Hydrostatic equilibrium

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Hydrostatic_equilibrium

Diagram of a newly formed planet in a state of hydrostatic equilibrium.

In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space.

Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System.

Mathematical consideration

If the highlighted volume of fluid is not accelerating, the forces on it upwards must equal the forces downwards.

For a hydrostatic fluid on Earth:

${\displaystyle dP=-\rho (P)\cdot g(h)\cdot dh}$

Derivation from force summation

Further information: Mechanical equilibrium

Newton's laws of motion state that a volume of a fluid that is not in motion or that is in a state of constant velocity must have zero net force on it. This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. This force balance is called a hydrostatic equilibrium.

The fluid can be split into a large number of cuboid volume elements; by considering a single element, the action of the fluid can be derived.

There are three forces: the force downwards onto the top of the cuboid from the pressure, P, of the fluid above it is, from the definition of pressure,

${\displaystyle F_{\text{top}}=-P_{\text{top}}\cdot A}$

Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is

${\displaystyle F_{\text{bottom}}=P_{\text{bottom}}\cdot A}$

Finally, the weight of the volume element causes a force downwards. If the density is ρ, the volume is V and g the standard gravity, then:

${\displaystyle F_{\text{weight}}=-\rho \cdot g\cdot V}$

The volume of this cuboid is equal to the area of the top or bottom, times the height — the formula for finding the volume of a cube.

${\displaystyle F_{\text{weight}}=-\rho \cdot g\cdot A\cdot h}$

By balancing these forces, the total force on the fluid is

${\displaystyle \sum F=F_{\text{bottom}}+F_{\text{top}}+F_{\text{weight}}=P_{\text{bottom}}\cdot A-P_{\text{top}}\cdot A-\rho \cdot g\cdot A\cdot h}$

This sum equals zero if the fluid's velocity is constant. Dividing by A,

${\displaystyle 0=P_{\text{bottom}}-P_{\text{top}}-\rho \cdot g\cdot h}$

Or,

${\displaystyle P_{\text{top}}-P_{\text{bottom}}=-\rho \cdot g\cdot h}$

P_top − P_bottom is a change in pressure, and h is the height of the volume element—a change in the distance above the ground. By saying these changes are infinitesimally small, the equation can be written in differential form.

${\displaystyle dP=-\rho \cdot g\cdot dh}$

Density changes with pressure, and gravity changes with height, so the equation would be:

${\displaystyle dP=-\rho (P)\cdot g(h)\cdot dh}$

Derivation from Navier–Stokes equations

Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where

${\displaystyle u=v=\frac{\mathrm{\partial }p}{\mathrm{\partial }x}=\frac{\mathrm{\partial }p}{\mathrm{\partial }y}=0}$

Then the only non-trivial equation is the ${\displaystyle z}$-equation, which now reads

${\displaystyle \frac{\mathrm{\partial }p}{\mathrm{\partial }z}+\rho g=0}$

Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.

Derivation from general relativity

By plugging the energy–momentum tensor for a perfect fluid

${\displaystyle T^{\mu \nu }=(\rho c^{-2}+P)u^{\mu }{u}^{\nu }+P{g}^{\mu \nu }}$

into the Einstein field equations

${\displaystyle R_{\mu \nu }=\frac{8\pi G}{c^4}\left(T_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }T\right)}$

and using the conservation condition

${\displaystyle {\mathrm{\nabla }}_{\mu }{T}^{\mu \nu }=0}$

one can derive the Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star in isotropic coordinates:

${\displaystyle \frac{dP}{dr}=-\frac{GM(r)\rho (r)}{r^2}\left(1+\frac{P(r)}{\rho (r)c^2}\right)\left(1+\frac{4\pi r^{3}P(r)}{M(r)c^2}\right){\left(1-\frac{2GM(r)}{r{c}^2}\right)}^{-1}}$

In practice, Ρ and ρ are related by an equation of state of the form f(Ρ,ρ) = 0, with f specific to makeup of the star. M(r) is a foliation of spheres weighted by the mass density ρ(r), with the largest sphere having radius r:

${\displaystyle M(r)=4\pi {\int }_0^{r}d{r}^{\prime }{r}^{\prime 2}\rho (r^{\prime }).}$

Per standard procedure in taking the nonrelativistic limit, we let c→∞, so that the factor

${\displaystyle \left(1+\frac{P(r)}{\rho (r)c^2}\right)\left(1+\frac{4\pi r^{3}P(r)}{M(r)c^2}\right){\left(1-\frac{2GM(r)}{r{c}^2}\right)}^{-1}\to 1}$

Therefore, in the nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium:

${\displaystyle \frac{dP}{dr}=-\frac{GM(r)\rho (r)}{r^2}=-g(r)\rho (r)⟶dP=-\rho (h)g(h)dh}$

(we have made the trivial notation change h = r and have used f(Ρ,ρ) = 0 to express ρ in terms of P). A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads:

${\displaystyle \frac{{\mathrm{\partial }}_{i}P}{P+\rho }-{\mathrm{\partial }}_i\ln u^t+u_t{u}^{\phi }{\mathrm{\partial }}_i\frac{u_{\phi }}{u_t}=0}$

Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates ${\displaystyle (t,r,\theta ,\phi )}$, the index i runs for the coordinates r and ${\displaystyle \theta }$).

Applications

Fluids

The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities. This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical motion at constant speed. It can also be a satisfactory approximation when flow speeds are low enough that acceleration is negligible.

Astrophysics

In any given layer of a star, there is a hydrostatic equilibrium between the outward thermal pressure from below and the weight of the material above pressing inward. The isotropic gravitational field compresses the star into the most compact shape possible. A rotating star in hydrostatic equilibrium is an oblate spheroid up to a certain (critical) angular velocity. An extreme example of this phenomenon is the star Vega, which has a rotation period of 12.5 hours. Consequently, Vega is about 20% larger at the equator than at the poles. A star with an angular velocity above the critical angular velocity becomes a Jacobi (scalene) ellipsoid, and at still faster rotation it is no longer ellipsoidal but piriform or oviform, with yet other shapes beyond that, though shapes beyond scalene are not stable.

If the star has a massive nearby companion object then tidal forces come into play as well, distorting the star into a scalene shape when rotation alone would make it a spheroid. An example of this is Beta Lyrae.

Hydrostatic equilibrium is also important for the intracluster medium, where it restricts the amount of fluid that can be present in the core of a cluster of galaxies.

We can also use the principle of hydrostatic equilibrium to estimate the velocity dispersion of dark matter in clusters of galaxies. Only baryonic matter (or, rather, the collisions thereof) emits X-ray radiation. The absolute X-ray luminosity per unit volume takes the form ${\displaystyle {\mathcal{L}}_X=\mathrm{\Lambda }(T_B){\rho }_B^2}$ where ${\displaystyle T_B}$ and ${\displaystyle {\rho }_B}$ are the temperature and density of the baryonic matter, and ${\displaystyle \mathrm{\Lambda }(T)}$ is some function of temperature and fundamental constants. The baryonic density satisfies the above equation ${\displaystyle dP=-\rho gdr}$:

${\displaystyle p_B(r+dr)-p_B(r)=-dr\frac{{\rho }_B(r)G}{r^2}{\int }_0^{r}4\pi r^2{\rho }_M(r)dr.}$

The integral is a measure of the total mass of the cluster, with ${\displaystyle r}$ being the proper distance to the center of the cluster. Using the ideal gas law ${\displaystyle p_B=k{T}_B{\rho }_B/m_B}$ (${\displaystyle k}$ is Boltzmann's constant and ${\displaystyle m_B}$ is a characteristic mass of the baryonic gas particles) and rearranging, we arrive at

${\displaystyle \frac{d}{dr}\left(\frac{k{T}_B(r){\rho }_B(r)}{m_B}\right)=-\frac{{\rho }_B(r)G}{r^2}{\int }_0^{r}4\pi r^2{\rho }_M(r)dr.}$

Multiplying by ${\displaystyle r^2/{\rho }_B(r)}$ and differentiating with respect to ${\displaystyle r}$ yields

${\displaystyle \frac{d}{dr}\left[\frac{r^2}{{\rho }_B(r)}\frac{d}{dr}\left(\frac{k{T}_B(r){\rho }_B(r)}{m_B}\right)\right]=-4\pi G{r}^2{\rho }_M(r).}$

If we make the assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density ${\displaystyle {\rho }_D={\rho }_M-{\rho }_B}$ satisfies the non-linear differential equation

${\displaystyle \frac{d}{dr}\left[\frac{r^2}{{\rho }_D(r)}\frac{d}{dr}\left(\frac{k{T}_D(r){\rho }_D(r)}{m_D}\right)\right]=-4\pi G{r}^2{\rho }_M(r).}$

With perfect X-ray and distance data, we could calculate the baryon density at each point in the cluster and thus the dark matter density. We could then calculate the velocity dispersion ${\displaystyle {\sigma }_D^2}$ of the dark matter, which is given by

${\displaystyle {\sigma }_D^2=\frac{k{T}_D}{m_D}.}$

The central density ratio ${\displaystyle {\rho }_B(0)/{\rho }_M(0)}$ is dependent on the redshift ${\displaystyle z}$ of the cluster and is given by

${\displaystyle {\rho }_B(0)/{\rho }_M(0)\propto (1+z{)}^2{\left(\frac{\theta }{s}\right)}^{3/2}}$

where ${\displaystyle \theta }$ is the angular width of the cluster and ${\displaystyle s}$ the proper distance to the cluster. Values for the ratio range from .11 to .14 for various surveys.

Planetary geology

See also: List of gravitationally rounded objects of the Solar System

Further information: Clairaut's theorem (gravity)

The concept of hydrostatic equilibrium has also become important in determining whether an astronomical object is a planet, dwarf planet, or small Solar System body. According to the definition of planet adopted by the International Astronomical Union in 2006, one defining characteristic of planets and dwarf planets is that they are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Such a body will often have the differentiated interior and geology of a world (a planemo), though near-hydrostatic or formerly hydrostatic bodies such as the proto-planet 4 Vesta may also be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly differentiated since their formation. Often the equilibrium shape is an oblate spheroid, as is the case with Earth. However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a scalene ellipsoid. Also, the purported dwarf planet Haumea is scalene due to its rapid rotation, though it may not currently be in equilibrium.

Icy objects were previously believed to need less mass to attain hydrostatic equilibrium than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 396 km, whereas the largest icy object known to have an obviously non-equilibrium shape is the icy moon Proteus at 420 km, and the largest rocky bodies in an obviously non-equilibrium shape are the asteroids Pallas and Vesta at about 520 km. However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus being made of mostly permeable ice and almost no rock. At 1,469 km Iapetus is neither spherical nor ellipsoid. Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge. Some icy bodies may be in equilibrium at least partly due to a subsurface ocean, which is not the definition of equilibrium used by the IAU (gravity overcoming internal rigid-body forces). Even larger bodies deviate from hydrostatic equilibrium, although they are ellipsoidal: examples are Earth's Moon at 3,474 km (mostly rock), and the planet Mercury at 4,880 km (mostly metal).

Solid bodies have irregular surfaces, but local irregularities may be consistent with global equilibrium. For example, the massive base of the tallest mountain on Earth, Mauna Kea, has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium.

Atmospheric modeling

Further information: Atmospheric model

In the atmosphere, the pressure of the air decreases with increasing altitude. This pressure difference causes an upward force called the pressure-gradient force. The force of gravity balances this out, keeping the atmosphere bound to Earth and maintaining pressure differences with altitude.

Gemology

Gemologists use hydrostatic balances to determine the specific gravity of gemstones. A gemologist may compare the specific gravity they observe with a hydrostatic balance with a standardized catalogue of information for gemstones, helping them to narrow down the identity or type of gemstone under examination.

Cannibalism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cannibalism

A slug, Arion vulgaris, eating a dead individual of the same species

Cannibalism is the act of consuming another individual of the same species as food. Cannibalism is a common ecological interaction in the animal kingdom and has been recorded in more than 1,500 species. Human cannibalism is well documented, both in ancient and in recent times.

The rate of cannibalism increases in nutritionally poor environments as individuals turn to members of their own species as an additional food source. Cannibalism regulates population numbers, whereby resources such as food, shelter and territory become more readily available with the decrease of potential competition. Although it may benefit the individual, it has been shown that the presence of cannibalism decreases the expected survival rate of the whole population and increases the risk of consuming a relative. Other negative effects may include the increased risk of pathogen transmission as the encounter rate of hosts increases. Cannibalism, however, does not—as once believed—occur only as a result of extreme food shortage or of artificial/unnatural conditions, but may also occur under natural conditions in a variety of species.

Cannibalism is prevalent in aquatic ecosystems, in which up to approximately 90% of the organisms engage in cannibalistic activity at some point in their life-cycle. Cannibalism is not restricted to carnivorous species: it also occurs in herbivores and in detritivores. Sexual cannibalism normally involves the consumption of the male by the female individual before, during or after copulation. Other forms of cannibalism include size-structured cannibalism and intrauterine cannibalism.

Behavioral, physiological and morphological adaptations have evolved to decrease the rate of cannibalism in individual species.

Benefits

In environments where food availability is constrained, individuals can receive extra nutrition and energy if they use members of their own species, also known as conspecifics, as an additional food source. This would, in turn, increase the survival rate of the cannibal and thus provide an evolutionary advantage in environments where food is scarce. For example, female Fletcher's frogs lay their eggs in ephemeral pools that lack food resources. Therefore, in order to survive, tadpoles within the same clutch are forced to consume each other and exploit their conspecifics as the only available source of nutrition. A study conducted on another amphibian, the wood frog, tadpoles showed that those that exhibited cannibalistic tendencies had faster growth rates and higher fitness levels than non-cannibals. An increase of size and growth would give them the added benefit of protection from potential predators such as other cannibals and give them an advantage when competing for resources.

The nutritional benefits of cannibalism may allow for the more efficient conversion of a conspecific diet into reusable resources than a fully herbaceous diet; as herbaceous diets may consist of excess elements which the animal has to expend energy to get rid of. This facilitates for faster development; however, a trade-off may occur as there may be less time to ingest these acquired resources. Studies have shown that there is a noticeable size difference between animals fed on a high conspecific diet which were smaller compared to those fed on a low conspecific diet. Hence, individual fitness could only be increased if the balance between developmental rate and size is balanced out, with studies showing that this is achieved in low conspecific diets.

Cannibalism regulates population numbers and benefits the cannibalistic individual and its kin as resources such as extra shelter, territory and food are freed, thereby increasing the fitness of the cannibal by lowering crowding effects. However, this is only the case if the cannibal recognizes its own kin as this won't hinder any future chances of perpetuating its genes in future generations. The elimination of competition can also increase mating opportunities, allowing further spread of an individual's genes.

Costs

Animals which have diets consisting of predominantly conspecific prey expose themselves to a greater risk of injury and expend more energy foraging for suitable prey as compared to non-cannibalistic species.

Predators often target younger or more vulnerable prey. However, the time necessitated by such selective predation could result in a failure to meet the predator's self-set nutritional requirements. In addition, the consumption of conspecific prey may also involve the ingestion of defense compounds and hormones, which have the capacity to impact the developmental growth of the cannibal's offspring. Hence, predators normally partake in a cannibalistic diet in conditions where alternative food sources are absent or not as readily available.

Failure to recognize kin prey is also a disadvantage, provided cannibals target and consume younger individuals. For example, a male stickleback fish may often mistake their own "eggs" for their competitor's eggs, and hence would inadvertently eliminate some of its own genes from the available gene pool. Kin recognition has been observed in tadpoles of the spadefoot toad, whereby cannibalistic tadpoles of the same clutch tended to avoid consuming and harming siblings, while eating other non-siblings.

The act of cannibalism may also facilitate trophic disease transmission within a population, though cannibalistically spread pathogens and parasites generally employ alternative modes of infection.

Diseases transmitted through cannibalism

Cannibalism can potentially reduce the prevalence of parasites in the population by decreasing the number of susceptible hosts and indirectly killing the parasite in the host. It has been shown in some studies that the risk of encountering an infected victim increases when there is a higher cannibalism rate, though this risk drops as the number of available hosts decreases. However, this is only the case if the risk of disease transmission is low. Cannibalism is an ineffective method of disease spread as cannibalism in the animal kingdom is normally a one-on-one interaction, and the spread of disease requires group cannibalism; thereby it is rare for a disease to have evolved to rely solely on cannibalism to spread. Usually there are different means of transmission, such as with direct contact, maternal transmission, coprophagy, and necrophagy with different species. Infected individuals are more likely to be consumed than non-infected individuals, thus some research has suggested that the spread of disease may be a limiting factor to the prevalence of cannibalism in the population.

Some examples of diseases transmitted by cannibalism in mammals include Kuru which is a prion disease that degenerates the brain. This disease was prevalent in Papua New Guinea where tribes practiced endocannibalism in cannibalistic funeral rituals and consume the brains infected by these prions. It is a cerebellar dysfunctional disease which has symptoms including a broad-based gait and decreased motor activity control; however, the disease has a long incubation period and symptoms may not appear until years later.

Bovine spongiform encephalopathy, or mad cow disease is another prion disease which is usually caused by feeding contaminated bovine tissue to other cattle. It is a neurodegenerative disease and could be spread to humans if the individual were to consume contaminated beef. The spread of parasites such as nematodes may also be facilitated by cannibalism as eggs from these parasites are transferred more easily from one host to another.

Other forms of diseases include sarcocystis and iridovirus in reptiles and amphibians; granulosus virus, chagas disease, and microsporidia in insects; stained prawn disease, white pot syndrome, helminthes and tapeworms in crustaceans and fish.

Foraging dynamics

Cannibalism may become apparent when direct competition for limited resources forces individuals to use other conspecific individuals as an additional resource to maintain their metabolic rates. Hunger drives individuals to increase their foraging rates, which in turn decreases their attack threshold and tolerance to other conspecific individuals. As resources dwindle, individuals are forced to change their behaviour which may lead to animal migration, confrontation, or cannibalism.

Cannibalism rates increase with increasing population density as it becomes more advantageous to prey on conspecific organisms than to forage in the environment. This is because the encounter rate between predator and prey increases, making cannibalism more convenient and beneficial than foraging within the environment. Over time, the dynamics within the population change as those with cannibalistic tendencies may receive additional nutritional benefits and increase the size ratio of predator to prey. The presence of smaller prey, or prey which are at a vulnerable stage of their life cycle, increases the chances of cannibalism occurring due to the reduced risk of injury. A feedback loop occurs when increasing rates of cannibalism decreases population densities, leading to an increased abundance of alternative food sources; making it more beneficial to forage within the environment than for cannibalism to occur. When population numbers and foraging rates increase, the carrying capacity for that resource in the area may be reached, thus forcing individuals to look for other resources such as conspecific prey.

Sexual cannibalism

Main article: Sexual cannibalism

Sexual cannibalism is present largely in spiders and other invertebrates, including gastropods. This refers to the killing and consumption of conspecific sexual partners during courtship, and during or after copulation. Normally, it is the female which consumes the conspecific male organism, though there have been some reported cases of the male consuming the adult female, however, this has only been recorded under laboratory conditions. Sexual cannibalism has been recorded in the female redback spider, black widow spider, praying mantis, and scorpion, among others.

In most species of spiders, the consumption of the male individual occurs before copulation and the male fails to transfer his sperm into the female. This may be due to mistaken identity such as in the case of the orb weaving spider which holds little tolerance to any spider which is present in its web and may mistake the vibrations for those of a prey item. Other reasons for male consumption before mating may include female choice and the nutritional advantages of cannibalism. The size of the male spider may play a part in determining its reproductive success as smaller males are less likely to be consumed during pre-copulation; however, larger males may be able to prevent the smaller ones from gaining access to the female. There exists a conflict of interest between males and females, as females may be more inclined to turn to cannibalism as a source of nutritional intake while the male's interest is mostly focused on ensuring paternity of the future generations. It was found that cannibalistic females produced offspring with greater survival rates than non-cannibalistic females, as cannibals produced greater clutches and larger egg sizes. Hence, species such as the male dark fishing spider of the family Dolomedes self-sacrifice and spontaneously die during copulation to facilitate their own consumption by the female, thereby increasing the chance of survivorship of future offspring.

Sexual dimorphism has been theorised to have arisen from sexual selection as smaller males were captured more easily than larger males; however, it is also possible that sexual cannibalism only occurs due to the difference in size between male and females. Data comparing female and male spider body length shows that there is little support for the prior theory as there is not much correlation between body size and the presence of sexual cannibalism. Not all species of spiders which partake in sexual cannibalism exhibit size dimorphism.

The avoidance of sexual cannibalism is present in males of certain species to increase their rate of survival, whereby the male uses cautionary methods to lower the risk of his consumption. Male orb weaving spiders would often wait for females to moult or to finish eating before attempting to initiate mating, as the females are less likely to attack. Males which are vulnerable to post-copulation consumption may gather mating thread to generate a mechanical tension which they could use to spring away after insemination, while other spiders such as the crab spider may tangle the female's legs in webs to reduce the risk of the female capturing him. Male choice is common in mantids whereby males were observed to choose fatter females due to the reduced risk of attack and were more hesitant to approach starved females.

Size-structured cannibalism

Nematode of the order Mononchida eating another Mononchid

Size-structured cannibalism is cannibalism in which older, larger, more mature individuals consume smaller, younger conspecifics. In size-structured populations, (where populations are made of individuals of various sizes, ages, and maturities), cannibalism can be responsible for 8% (Belding's ground squirrel) to 95% (dragonfly larvae) of the total mortality, making it a significant and important factor for population and community dynamics.

Size-structured cannibalism has commonly been observed in the wild for a variety of taxa. Vertebrate examples include chimpanzees, where groups of adult males have been observed to attack and consume infants.

Filial cannibalism

Main article: Filial cannibalism

Filial cannibalism is a specific type of size-structured cannibalism in which adults eat their own offspring. Although most often thought of as parents eating live young, filial cannibalism includes parental consumption of stillborn infants and miscarried fetuses as well as infertile and still-incubating eggs. Vertebrate examples include pigs, where savaging accounts for a sizable percentage of total piglet deaths, and cats.

Filial cannibalism is particularly common in teleost fishes, appearing in at least seventeen different families of teleosts. Within this diverse group of fish, there have been many, variable explanations of the possible adaptive value of filial cannibalism. One of these is the energy-based hypothesis, which suggests that fish eat their offspring when they are low on energy as an investment in future reproductive success. This has been supported by experimental evidence, showing that male three-spined sticklebacks, male tessellated darters, and male sphinx blenny fish all consume or absorb their own eggs to maintain their physical conditions. In other words, when males of a fish species are low on energy, it might sometimes be beneficial for them to feed on their own offspring to survive and invest in future reproductive success.

Another hypothesis as to the adaptive value of filial cannibalism in teleosts is that it increases density-dependent egg survivorship. In other words, filial cannibalism simply increases overall reproductive success by helping the other eggs make it to maturity by thinning out the numbers. Possible explanations as to why this is so include increasing oxygen availability to the remaining eggs, the negative effects of accumulating embryo waste, and predation.

In some species of eusocial wasps, such as Polistes chinensis, the reproducing female will kill and feed younger larvae to her older brood. This occurs under food stressed conditions in order to ensure that the first generation of workers emerges without delay. Further evidence also suggests that occasionally filial cannibalism might occur as a by-product of cuckoldry in fish. Males consume broods, which may include their own offspring, when they believe a certain percentage of the brood contains genetic material that is not theirs.

It is not always the parent that cannibalizes the offspring; in some spiders, mothers have been observed to feed themselves to their brood as the ultimate provision from mother to children, known as matriphagy.

The dinosaur Coelophysis was once suspected to practice this form of cannibalism but this turned out to be wrong, although Deinonychus may have done so. Skeletal remains from subadults with missing parts are suspected of having been eaten by other Deinonychus, mainly full-grown adults.

Infanticide

Main article: Infanticide (zoology)

Infanticide is the killing of a non-adult animal by an adult of the same species. Infanticide is often accompanied by cannibalism. It is often displayed in lions; a male lion encroaching on the territory of a rival pride will often kill any existing cubs fathered by other males; this brings the lionesses into heat more quickly, enabling the invading lion to sire his own young. This is an example of cannibalistic behaviour in a genetic context.

In many species of Lepidoptera, such as Cupido minimus and the Indian mealmoth, the first larvae to hatch will consume the other eggs or smaller larvae on the host plant, decreasing competition.

Intrauterine cannibalism

Further information: Oophagy

Intrauterine cannibalism is a behaviour in some carnivorous species, in which multiple embryos are created at impregnation, but only one or two are born. The larger or stronger ones consume their less-developed siblings as a source of nutrients.

In adelphophagy or embryophagy, the fetus eats sibling embryos, while in oophagy it feeds on eggs.

Adelphophagy occurs in some marine gastropods (calyptraeids, muricids, vermetids, and buccinids) and in some marine annelids (Boccardia proboscidia in Spionidae).

Intrauterine cannibalism is known to occur in lamnoid sharks such as the sand tiger shark, and in the fire salamander, as well as in some teleost fishes. The Carboniferous period chimaera, Delphyodontos dacriformes, is suspected of having practiced intrauterine cannibalism, also, due to the sharp teeth of the recently born (or possibly aborted) juveniles, and the presence of fecal matter in the juveniles' intestines.

Protection against cannibalism

Animals have evolved protection to prevent and deter potential predators such as those from their own kind. Many amphibian eggs are gelatinous and toxic to decrease edibility. Often, adults would lay their eggs in crevices, holes, or empty nesting sites to hide their eggs from potential conspecific predators which tend to ingest the eggs for an additional nutritional benefit or to get rid of genetic competition. In amphibians, the development of non-aquatic egg deposition has helped increase the survival rates of their young by the evolution of viviparity or direct development. In bees, worker policing occurs to prohibit worker reproduction, whereby workers cannibalize other worker laid eggs. Queen laid eggs have a different scent than worker laid eggs, allowing workers to differentiate between the two, allowing them to nurture and protect queen laid eggs rather than cannibalising them. Parental presence at nesting sites is also a common method of protection against infanticide committed by conspecific individuals, whereby the parent exhibits defensive displays to ward off potential predators. Parental investment in newborns are generally higher during their early stages of development whereby behaviours such as aggression, territorial behaviour, and pregnancy blocking become more apparent.

Morphological plasticity helps an individual account for different predation stresses, thereby increasing individual survival rates. Japanese brown frog tadpoles have been shown to exhibit morphological plasticity when they are in a high stress environment where cannibalism between tadpoles and more developed individuals were present. Shifting their morphology plays a key role in their survival, creating bulkier bodies when put into environments where more developed tadpoles were present, to make it difficult for the individuals to swallow them whole. Diet shifts between different stages of development have also evolved to decrease competition between each stage, thereby increasing the amount of food availability so that there is a decreased chance that the individuals will turn to cannibalism as an additional food source.

Cannibalism in the media

Cannibalism has been a subject for horror movies since the 1980s. This genre is called cannibal films. In Planet Dinosaur it shows two Majungasaurus fighting to eat each other.

Cannibalism has also been a subject of video games. More recently, cannibalism has been featured in a positive light, with video games like Ark: Survival Evolved incentivizing players' virtual characters to eat each other.