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PI curve
The PI (or 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. It is a plot of photosynthetic rate as a function of light intensity (irradiance).
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% 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.[citation needed]
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 argued that the PI curve can be best approximated by a hyperbolic tangent function, at least until photoinhibition is reached.[citation needed]
Subsequent work by Platt and colleagues extended the model to include photoinhibition using an exponential decay term, which became the dominant approach for the next several decades. However, analyses of large global datasets later revealed that this exponential formulation often underestimated the plateau region of photosynthesis and misrepresented the shape of inhibition. In 2025, Amirian, Devred, Finkel, and Irwin introduced a double-tanh formulation, known as Amirian model, that models photoinhibition as a saturating function of the reciprocal of irradiance. In comparisons against 16 alternative photoinhibition models, Amirian-tanh consistently outperformed existing approaches, capturing the initial light-limited slope, the photosynthetic plateau, and high-light inhibition within a single parsimonious framework .
Two classical formulations have been used for decades to study PI curves: a hyperbolic saturation model and an exponential photoinhibition model. Both provide useful approximations but historically failed to represent the complete range of observed light–response behavior.
The simplest formulation assumes photosynthesis increases with light until a maximum rate is reached and then remains constant:
where:
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PI curve AI simulator
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PI curve
The PI (or 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. It is a plot of photosynthetic rate as a function of light intensity (irradiance).
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% 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.[citation needed]
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 argued that the PI curve can be best approximated by a hyperbolic tangent function, at least until photoinhibition is reached.[citation needed]
Subsequent work by Platt and colleagues extended the model to include photoinhibition using an exponential decay term, which became the dominant approach for the next several decades. However, analyses of large global datasets later revealed that this exponential formulation often underestimated the plateau region of photosynthesis and misrepresented the shape of inhibition. In 2025, Amirian, Devred, Finkel, and Irwin introduced a double-tanh formulation, known as Amirian model, that models photoinhibition as a saturating function of the reciprocal of irradiance. In comparisons against 16 alternative photoinhibition models, Amirian-tanh consistently outperformed existing approaches, capturing the initial light-limited slope, the photosynthetic plateau, and high-light inhibition within a single parsimonious framework .
Two classical formulations have been used for decades to study PI curves: a hyperbolic saturation model and an exponential photoinhibition model. Both provide useful approximations but historically failed to represent the complete range of observed light–response behavior.
The simplest formulation assumes photosynthesis increases with light until a maximum rate is reached and then remains constant:
where: