Investments in photoreceptors compete with investments in optics to determine eye design
Curation statements for this article:-
Curated by eLife
eLife assessment
This paper makes a valuable contribution to our understanding of the tradeoffs in eye design - specifically between improvements in optics and in photoreceptor performance. The authors successfully build a formal theory that enables comparisons across a wide range of species and eye types. The conclusion from the modeling is that resources are split relatively evenly between optics and photoreceptors, and hence that both must be considered in eye design. Evidence for this conclusion is solid, and could be strengthened with a more complete comparison with the experiment.
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Abstract
When an animal invests space, materials and energy in an eye to meet behavioural needs, the eye’s optics and photoreceptor array compete for these resources to improve the eye’s performance. To discover how this competition influences eye design, we introduce a new and superior measure of cost, specific volume in µm 3 sr −1 , that depends on the dimensions of the eye’s components, applies to both optics and photoreceptor array, accounts for space, materials and energy (including photoreceptors’ high metabolic rates), and links investments to an eye’s performance via optical, physiological and geometrical constraints. Specific volume enables us to construct a performance surface across the morphospace of an eye of given type and total cost by modelling all of its configurations and determining each model’s information capacity. We model three eye types, neural superposition and fused-rhabdom apposition compound eyes and a simple (camera type) eye, across a 10 5 -fold range of total cost. Performance surfaces are flat-topped, therefore the optimum configuration lies in a broad high-efficiency zone within which eyes adapted for specific tasks loose <5% of information. This robust region will increase adaptability by reducing loss of function. Comparing optimised models: simple eye information capacity increases as (total cost) 0.8 and (total cost) 0.55 in apposition eyesm and simple eyes are x10 to x100 more efficient than apposition eyes of the same total cost. In both eye types 30%-80% of total cost is invested in photoreceptor arrays, optimum photoreceptor length increases with total cost and is reduced by photoreceptor energy consumption. Simple eyes’ photoreceptors are much shorter than apposition eyes’ and their length more sensitive to energy consumption. We analyse published data that cover the same range of total specific volumes. The apposition eyes of fast-flying diurnal insects follow three trends predicted by our models: photoreceptor arrays are allocated 40% - 80% of total specific volume, spatial resolution and photoreceptor length increase with increasing specific volume, and apposition photoreceptors are much longer than simple. We conclude that photoreceptor costs are considerable and often exceed optical costs. Thus, competition between optics and photoreceptors for resources helps determine eye design, photoreceptor energy cost plays a major role in determining an eye’s efficiency and design, and matching investments in optics and photoreceptors to improve efficiency is a design principle. Our new methodology can be developed to view the adaptive radiation of eyes through a cost-benefit lens.
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eLife assessment
This paper makes a valuable contribution to our understanding of the tradeoffs in eye design - specifically between improvements in optics and in photoreceptor performance. The authors successfully build a formal theory that enables comparisons across a wide range of species and eye types. The conclusion from the modeling is that resources are split relatively evenly between optics and photoreceptors, and hence that both must be considered in eye design. Evidence for this conclusion is solid, and could be strengthened with a more complete comparison with the experiment.
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Reviewer #1 (Public Review):
Summary:
Two important factors in visual performance are the resolving power of the lens and the signal-to-noise ratio of the photoreceptors. These both compete for space: a larger lens has improved resolving power over a smaller one, and longer photoreceptors capture more photons and hence generate responses with lower noise. The current paper explores the tradeoff of these two factors, asking how space should be allocated to maximize eye performance (measured as encoded information).
Strengths:
The topic of the paper is interesting and not well studied. The approach is clearly described and seems appropriate (with a few exceptions - see weaknesses below). In most cases, the parameter space of the models are well explored and tradeoffs are clear.
Weaknesses:
- Light level
The calculations in the paper …Reviewer #1 (Public Review):
Summary:
Two important factors in visual performance are the resolving power of the lens and the signal-to-noise ratio of the photoreceptors. These both compete for space: a larger lens has improved resolving power over a smaller one, and longer photoreceptors capture more photons and hence generate responses with lower noise. The current paper explores the tradeoff of these two factors, asking how space should be allocated to maximize eye performance (measured as encoded information).
Strengths:
The topic of the paper is interesting and not well studied. The approach is clearly described and seems appropriate (with a few exceptions - see weaknesses below). In most cases, the parameter space of the models are well explored and tradeoffs are clear.
Weaknesses:
- Light level
The calculations in the paper assume high light levels (which reduces the number of parameters that need to be considered). The impact of this assumption is not clear. A concern is that the optimization may be quite different at lower light levels. Such a dependence on light level could explain why the model predictions and experiment are not in particularly good agreement. The paper would benefit from exploring this issue.- Discontinuities
The discontinuities and non-monotonicity of the optimal parameters plotted in Figure 4 are concerning. Are these a numerical artifact? Some discussion of their origin would be quite helpful.- Discrepancies between predictions and experiment
As the authors clearly describe, experimental measurements of eye parameters differ systematically from those predicted. This makes it difficult to know what to take away from the paper. The qualitative arguments about how resources should be allocated are pretty general, and the full model seems a complex way to arrive at those arguments. Could this reflect a failure of one of the assumptions that the model rests on - e.g. high light levels, or that the cost of space for photoreceptors and optics is similar? Given these discrepancies between model and experiment, it is also hard to evaluate conclusions about the competition between optics and photoreceptors (e.g. at the end of the abstract) and about the importance for evolution (end of introduction). -
Reviewer #2 (Public Review):
Summary:
In short, the paper presents a theoretical framework that predicts how resources should be optimally distributed between receptors and optics in eyes.
Strengths:
The authors build on the principle of resource allocation within an organism and develop a formal theory for optimal distribution of resources within an eye between the receptor array and the optics. Because the two parts of eyes, receptor arrays and optics, share the same role of providing visual information to the animal it is possible to isolate these from resource allocation in the rest of the animal. This allows for a novel and powerful way of exploring the principles that govern eye design. By clever and thoughtful assumptions/constraints, the authors have built a formal theory of resource allocation between the receptor array and the …
Reviewer #2 (Public Review):
Summary:
In short, the paper presents a theoretical framework that predicts how resources should be optimally distributed between receptors and optics in eyes.
Strengths:
The authors build on the principle of resource allocation within an organism and develop a formal theory for optimal distribution of resources within an eye between the receptor array and the optics. Because the two parts of eyes, receptor arrays and optics, share the same role of providing visual information to the animal it is possible to isolate these from resource allocation in the rest of the animal. This allows for a novel and powerful way of exploring the principles that govern eye design. By clever and thoughtful assumptions/constraints, the authors have built a formal theory of resource allocation between the receptor array and the optics for two major types of compound eye as well as for camera-type eyes. The theory is formalized with variables that are well characterized in a number of different animal eyes, resulting in testable predictions.
The authors use the theory to explain a number of design features that depend on different optimal distribution of resources between the receptor array and the optics in different types of eyes. As an example, they successfully explain why eye regions with different spatial resolution should be built in different ways. They also explain differences between different types of eyes, such as long photoreceptors in apposition compound eyes and much shorter receptors in camera type eyes. The predictive power in the theory is impressive.
To keep the number of parameters at a minimum, the theory was developed for two types of compound eye (neural superposition, and apposition) and for camera-type eyes. It is possible to extend the theory to other types of eyes, although it would likely require more variables and assumptions/constraints to the theory. It is thus good to introduce the conceptual ideas without overdoing the applications of the theory.
The paper extends a previous theory, developed by the senior author, that develops performance surfaces for optimal cost/benefit design of eyes. By combining this with resource allocation between receptors and optics, the theoretical understanding of eye design takes a major leap and provides entirely new sets of predictions and explanations for why eyes are built the way they are.
The paper is well written and even though the theory development in the Results may be difficult to take in for many biologists, the Discussion very nicely lists all the major predictions under separate headings, and here the text is more tuned for readers that are not entirely comfortable with the formalism of the Results section. I must point out though that the Results section is kept exemplary concise. The figures are excellent and help explain concepts that otherwise may go above the head of many biologists.
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Reviewer #3 (Public Review):
Summary:
This is a proposal for a new theory for the geometry of insect eyes. The novel cost-benefit function combines the cost of the optical portion with the photoreceptor portion of the eye. These quantities are put on the same footing using a specific (normalized) volume measure, plus an energy factor for the photoreceptor compartment. An optimal information transmission rate then specifies each parameter and resource allocation ratio for a variable total cost. The elegant treatment allows for comparison across a wide range of species and eye types. Simple eyes are found to be several times more efficient across a range of eye parameters than neural superposition eyes. Some trends in eye parameters can be explained by optimal allocation of resources between the optics and photoreceptors compartments of …
Reviewer #3 (Public Review):
Summary:
This is a proposal for a new theory for the geometry of insect eyes. The novel cost-benefit function combines the cost of the optical portion with the photoreceptor portion of the eye. These quantities are put on the same footing using a specific (normalized) volume measure, plus an energy factor for the photoreceptor compartment. An optimal information transmission rate then specifies each parameter and resource allocation ratio for a variable total cost. The elegant treatment allows for comparison across a wide range of species and eye types. Simple eyes are found to be several times more efficient across a range of eye parameters than neural superposition eyes. Some trends in eye parameters can be explained by optimal allocation of resources between the optics and photoreceptors compartments of the eye.
Strengths:
Data from a variety of species roughly align with rough trends in the cost analysis, e.g. as a function of expanding the length of the photoreceptor compartment.
New data could be added to the framework once collected, and many species can be compared.
Eyes of different shapes are compared.
Weaknesses:
Detailed quantitative conclusions are not possible given the approximations and simplifying assumptions in the models and poor accounting for trends in the data across eye types.
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