The Metabolic Cost of Information - a Fundamental Factor in Visual Ecology
173
the eye. The cost of carriage approximates the total rate of consumption of
metabolic energy required for locomotion multiplied by the fraction of body mass
that is eye. Given that the costs of building, maintaining and carrying the eye are
proportional to eye mass, we can examine relationships between costs and
benefits.
3 Costs and Benefits in Image Formation
Take a simple (single-lens) eye. Define its cost as its mass, and its benefit as the
quantity of information that it captures (Laughlin 1998). Each photoreceptor is
one pixel on the retinal image. The information captured depends upon the
number of photoreceptors (pixels) in the retina and the signal-to-noise ratio
(SNR) in each pixel. Now make two simplifying assumptions. (1) All eyes have
the same F-ratio (focal length/lens aperture), irrespective of size. (2) The number
of receptors increases in proportion to focal length squared, to maintain retinal
coverage, but photoreceptor length and diameter are held constant. Because
these assumptions tend to maintain the SNR in photoreceptors, independent of
eye size, the information gained increases in proportion to the number of
photoreceptors on the retina, as (eye length) 2 • Metabolic cost increases with
mass, as (eye length/. Therefore the unit cost of information, the cost per pixel of
the image, rises with eye size, and hence with the total number of pixels coded
per unit area (Fig. 1 ).
The shallow optimum, a minimum cost per pixel, is for small eyes containing a
few hundred pixels and is due to a tradeoff between investment in image quality
(focal length and lens aperture) and investment in photoreceptors. We conclude
that basic optical principles dictate that the unit cost of information (the cost per
pixel) increases with eye size and hence with the total amount of information
coded (the total number of pixels). In other words, this optical cost-benefit
relationship follows the law of diminishing returns. A similar analysis has been
applied to apposition compound eyes (Laughlin 1998), and its result draws
attention to the hopeless inefficiency of this widespread optical mechanism
(Fig. 1 ). The law of diminishing returns increases the pressure to minimize
investment because the unit cost is rising with total expenditure.
4 Efficiency and Cost
Costly mechanisms should be adapted for efficient usage. Indeed, the assumption
that improvements in efficiency promote mechanisms that perform better
underpins adaptationist explanations of sensory structure and function.
Adaptations that maximize the effectiveness of structures are common-place in
vision (Walls 1942). Such excellent engineering is made possible because
biological systems are highly adaptable. The variety and variability of
173
the eye. The cost of carriage approximates the total rate of consumption of
metabolic energy required for locomotion multiplied by the fraction of body mass
that is eye. Given that the costs of building, maintaining and carrying the eye are
proportional to eye mass, we can examine relationships between costs and
benefits.
3 Costs and Benefits in Image Formation
Take a simple (single-lens) eye. Define its cost as its mass, and its benefit as the
quantity of information that it captures (Laughlin 1998). Each photoreceptor is
one pixel on the retinal image. The information captured depends upon the
number of photoreceptors (pixels) in the retina and the signal-to-noise ratio
(SNR) in each pixel. Now make two simplifying assumptions. (1) All eyes have
the same F-ratio (focal length/lens aperture), irrespective of size. (2) The number
of receptors increases in proportion to focal length squared, to maintain retinal
coverage, but photoreceptor length and diameter are held constant. Because
these assumptions tend to maintain the SNR in photoreceptors, independent of
eye size, the information gained increases in proportion to the number of
photoreceptors on the retina, as (eye length) 2 • Metabolic cost increases with
mass, as (eye length/. Therefore the unit cost of information, the cost per pixel of
the image, rises with eye size, and hence with the total number of pixels coded
per unit area (Fig. 1 ).
The shallow optimum, a minimum cost per pixel, is for small eyes containing a
few hundred pixels and is due to a tradeoff between investment in image quality
(focal length and lens aperture) and investment in photoreceptors. We conclude
that basic optical principles dictate that the unit cost of information (the cost per
pixel) increases with eye size and hence with the total amount of information
coded (the total number of pixels). In other words, this optical cost-benefit
relationship follows the law of diminishing returns. A similar analysis has been
applied to apposition compound eyes (Laughlin 1998), and its result draws
attention to the hopeless inefficiency of this widespread optical mechanism
(Fig. 1 ). The law of diminishing returns increases the pressure to minimize
investment because the unit cost is rising with total expenditure.
4 Efficiency and Cost
Costly mechanisms should be adapted for efficient usage. Indeed, the assumption
that improvements in efficiency promote mechanisms that perform better
underpins adaptationist explanations of sensory structure and function.
Adaptations that maximize the effectiveness of structures are common-place in
vision (Walls 1942). Such excellent engineering is made possible because
biological systems are highly adaptable. The variety and variability of