# Predation relationship definition math

### Predator–Prey Relationships | gtfd.info

The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of in by Vito Volterra, a mathematician and physicist, who had become interested in mathematical biology. . yields the implicit relationship. V = δ x. Lotka-Volterra models of Predator-Prey Relationships. Author: Tyler As with many other mathematical models, many assumptions were . Further Examples. Predator-prey relationships are essential to maintaining the balance of organisms in an ecosystem. Examples of predator-prey relationships.

The African wild dog is an extreme persistence predator, tiring out individual prey by following them for many miles at relatively low speed, compared for example to the cheetah 's brief high-speed pursuit. These very large marine predators feed on planktonespecially krilldiving and actively swimming into concentrations of plankton, and then taking a huge gulp of water and filtering it through their feathery baleen plates. Osprey tears its fish prey apart, avoiding dangers such as sharp spines.

Once the predator has captured the prey, it has to handle it: Some catfish such as the Ictaluridae have spines on the back dorsal and belly pectoral which lock in the erect position; as the catfish thrashes about when captured, these could pierce the predator's mouth, possibly fatally.

Some fish-eating birds like the osprey avoid the danger of spines by tearing up their prey before eating it. Cooperative hunting In social predation, a group of predators cooperates to kill prey.

## Predator–Prey Relationships

This makes it possible to kill creatures larger than those they could overpower singly; for example, hyenasand wolves collaborate to catch and kill herbivores as large as buffalo, and lions even hunt elephants.

For example, when mixed flocks of birds forage, the birds in front flush out insects that are caught by the birds behind. Spinner dolphins form a circle around a school of fish and move inwards, concentrating the fish by a factor of Predators of different species sometimes cooperate to catch prey. In coral reefswhen fish such as the grouper and coral trout spot prey that is inaccessible to them, they signal to giant moray eelsNapoleon wrasses or octopuses.

These predators are able to access small crevices and flush out the prey. Solitary predators have more chance of eating what they catch, at the price of increased expenditure of energy to catch it, and increased risk that the prey will escape.

These include speed, agility, stealth, sharp senses, claws, teeth, filters, and suitable digestive systems. Many predators have acute hearing, and some such as echolocating bats hunt exclusively by active or passive use of sound. Some predators such as snakes and fish-eating birds like herons and cormorants swallow their prey whole; some snakes can unhinge their jaws to allow them to swallow large prey, while fish-eating birds have long spear-like beaks that they use to stab and grip fast-moving and slippery prey.

Lions can attack much larger prey, including elephants, but do so much less often. Predators are often highly specialized in their diet and hunting behaviour; for example, the Eurasian lynx only hunts small ungulates. When prey have a clumped uneven distribution, the optimal strategy for the predator is predicted to be more specialized as the prey are more conspicuous and can be found more quickly; [78] this appears to be correct for predators of immobile prey, but is doubtful with mobile prey.

This has led to a correlation between the size of predators and their prey. Size may also act as a refuge for large prey. For example, adult elephants are relatively safe from predation by lions, but juveniles are vulnerable. Members of the cat family such as the snow leopard treeless highlandstiger grassy plains, reed swampsocelot forestfishing cat waterside thicketsand lion open plains are camouflaged with coloration and disruptive patterns suiting their habitats.

Female Photuris firefliesfor example, copy the light signals of other species, thereby attracting male fireflies, which they capture and eat. Venom and Evolution of snake venom Many smaller predators such as the box jellyfish use venom to subdue their prey, [86] and venom can also aid in digestion as is the case for rattlesnakes and some spiders.

Cattle that graze on grass are not considered a predator-prey relationship, as only a portion of the grass is eaten, with the intact roots permitting re-growth of the grassy stalk to occur. A predator and its prey can both be microscopic, as is the case with the bacterium Bdellovibrio and other Gram-negative bacteria.

But, the size difference between predator and its prey can be immense. Predator-prey relationships can be more complex than a simple one-to-one relationship, because a species that is the predator or the prey in one circumstance can be the opposite in a relationship with different species.

For example, birds such as the blue jay that prey on insects can become the prey for snakes, and the predatory snakes can be the prey of birds such as hawks.

This pattern is known as a hierarchy or a food chain. The hierarchy does not go on indefinitely, and ends at what is described as the top of the food chain. For example, in some ocean ecosystems, sharks are at the pinnacle of the food chain. Other than humans, such so-called apex predators are not prey to any other species.

This relationship applies only to the particular ecosystem that the apex predator is in. If transferred to a different ecosystem, an apex predator could become prey. For example, the wolf, which is at the top of the food chain in northern forests and tundra environments, could become the prey of lions and crocodiles if it were present in an African ecosystem. Predator-prey relationships involve detection of the prey, pursuit and capture of the prey, and feeding.

Adaptations such as camouflage can make a prey species better able to avoid detection.

By blending into the background foliage or landscape and remaining motionless, an insect or animal offers no visual cue to a predator since it mimics its surroundings. There are many examples of mimicry in predator-prey relationships.

Some moths have markings on their outer wings that resemble the eyes of an owl or that make the creature look larger in size. Insects popularly known as walking sticks appear similar to the twigs of the plants they inhabit.

Another insect species called the praying mantis appears leaflike. The vertical stripes cause individual zebras in a herd to blend together when viewed for a distance. To a predator like a lion, the huge shape is not recognized as a potential source of food. Camouflage can also be a strategy used by a predator to avoid detection by prey. An example is the polar bearwhose white color blends in with snow, reducing the likelihood that the bear will be detected as it approaches its prey.

In this case, the same strategy and color can be utilized by young seals, since their color allows them to be invisible as they lie on the snowy surface. The community of individuals and the physical components of the environment in a certain area. A sequence of organisms, each of which uses the next lower member of the sequence as a food source.

An interconnected set of all the food chains in the same ecosystem.

### Lotka–Volterra equations - Wikipedia

The natural location of an organism or a population. Factors that influence the evolution of an organism.

An example is the overuse of antibiotics, which provides a selection pressure for the development of antibiotic resistance in bacteria. The opposite of camouflage can occur. A prey can be vividly colored or have a pattern that is similar to another species that is poisonous or otherwise undesirable to the predator. A successful predator must judge when pursuit of a prey is worth continuing and when to abandon the chase.

This is because the pursuit requires energy. A predator that continually pursues prey without a successful kill will soon become exhausted and will be in danger of starvation.

Predatory species such as lions are typically inactive during the hot daytime hours, when prey is often also resting, but become active and hunt at night when conditions are less energy taxing and prey is more available. Similarly, bats emerge at night to engage in their sonar-assisted location of insects that have also emerged into the air.

When supplied with food in a setting such as a zoo, predators will adopt a sedentary lifestyle. Predation is an energy-consuming activity that is typically done only when the creature is hungry or to supply food for offspring. In settings such as an aquarium, predators and prey will even co-exist.

Being a prey does not imply that the creature is completely helpless. The prey may escape from the predator by strategies such as mimicry, or can simply outrun or hide from the predator. Some species act coordinately to repel a predator.

For example, a flock of birds may collectively turn on a predator such as a larger bird or an animal such as a cat or dog to drive off the predator. This mobbing type of repulsion can be highly orchestrated.

As well, some bird species use different calls, which are thought to be a specific signal to other birds in the vicinity to join the attack. Even birds of a different species may respond to such a call. The fluctuation in the numbers of a predator species and its prey that occurs over time represents a phenomenon that is known as population dynamics.

The dynamics can be modeled mathematically. The results show that a sharp increase in the numbers of a prey species an example could be a rabbit is followed soon thereafter by a smaller increase in numbers of the relevant predator in this case the example could be the fox. As the prey population decreases due to predator killing, the food available for the predators is less, and so their numbers subsequently decline.

With the predator pressure reduced, the numbers of the prey can increase once again and the cycle goes on. The result is a cyclical rising and falling of the numbers of the prey population, with a slightly later cyclical pattern of the predator.

### Predation & herbivory (article) | Ecology | Khan Academy

A famous predator-prey model is the Lotka-Volterra version. The two equations were formulated in the mids by Italian mathematician Vito Volterra — to explain the decline in a fish population observed in the Adriatic Sea during World War I — At the same time, American mathematician Alfred Lotka — was using the equations to explain the behavior of some chemical reactions.

Their efforts were recognized as the Lotka-Volterra model, which represents one of the first examples of ecological modeling. Other examples include the Kermack-McKendrick model and the Jacob-Monod model used to model predation of one bacterial species on another.