# Honeybees' altitude control relies on same optical invariants as pilots

Julien Serres, Aimie Berger Dauxère, Gilles Montagne

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Julien Serres, Aimie Berger Dauxère, Gilles Montagne. Honeybees' altitude control relies on same optical invariants as pilots. 53ème Colloque de la Société Française pour l'Etude du Comportement Animal (SFECA), May 2024, Albi, France. , 37, 2024. hal-04585486

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Submitted on 23 May 2024

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# Honeybees' altitude control relies on same optical invariants as pilots*

Julien R Serres, Aimie Berger Dauxère, and Gilles Montagne

Aix Marseille Univ, CNRS, ISM, Marseille, France

Corresponding author: julien.serres@univ-amu.fr

**Main question:** Perceiving a complex visual environment, what optical invariant does *Apis mellifera* focus on to stabilize its altitude?

<figure><img src="image_1.png" /></figure>

## Bases and aims

**Optic flow:** vector field of the apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an agent and the scene.

**Optical invariants:** particular properties of the optic flow unaltered when the agent is moving.
Two optical invariants are particularly relevant for a ground-following task:

* optical speed rate of change $\dot{\omega}$ [used by bees and pilots]

* splay angle rate of change $\dot{s}$ [used by pilots]

**Aims:**
(1) To determine if bees also use splay angle rate of change for performing ground-following tasks
(2) To set the priority and weight system by which bees use these two optical invariants to control their altitude

<figure><img src="image_2.png" /><figcaption>Optic flow field perceived by a flying agent (Gibson 1950, 1979)</figcaption></figure>

<figure><img src="image_3.png" /></figure>

## Optical speed (OS) experienced by a flying agent

OS ($\omega$) is the speed of environment's image scrolling the retina when an agent is moving.

* OS increases for an agent going down ($\dot{\omega} > 0$)

* OS decreases for an agent going up ($\dot{\omega} < 0$)

--> optical speed rate of change ($\dot{\omega}$) is informative about altitude change

altitude

<figure><img src="image_4.png" /></figure>

$\omega = \text{OS}$

$\dot{\omega} = \text{OS rate of change}$

$Vx = \text{agent's speed}$

$z = \text{agent's altitude}$

To maintain a constant flight altitude --> keep $\dot{\omega} = 0$

observed in bees [1, 2, 3, 4, 7, 8]

<figure><img src="image_5.png" /></figure>

## Splay angle rate of change experienced by a flying agent

Base lines join at the image's focus of expansion forming the splay angle ($\dot{s}$):

* angle's value increases in the visual field of an agent going down ($\dot{s} > 0$)

* angle's value decreases in the visual field of an agent going up ($\dot{s} < 0$)

--> splay angle rate of change ($\dot{s}$) is informative about altitude change

altitude

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

horizon
base line

$s = 1/2$ angle formed by base lines

To maintain a constant flight altitude --> keep $\dot{s} = 0$

observed in humans [5, 6]

<figure><img src="image_8.png" /></figure>

## Experimental setup [9]

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

Weak OS available
Regular splay angle

Weak OS available
Narrow splay angle

<figure><img src="image_12.png" /></figure>

## Highlights

* An experimental setup was designed to investigate whether the splay angle rate of change is implicated in bees' altitude control

* A flight tunnel was built enabling specific manipulations of two optical invariants

* Splay angle rate of change is used by bees to control their altitude in a ground-following task

* Splay angle rate of change is used by bees only if the optical speed rate of change is less accessible

<figure><img src="image_13.png" /></figure>

* A bee perceiving a splay's enlargement will interpret a loss of altitude, so it will go up to maintain a null splay angle rate of change.

* A bee perceiving a splay's narrowing will interpret a gain in altitude, so it will go down to maintain a null splay angle rate of change.

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

APIS
AMU

*This project was supported by a doctoral grant awarded to Aimie Berger Dauxère from Aix Marseille University.

[1] J. Lecoeur, M. Dacke, D. Floreano and E. Baird (2019), Scientific Reports (9), 7707

[2] G. Portelli, J.R Serres and F.Ruffier (2017), Scientific Reports (7) 9231

[3] J.R Serres and F.Ruffier (2017), Arthropod Structure & Development (46) 5, 703-717

[4] M.V Srinivasan (2011), Current Opinion in Neurobiology (24) 4, 535-543

[5] A.P Duchon and W.H Warren (2002), Psychological Sciences (13) 3, 272-278

[6] J.M Flach, R. Warren, S.A Garness, L. Kelly and T.Stanard (1997), Journal of Experimental Psychology (23) 6, 1764-1782

[7] J.R Serres et al. (2022), Biology Letters (18) 3, 20210534

[8] A. Berger Dauxère, J.R. Serres, & G. Montagne, (2021), Insects, 12(12), 1075.

[9] A. Berger Dauxère, G. Montagne, & J.R. Serres (2022), Journal of Insect Physiology, 143, 104451.

[10] A. Berger Dauxère, G. Montagne, & J.R. Serres (2023), Insects, 14(4), 313.
# Honeybees' altitude control relies on same optical invariants as pilots*

Julien R Serres, Aimie Berger Dauxère, and Gilles Montagne

Aix Marseille Univ, CNRS, ISM, Marseille, France

Corresponding author: julien.serres@univ-amu.fr

**Main question:** Perceiving a complex visual environment, what optical invariant does *Apis mellifera* focus on to stabilize its altitude?

<figure><img src="image_2.png" /></figure>

## Bases and aims

**Optic flow:** vector field of the apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an agent and the scene.

**Optical invariants:** particular properties of the optic flow unaltered when the agent is moving.
Two optical invariants are particularly relevant for a ground-following task:

* optical speed rate of change $\dot{\omega}$ [used by bees and pilots]

* splay angle rate of change $\dot{s}$ [used by pilots]

**Aims:**
(1) To determine if bees also use splay angle rate of change for performing ground-following tasks
(2) To set the priority and weight system by which bees use these two optical invariants to control their altitude

<figure><img src="image_3.png" /><figcaption>Optic flow field perceived by a flying agent (Gibson 1950, 1979)</figcaption></figure>

<figure><img src="image_4.png" /></figure>

## Optical speed (OS) experienced by a flying agent

OS ($\omega$) is the speed of environment's image scrolling the retina when an agent is moving.

* OS increases for an agent going down ($\dot{\omega} > 0$)

* OS decreases for an agent going up ($\dot{\omega} < 0$)

--> optical speed rate of change ($\dot{\omega}$) is informative about altitude change

<figure><img src="image_5.png" /><figcaption>altitude</figcaption></figure>

$\omega = \text{OS}$

$\dot{\omega} = \text{OS rate of change}$

$Vx = \text{agent's speed}$

$z = \text{agent's altitude}$

To maintain a constant flight altitude --> keep $\dot{\omega} = 0$

observed in bees [1, 2, 3, 4, 7, 8]

<figure><img src="image_6.png" /></figure>

## Splay angle rate of change experienced by a flying agent

Base lines join at the image's focus of expansion forming the splay angle ($\dot{s}$):

* angle's value increases in the visual field of an agent going down ($\dot{s} > 0$)

* angle's value decreases in the visual field of an agent going up ($\dot{s} < 0$)

--> splay angle rate of change ($\dot{s}$) is informative about altitude change

<figure><img src="image_7.png" /><figcaption>altitude</figcaption></figure>

observed in humans [5, 6]

To maintain a constant flight altitude --> keep $\dot{s} = 0$

<figure><img src="image_8.png" /></figure>

## Experimental setup [9]

<figure><img src="image_9.png" /></figure>

Weak OS available
Regular splay angle

Weak OS available
Narrow splay angle

<figure><img src="image_10.png" /></figure>

## Highlights

* An experimental setup was designed to investigate whether the splay angle rate of change is implicated in bees' altitude control

* A flight tunnel was built enabling specific manipulations of two optical invariants

* Splay angle rate of change is used by bees to control their altitude in a ground-following task

* Splay angle rate of change is used by bees only if the optical speed rate of change is less accessible

<figure><img src="image_11.png" /></figure>

* A bee perceiving a splay's enlargement will interpret a loss of altitude, so it will go up to maintain a null splay angle rate of change.

* A bee perceiving a splay's narrowing will interpret a gain in altitude, so it will go down to maintain a null splay angle rate of change.

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

APIS
AMU