 και κονέκτος. Και, ναι, είναι σαν να είμαστε βασικές. Ευχαριστούμε, όλοι, και ευχαριστούμε another session of our SussexVision Seminar Series, always within the World Wide Neuro Initiative. Είμαι ο Γιώργος Καφετζής, ένας φορμιστικός μάστος στην Τόμα Σοήλειο's Lab, και, σχετικά, νιολογικά, έγινε η ΠΕΙΤΟΡΙΤΟΡΙΤΟΡΙΤΟΡΙΤΟΡΙΤΟΡΙ. Είμαι ο Γιώργος Καφετζής. Θα ήθελα να ξεκινήσω μετά, να ευχαριστούμε τον Βόγγελς και τον Πάνος Βοζέλος, για να παίρνουμε αυτό το very initiative toward the greener and much more accessible seminar world. Και, φυσικά, όχι αυτό, ευχαριστούμε να πάμε back to the reason we all gathered here for today and introduce our guest from the University of Cambridge, Prof. Simon Laughlin. Φollowing a bachelor degree in geology from Cambridge, he then moved for his PhD in neurobiology to Canberra in Australia, where he worked with Alan Horridge on visual processing in insects and more specifically, I think, dragonflies and bees. During his time there and in close interaction with mathematicians, physicists and engineers, he spearheaded the application of information theory on neural coding, acquired data on natural image statistics and according to Horridge himself, virtually dealt with all the signal-to-noise ratio stuff. Following postdoctoral years at Yale and Berlin universities, with William Miller and Randolph Menzel respectively, he then returned in 1984 to the geology department of Cambridge, where he has been located ever since and nowadays is holding the title of emeritus professor of neurobiology. Deservedly, he is best known for his pioneering and seminal work on relating through basic biophysics, energy usage to neural performance and what that implies for neural design and evolution. A fellow of the Royal Society since 2000, recipient of many personal awards and co-author with Peter Sterling of the award-winning book Principles of Neural Design. It is with great pleasure that I am leaving the stage for him, Professor Simon Laughlin, for a talk entitled Receptor Costs Determine Retinal Design. So, without any further ado from my side, please all welcome Professor Laughlin. This stage is all yours. Simon, yeah, you can begin by screen sharing Can people all see my screen? Yes, though we still see the presenter's mode, you can swap it from the top left corner again, like from the display settings. Now we cannot see it again. Did you stop screen sharing? Oh right, I didn't put it back in, I didn't leave presenter's mode. Okay, right now we cannot even see your screen sharing. So I think you also stopped that, right? I stopped screen sharing, yes. Okay, so you can restart it if you wish and we can figure it out together. Okay, so here we are. This worked before. Share PowerPoint. Great, now try going into presentation mode. Yeah, and now if you see at the top left corner, Okay, there we go. Excellent, yeah, so we are good to go. Okay, well thank you very much for inviting me George and thanks in particular to Sussex Vision Group and to Worldwide Neuro for giving me the opportunity to speak to such a worldwide audience. It's a first time for me. So I'm going to return to my roots in actually to work which dates back to my PhD looking at eye design, but in this particular case I'm going to factor in some of the insights that I got looking at costs. Now receptors are very costly, photoreceptors are very costly and they for example in a blowfly they're responsible for something like 6% of the resting energy consumption and they occupy as we will see quite a considerable amount of volume. The retina of a blowfly of its two eyes which includes the optics that accounts for something like 15% of the body weight. So insects invest very heavily in eyes and particularly especially heavily in photoreceptors and in view of this Francisco Hernandez-Harras and I decided to take a new approach to understanding eye design and we asked a question that anybody who's built an imaging system on a small budget will have asked and that is how much of my small budget should I give to the optics which forms the image and how much should I give to the receptors the sensors which actually capture the image is there some optimum resource allocation that will maximise the performance of the whole system and short answer is that yes there is but to demonstrate this to you and for you to understand what I'm on about we have to start off with a few basics about eye design and how performance of an eye is important in its particular components so we'll start with Landon Nielsen's book on animal eyes and they have a chapter called what makes a good eye and in that chapter they show they explain that three factors make good eye so the first is when the lens focuses light onto the retina the light the parallel rays from a point do not form a single point on the image plane they form their spread out to form this point spread and the second factor is that there's a discrete spacing of the receptors and the third factor is that there is photon noise introduced when photoreceptors absorb photons because that's a stochastic process and it creates on the performance of an eye so first of all the angle between photoreceptors well in a simple lens eye that simply depends on the focal length and the angular diameter of the photoreceptor aperture so the angle is the aperture of the photoreceptor divided by photoreceptors determines your ability to resolve whether you measure that by your highest or by two point resolution okay so that's and the they have an interreceptor spacing which is now the spacing between the optical units the lens is on the lens on each armatidium of the eye which is where all of these axes eventually would converge and the angle is the diameter of the optical radius and it's obvious that if both these eye types that if you make a larger radius or a larger focal length a larger eye you can use your lens with our guests internet connection because he Simon your you are muted again can you hear me let me unmute you are muted Simon okay I'll unmute you great great so I think your connection might be right here we go so I think I've stopped screen sharing right yeah so try restarting it please I mean I've had a lot of problems with our internet recently and everybody in our streets has been having problems yeah I can imagine no worries like what I would suggest just for the beginning like maybe start screen sharing and what we can do is you will switch off your own video yeah I can do that great so let's try that I probably only look like a crazy puppet okay so let's go to screen share you got that yes try again presenters and slide presentation mode swap the two displays again please like from the top left corner like to try like switching off your video for now like maybe that's I think I would have to do that before I go into oh no I got it up here stop video great so hopefully now all your internet will be devoted you know to your voice and your slide presentation yeah let's try it like that and see how it goes so sorry about that folks okay so this is the this is the constraint of interceptor spacing as you can see it pixelates the image and has an obvious deleterious effect on image quality and you want to minimize this angle between photoreceptors delta phi the second constraint is the point spread function and this diagram just shows how the point spread function that it basically takes bright light from the bright points and spreads it to the dark points so it reduces image contrast and as these line scans through the image show it removes fine detail from the image the final constraint so that's the point spread function the final constraint is noise from photon absorption which just makes everything more difficult to see okay so by investing more in optics and photoreceptors an animal can improve the quality of the captured image by reducing what are inviolable optical geometrical and cell biological constraints on delta phi the point spread function and noise and I thought the best way to illustrate this was to look at some really cool insects which have specialized to improve the performance of their eye for particular tasks by investing very heavily in optics and in photoreceptors and the first example is the predatory robberfly holosephala which has been studied in a really nice paper by Trevor Warthel and Paloma Gonzalez and Duke of Stavanger and others where they looked at the behavior of this fly and also looked at the specialization of its eye so the robberfly is very small its head is about 2mm across and it detects prey at about the distance of 28cm which doesn't seem very far but its prey are also very small and then it flies up and intercepts them and in order to locate and track its prey it has a fovea a small area on its compound eye where the facets are very very large and there is a section through the fovea shown here and you can see that the layer of the compound eye which constitutes the optics which is the lens plus the crystalline cone through which it focuses light down onto the photoreceptors that volume of optics is greatly increased and the volume of the eye in this region of the fovea is large the lenses are very large, they are the largest known in any insect at the moment and their focal lengths along their focal distance from the top of the lens down to the focal plane is about 170 microns the angle between receptors is very small and that means that with a large d and a small angle about 20% of the eye volume is used to monitor about 1.1% of visual space so this is a huge investment and largely in the optics so what does it gain from that well there are two fundamental limits to the angular sensitivity of a photoreceptor the first is diffraction at the lens aperture which generates an airy disc which has a half width of lambda wavelength of light divided by d so if you increase lens diameter you narrow this component the airy disc of the blur function the second constraint is the angle subtended by the entrance aperture of the photoreceptors waveguide, the so called which in these flies is called the raptomir the diameter of the raptomir as we've seen divided by the no it should be the diameter of the raptom divided by the focal length so if you make the focal length longer you get a small this angle reduces and these two effects combine together in a very complicated way because this is diffraction coupling of a waveguide to a diffraction pattern and there's a very simple approximation to Alan Snyder which is you assume that these two functions are Gaussian and you simply sum them together and it works moderately well for some insects but is complete rubbish for others but for the basis of a general study this is the best we've got but it emphasises the point that when you invest in optics you reduce the effects of blur by narrowing the angular sensitivity so now what happens when you invest in photoreceptors well the animals in the animal kingdom the largest investments in photoreceptors of the volume that they occupy in an eye is probably made by dragonflies and this is the dragonfly I did my Ph.D. on and you can see in this photograph that its eye is divided into a dorsal area which looks at the sky and a ventral area which looks at the ground and in the dorsal area the light guides formed by individual photoreceptors and this compares with this 40 times longer than a human cone out of segment it's about 3 times longer than the longest known out of segments which are in deep sea fish rods and it's a bit longer than deep sea squid photoreceptors so this goes against what you learn in the textbooks that animals have long photoreceptors to get more photons and therefore this is a specialisation for vision in dim light and in fact the longest photoreceptors known in the animal kingdom are in the dorsal phobia the part of the dorsal eye which is used for tracking objects in the dragonfly simpetrum are 1.1mm long and this dorsal phobia has been studied in considerable detail by Don Eric Nielsen and Thomas Labhart and the function of the phobia has been studied in particular in the lab of Antony Leonardo previously at Janelia Farm and they showed by amazing techniques for tracking single dragonflies intercepting prey that when a dragonfly first sees a prey it flies up towards it and it locks its phobia onto its prey target and as it approaches the prey it moves its head to keep it centred the phobia centred on the target to align with the head and it's using a really fancy control system so we know exactly what this phobia is being used for in behaviour and Don Eric Nielsen and Thomas Labhart showed that it has unusually narrow so they measured the interometrial angle and facet diameter across the eye and in the region of the phobia their interometrial angles are very small to give you very good spatial resolution and the facets are very large and so are their focal lengths to give you a very narrow blur circle and in addition the photoreceptors in the phobia are greatly elongated and this doesn't look like a big deal when you look at it in angular space but on the tidier density is very high in the phobia the area of retina taken up by the phobia is quite large so again this is a big investment for the dragonfly so why has it bothered to make such long raptomias, what does a strictly diurnal animal gain from having such long photoreceptors and the answer to this as Labhart and Nielsen pointed out is that it reduces a cell biological constraint on photoreceptor signal-to-noise ratio and this cell biological constraint is the fact that photons are transduced by microvilli these are little tubes of membrane and each microvillus acts as an independent unit that responds to a photon by recruiting its phototransduction machinery to produce an all-or-nothing event rather like a mini-action potential called a quantum bump and each microvillus can only transduce one photon at a time and the transduction from absorption here to the formation of the bump and then the recovery, the resetting of the microvillus takes some time between 10 to 50 microseconds and milliseconds and what this means is that at very high light levels many of the phototrans... many of the microvilli are in this refractory phase and are unable to produce photons and you can see that this effect in blow-fly photoreceptors in this study I did with John Anderson we used noise analysis to estimate the rate at which photoreceptors were transducing photons and we plotted this against the rate at which they were absorbing photons calibrated from quantum bumps and what you can see is that at high light levels the absorption falls below the rate of absorption and this is due to two effects one is an intracellular pupil which brings up pigment granules to attenuate the light and the other is the saturation of transduction units and in fact the pupil is mitigating the constraint imposed by transduction units and this was shown by Joe Howard back in the 1980s where we took a blow-fly photoreceptor and we measured the signal-to-noise ratio in the wild type as a function of the light intensity photons per second coming in per receptor per second and in full daylight you can see that it's operating at this level here then if you have a white-eyed mutant then it has no intracellular pupil so it's unable to attenuate the light and the white-eyed mutant response signal-to-noise ratio goes up and up and up, reaches a peak and then comes crashing down when you get to higher photon absorption rates because the transduction units have saturated and you can fit this curve here quite well with a binomial distribution and when you do that you find that the maximum signal-to-noise ratio is proportional to the square root of the number of microvilli divided by 4 so the number of microvilli in that raptomere determine the maximum signal-to-noise ratio that you can get and the action of the pupil is to prevent you from getting to saturation and to hold you close to this maximum signal-to-noise ratio so when we model this constraint we model the benefit of having a longer photoreceptor is that if it has a constant cross-section the number of microvilli increases in proportion to the length of the photoreceptor and that sets the transduction unit limit to signal-to-noise ratio and we assume that in the eyes that we're going to model that they have some sort of mechanism for holding the photoreceptor close to this optimum so this is the benefit of a long photoreceptor but there's a puzzle and the puzzle is if you go to the ventral eye region here you still have very long photoreceptors but you can't really explain that as an adaptation for detecting very small targets in a fovea there must be some other advantages of having these long photoreceptors and in fact having long photoreceptors outside of a foveal region is very common this is the praying mantis where Horigen dueli took sections through and showed that in the region of the fovea which is forward looking you've got large lenses long, long focal lengths but also very long photoreceptors and as you move away the investment in optics goes down this band gets narrower and so does the investment in photoreceptors they get shorter and Sam Russell showed that there's a very neat co-variation but you can see that there's a difference between the photoreceptors and the lens diameter and this led Fran and I to the idea that maybe the investment in photoreceptors which depends on L is matched to the investment in optics which depends on D and in fact this correlation between photoreceptor length and lens diameter is widespread among insects you can observe it very easily in slides but photoreceptor lengths have not been measured very often in insect compound eyes and related to lens diameter there are stacks of studies which look at resolving power but very few of them correlate these with also measure photoreceptor length and so the data we were able to mine from the literature which is these points here is really quite limited but you can see that there's a very nice trend and a very heavy investment of optics and relatively short photoreceptors is an anomaly and you can explain the short photoreceptors because the head is only about half a millimetre deep and so photoreceptors of 500 microns simply wouldn't fit inside the head so this reminds us that there are other constraints nonetheless there is the systematic trend and it's a general trend so we set out to test this hypothesis by calculating investments and then determining their effects on performance and the method for calculating investments is really very simple we assume that in a small region of the eye is locally spherical with an optical radius defined by d and delta phi the investment in the optics then is the volume of this outer shell of depth f' where f' is the focal distance from the top of the lens down to the focal plane the investment in the optics is the volume of this shell here from the focal plane down to the bottom and photoreceptors is determined by this shell here which has a depth by the length of the photoreceptor and it's very easy to calculate these from the volume formulae for the volumes of the sphere I won't grind through the formulae but note that these formulae only contain three variables which are the optical radius the length of the photoreceptor we assume that f' the focal length of the photoreceptor is that the system has a constant f ratio then diameter also gives you focal length and it's been found empirically as one might expect from very simple theory that in fact this distance here the focal distance is times the refractive index of the internal medium and what this means is that if I give you v total lens diameter and L you can determine, delta phi the investment in optics and the investment in photoreceptors and we know that d and f determine delta rho and L determines the signal to noise ratio all three of our quality factors just related to the investments in volume of optics and volume of photoreceptors and we also know that's explained here how changing these investments will improve or decrease will improve performance or decrease performance so we can now examine the trade-offs let's say what about photoreceptor energy costs I've said that energy is very costly and yet the optics are relatively inert and in order to get an estimate of the extra cost of energy we made a very simple and probably very foolhardy we took a very simple approach which contains a lot of problems but at the moment it's the only thing you can do so our cost of volume is our volume cost if you assume constant density is also a cost of mass and when a flying insect its oxygen consumption in flight is very high so its metabolic rate in flight is very high and a part of that metabolic rate is devoted to carrying the eye around so it's going to be proportional to the mass of the photoreceptors and the mass of the optics and this gives you a method of converting energy which is from metabolic rate into mass and therefore volume so we can come up with an extra energy cost from electrical currents and photoreceptors which increases with the number of microvilli because that's the number of transduction units consuming energy so the total cost is going to be the eye volume plus this energy factor which is the number of microvilli multiplied by this conversion factor is the number of cubic microns per microvillus and this is calculated from the energy consumption of a single microvillus which has actually been estimated in some quite accurately in flies and measurements of energy per unit volume and therefore mass in flying insects this is a very fraught calculation how much of the day a microvillus is illuminated and how much of the day an insect spends in flight and it's species specific because it's going to depend on the flight mechanics and body mass of the insect as well but in fly prolifera we can make a very rough estimate and this factor seems to vary depending on how much the fly flies and how much during the day but that's our method of getting an energy discount factor and it's not a very good method but it at least enables you to show how the design of the eye will change with photoreceptor energy costs and we can get it into the right ballpark but this conversion David O. Carroll and I first discussed it years ago when we measured the masses of our eyes but it's since been independently hit upon by people working on weapons in beetles so some species of stag beetle carry huge horns on their head which are very heavy and they wanted to work out what the cost to the beetle was so they used this method here to convert the mass of the horn into an energy consumption okay so this is our method for taking account of energy costs of photoreceptors now let's look at our trade off so just to recap on what the trade off is if you invest more in photoreceptors you will get a more blurred image and both of these configurations have equal total volumes and this emphasises that the volume on the outside towards the outside of a sphere equal volume on the inside of the sphere and the outside of the sphere involve very different distances from the centre and so it's difficult to believe that this really is the same volume of that but if you invest in photoreceptors you must invest less in optics so you get a very blurry image but there's not much noise and the opposite happens when you go for optics now it's very difficult to look at these two images and decide which one is really best and so when we set up this trade off we need some method of evaluating the performance the quality of the image and therefore the performance of the eye and so we used a model a method developed by Hans van Hatteren for calculating information rates in bits per solid angle per second based on those quality factors that we've deduced, delta-5, delta-row and the signal-to-noise ratio and we model two similar types of opposition eye of compound eye the opposition eye in which the lens drives a group of photoreceptors which contribute microvilli to a single wave guide and the others are the neural superposition eyes of particular flies in which the wave guides of the photoreceptors entrance apertures are distributed across the image plane so each one is looking out through the lens in a different direction but the angles between photoreceptors within an armatidium are the same as the angles between armatidia so there are always adjacent photoreceptors which align and the axons from those aligning photoreceptors that align are brought together to a single point at the first optic so you get a neural superposition of the image that they've collected and that's the neural superposition eye and the advantage of the neural superposition eye is that it collects more light and also as we show here that you get more microvilli per unit length so this constant B that relates length to numbers of microvilli is in fact because each one of these segments here is roughly equivalent to one of those and there are three of these and six of these outer red domains here so in everything that follows you'll see sets occurs for neural superposition and apposition eyes and that's what they mean and so we go now and we look at image capture we're considering in the Vanhateron method one considers an image a certain intensity distribution in space and that follows natural scene statistics one over F squared and this image jitters backwards and forwards so that when it's viewed by a single omatidium the photoreceptors in a single omatidium the photoreceptors generate get an optical signal which moves up and down with the jitter of the image and the point of using jittery image is that it actually tends to decorrelate the spatial frequencies in here and the temporal frequencies which is what you need in information theory then this intensity signal in the photoreceptor is transduced into an electrical signal and this adds photon noise which is ultimately limited by the length of the photoreceptor as we've seen and this model came up with this hideous looking formula which taking these quality factors gives you an information rate and I don't have the time or inclination to ride through the formula but if anybody wants to discuss it we can come back to this this to this slide and this model then allows us to address our question how does performance change when resources are transferred between photoreceptor optics and the way in which we do this is that we fix the volume invested in the eye and we consider different energy surcharges and for each volume the total we pick pairs of combinations of pairs of lens diameters and receptor lengths which fit into the which you can be accommodated in an eye of that particular volume and each DL pair specifies a particular eye configuration and as we've seen specifies the quality factors so for each DL pair we can calculate the information capacity and so we can plot that out as you vary D how the information capacity varies and what you can see is this surface is the performance surface that covers the complete design space of all possible configurations of eye of this particular volume with this particular geometry and you can see that the performance surface is actually flat topped and elongated and when you increase the energies and there's an optimum around here somewhere where efficiency is maximum and when you increase the energy surcharge the optimum photoreceptor gets shorter in length which is what you would expect but the interesting thing about this performance surface is it's actually very smooth and flat on its top but it's very more clearly seen by looking at contour plots so here are contour plots at three different energy surcharges and this red area here and you can see that there's an optimum here and here and here and that sits in this red area which is a robust high performance zone in which efficiency is greater than 95% because they're going to be very messy as you will see but it's great news for insects because what this means is you can vary the parameters you can vary DNL within this high performance zone for a particular task getting more larger D or larger L and yet lose very little capability for general purpose vision but this information theory gives you and you'll see that the shapes of the surface depend on the energy surcharge factor that as you increase the when the energy surcharge factor is low you want the longest possible photoreceptor and as you increase the energy surcharge the high performance zone and the optimum point of high maximum efficiency increase moves to lower lengths and eventually at the highest energy surcharge factors then you can see the performance zone is also contracted to shorter photoreceptors now in order then so this means for any particular investment we can work out what is the optimum combination of investment in optics and investment in photoreceptors which maximizes efficiency and how sensitive is one is the system to deviations away from the optimum and one can do that for different energy surcharge factors so now we can perform this procedure for over a range of total investments to see how these d and l scale and in particular l scales for total investment and therefore how l changes with the acuity of the i and how this shows how whether l is matched to total investment and therefore matched to the optics and what we find is that as you increase the total investment the specific volume of the i increases that's the volume of i per unit solid angle and the optimum specific investment decreases with energy optimum investment in photoreceptor length decreases with energy surcharge and you can see there's a bit of instability in the model but nonetheless there are clear limits between the two energy surcharge factors which are our lowest and highest estimates and these are these spots are data points that we mined from the literature showing variety of species that's califras frontal i that is califras lateral i these are the two values for muska and down here and you can see that these points fall within the zone of high efficiency and also you can see that matching the optics captures the general trend that you see in real i's but of course you can't see very well what's going on down here so if we put it on a log plot you can now see these smaller i's that's that might be holosephala and we haven't gone out to very long raddoms not to have holosephala here but you can see that the model captures the trend of the data so it looks as if this lengthening of raddomias with increase in lens diameter and increase in acuity that you observe in i's is in fact representing efficient allocation of resources for the general purpose vision and it's not simply a specialisation for high signal to noise ratio but it's not specialised for a task which is particularly demanding of high signal to noise ratio but it's worthwhile investing in that to make efficient use of your entire investment when you look at the acquisition i's again these are the theory curves for low and high energy surcharge and again you see this instability in the theoretical curve which is skating around on the top of that flat high performance zone and here is data from three different apposition i's Sympetrum and Tenodora which we've already seen come from Laphart and Nielsen and Tenodora from Sam Russell and Horridge and Durelli and this is the Honey Bee where the data comes from a paper by Menzel and Stavanger and Timbergen I think and you can see again for the most efficient photoreceptor length to increase with specific volume and this trend is kind of captured by the model so the model also tells us how much of what percentage of the total investment should be in the photoreceptors and therefore in the optics and again you see that the percentage tends to increase in theory with specific volume percentage in the photoreceptors and this trend is captured by this trend is demonstrated by the same trend as shown in the empirical data both in neural superposition and in apposition i's but the fit isn't terribly good and again that's because you have this flat surface on the top which militates against a very good fit of an optimization model to observe data plus the fact that you have a robust zone so there's plenty of evolution is free to wander around with different i-configurations without losing too much information finally for affectionados there is a factor called the i-parameter which takes into account under sampling so the i-parameter invented by Alan Snyder is the diameter of the lens times the interometrial angle now the diffraction limit when the interometrial angle is set to the diffraction limit this turns out P turns out to be half the wavelength sorry it turns out to be the wavelength of light divided by a factor of 2 which is 0.25 here at the diffraction limit P is 0.25 and in apposition i's and neural superposition i's only the fovea of tenodora and the fovea of simpetrum get close to this diffraction limit but most i's have a P which is quite a bit larger than 0.25 and this P this means that they've got much larger lenses with much better diffraction limited resolving power than the can be catered and much larger interometrial angles which means that the interometrial angles are too wide to retrieve all of the spatial information provided by the spatial resolving power of the lens and as has been observed by many people before the majority of insects under sample they have a P quite a bit lower than the diffraction limit and our model predicts that the P should not approach the diffraction limit for efficiency many values of P are considerably larger than are predicted by our model and it's worth noting that P varies enormously within a single eye so there's lots of factors deciding the exact balance between diameter of receptors and interometrial angles and so there's lots of variation but within those variations as we've seen there's a trend for photoreceptor length to get larger as predicted by our model so we conclude that we have quite good evidence for there being a matching efficient resource allocation can explain why in general insects have long photoreceptors and the length of the photoreceptor increases with the acuity of the eye but why are they so much longer than photoreceptors in single eyes well Fran went back and used this equivalence of photoreceptors of sorry simple and compound eyes where again you've got d and delta phi and r and delta phi but we've got a very simple photoreceptor length and he reconfigured the model for a simple eye a very simple simple eye with a simple lens and worked out what the optimum photoreceptor lengths were so these are the optimum photoreceptor lengths as a function of investment and we can see that we have a very simple eye with a low energy surcharge and a high energy surcharge and here are the equivalent curves for a simple eye and you can see that efficient resource allocation can account for the fact that simple eyes have much shorter photoreceptors but they encounter in insects out to about one times 10 to the 11 cubic microns per steradian where the equivalent curves for a neural superposition eye and a simple eye are separated by a factor of approaching a log unit and in both cases the research arch factor decreases the length of the optimum photoreceptor and of course this model predicts that in a simple eye if you invest more in optics then you should have longer photoreceptors and observations in jumping spiders suggest that that is indeed the case but here jumping spiders have four different eyes and one of them, the frontal eye they pair of frontal eyes have very large lenses with long focal lengths so they invest heavily in optics and they have longer photoreceptors shown here than the other eyes which invest less in optics and in fact you can see that the photoreceptor length tends to decrease with the investment in optics but there is one indication that efficient resource allocation can explain the short photoreceptors in simple eyes finally our model confirms what is already well known that the compound eye is very inefficient that compound eyes are very inefficient these are the information rates as a function of total investment calculated using our model for simple eyes with high and sorry low and high energy surcharges and neural superposition eyes and also apposition eyes and you can see that say the size of eye of sympetrum which is here then the efficiency is about 100 times less than in a high energy surcharge simple eye and if the energy surcharge is very low the efficiency is in fact 10,000 times less which was first of all pointed out this inefficiency was first of all pointed out also if you were to look at the how you would have made a curved field that constructed this diagram showing how large your eye would have to be if it was a compound eye and the reasoning is very simple but if you want to double the resolution of a simple eye as you can see you just double the focal length Okay, but. But you have to. So you have to double the size of the eye again and have twice as many lenses. And so you get this massive inefficiency. Well, after all of this, what have we learned? Well, we've taken a new approach to understanding eye design by considering the cost of investing in eye Βεχύουμε και as a new approach to understanding eye design. By considering the cost of investing in optics and photoreceptors. and examining the effects of resource allocation and transferring the investment between optics and photoreceptors. We find that the total investment in the eye can be divided, can be allocated, to improve the eye's overall performance. και there's an optimum and also there's a robust zone and this favours long photoreceptors in compound eyes. Efficient investment depends on the cost-benefit relationships of both optics and photoreceptors which is why simple eyes and compound eyes are different and why the energy surcharge tends to reduce investment in photoreceptors. και πάνω από το κομμάτι της υποσιασμής εξοπλότητας, πιο πιο εξοπλότητας είναι αντιμετωπίζονται στη φωτοριασμή. Αυτό significa ότι η εξοπλότητα της υποσιασμής εξοπλότητας εξηγεί ένα πιο πιο εξηγημένο στους που δεν έχει πραγματικά been remarked upon very much. Αυτό είναι το πιο εξοπλότητας του διελμούς εξοπλότητας που έχουν τα κόσμια πιο εξοπλότητας του διελμού. Αυτό είναι ο απόλυνης ουδεσσοχός συμπορίας και εξοπλότητας στους που έχουν τα κόσμια πιο εξοπλότητας. Γιατί υπάρχουν πιο εξοπλότητας, ένα σύμπωνο στους που έχουμε δει πολλά διάλεγμα για να κοινωνήσεμε τον καλύτερο επειμερικό. Το πρώτο είναι ότι οι ώρες δημιουργούνται στους δεύτερες, γιατί μπορούμε να δημιουργήσουμε αυτό για να δημιουργήσουμε στους δεύτερες λευτεί. One of the ways in which one would do this is to relax the assumption that the F number is kept constant, and this allows you to trade sensitivity for a purity within the optics, within the constraint of cost. We could disregard exponential absorption, we've disregarded exponential absorption in raptomiers and gone for vision in high light, because at low light levels you need to relax that and include exponential absorption, and in fact Fran has already done this for a model of polarization sensitivity in photoreceptors that we published some time ago. We've assumed constant photoreceptor cross-section, this can be relaxed to adjust the width of the raptomier to make the best use of microvillia along the length of the raptomier. Again, this can all be done within the trade-offs between performance and cost, which we've been able to set up by estimating volumes. I'll just say in passing that although we've estimated volumes, new techniques for measuring three-dimensional tissue structure, particularly new imaging techniques, X-ray imaging techniques are going to make it possible to measure volumes invested quite accurately with much less effort previously, and so this cost-benefit approach might very well take off. We've also assumed that the temporal parameters, image speed and photoreceptor response dynamics were the same, and one can relax these to investigate the effects of photoreceptor response dynamics and image speed, and we've also assumed that energy consumption for microvillus is constant across species, and in fact we have to relax this because some species have faster responding to photoreceptors with higher energy costs per microvillus, and maybe spatial and temporal coding co-vary to improve efficiency. And finally, of course, one needn't use bit rate as a measure of performance. One could apply this same cost-benefit approach to say the detection and tracking of small targets, and so all of these possibilities in fact can be investigated within this cost-benefit framework that we've started to construct. And so really it only remains for me to say thank you Fran. This actually was Fran's master's thesis originally and over the years we kind of worked it up a bit and Fran is now working in the Champalamo Center in Lisbon on schooling in zebrafish, but we're still plugging away at this project and we hope to have a manuscript out in by Easter. So okay, over to you for questions and thank you very much for listening. Thank you very much Simon for this enlightening talk. I mean lots to unpack and I believe you can now try to switch on your video. It was quite sad that we couldn't see you while you were giving us the presentation, but nevertheless at least the audio quality became quite stable throughout. So there are already a couple of questions on the chat and you have definitely scratched the surface of most of them. I just want to remind to the audience that you can either type your questions there or wait for the post-talk informal discussion that will soon follow. We will shortly also post the Zoom Room link that we are currently sitting in so you can join us. A lot of people are already congratulating you on the YouTube chat, I assume you don't have it open and I will begin with the questions. The first one is from Bobbert Job and he asks, what's the absorption length of an insect photoreceptor? In vertebrates, I seem to remember 50 micrometers or so. In that case, a millimeter long photoreceptor was only light near the bottom. That's a very good question. So the absorption coefficient in an insect photoreceptor is, as I remember it, something like 0.08 per micron compares with about slightly higher value in rods and cones and the peak wavelength, you're absolutely right, it's dark at the bottom of an 800 magrabdom. So there seems to be no point in lengthening it. But Darn Eric Nielsen and Thomas Labhart addressed this problem and showed that for, because what the long rabdom here does is it's actually capturing the wavelengths for which are inefficiently absorbed. So it's getting more photons by going out and collecting the photons for which the absorption coefficient is much less. And so you carry on getting more light even when you, you could make the rabdom here even longer. And actually their paper is really well, if you're into absorption coefficients and photopigments, their paper is well worth looking at because they also suggested that there could be differences in the density of the pigment along the rabdom, which meant that in fact the probability of a microvillus absorbing a photon tends to be equalized. So you have less photopigment density at the top and more at the bottom. And they're all, and you can play with the rabdomia geometry as well to try and equalize. And in fact, I'd suggested back in 1978 that light was travelling in the photoreceptors and being reflected by the little sheets around the e-traumatidium. And they tested that and that turned out to be wrong. But, yeah. I see. I will try to stick to the questions for now even though I also have some of mine that I would like to ask. Next one is Tobi Delbruc and he asks, but does the method of signal to noise ratio cost in bits per second account for motion blur effects? Yes. So that's a good point, Tobi. Nice to hear that you're here from you. Yeah. So the motion blur is accounted for in the Van Hateren model by setting a photoreceptor time constant, a phototransduction time constant. Like Van Hateren, like hands, we used the value that was used that's been determined experimentally for fully light adapted eyes, which is off the top of my head, something like 4 milliseconds or so. They're very fast responses. But of course, that is one of the variables. And in fact, that time constant is related to energy cost. I mean, we showed that slow photoreceptors use much less energy than fast responding photoreceptors. So the trade-off, in fact, extends from space into time and space and time interact because temporal frequency is related to spatial frequency of constant velocity and so on. So there's a whole area there to be looked at. Yeah. So that's a good point. Next one up is Gregor Belouzic. He has one question and one remark. So the question is, the efficiency contours only partially explain the urge for very long photoreceptors in large diurnal flyers. Could the length be explained also by its ability to prevent bleaching? For example, when looking into the sun? Yeah, I mean, possibly. I think there are other constraints. And so I think, for example, that there's a very... So when you have a large eye, as we've seen in, as you see in both Holosephala, and you have a phobia in which there's a large investment of specific volume, the surface area of the eye is very large. And that's going to be a constraint for a flight, particularly for a flying insect. And so there may be pressure to reduce the surface area by reducing facet diameter and density of facets, enterometrial angle, that you partially compensate for by having longer photoreceptors. So I mean, once you start getting away from one constraint, like the absorption curve of a photopigment, and you start considering several constraints interacting, everything quickly becomes multidimensional. And it's very easy to get lost and run around in circles. But yeah, that's a distinct possibility. Yeah, the second one, which is a remark, and I see it's written from Gregor Belusitz, but in bracket it says primos here. I would remark that both eyesight and if is in butterflies do not speak in favor of under sampling. Acceptance angles in the acute zone are two degrees and interometrial angles 1.5 degrees. Would you like to comment on that? Yeah, so that, so that are so that there are zones in eyes which go for maximum spatial resolution by approaching the fraction in it. There's no question about that. And again, this may be, so the problem with the virtue of, it's a bit like politicians, the virtue of using information theory is that it's relevant for everybody. But actually, it's not particularly good for specific things. So you can appeal to everybody and be bad at everything. So, but so, I think we used information theory because we wanted to general measure. But I would urge people to start thinking about using this cost-benefit approach for specific tasks such as the detection of a small target or the resolution of the gap through a footage at the great distance or whatever. The next one and the last one that I see appearing on the YouTube chat and may I remind to people at this time that they can follow the zoom room link that we have posted to enter this very space that we are sitting in. So the last question is from Jesse S. Cost efficiency of flight is an interesting study, cost versus efficiency. What can be said about terrestrial, non-flight insects with the same estimations? That's a very good point. Yeah, so basically the energy costs of photoreceptors are high and if an animal is very active in locomotion so is the energy cost of moving around its body volume. So if you have a high field metabolic rate and an active animal then the energy cost of the photoreceptor translates into a smaller volume than if you have a low specific metabolic rate or field metabolic rate rather and what that means is that the less the animal expends on locomotion the more significant the photoreceptor energy costs become. The larger the volume of the animal they correspond to and I've been thinking about this as to why in a lot of large simple eyes photoreceptors are actually still smaller than we shorter than we predict and one thing is that for example if you're a fish then the energy cost of supporting your body in locomotion is actually much less and that makes the relative cost of the photoreceptors much higher so you make them shorter. Yeah, the constraints are absolutely intertwined So yeah, like I would like to ask people to start joining the room I would like to ask one of my own probably naive questions So like we are talking about photoreceptor costs and they assume like different types of photoreceptors come with different costs. Is that right? Yes, that is right. So have you tried to make a more complex model in that regard as well to see how a different photoreceptor would change the trade-off between lens, investment and photoreceptor lens? No, we haven't because again it's introducing more free parameters. So we haven't tried that but we're aware that one could do that and there probably are some very important trade-offs and people have considered for example so in flies where we've where we've assumed that the photoreceptor is basically cylindrical it has a uniform cross-section in fact it's known that the rhabdemeers taper, they're wider at the top and narrower at the bottom and in fact it was pointed out by Boschek in 1971 that this would tend to concentrate light towards the bottom but it would tend to counteract the effects of exponential absorption so that all sorts of once you start thinking I don't know if my connection is safe or if all of us lost you judging from transducers then you can play around with the geometry of the rhabdeme in lots and lots of different ways Thank you very much for that as you can see people are already here and we will shortly interrupt live transmission so make sure if you want to join us in this post-talk informal get-together given that conferences are not happening for the time being, I mean this is the best alternative we have in our hands. I would like to thank you Simon once again for accepting our invitation it was great, like definitely an honour to be hosting you and yeah, like I would like to thank the audience as well and as I said make sure to join the room in case you still want to remain a part of it so officially now I have surrendered my moderator responsibilities people can you know freely interact don't wait for me and the go signal Hi Tom Awesome talk I just made it Tom, we didn't hear you Sorry Can you hear me now Yeah, can you repeat Yeah, I just said it was good to see Tom No, we couldn't hear Tom I couldn't hear Tom but actually it's a bit laggy Yeah I was going to get his other mic Sorry Can you hear me now I just said it was good to see Tom No, we couldn't hear Tom I couldn't hear Tom Okay, guys someone probably has still the live transmission on I would suggest you turn it off because we are getting the feedback that is already improved I think, yeah, thank you Are you such silence? Hello Petri, hello Tomas Okay, I think now I can talk Is that right, can you hear me now There is still the live transmission on I would suggest you turn it off because