Population coding is a means by which information is coded in a group of neurons. In population coding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs. In one classic example in primary motor cortex, Georgopoulos and colleagues trained monkeys to move a joystick in one of several directions towards a target. Neurons in primary motor cortex responded maximally during movements to their preferred direction, and their response decreased if the animal made movements towards directions increasingly different from the preferred direction. Kenneth Johnson originally derived that if each neuron represents movement in its preferred direction, and the vector sum of all neurons is calculated (each neuron has a firing rate and a preferred direction), the sum points in the direction of motion. In this manner, the population of neurons codes the signal for the motion. This particular population code is referred to as population vector coding. This particular study divided the field of motor physiologists between Evarts' "upper motor neuron" group, which followed the hypothesis that motor cortex neurons contributed to control of single muscles, and the Georgopoulos group studying the representation of movement directions in cortex.

Typically an encoding function has a peak value such that activity of the neuron is greatest if the perceptual value is close to the peak value, and becomes reduced accordingly for values less close to the peak value.

It follows that the actual perceived value can be reconstructed from the overall pattern of activity in the set of neurons. The Johnson/Georgopoulos vector coding is an example of simple averaging. A more sophisticated mathematical technique for performing such a reconstruction is the method of maximum likelihood

Maximum likelihood

In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters....

 based on a multivariate distribution of the neuronal responses. These models can assume independence, second order correlations
, or even more detailed dependencies such as higher order maximum entropy models

Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution is a probability distribution whose entropy is at least as great as that of all other members of a specified class of distributions....

 or copulas

Copula (statistics)

In probability theory and statistics, a copula can be used to describe the dependence between random variables. Copulas derive their name from linguistics....

.

Contrast this with sparse coding

Sparse coding

The sparse code is a kind of neural code in which each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons....

.

See also

• Rate coding
• Temporal coding
  Temporal coding
  The temporal coding is a type of neural coding which relies on precise timing of action potentials or inter-spike intervals.Combined with traditional rate coding models, temporal coding can provide additional information with the same rate....
  
  
• Sparse coding
  Sparse coding
  The sparse code is a kind of neural code in which each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons....
  
  
• Independent-spike coding
  Independent-spike coding
  The independent-spike coding model of neuronal firing claims that each individual action potential, or "spike", is independent of each other spike within the spike train.Contrast this with correlation coding.-References:...
  
  
• Neural coding
  Neural coding
  Neural coding is a neuroscience-related field concerned with how sensory and other information is represented in the brain by networks of neurons. The main goal of studying neural coding is to characterize the relationship between the stimulus and the individual or ensemble neuronal responses and...