Superorganism in Flight: The Physics Behind Starling Murmurations

Maeve Ding, Matt Levasseur, Nicole Shen, Rachael Zhang

Abstract

Across ecosystems, certain species exhibit behaviors that make them appear as more than just individual organisms, functioning instead as part of a larger collective entity. These so-called “superorganisms” are marvelous displays of highly coordinated behavior where individuals’ ability to communicate information effectively enhances survival for the group. Starlings, members of the family Sturnidae, and of the larger order Passeriformes, are a species that exemplifies this phenomenon through murmurations. These black birds with short tails, long, pointed bills, and triangular wings function collectively to navigate complex environments with precision.

In this paper, we explore murmurations of starlings from a physical perspective. We analyze the physical characteristics of starlings, the aerodynamics of avian flight, the optical properties of starling plumage, as well as the energetic favourability and evolutionary advantage of flocking and murmurations. An analysis of starling murmuration behavior from a physical perspective allows us to deepen our understanding of how their lifestyle as a superorganism allows them to thrive.

Introduction

The phylogeny of starlings (Fig. 1) suggests a root in tropical Asia before dispersing throughout Europe, Africa, and Australia. However, their introduction to North America is a relatively recent event, beginning in 1890 when approximately 80 European Starlings were released in New York City’s Central Park (Vickers, n.d.). The release of the birds was part of an effort to introduce all the bird species mentioned in Shakespeare’s works to the United States. Remarkably, they were able to survive the winter and have since proliferated. The starlings moved westward, expanding to the Midwest and eventually spreading to every U.S. state and province of Canada. Their population reached an estimated high of 200 million in the 20th century.

Genetic tests showed that the differences in starling populations from around the United States are subtle. However, genome sequencing shows a notable change in the genetic signature that controls their adaptability to temperature and rainfall. Their success in such varying environments is largely attributed to their genetic predisposition for adaptability, allowing them to proliferate in both native and introduced habitats. Starlings can now be found on six of the world’s continents and are contradicting the long-held belief that evolutionary changes at the genetic level take millions of years. The intrinsic adaptability of starlings also contributes to their being referred to as pests. They usually inhabit densely to mildly human-populated regions, where they are found most abundantly in fields, parks, farms and cities, although they can adapt to most wild habitats. As they proliferate in various non-native habitats, they compete with other birds for nesting sites. Such is the case with bluebirds and Red-headed Woodpeckers in North America.

Fig. 1. The Common Starling, Sturnus Vulgaris (Baca & Sartarelli, 2024).

About 22 centimeters in height, male starlings are distinguishable by their green and purple iridescent plumage dotted with regular flecks of white. In contrast, their female counterparts are much less brilliant, with only a few bright spots. Male bills are bright yellow during prime mating season, and they become progressively duller in color as the mating season wears on. During the spring and summer, the male and the female are discerned by the color of the base of the bill: blue in males and pink in females. Their wings are pointed and tapered in shape, whereas their tail is short and square tipped. Starlings, like other avians of the same family, are also notable for their expert vocal mimicry. They can replicate a wide range of sounds, including bird calls, human-made noises, and environmental sounds.

Murmurations (Fig. 2), fittingly named for the murmuration “cloud” created by thousands of flapping wings, are one example of notable collective animal behavior. Made up of around 30,000 birds on average, they form spectacular shapes ranging from spheres, planes, and waves (Goodenough, 2017). Their choreographed movements have been a topic of discussion for biologists, physicists, and mathematicians alike and are often compared to behavior of swarming insects, herding mammals, or schools of fish. To fully understand the significance of these murmurations, we must first discuss collective animal behavior and the potential adaptive purposes by which it transpires (Hindmarsh, 1984).

Fig. 2. Starling murmuration in flight (Worldphoto, 2018).

Physical characteristics and adaptations of starlings

Birds have evolved specific anatomical features to adapt to their behavioral habits. Flight as a means of locomotion has evolved to minimize energy loss, while retaining the characteristic flamboyance of bird appearance for mating. Flight has several advantages as an evolutionary adaptation. First, the aerosphere provides a less obstructed means of locomotion than the grounds. Organisms that rely on flight benefit from a more dependable means of transport as geographical and distance barriers do not hinder them as much. Similarly, the ability to fly boasts the advantage of evading land predators. As a result, defensive strategies among flying and gliding animals primarily deter aerial predators. Other advantages of flight include improved detection of mating partners, greater displacement velocity compared to land animals of comparable size, evasion of atmospheric and environmental conditions, increased efficiency in acquiring food, and several others. Such benefits are inevitably weighed by significant changes in the anatomy of birds (Dvorák 2016).

Skeletal and urogenital adaptations

The anatomical adaptations of flying and gliding animals serve the purpose of facilitating the energy-intensive process of flight. Efficient adaptations in flying organisms will improve said organism’s aerodynamics – its interactions with air – or its endurance during flight, via metabolic processes. Here, improve is meant as a generic term to describe the desirable work that can be done by the fluid on the object in question, in this case a flying animal. With respect to aeronautics, desirable work refers to the amount of lift that can be exerted on the object simply by virtue of its design and motion. Thus, to maximize aerodynamic lift, birds have evolved lightweight yet sturdy bones that balance strength and minimize weight to reduce the metabolic cost of flight (Dumont, 2010). The high moment of inertia of bird bones, namely their weighted mass distribution in relation to the bone’s principal axis, is due to their hollow cylindrical shape. Flexural rigidity, a material property characterizing bending resistance, is positively correlated to moment of inertia. Additionally, because birds’ bones are comparable in weight to the bones of other mammals but have a thinner walled diaphysis, it is suggested that they exhibit higher flexural rigidity than those of other mammals (Fig. 3). This is to be attributed to the reduced porosity of their cortical bone (Dumont, 2010). These structural adaptations give birds’ skeletons a high strength-to-weight ratio and stiffness-to-weight ratio, enabling them to withstand the forces encountered by them during flight.

Fig. 3. Bird bone cross section. Thinner cortex is apparent along diaphysis, and a thicker cortex along the epiphysis (The George Washington University, n.d.).

The mass relative to the lift-generating surface, rather than total body mass alone, determines the metabolic cost of flight. The combination of density and bone shape (Fig. 4) allows birds’ bones to achieve the optimal balance between stiffness, strength, and toughness, hence making them highly efficient for the demands of flight.

Fig. 4. Diagram of the effects of bone density and shape to bone stiffness and strength for a given piece of bone. Density is proportional to stiffness and strength. The dashed lines represent regions of equal strength and stiffness (Dumont, 2010).

Air sacs and other adaptations

The respiratory system of birds is optimized for their high metabolic needs. Resultingly, avian lungs are connected to multiple air sacs located along their clavicle, thorax, and abdomen (Fig. 5). These extra chambers, along with the lungs, allow for the unidirectional and constant flow of air. Thus, bird respiration consists of two cycles. When the bird first inhales, external air is brought to the caudal air sacs. As the bird exhales, this air is brought to the lungs. Through the subsequent inhalation, the air exits the lungs to fill the cranial air sacs. Upon the last exhale, this air is expulsed to the exterior. These two cycles occur simultaneously, allowing for a constant supply of oxygen to the lungs (Maina, 2022). Hence, the voluminous air sacs of birds allow for a larger quantity of air to circulate through their respiratory system despite their relatively small lungs. Efficient gas-exchange is crucial to sustain the muscles’ increased demand for oxygen during flight. Breath rate increases during flight as a compensatory measure. However, it remains unclear if birds actively use their air sacs to optimize aerodynamic efficiency during flight.

Furthermore, birds generally possess pneumatic bones, which are hollow (Maina, 2022). These bones play a role in the bird’s respiratory system, as air sacs can extend through them. It has been suggested that pneumatic bones, along with air sacs, could have contributed to the overall lightening of bird skeletal frames, thought to have been crucial for flight development (Apostolaki et al., 2015). However, this belief could be misleading, as pneumaticity has evolved independently among different lineages of archosaurs, ancestors of birds, before the development of avian flight. Some studies suggest that these adaptations simply allowed for a “higher performance” endothermy (Schachner et al., 2013). Additionally, some migratory birds, such as loons and grebes, lack such an extensive characteristic. Bats, too, are capable of flight despite their lack of pneumatic bones. Thus, the development of pneumatic bones may not have been crucial for avian flight (Machado et al., 2016).

Fig. 5. Avian respiratory system. The cranial air sacs are located towards the bird’s head, whereas the caudal air sacs are located towards the tail (Sereno, 2008).

Flying animals have grown smaller as evolution has occurred (Dumont, 2010). The energy intensity of flight is such that the lighter animals boast a major metabolic advantage over their heavier counterparts. Thereby, evolution in avian species has favored a lighter and simplified skeleton. This materializes in birds as fewer bones and the fusion of many of those that remain. For instance, bird vertebrae have fused over time to form a rigid spinal column, optimal for flight (Scanes & Dridi, 2022). Fused bones possess fewer movable joints, which provides a rigid internal framework that can resist a greater force without deformation.

The weight of birds has also been reduced via their streamlined urogenital anatomy (Dvorák, 2016). For instance, as birds have neither urinary bladder nor urethra, their urine exits the ureters into the cloacal chambers and directly mixes with their feces. Furthermore, urogenital adaptations in birds arise in the female’s sole ovary, while most female terrestrial mammals have two. Birds have also sacrificed their dentition for weight loss to minimize the cost of flight.

Vocal mimicry

There are several hypotheses to explain vocal mimicry in starlings (Dudeck, 2016). This includes interspecific territoriality: how birds can deter competition from food or resources by imitating aggressive or territorial calls of competing species. Batesian mimicry is another hypothesis for this phenomenon, which describes how the imitation of calls from predatory species can be used to deter individuals of the same or different species. Others suggest that a large repertoire of mimicry is a method by which females can be attracted by the males, which would ascribe vocal mimicry to sexual selection in birds.

Ocular

The optical system of birds, including starlings, features specialized eyes that allow them to excel in foraging, navigating, and evading predators. These specialized eyes have increased light sensitivity to improve night-vision as well as modified geometric proportions for improved visual acuity. Visual acuity corresponds to the observer’s ability to distinguish the details of an image at a distance.

Vision is the process during which light penetrates the cornea, refracts into the lens and projects an image onto the retina for detection by specialized neurons. Several geometric parameters affect the result of this process. The axial length of the eye is the distance from the front of the cornea to the back of the eye (Fig. 6). The axial length affects the posterior nodal distance (PND), namely the distance between the lens and the retina. Longer axial length and longer PND result in a larger projected image onto the retina, which improves visual acuity in birds (Hall & Ross, 2006). Bird species adapt different eye shapes based on their activity patterns: nocturnal or diurnal. Nocturnal birds performing activities at night have larger corneal diameters relative to their axial length. This adaptation allows more light to enter the eye and thus propagate to the photoreceptors in the retina. In contrast, diurnal birds performing activities during the day prioritize clear and sharp vision. These birds’ eyes have a longer axial length relative to their corneal diameter to project a larger image onto the retina. This adaptation helps diurnal birds focus on precise and detailed images in bright light.

Fig. 6. Illustration presenting various measurements relevant to the discussion of the camera eye shape (Hall & Ross, 2006).

Aerodynamics of avian flight and avian biomechanics

In the study of aerodynamics, an airfoil is an object which, upon interaction with a surrounding fluid, will generate much greater upwards force – perpendicular to the direction of movement – than drag, which acts opposite motion, due to its structure (Serway et al., 2014). Thus, an airfoil is a property of shape rather than function. The mechanical properties given to an airfoil by its shape enable it to serve important functions in many fields such as aeronautics. Additionally, viscosity is an inherent property of a fluid. It is defined as the fluid’s stiffness, its resistance to deformation, at a given rate. This resistance applies both to direct and indirect deformation: respectively, deformation by a force exerted directly onto the object and deformation as results from long-range forces such as gravity.

Aerodynamics

In flight, the aerodynamic force is the main source of interest and is defined as the net force exerted on an airfoil by the surrounding fluid (Fig. 7). The individual components of this force are called lift and drag. As prescribed by Newton’s third law, the corresponding antiparallel forces are called weight and thrust, respectively.

Fig. 7. Free-body diagram of the forces acting on an airfoil (a wing in this case) during flight. The aerodynamic force can be described as the sum of its components (Dvorák, 2016).

Lift itself is a consequence of the airfoil’s structure, the Bernoulli principle, and Newton’s third law (Serway et al., 2014). Thus, as an airfoil thrusts itself into a fluid, regions of lower and higher pressure are created above and below the airfoil, respectively. This can be explained in tandem by the Coandă effect and Bernoulli’s principle. The Coandă effect (Fig. 8) corresponds to a fluid’s tendency to linger around a surface as it moves around and past it. If the fluid within a region has a net velocity, due to viscosity, particles around this “fluid jet” will experience a net force in the same direction resulting in their net displacement. As fluid particles collide directly onto one face of the object and are driven away from the other, a net pressure gradient is created around the object’s surface. Resultingly, fluid particles in motion, as they brush past the object, are driven to accelerate toward the lower-pressure region. Thus, there is a net increase in the fluid’s velocity during curved flow as it is the product of acceleration due to a pressure differential.

Fig. 8. Illustration of the Coandă effect. The Coandă effect is defined as the net acceleration of fluid particles toward a lower-pressure region induced by a moving fluid brushing past an object (Katopodes, 2019).

Bernoulli’s principle, Equation 1, reinforces this effect to produce lift. Indeed, the Bernoulli equation relates the pressure P, the density 𝜌 , the speed v, the gravitational constant g as well as the relative height h of a fluid in some defined region and determines them to be constant throughout space.

(1) $P+\frac{1}{2}pv^2+pgh=C$

Consider a region of space where pressure is constant and the gravitational force on fluid particles is homogenous. Then, Bernoulli’s principle states that the change in pressure is equal to the negative of the difference in square velocities times a constant. Otherwise put, pressure decreases as velocity increases. From the Coandă effect, it follows that the increase in speed near the radius of curvature of the wing in starlings’ results in a pressure gradient that produces lift. This same speed differential observed above the wing – or airfoil – does not occur on its downward face as it has a net positive angular component antiparallel to the fluid flow direction. This means that the fluid will come into direct contact with the wing, which will produce an action-reaction pair per Newton’s third law, and a region of greater pressure. This higher-pressure region below the wing further contributes to the positive lift component of the aerodynamic force.

The Kutta-Joukowski theorem

In most applications, the net lift (Fig. 9) exerted on an airfoil can be represented using the Kutta-Joukowski theorem (Neuenschwander, 2015). Being an inviscid theory, namely a theory describing phenomena occurring in non-viscous environments, the Kutta-Joukowski theorem, given by Equation 2, can realistically be applied to lift contribution on wings due to the low viscosity of the atmosphere.

(2) $L=\rho V\oint V\bullet ds$

Where L represents the lift, 𝜌 is the fluid density, V is the speed of the airfoil relative to the fluid, and the surface integral corresponds to the fluid’s circulation around the airfoil. Several assumptions must be made about the fluid’s properties and the airfoil’s displacement for the equation to accurately model lift generation. Among these, the Kutta condition stipulates that the fluid flow must be steady and tangential to the airfoil at its trailing edge, and the fluid must be incompressible (Serway et al., 2014). While the latter certainly does not apply to the atmosphere and the former is certainly not true of a wing during takeoff or landing, the equation is still applicable during gliding, when the pressure gradient about the wing is smallest, and the fluid flow is reasonably steady.

Fig. 9. The net lift exerted on an airfoil is a product of a pressure gradient caused in tandem by the Coanda effect and the Bernoulli principle. The Kutta-Joukowski equation can quantify the lift in relation to various fluid parameters (Airfoils and Aerodynamics – A Basic Overview, 2012).

Biomechanical adaptations for avian flight

Avian biomechanics are also highly relevant to the study of aerodynamics in flight. The efficient use of energy to power the dynamic motion of flight as well as the anatomical adaptations evolved to maximize power distribution to the wings are of primary concern (Greij, 2014). Flapping in wings is governed by repeated cycles of contraction and elongation of the two largest muscles in the bird’s body: the pectoralis major and the supracoracoideus (Fig. 10). The pectoralis major is responsible for downstroke and is attached to the keel of the sternum and the humerus. To adapt to the large size of their pectoralis major, birds have evolved a vertical keel which greatly increases the sternum’s surface area for muscle attachment.

Fig. 10. Musculoskeletal adaptations in birds. The vertical keel of the sternum and the large supracoracoideus muscle for upstroke are major adaptations for flight (Shyamal, 2024.).

The supracoracoideus governs upstroke during flight and is located laterally above the pectoralis major. While most mammals make use of their relatively small deltoids to raise their arms, the energy intensive upstroke in birds requires a muscle with much greater surface area. This anatomical challenge is solved by fixing the supracoracoideus to the vertical keel of the sternum in birds and looping its tendon around the coracoid for attachment to the humerus. In this way, birds employ their two largest muscles, first the pectoralis and second the supracoracoideus, for downstroke and upstroke, respectively.

Energetic cost of flight

It is estimated that muscle mass-specific mechanical power output of birds during flight varies between 60-150 W/kg and 400 W/kg for cruising flight and take-off, respectively (Tobalske, 2007). This power output can be further described according to types of energy expense during flight, as shown by Equations 3 and 4.

(3) $P_{musc}=P_{inner}+P_{aero}$

(4) $P_{aero}=P_{ind}+P_{pro}+P_{par}+\frac{\Delta E}{\Delta t}$

Where $P$ denotes power and the subscripts musc, inner, and aero denote energy expenditure by the muscle, energetic requirement to act against the inertial forces of the musculoskeletal body and aerodynamic power expenditure, respectively. The aerodynamic power expenditure is further distributed as the cost of lift production (ind), the cost of overcoming drag on the wings (pro), and the cost of overcoming drag on the entire body (par). The remaining term denotes loss of energy due to changes in the kinetic and potential energies of the bird as a function of time.

The pectoralis major being the largest muscle in the bird’s body, it is of consensus that it contributes most significantly to $P_{musc}$ (Fig. 11B). Furthermore, $P_{aero}$ will vary according to the speed and conditions of flight. $P_{aero}$ consists of a U-shaped curve describing the energy minimizing and maximizing constraints of flight (Fig. 11A). While the U-shaped trend is common for all flying animals, the actual predicted values of this energy-consumption model also vary according to anatomical aspects of the bird. Thus, all individual components of the aerodynamic power expenditure equation may change according to the bird’s profile and weight.

Fig. 11. A) Representation of the aerodynamic mechanical power output of birds during flight. The signature U-shaped energy curve is evident. $V_{mp}$ denotes the velocity for minimum power, whereas $V_{mr}$ denotes the velocity for maximum range (greatest balance between flight speed and endurance). B) Work loop of the pectoralis major during a single contraction and relaxation cycle for a cockatiel Nymphicus hollandicus. The arrows point counterclockwise to denote positive work done on the muscle. Muscle and bone strain during the cycle are also shown (Tobalske, 2007).

Structural coloration: an iridescent plumage

Morphology of feathers

As an extreme example of positive evolutionary feedback in mammals, bird plumages have evolved luxurious colors and intricate motifs for courtship (Kinoshita, 2008). Depending on the species, this adaptation reflects several different physical mechanisms. Among them, light scattering is most prevalent in birds with blue or violet plumages, whereas more vibrant monochromatic plumages, of red or orange hue for instance, are due to pigments, carotenoids, deposited in the microstructural assembly of the feather (Delhey et al., 2022). Melanocytes are epidermal cells that synthesize melanin, a pigment found in most mammals and birds, including starlings. Melanin is responsible for the brownish coloration of starlings’ plumage. Relatedly, coloring via chemical properties of compounds consists of cell pigmentation. In contrast, light phenomena caused by the interactions of light with specific morphological structures in biological organisms are collectively referred to as structural coloration. Structural coloration arises merely as a byproduct of light’s physical properties and its ensuing propagation in matter. Here, we discuss structural coloration in starlings.

Starlings have evolved a specific mechanism for their iridescent plumage (Norden et al., 2021). Iridescence refers to the optical property of a material that reflects different wavelengths relative to the angle at which it is observed. This phenomenon is attributable to the specialized assembly of keratin in the starling’s feather. As described in Feather Structure and Assembly (Bouslama et al., n.d.), a feather’s morphology can be grossly summarized as a central shaft, the rachis, with branching segments called barbs (Fig. 12). Barbs possess their own branching components called barbules, which are themselves responsible for the iridescent phenomena observed in bird species. As observed in Figure 12, each barbule contains melanosomes arranged in various assemblies, and the β-keratin molecule of which feathers are made of. The assortment and morphology of the feather components exhibits a wide variety among different species due to diverging evolution.

Fig. 12. Morphology of the feather and cross-section of a feather barbule illustrating the photonic crystal-like arrangement of melanosomes and β-Keratin (Norden et al., 2021).

Interference and diffraction

Iridescence is a product of thin-film interference in the feather barbules of starlings. To illustrate this, consider a sheet of some material of thickness d with index of refraction $n_2$ where $n_2$ > $n_1$ . From the properties of reflectance and transmittance, light interacting with a material boundary will be partially reflected and partially refracted (Serway et al., 2014). Consider Figure 13, the light incident to the material will have a π phase shift upon reflection. The remaining light, refracted into the translucent material, will be partially reflected upon interaction with the other boundary of the material, a distance d away. Light traveling from a material boundary of higher refractive index will not have a π phase shift when reflected (assuming $n_3$ = $n_1$ ). The level of coherence of light as it exits $n_2$ will determine the predominantly observed color as a product of iridescence. Light waves whose peaks and troughs perfectly align will observe maximum constructive interference.

Two reflected light waves will interact once the initially refracted light wave travels an additional distance of 2d. This phenomenon can produce a range of interference patterns. Indeed, different wavelengths will be observed at different angles because interference patterns are dependent upon the distance travelled by light within the material. This phenomenon is highlighted by Equations 5 and 6.

(5) $2d=2\left(m+\frac{1}{2}\right)\cdot\lambda$

(6) $2d=m\lambda$

This model varies only slightly if light is observed at an angle. The first equation represents maximum destructive interference in the case where the initially reflected light beam undergoes a single-phase shift of 𝜋; the second represents maximum constructive interference. Different angles of light incidence – equivalent to different angles of observation – will correspond to slight changes in the distance travelled by light within the material, which will affect the magnitude of the wavelengths required for maximum constructive interference.

Fig. 13. Diagram of the interaction of light with materials of varying refractive indices. Suppose $n_2$ > $n_1$ and $n_3$ = $n_1$ . The overall reflected ray will be a product of interference between the two light waves (Thin Films – Wize University Physics Textbook (Master), 2024).

Feather barbules contain a variety of characteristics that enable thin-film interference. Melanosomes, which are the organelles tasked with storage and synthesis of melanin within the melanocytes, have an index of refraction of approximately 1.7 whereas β-keratin, the molecule which envelopes melanosomes within the barbule, has an index of refraction of 1.55. This difference enables interference as light can be both reflected and refracted upon interaction with a material of higher refractive index from a medium of lower refractive index. Furthermore, melanosome arrangement in the barbule facilitates bright interference patterns. Indeed, the uniform melanosome and keratin layers within the barbule bring about formation of photonic crystal-like structures, which are characterized by their periodic refractive index changes (Freyer et al., 2021). Photonic crystals amplify color saturations due to the multiple reflective surfaces, thus making the bird’s plumage appear brighter and more colourful.

Murmurations: an evolutionary perspective

Omnipresence in nature

Collective animal behavior refers to the coordinated, synchronized actions of large groups of animals. Collective behavior is widespread in nature, seen in schools of fish, ants marching in a line, or swarms of locusts. While each individual may be acting independently, their movements inadvertently contribute to a much larger picture. The key to understanding such behaviors is to examine the adaptive nature of which they formed. Generally, these behaviors often follow simple rules. The three guidelines are as follows (Sumpter, 2006):

Move away from very close individuals.

Adopt the same direction as those that are close by.

Avoid becoming isolated.

These simple principles enable large groups to move in such a coordinated manner without any centralized control; each animal adjusts its behavior based on its immediate neighbors. This allows for real-time adaptability to environmental stimuli (Sumpter, 2006).

The dynamic behavior of the coordinated flight patterns is an incredible evolutionary adaptation. It makes it difficult for predators to single out individual birds, thus reducing the risk of predation. In fact, predatory birds’ hunting behavior consists mainly of targeting a specific individual in a flock. The inability for a predator to discern an individual from the crowd is known as “target degeneracy”, a phenomenon harnessed by such colonial species to evade aerial predators (Pearce et al., 2014). Starlings’ immense murmurations are continuously moving, creating dynamic streaks of darkness in the sky (Fig. 14). This perpetual motion confuses predators by intensifying target degeneracy (Goodenough, 2017).

Fig. 14. Representation of the dynamic behaviour of starling murmurations. Regions of greater and lower opacity in response to stimuli are evident (Hemelrijk et al., 2015).

Herd behaviours

Starling murmurations display several patterns of formation depending on the severity of the perceived threat. One notable pattern used by flocks in response to predators is the formation of waves within the murmuration. Numerous theories attempt to explain individual motivation within a group, such as the “selfish herd” theory, which states that individuals will continuously aim to occupy the safest, most advantageous spot in a collective at signs of danger to favor their chances of survival (Fig. 15). Thus, this theory states that preyed individuals within a collective will distance themselves from predators at the expense of their fellow members. Certain species of the animal kingdom exhibit this selfish herd behavior, such as European minnows. Despite this fact, there is no significant evidence that starlings desire to occupy the centermost position of the flock, which is synonymous with safety, despite being aware of the risks (Vallee, 2021). One can hypothesize that starlings do not exhibit selfish herd behavior. This counterintuitive notion is also observed in other members of the avian class, such as pigeons and penguins. In fact, a study simulating aerial attacks on pigeons with a robotic falcon found that, when threatened, pigeons formed highly aligned flocks rather than fleeing toward the center in a selfish manner. This study brought to light hypotheses for selfless actions in response to danger (Sankey et al., 2021; see also Hammer et al., 2023). One such hypothesis states that the alignment and coordination of birds in flight allows for more efficient predator evasion for the entire flock, thus outweighing the benefits of protecting individual members.

Fig. 15. Illustration depicting the centroid and a representation of selfish herd theory. The flock of birds (red) is in direct alignment and its greater mode of survival is coordination. The approach of a predator (green) towards the focal bird (gray) forces it to adopt an angle of escape $\theta_t$ at $t_0$ to reach its new position at $t_1$ . $\theta_{ali}$ : angle of alignment with flock, $\theta_{ca}$ : angle of alignment with the “predicted future centroid” $C_f$ , $C$ : the instantaneous centroid, $\theta_{rpf}$ : angle to predator position, $\theta_{rfo}$ : angle to predator orientation, $\theta_h$ : angle to home (Sankey et al., 2021).

Indeed, coordination such as observed in the aforementioned study could allow for faster information transfer among individuals within the flock, which might explain why this mechanism could have been passed on through natural selection for pigeons, and indeed other birds such as starlings. By simply aligning with its neighbors, the individual does not need to sense a predator to evade. Instead, it can adjust itself to the evasive movements of its neighbors who have sensed it: thus, allowing for heightened information transmission in large masses. It is also riskier for birds to exhibit centroid attraction as opposed to fish, as it could lead to collisions near the center of the flock, which are more costly for birds in high altitudes than for fish in water. This explanation is supported by the fact that collision avoidance is an important element of starling flock cohesion. It is suggested that at high speeds, highly aligned configurations are more advantageous than selfish herds displaying centroid attraction, based on a simulation model created by Wood & Ackland (Sankey, 2022). When comparing evasion tactics, individuals exhibiting centroid attraction consistently ended up at the rear of the flock, closer to the predator and thus at greater risk than highly aligned individuals. In contrast, highly aligned individuals were able to evade predators more effectively at high speeds. For slow-moving species, such as crabs, centroid-based tactics are thought to be more effective, as escaping from fast-moving predators is harder, making the protective benefits of clustering more advantageous. In such a case, selfish herd theory prevails, as the group benefits more from another member being preyed upon. Starlings are fast fleeing, however, which could explain why they do not seem to display selfish herd behaviors. In short, high-alignment mechanisms in flocking birds could have been retained from natural selection due to its advantages as opposed to a selfish herd mechanism. It is important to note that these hypotheses, while based on empirical evidence, are validated by models which might not accurately represent the mechanisms of collective animal behavior, and they must thus be considered appropriately.

Energetic favourability of flocking

Murmurations are energetically favourable. Indeed, during cold winter months, large roosts made up of thousands of starlings offer thermal benefits to their members. The sole act of congregating many of these warm-blooded individuals can contribute to raising local ambient temperatures by 5℃, ensuring the survival of the flock in harsh weather. Additionally, the act of huddling reduces the surface area of their bodies exposed to the elements, which in turn helps them conserve heat. According to experimental data, a study conducted on starlings concluded that by resting in a large roost overnight, each individual starling could save up to 4-6 kcal of energy which is roughly equivalent to the energy spent on a 31 km flight. The energy expenditure of flight is given by Equation 7.

(7) $C=1.25W^{0.773}$

Where C denotes the cost of flight (kcal/km) and W represents the starling’s weight (kg), which was generalized to be around 80g (Yom-Tov, 2008). Even marginal energy savings are highly important to the survival of the species as unwanted energy loss can lead to untimely death, which is why its optimization is promoted. However, starlings were often found to fly beyond 31 km to attain the roosts, indicating that other benefits to roosting in a collective, such as offering protection from predators, outweigh energetic benefits, if there are any. Large roosts can also act as communication centers for food, an important display of information. The large-scale spread of information is made possible by the congregation of numerous individuals into a group. This is greatly beneficial to the individual members of large flocks, which supports why starlings form such large congregations.

Ocular adaptations: a fundamental feature in starlings

Optics and visual mechanisms

Prey species of birds typically have eyes that are located laterally on their heads. This results in their optical axes pointing toward the sides. Predatory birds generally have forward-oriented eyes, a phenomenon that is also prevalent among mammalian predators, allowing for performant stereoscopic vision (Yong, 2022). Stereoscopic vision refers to the depth perception provided by both eyes. The total visual field is a combination of the visual fields of both eyes, with an overlap region between the two fields known as the binocular region. Prey bird species have a wide visual field, with greatest resolution in the lateral fields (Martin, 2022). Due to poor forward vision, these birds use a mechanism called optic flow to control flight. This refers to the pattern of motion perceived as a bird flies through its environment. Thus, prey bird species adapt to visual cues in their environment to adapt flight motion and mechanics. For example, as an object is approached by the bird, the optic flow expands outward from that object, therefore the object’s relative velocity is opposite that of the bird’s motion. The rate of expansion signals the bird of the object’s distance and its relative rate of approach. Faster expansion means the object is near, while slower expansion means it is farther away. This concept is analogous to the perceived velocity of objects while driving on the highway: the closer one drives to the highway’s shoulder, the faster approaching signs seem to move while one drives past them. Thus, prey bird species rely solely on this flow to estimate the relative distances of objects. Their lateral vision is therefore essential to locate predators at a distance.

Monitoring of neighbours in murmurations

Starlings typically rely on their retinal periphery to monitor conspecifics because this low-acuity vision requires less energy and attention as opposed to their high-acuity center of vision (fovea), which is often used when monitoring threats (Butler et al., 2016). This region of the visual field which offers higher resolution is only a minuscule portion of a starling’s field of vision which is why relying solely on the fovea is not advantageous (Fig. 16). Starlings’ visual periphery allows them to have a wider field of view for stimulus detection, at the expense of visual clarity. Indeed, starlings have a field of vision of around 296°. Using the retinal periphery to monitor movements of neighbors can increase the uncertainty of the information gathered since the resolution is lower. After detecting stimuli in their visual periphery, starlings tend to orient their heads such that their center of acute vision corresponds with the direction of stimuli to receive a higher resolution image. Birds typically move their heads at a higher frequency and a greater angle than they would their eyes to gather more enhanced information. Moving their heads allows for better resolution of images due to birds’ fronto-lateral centers of high visual acuity. Head movements in birds are analogous to gaze fixation in humans. Thus, upon reception of an action-inducing signal, such as a predator or food, birds exhibit more lateral head movement than at rest to assess their velocity, angle, and potential attack maneuver.

Fig. 16. Wheel on the left describes the field of vision of starlings. Dark regions are binocular vision, light grey regions are regions of independent field of view, and black region is blind spot. Wheel on the left: A) Resting binocular field, B) Front periphery, C) Foveal region → high acuity vision, D) Rear periphery, E) Blind area (Butler et al., 2016).

Starlings can harness the characteristics of their visual field to restrict different portions of their attention to different fields of view, such as the use of their high-acuity field of vision for foraging while monitoring their conspecifics via their low-acuity centers. Studies have shown that using peripheral vision allows starlings to monitor multiple neighbors’ behaviors at the same time since they have a broad field of vision. Their prevalent use of peripheral vision makes predator-evading maneuvers more efficient, while diminishing the probability of false-alert maneuvers due to the continuous monitoring of neighboring members of the murmuration.

It is also shown that starlings which are positioned at the edge of a flock are typically more wary of danger than the ones in the center as their head movements increase in frequency, which is synonymous with alertness. This is due to the outermost positions in the flock being riskier to predation than central positions (Fig. 17). Increased vigilance is inversely correlated to time spent feeding. Vigilance is also inversely proportional to flock size. Bigger flocks are correlated with lower time spent vigilant and more time feeding during foraging events for all positions in the flock (Jennings & Evans, 1980).

Fig. 17. Chart displaying the correlation between flock size and time spent vigilant for birds in various locations in the flock (Jennings & Evans, 1980).

Since starlings must monitor their neighbors, during flights, most of their visual inputs are solely silhouettes and shadows due to the fast movement of the flock. It is thus difficult to distinguish clear contours during such activities, but contrast is apparent. They must therefore rely on a visual binary code of light and dark to infer information. Light represents the sky, an opening in the murmuration, and dark represents other members of the flock. This form of primary sensory input allows starlings to quickly detect its neighbors’ positions and make rapid decisions which is crucial for predator evasion since an effective fleeing maneuver requires the entire flock to coordinate and align to a high degree.

Scale-free correlations of information transduction in murmurations

Predator evasion and information transduction: a qualitative analysis

A model of starling murmurations (Pearce et al., 2014) demonstrates that flocks of starlings tend to self-organize into a level of maximal density which is still marginally opaque. Swarm opacity offers evolutionary advantage to the flock as it allows for greater target degeneracy and dilution of the individual in the crowd, making it more difficult for predators to single out individual members. However, too opaque of a swarm would hinder information transfer as it would create too much noise in the starling’s field of view, making it harder to distinguish a predator from conspecifics. It would also decrease contrast between neighbors, making it difficult to coordinate movements. Since views would be obstructed, only a few members on the periphery would have a clear line of sight on incoming predators, and information transfer within the murmuration would slow down due to the need for information processing by individual members. As a result, transduction of information to individuals at the center of the flock would not occur at the speed of light, the speed of optical signalling, but rather at the speed at which individuals at the periphery could react to the signal, which is much less efficient. There would thus be greater delay between detection of the predator and the evading reaction of the flock. One can infer from this that there is no advantage for opacity past a certain threshold. Sparse swarms have an advantage of allowing its members to have a better view of the flock which allows for more information to be acquired by all members about the flock’s condition. The individual birds would also be able to see in all directions, allowing for better detection of predators or better detection of another member’s reactions. However, sparse flocks are more vulnerable to threats since predators can distinguish individual targets more easily, which negates the benefits of being sparse. There is an equilibrium point which balances the benefits of sparsity and opacity: marginal opacity. If the flock were to be marginally opaque, individuals in the center would have faster signalling speeds of the murmuration’s overall condition since they would have visual access to the peripheries of the flock.

Although marginal opacity offers benefits to members of flocks, there is still an unequal distribution of risk among individuals in a murmuration. Indeed, it is known that positions near the edge of the flock are riskier to adopt than positions near the center, as the periphery is more vulnerable to predators. However, starlings are not known to desire the centermost position, indicating that they might not exhibit selfish herd behavior. If the benefit of staying in a group is less than the cost of being a member, the group will break off. This ratio of risk and reward must be balanced for a murmuration to be viable. To maintain flock integrity, the risk associated with each individual’s position must be redistributed. There is currently no known mechanism of starlings on the edge of the murmuration moving towards the center to redistribute risk. More studies must be conducted to determine if such movement occurs. Instead, studies have found that starlings occupying the outermost positions exchange positions among themselves continuously, thus redistributing the risk of being at various positions on the edge. The boundaries of the murmuration are therefore unstable positions as they are constantly being changed (Ballerini et al., 2008).

Conclusion

Starlings have evolved complex mechanisms to interact with their environment. Their ability to coordinate as a group is a result of individual responses to stimuli, their expert communication, and visual processing skills. Their movements as a group not only allow them to conserve energy but offer an important defense mechanism. Their prevalence across the globe is a testament to their genetic predisposal for adaptability. In an ever-changing world, understanding how species adapt is becoming critical.

While the evolutionary benefits of starling murmurations are noteworthy, it is also important to consider the physical aspects of bird species which allow such behaviors in the first place. For instance, birds’ large field of vision, their anatomical adaptations which enable flight, and their extravagant appearances are all products of millions of years of refinement of engineering design for improved efficiency in flight and the appropriate manifestations of their mating behaviors. Studying bird morphology, as well as avian biomechanics and the general coherence of murmurations could thus contribute to invaluable breakthroughs in various fields of engineering.

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