Baysean identification of controlled variables

Research Ethology
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Mosquitoes are attracted to dark objects and slow down when they get within about 40 centimeters, but the visual variable alone is insufficient. Without other perceptions (e.g. body odor, humidity, heat) mosquitoes often flew away even after approaching their target. “We interpret the movement away from the target as rejection of it in the absence of essential cues—such as body odor, humidity, and heat—to induce landing and blood feeding.”

Mosquitoes can detect carbon dioxide concentrations as low as 0.1 percent and that their detection range extends to approximately 50 centimeters from the source. In presence of a source of carbon dioxide, mosquitoes normally flying at 0.7 m/s enter within a radius of about 40 centimeters of the carbon dioxide source, suddenly slow to 0.2 m/s, and begin swaying erratically without a clearly observed direction.

With both visual and CO2 perceptual input, mosquitoes began to circle around the target, and significantly more mosquitoes concentrate near the target than when just one variable is present.

Once in direct contact with the host, cues like skin odor, heat, and humidity aid the mosquito in landing and choosing a spot to probe for capillaries.

https://www.science.org/doi/10.1126/sciadv.adz7063

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Very interesting. Of course, they are not really identifying controlled variables since they aren’t testing for them. As noted in their abstract, they are trying to identify “how visual and other sensory cues guide mosquitoes to their targets…”. That is, they are identifying variables that they see as the causes of mosquito behavior. The authors note this later in their paper where that note that the “learned forces [in their model of mosquito behavior] represent different responses to visual and CO2 cues .”. So, what they are seeing is the behavior of mosquitoes in response to stimuli (visual and chemical). And since they are finding a clear stimulus-response relationship between these variables we can be pretty sure (based on our understanding of PCT and a careful reading of all of Powers’ and my descriptions of “the behavioral illusion” ) that these stimulus variables (dark versus light target and CO2 concentration at target) are – or are closely related to variables that are being controlled. So, once you cut through all S-R and Bayesian junk you can see that this research could provide a good basis for a start at research aimed at identifying the controlled variables around which the behavior of mosquitos is organized.

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But of course they are. If there were one mosquito, you would see it. CO2 and dark color (and a headlike shape helps), are variables because they vary them. The mosquitoes’ ability to control landing and seeking a capillary varies accordingly. The authors did not test for mosquitoes’ control of drawing blood by means of landing and seeking a capillary, but no one who had ever swatted at a mosquito and found it persistent could doubt that this is a CV. Just as landing and seeking a capillary are examples of control, so also is finding a target on which to land and seek a capillary. Block both variables, and the mosquito looks for those variables elsewhere. (Other variables were discussed as well.)

The cloud of mosquitos over a nice dark CO2-breathing head is a Bayesean result of individual control, just as the arcs and rings in the CROWD demo are Bayesean results of individual control—Bayesean in that the location of any given agent is probabilistic at any given moment including when the last one has stopped..

It would be possible to constrain the environment around the target agent, the ‘speaker’, so that approach was possible only through radial tunnels. You would see radial lines rather than rings and arcs. By varying the tunnel widths you could determine the proximity CV precisely, even in so impoverished an environment as compared to that of the mosquito.

You could perhaps show that the paths and/or the ultimate destinations of the agents were deterministic with a map correlating starting positions with ending positions on successive runs.

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No, they are not.

I would see the same thing with one mosquito as I see with the group of mosquitoes tested in this study. These researchers are identifying S-R relationships, not controlled variables.

CO2 and color are physical variables; controlled variables are perceptual variables. Therefore, the role of CO2 and color in the mosquitoes’ behavior must be that of disturbances to controlled variables. Per PCT, the mosquitoes’ controlled landings result from acting to oppose the disturbing effects of variables like CO2 and color on these controlled variables.

The researchers, unaware of the existence of controlled variables, see the oppositional relationship between disturbance and action as causal; the disturbance is seen as a stimulus (S) that causes (cues, guides) the action or response (R). For example, CO2 (actually, distance from the CO2 source) is seen as an S that guides the mosquitoes’ movement trajectory (R). Seeing the observed relationship between S and R this way is one type of behavioral illusion.

Behavioral illusions like this have been the main obstacle to what I call “doing research on purpose”, the main goal of which is to find, describe and classify the controlled variables around which behavior is organized. But, as I noted in a recent paper, there are ways to “get around” these obstacles. Behavioral illusions can provide hints about what the controlled variables involved in this behavior might be.

When an observed S-R relationship is seen as the disturbance-output relationship of a process of control, the hint about the possible controlled variable is that it is something that is “pushed” one way by S and the opposite way by R. In the mosquito flight study distance from CO2 is directly related to velocity of movement: speed decreases as distance to the CO2 source decreases. One possible controlled variable here is CO2 molecules/unit time – or simply CO2/dt. Since the spatial density of CO2 decreases with distance from the source, the mosquito must move faster when it’s far away from the source in order to keep CO2/dt constant.

There are surely several possible definitions of the CO2 related perception controlled by mosquitos but I hope this makes the point. CO2 per se is not a perception; it can’t be controlled. But some variable aspect of CO2 – its weight, spatial density, etc – can be. CO2 molecules/unit time is a perception that has to be created by a perceptual function in the mosquito. This is the kind of variable – a perceptual variable – that we want to discover based on our understanding of how control systems work.

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Oh of course one can drill down to molecule level and atomic level variables and cellular membranes in the anatomy of sensory organs. In a model of controlling spatial relationship of objects we have no problem using measurements of the positions of the objects—physical properties—as a surrogate for the complexity in the retina which produces the experience of an object at a position.

They are not framing their work in PCT terms (big surprise), and I do not say that they are. All I am doing is showing how they could have.

Take as a given that mosquitos control landing, locating a capillary, and drawing blood. It is pretty thoroughly demonstrated that if they do not do so they do not propagate.

Prior to that, they must control locating a surface that is likely to bear capillaries. The paper focalizes two of the variables which have been identified in prior research, without which mosquitos do not do so: color and CO2. Research on the CO2 receptors is easy to find, e.g.:

Xu P, Wen X, Leal WS. CO2 per se activates carbon dioxide receptors. Insect Biochem Mol Biol. 2020 Feb;117:103284. doi: 10.1016/j.ibmb.2019.103284. Epub 2019 Nov 22. PMID: 31760135; PMCID: PMC6980743.

Kumar A, Tauxe GM, Perry S, Scott CA, Dahanukar A, Ray A. Contributions of the Conserved Insect Carbon Dioxide Receptor Subunits to Odor Detection. Cell Rep. 2020 Apr 14;31(2):107510. doi: 10.1016/j.celrep.2020.03.074. PMID: 32294446; PMCID: PMC7552916.

Shadi Charara, Jonathan Choy, Kalyani Cauwenberghs, +7 , and Chih-Ying Su. Morphological specializations of mosquito CO2-sensing olfactory receptor neurons. October 23, 2025. PNAS 122(43)e2514666122 https://doi.org/10.1073/pnas.2514666122

“Carbon dioxide (CO2) emitted by human hosts is a critical cue that mosquitoes use for host detection, yet the nanoscale three-dimensional (3D) structure of their CO2-sensing neurons and associated cells remains unclear. Elucidating the anatomy of these cells will yield structural insight into the sensory biology which drives mosquito−host interactions. Using volume electron microscopy, we reveal that Aedes aegypti CO2-sensing neurons exhibit striking structural specializations—including enlarged CO2-sensing surface areas, unique axonal architecture enriched with mitochondria, and unusual somatic ensheathing by support and glial cells—that likely enhance CO2 detection and support signal transmission. Our detailed anatomical characterization provides a structural basis for the mosquito’s exceptional host-seeking capabilities.”

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I wasn’t drilling down to the molecular level. Indeed, I was going the opposite way, describing a possible higher level perceptual aspect of CO2 – CO2 density/dt – that might be the variable under control in this study. The researchers had interpreted their observations as showing that mosquito flight is “guided” by CO2. This is obviously an example of a behavioral illusion of the S-R kind. What the researchers observed was actually the relationship between a disturbance to a controlled variable (the CO2) and the compensating output (movement trajectory). I noted that the controlled variable was a perceptual function of CO2, such as CO2 density/dt.

The spatial relationships of objects (lines on the screen) that we use in our tracking studies are described by functional representations of the actual physical events “out there”. For example, the same physical location of a line of pixels on a screen can be represented as perceptions in a model of tracking behavior in terms of Cartesian or polar coordinates. And these different perceptual representations make a difference in how well the model accounts for the behavior; see the experiment described on pp. 200 - 202 in my book Mind Readings: Experimental Studies of Purpose (1992) as well as the series of experiments described on pp. 77-95 in my book Doing Research on Purpose: A Control Theory Approach to Experimental Psychology (2014). I imagine you have the books but maybe you skipped over or didn’t remember those sections.

You start off your “framing” by saying “Mosquitoes are attracted to dark objects…” This is the exact opposite of a PCT framing, as is your final statement that “…cues like skin odor, heat, and humidity aid the mosquito in landing and choosing a spot to probe for capillaries”. All of this “framing”, suggests that the perception of environmental events – dark objects, skin odor, heat, and humidity – causes (attracts, cues, aids) the landing behavior of the mosquito.

I gave the correct PCT “framing” of their results, which is really just a matter of looking at their results through control theory glasses: What they thought they found – that variations in CO2 causing variations in flight trajectory – was actually an example of a behavioral illusion because they didn’t test to determine the perceptual (controlled) variables around which the landing behavior is organized.

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CO2 tends to settle below nitrogen and Oxygen in the atmosphere, but disturbances mix them up until you get up to the turbopause at about 13 km. There’s a nice description here. In an undisturbed closed room it settles to the floor, along with the propane from a gas range.

Above a breathing person, however, is a rising plume of warmer air, carrying exhaled CO2 with it, and other molecules to which piezoelectric molecules in olfactory sensors respond (odors). ‘Respond’ is an appropriate word, by the way, because these are molecular interactions in the realm of physics still.

Just as raptors control differential lift on their wings to find updrafts, circle and go up, or gradually descend as they increase gain in control of other perceptions, mosquitoes control intensity of perception of CO2 to find updrafts of CO2 and descend them until they get close enough for other perceptions such as odor and heat to be controlled. Disease-bearing mosquitos have been a hot research area for a long time. There is abundant evidence that mosquitos have the necessary sensory equipment and that their behavior is consistent with controlling those perceptions.

Seeking a plume and following it down, and then seeking a landing place and a capillary, is well described by a PCT model of random-walk chemotaxis. Unlike e.coli, the mosquito does have a brain, though it’s tiny. So unlike e.coli it can have more than one such perception under random walk control at the same time.

The discovery of the role of piezoelectric molecules in sensory organs won David Julius and Ardem Patapoutian a nobel prize in 2021. PIEZO proteins are excitatory ion channels in a cell membrane which are directly gated by mechanical force. The mechanical force of one molecule encountering another is very subtle indeed from our point of view. Photons are too subtle, the retina has photoreactive molecules for that. The retina does have piezoelectric cells whose generated signals are controlled to regulate grosser mechanical pressures and stresses.

The mosquito has many thousand molecular piezoelectric tripwires, specialized gateways in the environment-facing cell membrane of nerve endings. Many such endings constitute a sensory organ. Impact of a molecule of CO2 contributes to an electrical pulse along a nerve fiber. Signals from the many thousand of such fibers may be presumed to synapse to a unitary signal which from our observer’s point of view we can call a perception of the density of CO2 at the sensory surface of the mosquito. Itt is convenient to adopt the conceptual simplification articulated by Bill Powers (sometimes likened to Galileo’s inclined planes), and think of the many molecular piezoelectric tripwires with their connections to dendrites as a single sensory organ, and to treat the thousands dendrites as a bundle and call that bundle a single ‘nerve fiber’ (though they need not be and often are not physically parallel in a bundle). Or for terminological consistency applicable across different organizational levels we could call them, respectively, a giant virtual molecule sensor with its giant virtual dendrite which provides sensory input to a control loop which can be block-diagramed with the convenient fiction of single lines..

Measures of the physical variables are the only available surrogate for the neural signals generated by this appartus. (Not even Henry could work with fibers inserted into the brains of free-flying mosquitos the way he does with mice.) Guo et al. are well aware that what is relevant is not the physical variables which they can measure in the environment, but rather the mosquito perceptions of them which are essential.

A great deal of research has investigated such variables. Guo et al. cite, for example,

L. E. Muir, M. J. Thorne, B. H. Kay, Aedes aegypti (Diptera: Culicidae) vision: Spectral sensitivity and other perceptual parameters of the female eye. J. Med. Entomol. 29 , 278–281 (1992).

S. Majeed, S. R. Hill, T. Dekker, R. Ignell, Detection and perception of generic host volatiles by mosquitoes: Responses to CO2 constrains host-seeking behaviour. R. Soc. Open Sci. 4 , 170189 (2017).

W. J. Laursen, G. Budelli, R. Tang, E. C. Chang, R. Busby, S. Shankar, R. Gerber, C. Greppi, R. Albuquerque, P. A. Garrity, Humidity sensors that alert mosquitoes to nearby hosts and egg-laying sites. Neuron 111 , 874–887 (2023).

They say “mosquitoes use the time-integrated response of their sensory information to make a host-seeking decision,” citing

T. Dekker, R. T. Cardé, Moment-to-moment flight manoeuvres of the female yellow fever mosquito (Aedes aegypti L.) in response to plumes of carbon dioxide and human skin odour. J. Exp. Biol. 214 , 3480–3494 (2011).

D. Alonso San Alberto, C. Rusch, Y. Zhan, A. D. Straw, C. Montell, J. A. Riffell, The olfactory gating of visual preferences to human skin and visible spectra in mosquitoes. Nat. Commun. 13 , 555 (2022).

T. Dekker, M. Geier, R. T. Cardé, Carbon dioxide instantly sensitizes female yellow fever mosquitoes to human skin odours. J. Exp. Biol. 208 , 2963–2972 (2005)

C. J. McMeniman, R. A. Corfas, B. J. Matthews, S. A. Ritchie, L. B. Vosshall, Multimodal integration of carbon dioxide and other sensory cues drives mosquito attraction to humans. Cell 156 , 1060–1071 (2014).

B. D. Sumner, R. T. Cardé, Primacy of human odors over visual and heat cues in inducing landing in female Aedes aegypti mosquitoes. J. Insect Behav. 35 , 31–43 (2022).

M. Z. Liu, L. B. Vosshall, General visual and contingent thermal cues interact to elicit attraction in female Aedes aegypti mosquitoes. Curr. Biol. 29 , 2250–2257 (2019).

F. Van Breugel, J. Riffell, A. Fairhall, M. H. Dickinson, Mosquitoes use vision to associate odor plumes with thermal targets. Curr. Biol. 25 , 2123–2129 (2015).

A. Hinze, S. Hill, R. Ignell, “Chapter 9: Odour-mediated host selection and discrimination in mosquitoes,” in Sensory Ecology of Disease Vectors (Wageningen Academic Publishers, 2022), pp. 253–276.

C. S. McBride, F. Baier, A. B. Omondi, S. A. Spitzer, J. Lutomiah, R. Sang, R. Ignell, L. B. Vosshall, Evolution of mosquito preference for humans linked to an odorant receptor. Nature 515 , 222–227 (2014).

This work is usually phrased in the customary legacy terms, very possibly as a prerequisite for being understood, accepted, and published. So they use observer terms for measurable physical properties, such as ‘cue’ and ‘stimulus’. It is obvious, or should be, that a physical variable cannot be a ‘cue’ or a ‘stimulus’ to an organism unless the organism is capable of creating a perception correlated to that observed variable, and at relevant times nothing is preventing such perception.

When Guo et al. experimentally blocked the perceptibility of these variables, mosquitos observed activity was different, but their random-walk chemotaxis control was unchanged. When they blocked CO2 from ascending in a plume, mosquitos “wandered off”, that is, they continued their random-walk chemotaxis.

So, did Zuo et al identify and test a CV related to the physical presence of CO2? Yes, I hold that they did, and whether or not they had the theoretical apparatus to know that this was what they were doing is irrelevant.

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Nice post. Thanks.

I think it’s very possible that some of the studies cited by Guo et al do something like a test for the controlled variable (TCV). But Guo et al don’t. My criterion for seeing research as having involved the TCV is whether it in some way tested at least two different definitions of the CV to see which, when place in a control model, gives the best fit to the data.

A good example of such research is described in this paper on Object Interception, where we test three different definitions of the variable people are controlling when they run to intercept moving objects. While the Guo et al paper (and probably most of the papers they cite) provide strong hints about the variables mosquitos are controlling when they fly to a target, I would like to see research aimed at getting a more precise definition of these variables, just as we did in the Object Interception research.

The relevant difference between E. coli and mosquitoes is that the latter can steer, while the former can’t. Mosquitoes can use their wings to fly in any desired direction while E. coli can only randomly change direction by unwinding their flagella and tumbling. This means that the apparently random walk behavior of the mosquitoes might not be random at all but, rather, appropriate variations in control actions (flight trajectory) aimed at keeping a perceptual variable, such as the angular gradient of CO2 density (a possible CV), under control.

Of course. And the different possible “measures” of those physical variables are the possible CVs that the organisms control.

This statement betrays a view of perception that is completely at odds with the PCT view. It is the conventional view of the role of perception in behavior. Yes, Guo et al, like all conventional behavioral and social scientists, think of physical variables as a surrogate for the perceptions that are the “relevant” cause of the observed behavior. You seem to think that Guo et al (and all the other researchers cited) are discovering controlled variables because they know that it’s actually perceptions and not the physical variables they measure, that are the cause of the observed variations in mosquito behavior. But to be considered a CV a variable has to be more than a perception; it also has to be shown to be controlled.

I’ll probably never convince you otherwise. But keep those papers coming that you think are tests for CVs because I would like to have a lot of examples of conventional research that provide hints about the variables organisms control.

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This should probably go into a separate thread, but I just wanted to quickly mention one obvious (and very significant) way your view of controlled perceptual variables differs from the PCT (Powers’ Control Theory) view.

Based on this statement of yours:

it’s clear that you think of controlled variables as neural signals that correspond to physical variables; the physical variables are “surrogates” for the neural signals that are the actual controlled perceptions. So, when mosquito researchers find a physical variable that mosquitos respond to in a way that seems to be keeping it under control, then they have discovered a physical variable this is a surrogate of the perception that is the actual controlled variable.

The problem with this view of controlled variables is that there are many controlled variables that have no obvious physical variables as surrogates. (And there are other controlled variables that are actually different perceptions based on the same physical variables, such as the perimeter and area of a rectangle in my “What s Size” demo). Indeed, PCT hypothesizes a whole hierarchy of such controlled variables and Powers and others have presented both physiological and behavioral evidence for many of them. For example, what physical variable is the surrogate for “self-concept” or “honesty” or, of course, “the taste of lemonade”.

The mistake is in thinking that perceptual variables correspond to physical variables or entities that are “out there” in the environment. There certainly are physical variables out there in the environment – they are the variables we find in the models of reality provided by physics and chemistry – the “hard” sciences. But our perceptions of that reality are FUNCTIONS of physical variables. So, perceptions of “self-concept”, “honesty” and “the taste of lemonade” don’t correspond to physical entities out in the environment; they are FUNCTIONS of those physical entities: they are CONSTRUCTED by afferent neural networks in our nervous system that are the perceptual functions of the PCT model of behavior.

Hopefully, this little treatise on perception will help you to better evaluate what conventional researchers have – and haven’t! – discovered about the purposeful behavior of organisms. The problem is not that these researchers have done poor research; the research is often brilliant. The problem is that they are using research methods that are appropriate to the study of open-loop rather than closed-loop systems.