Journal Article

# Negentropy Flow in Communities of Plankton

Bernard C. Patten

Limnology and Oceanography

Vol. 6, No. 1 (Jan., 1961), pp. 26-30

https://www.jstor.org/stable/2832780

Page Count: 5

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**Topics:**Entropy, Plankton, Photosynthesis, Luminous intensity, Bays, Ecosystem models, Respiration, Cost efficiency, Biomass production, Probabilities

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## Abstract

A model generalizing negentropy flux in plankton communities is presented. The biomass information equivalent B (I) at time t is $B_t (I) = B_0 (I) \exp [(\pi - \rho) / B(I)]t$, where $\pi$ (gross production) and $\rho$ (respiration) represent rates of negentropy gain and loss, respectively. From this equation is derived an expression for the total community information in a homogeneous water column of depth z assuming a logistic relationship between photosynthesis and light intensity: $[B_t (I)]_ {0\rightarrow_z} = [B_0(I)]_{0\rightarrow_z} exp \phi I_0\{\delta^-1} \{[1/2 (1 + e^-2\{\delta z}) - e^-\{\delta z}] - zc^-1 [1/2 (1 + e^-2\{\delta c}) - e^-\{\delta c}]\} t$, where $\phi$ is a photosynthetic constant, $I.$ is environmental negentropy concentration at the surface $\delta$ is a decay coefficient expressing the rate of diminution of $I.$ with depth, and c is the compensation depth. Various transformations of this equation yielded for gross production in the whole watercolumn: $(\pi){_0\rightarrow_z} = \rho c[1/2 (1 + e^{-2\delta z}) - e^-\delta z] [1/2 (1 + e^{-2\delta c}) -e^{-\delta c}]^-1$ for respiration: (\rho)_{\rightarrow_z} = \rho z$, and for net production: (\pi - \rho)_{0 rightarrow z} = \rho \{c[1/2(1 + e^{-\delta z}) - e^{-\delta z}] [1/2(1 + e^{-\delta c}) - e^{-\delta c}] ^-1 - z\}$. The cost in community negentropy to procure a unit of biotope negentropy was formulated as $(\rho/\pi)_{0\rightarrow_z} = zc^-1[1/2(1 + e^{-2\delta c}) - e^{-\delta c}] [1/2(1 + e^{-2\delta z}) - e^{-\delta z}]^-1$. Empirical data are provided for a station in Raritan Bay which indicate a net loss of planktonic negentropy during the summer of 1959 amounting to $ 5.46 \times 10^20 bits/cm^2/ day$. A comparison of observed costs with expected values computed from the model indicated no significant difference between expectation and observation, demonstrating the efficacy of the model even under conditions where the assumption of perfect homogeneity throughout the water column was only partially realized.

Limnology and Oceanography