of total global carbon fixation and are important suppliers to the marine food web.

Within the scientific community, the curve can be referred to as the PI, PE or Light Response Curve. While individual researchers may have their own preferences, all are readily acceptable for use in the literature. Regardless of nomenclature, the photosynthetic rate in question can be described in terms of carbon (C) fixed per unit per time. Since individuals vary in size, it is also useful to normalise C concentration to Chlorophyll a (an important photosynthetic pigment) to account for specific biomass.


As far back as 1905, marine researchers attempted to develop an equation to be used as the standard in establishing the relationship between solar irradiance and photosynthetic production. Several groups had relative success, but in 1976 a comparison study conducted by Alan Jassby and Trevor Platt, researchers at the Bedford Institute of Oceanography in Dartmouth, Nova Scotia, reached a conclusion that solidified the way in which a PI curve is developed. After evaluating the eight most-used equations, Jassby and Platt revealed that an adaptation of the Michaelis-Menten equation, previously used in enzyme kinetics, best served the relationship demonstration. Their findings were so conclusive that the Michaelis–Menten equation remains the standard for PI curve generation.


There are two simple derivations of the equation that are commonly used to generate the hyperbolic curve. The first assumes photosynthetic rate increases with increasing light intensity until Pmax is reached and continues to photosynthesise at the maximum rate thereafter.

P = Pmax[I] / (KI + [I])
  • P = photosynthetic rate at a given light intensity
    • Commonly denoted in units such as (mg C m-3 h-1) or (µg C µg Chl-a-1 h-1)
  • Pmax = the maximum potential photosynthetic rate per individual
  • [I] = a given light intensity
    • Commonly denoted in units such as (µMol photons m-2 s-1 or (Watts m-2 h-1)
  • KI = half-saturation constant; the light intensity at which the photosynthetic rate proceeds at ½ Pmax
    • Units reflect those used for [I]

Both Pmax and the initial slope of the curve, ΔP/ΔI, are species-specific, and are influenced by a variety of factors, such as nutrient concentration, temperature and the physiological capabilities of the individual. Light intensity is influenced by latitudinal position and undergo daily and seasonal fluxes which will also affect the overall photosynthetic capacity of the individual. These three parameters are predictable and can be used to predetermine the general PI curve a population should follow.

PI curve Chalker et al 1983

As can be seen in the graph, two species can have different responses to the same incremental changes in light intensity. Population A (in blue) has an initial rate higher than that of Population B (in red) and also exhibits a stronger rate change to increased light intensities at lower irradiance. Therefore, Population A will dominate in an environment with lower light availability. Although Population B has a slower photosynthetic response to increases in light intensity its Pmax is higher than that of Population A. This allows for eventual population dominance at greater light intensities. There are many determining factors influencing population success; using the PI curve to elicit predictions of rate flux to environmental changes is useful for monitoring phytoplankton bloom dynamics and ecosystem stability.

The second equation accounts for the phenomenon of photoinhibition. In the upper few meters of the ocean, phytoplankton may be subjected to irradiance levels that damage the chlorophyll-a pigment inside the cell, subsequently decreasing photosynthetic rate. The response curve depicts photoinhibition as a decrease in photosynthetic rate at light intensities stronger than those necessary for achievement of Pmax.

Terms not included in the above equation are:

  • βI = light intensity at the start of photoinhibition
  • αI = a given light intensity


Data sets showing interspecific differences and population dynamics.


The hyperbolic response between photosynthesis and irradiance, depicted by the PI curve, is important for assessing phytoplankton population dynamics, which influence many aspects of the marine environment.


  • Chalker B.E., Dunlap W.C. and Oliver J.K., 1983. Bathymetric adaptations of reef building corals at Davies Reef, Great Barrier Reef, Australia. II. Light saturation curves for photosynthesis and respiration. J Exp Mar Biol Ecol 73:37–87.
  • Lalli C.M. and Parsons T.R., 1997. Biological Oceanography: An Introduction, 2nd edn. Butterworth–Heinemann, Oxford.
  • Marra J., Heinemann K. and Landriau G. Jr., 1985. Observed and predicted measurements of photosynthesis in a phytoplankton culture exposed to natural irradiance. Mar. Ecol. 24:43–50.
  • Miller C.B., 2004. Biological Oceanography, Blackwell.
  • Jasby A.D. and Platt T., 1976. Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. Limnol. Oceanogr. 21:540–547.
  • Platt T. and Jasby, A.D., 1976. The relationship between photosynthesis and light for natural assemblages of coastal marine phytoplankton. J. Phycol. 12:421–430.


  1. ^ Field et al. 1998

External links

Daily light integral

Daily light integral (DLI) describes the number of photosynthetically active photons (individual particles of light in the 400-700 nm range) that are delivered to a specific area over a 24-hour period. This variable is particularly useful to describe the light environment of plants.


Ecophysiology (from Greek οἶκος, oikos, "house(hold)"; φύσις, physis, "nature, origin"; and -λογία, -logia), environmental physiology or physiological ecology is a biological discipline that studies the adaptation of an organism's physiology to environmental conditions. It is closely related to comparative physiology and evolutionary physiology. Ernst Haeckel's coinage bionomy is sometimes employed as a synonym.

Grow light

A grow light or plant light is an artificial light source, generally an electric light, designed to stimulate plant growth by emitting a light appropriate for photosynthesis. Grow lights are used in applications where there is either no naturally occurring light, or where supplemental light is required. For example, in the winter months when the available hours of daylight may be insufficient for the desired plant growth, lights are used to extend the time the plants receive light. If plants do not receive enough light, they will grow long and spindly.

Grow lights either attempt to provide a light spectrum similar to that of the sun, or to provide a spectrum that is more tailored to the needs of the plants being cultivated. Outdoor conditions are mimicked with varying colour, temperatures and spectral outputs from the grow light, as well as varying the intensity of the lamps. Depending on the type of plant being cultivated, the stage of cultivation (e.g. the germination/vegetative phase or the flowering/fruiting phase), and the photoperiod required by the plants, specific ranges of spectrum, luminous efficacy and colour temperature are desirable for use with specific plants and time periods.

Russian botanist Andrei Famintsyn was the first to use artificial light for plant growing and research (1868).


In radiometry, irradiance is the radiant flux (power) received by a surface per unit area. The SI unit of irradiance is the watt per square metre (W·m-2). The CGS unit erg per square centimetre per second (erg·cm−2·s−1) is often used in astronomy. Irradiance is often called intensity because it has the same physical dimensions, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity.

Spectral irradiance is the irradiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The two forms have different dimensions: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz (W·m−2·Hz−1), while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre (W·m−3), or more commonly watts per square metre per nanometre (W·m−2·nm−1).

Shade tolerance

In ecology, shade tolerance refers to a plant's ability to tolerate low light levels. The term is also used in horticulture and landscaping, although in this context its use is sometimes sloppy, especially with respect to labeling of plants for sale in nurseries.Shade tolerance is a relative term, a complex, multi-faceted property of plants, not a single variable or simple continuum. Different plant species exhibit different adaptations to shade. In fact, a particular plant can exhibit varying degrees of shade tolerance, or even of requirement for light, depending on its history or stage of development.

Solar irradiance

Solar irradiance (SI) is the power per unit area (watt per square metre, W/m2), received from the Sun in the form of electromagnetic radiation as reported in the wavelength range of the measuring instrument.

Solar irradiance is often integrated over a given time period in order to report the radiant energy emitted into the surrounding environment (joule per square metre, J/m2), during that time period. This integrated solar irradiance is called solar irradiation, solar exposure, solar insolation, or insolation.

Irradiance may be measured in space or at the Earth's surface after atmospheric absorption and scattering.

Irradiance in space is a function of distance from the Sun, the solar cycle, and cross-cycle changes.

Irradiance on the Earth's surface additionally depends on the tilt of the measuring surface, the height of the sun above the horizon, and atmospheric conditions.

Solar irradiance affects plant metabolism and animal behavior.The study and measurement of solar irradiance have several important applications, including the prediction of energy generation from solar power plants, the heating and cooling loads of buildings, and in climate modeling and weather forecasting.


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