Predation Models- introduction & problems

Note: on the bottome there are the 2 problems to be solved before your next exam

Classical Models of Predation:

1. Lets start out with one of the simplest population models ( dN/dT = rN; exponential growth) and build a starter model of predator-prey dynamics.
  • As predation can only occur when a predator actually encounters a prey we must include both the number of prey (N) and predators (C),

    and as not every encounter results in an attack we must estimate an attack rate ( a') which approximates the proportion of times that an encounter results in an actual successful attack.

  • Then the change in the number of prey would be a function of:

    dprey/dt = r*N - [a'CN] or in words.... the growth rate * then number of prey at that time minus the attack rate * number of predators (C) * of prey (N). When you use your logic here, even if you have a lot of prey or predators alone you will not get many attacks. Only when both are in moderate to high densities will many prey be killed off ( akin to atoms meeting in a gas.. then can only react in proportion to their numbers)

    2. The change in the number of predators is a function of:

    dC/dt = f[a'CN] -qC'

  • where f = food conversion of actual prey caught [ a"*C*N] into offspring of predator ( how many rabbits equals the successful rearing of one bobcat?) and

    we account for the natural death of the predators themselves: q = mortality rate of predator - as they must die not only due to lack of food but for other reason.

  • At equilibrium, both dN/dt and dC/dt are equal to 0; (there is no change in number in either population) . We can solve for both equations ( as we did in the competition class) by setting both to 0 to solve for equilibrium population sizes.

    When dN/dt = 0 then rN = a'CN and C ( predator #) = r/a'
    As this relationship is independent of N, r/a' or C remains a constant at least at equilibrium.

    If the actual C is higher than the equilibrium value, then prey (N) will decrease <----- and if the actual C is lower than the equilibrium value, then N will increase.--->

 

When dC/dt = 0 then fa'CN = qC and N ( prey #) = q/ fa'
As this relationship if independent of C, q/fa' or N remains a constant. If N the # of prey is below the equilibrium value (q/fa') then predator number will decrease and the reverse when greater than eq. value.

Use the following isoclines to better visualize this estimation process:


If we overlay the isocline for C at equilibrium and that for N at equilibrium, then we can interpret the graph. As the prey number increase, then predators will also increase. As predators increase, then prey will begin to decrease. As prey decrease, so do predators......
The result is a neutrally stable cycle but not a stable limit cycle. That is, fluctuations in population size will vary.

Building a stronger model:


Although a good start in attempting to simulate predator-prey dynamics, there are several weaknesses in this starter model. How can we strengthen it?

A. Remember from the population growth models, how time lags in ability to recognize current size could crash a population if the lags were too long. Same goes here.... If the predator does not sense decreases in prey size, he may end up eliminating the prey population, and thus his own.
Sensitivity to lag will result in stabilization of both populations.

B. Outside influences:

Role of other species interactionlves roam the woods."Our goal for the recovery includes establishing at least three self-sustaining wild populations, one of which we had hoped would be in the park," said Hamilton.

"Of 28 pups known to be born in the wild and not removed, we don't know of any that have survived their first year, so we no longer expect to achieve the recovery goal in the park," he said.

While the precise cause of the pup mortality is unknown, disease, predation, malnutrition and parasites are suspected to have contributed to their death, said project biologists.

In 1990, the federal agencies selected the park as a potential restoration site because of the large tracts of federal land that make up the park and surrounding national forests.

The red wolf project began in late 1991 with the release of one family group to assess the interactions between red wolves and people, livestock, and coyotes. Results of that initial release showed that restoration was feasible, and biologists subsequently released 37 red wolves from late 1992 through 1996.

While the precise cause of the pup mortality is unknown, disease, predation, malnutrition and parasites are suspected to have contributed to their death, said project biologists.Of the 37 released red wolves, 26 later died or were recaptured after straying onto private lands outside the park. Biologists suspect a scarcity of prey in the steep, heavily forested slopes that make up most of the park's 500,000 acres is the likely reason the wolves strayed.

"Low food availability can cause wolves to wander widely and expand their range," said Hamilton. "The fact that this was the typical response of red wolves when released in the park suggests that it is less preferred habitat when compared to the lower-elevation agricultural land of the surrounding area."

The Fish and Wildlife Service is in the process of relocating the park's six captive red wolves and plans to recapture the remaining four free-ranging red wolves by late fall 1998.

Biologists are analyzing information gathered as part of the restoration project over the last 11 years to aid in the selection of future release sites.

"The selection of the next release site will be a very complex process, a process that must balance biological, logistical, and socio-political factors, all of which can contribute to the success or failure of individual red wolves and, ultimately, to the overall recovery of the species." Hamilton said.

All large federally owned land bases -- 170,000 acres or more -- within the red wolf's historic range are being included in the assessment of potential release sites.

The Fish and Wildlife Service hopes to develop a "short list" of potential areas that offer the greatest biological potential and then further refine the selection process based on the interests, land use, and attitudes of the public surrounding a particular federal site

Home work!! From the Nebraska wild life pages: (http://www.ngpc.state.ne.us/wildlife/coyote.html

DESCRIPTION The coyote's name is derived from the Aztec word "coyotl". It is a member of the dog family (canids) which includes wolves, dogs and foxes, and resembles a small German Shepherd. Adults coyotes weigh an average of 20 to 35 pounds, with males being about 4 pounds heavier than females. Coyotes weighing over 50 pounds are more common in the northern and northeastern portions of their range than elsewhere. An adult coyote is four to five feet long from the tip of its nose to the tip of its tail. In Nebraska, coyote pelts show a great variety of color and texture. Eastern Nebraska coyotes generally have a coarse coat that is brownish gray to buff in color, while coyotes from the Sandhills and Panhandle are much lighter gray with dense, soft underfur. Coyote tracks are more elongated than dog tracks and are about 1 Ih times as long as they are wide. Coyotes have bushy black-tipped tails, broad, pointed, erect ears and yellow eyes. They have relatively large brains, and exceptional senses of smell, sight and hearing. Although coyotes avoid wolves and dogs under normal conditions, they occasionally mate with them and create hybrid offspring that are usually larger than a typical coyote. This usually happens where wolf densities are low or on the edge of the coyote's range.

Distribution and abundance During the early 1800's, coyotes were limited to the Great Plains and western regions of North America. Since then, they have expanded their range north and east. This is primarily the result of the eradication of wolves by humans and the coyote's ability to adapt to various habitats, including living very close to human populations. Coyotes in New England have hybridized with gray wolves and are generally larger than western coyotes. Range expansion in the southeastern United States has been aided by translocation for sport hunting. Coyotes are generally more abundant in the Southwest and Midwest than in other regions of North America In Nebraska, coyotes are more abundant in western Nebraska and the Sandhills, regions where ranching predominates over crop farming. Habitat and home Coyotes are extremely adaptable and live in a wide variety of vegetative types, from grassland to northern boreal forest. Almost any area that supports good populations of small prey will support coyotes. As prey abundance increases, coyote abundance generally increases. Coyotes require a minimum of shelter during most of the year. They usually simply curl up in a concealed, protected spot, though they do use dens for whelping and rearing pups. A coyote seldom digs its own den, instead, it uses natural cavities or modifies abandoned woodchuck or badger dens. The female coyote usually selects several den sites in concealed locations and moves her litter if she is disturbed in one location. Habits The coyote is perhaps the most vocal mammal in Nebraska. Its howling and yipping serves to communicate with family members and to notify neighboring coyotes of its presence in the area. Numerous displays and postures are used to show antagonism, dominance and greetings.

Coyote densities have been reported as high as five animals per square mile in the Southwest United States, but are more likely to be one to two per square mile in Nebraska. Both parents help care for young and may mate for life. Home ranges are usually occupied by mated pairs although the male may move more extensively than the female. Coyotes are known to form packs consisting of the adult pair and young from more than one generation, although this seldom occurs in Nebraska. The size of the coyote's range depends on population density and varies between eight and 12 square miles. Where coyotes are numerous, their home ranges are small. A mated pair defends its home range from adjacent pairs but is somewhat tolerant of unmated transient coyotes that pass through the range. Unmated transient coyotes move great distances and comprise up to 20 percent of the total coyote population. A coyote marks his territory with scent by depositing droppings and urine on the perimeter of the area. Coyotes may be active and observed throughout the day, but are most active at dusk and dawn. The daytime activity increases during breeding and pup rearing. Coyotes hunt in areas where small prey are likely to occur. They rely on sight, smell and sound to locate prey. Rabbits are typically flushed from cover and chased down and mice are usually caught by the coyote pouncing upon them with its front feet.

Foods Coyotes are opportunistic carnivores and take advantage of seasonal changes in the abundance of food items. Rabbits, deer fawns, various plants and assorted birds and invertebrates are important summer food. Their winter diet emphasizes larger prey, such as deer (prey or carrion), livestock carrion, rabbits and hares. Occasionally, an individual coyote learns that sheep, lambs and calves are easy prey.

Reproduction Coyotes reproduce once a year. Pairs are formed and breeding occurs in January-February. Coyotes are capable of breeding at one year of age but do so infrequently. Most are two years old when they breed for the first time. The percentage of females that breed is dependent on food availability and coyote density. Pups are born nine weeks after breeding occurs. The litter size depends on the age of the mother and the amount of available prey in the area. A scarcity of prey results in fewer females breeding and producing smaller litters. There are usually four to seven pups in a litter under average conditions. The pups join parents on hunting trips when they reach eight to 10 weeks of age and they begin to disperse in the fall, but some pups may not leave the family group for up to two years. When a pup leaves the family group it usually relocates within five to 10 miles, but records show some have traveled in excess of 300 miles.

Mortality As many as 50 to 70 percent of all juvenile coyotes die before they reach adulthood. Those that become adults typically live three to five years, and 30 to 50 percent of the adult population dies each year. Under most conditions, human-related causes, including hunting, trapping and vehicle collisions are responsible for most coyote mortality. Coyotes compensate for that heavy harvest by breeding at younger ages and having larger litters. More one-year-old females breed during periods of heavy harvest and their litter size can rise to as many as 17 pups. Sarcoptic mange occurs in coyote populations throughout Nebraska. Mange outbreaks occasionally become severe and can seriously reduce coyote populations over large areas for a number of years. Other important diseases and parasites that effect coyotes include canine distemper, canine hepatitis and heartworm. Surprisingly, rabies is not an important disease in coyotes, although they are susceptible to that disease.

 

Importance Several million dollars worth of livestock losses are annually attributed to coyote depredation nationwide and several million dollars are spent trying to control those losses. In Nebraska, the coyote is among the top three wildlife species that are responsible for depredation complaints. Livestock losses are predominantly for sheep and young calves. Attempts to control losses involve short-term coyote population reduction and the removal of offending individuals by shooting, trapping, or poisoning. Poisoning must be done only by trained professionals. Changes in animal husbandry practices have proven effective in reducing losses to coyotes. As Nebraska's dominant terrestrial predator, coyotes can influence the abundance of their competitors. The abundance of coyotes is inversely related to the abundance of red foxes and bobcats. When coyote numbers increase, fox and bobcat numbers decrease and when coyote numbers decrease, fox and bobcat numbers can increase. The coyote is an extremely cunning animal that provides thousands of days of hunting and trapping recreation each year. From 1941-89, 540,000 coyotes were harvested by fur trappers and hunters. Harvest totals 1980-89 indicated an average annual harvest of 20,900 coyotes, their pelts valued at $521,000.

Coyotes move east, make homes in Virginia...........Wednesday, October 14, 1998

Nancy Jones, on a farm outside of Windsor, Va., spent much of the summer watching coyotes grow, along with the cotton.

They first appeared in the spring, just after the cotton was planted, Jones said. As the plants sprouted, so did the three pups whose parents frolicked with them daily.

"We didn't know what they were at first," said Jones, whose family has lived on the same 156-acre farm since the mid 1930s. "We watched them through the kitchen window with binoculars. They didn't bother us, so we didn't bother them. It was kind of fun watching them."

Coyotes have been anything but fun for Gates County, N.C., resident Harry Tyler, who lives about six miles south of the Suffolk border.

"They're here, all right," said Tyler. "They're scroungy-looking things. Coyotes have eaten just about all my chickens. I can't keep biddies. The last thing I lost was a grown goose."

Mangy nuisances or intriguing visitors, coyotes are moving into the western reaches of Hampton Roads. They're in Isle of Wight, they've been spotted in Suffolk, and they're frequently seen in Gates County.

It's part of the animals' migration east, said Glenn Askins, regional wildlife biologist with the state Department of Game and Inland Fisheries. With natural predators, like wolves, mostly gone in this state, coyotes are expanding their habitat.

"They're extremely adaptive," he said. "They live very well close to people."

The first time Nancy Jones and her husband saw the animals, they thought it was a family of foxes. They knew that was wrong when their dog started barking, she said, and the older animals barked back.

"Some nights, after dark, we'd go out and just listen for them," Jones said.

And there's no mistaking a coyote's howl, Askins said.

"It's kind of a yodel, a high whistle," he said. "If they're trying to pack up, one will yodel, and another will yodel back."

Jones hopes to see more of her coyote family once the cotton is harvested, but other local farmers aren't so welcoming.

"They look like skinny, long-legged, mangy dogs," said William A. Gwaltney, another farmer in the Windsor area. "If you're working in a field on a tractor, they'll hang out at the edge of the field. But if you walk toward them, they'll run."

Local game warden Jerry Barwick said he's heard about coyote sightings in Isle of Wight for a couple of years. So far, they don't seem to have created as much of a nuisance locally as they have in the western part of the state, where coyotes are notorious for killing livestock.

Coyotes, natives of the U.S. plains, probably moved into Virginia sometime in the early 1980s, Askins said. The first hint came from road kill and hunters' reports.

"They're pretty much statewide now," he said. "People are beginning to see them, and they're likely to see a lot more."

An adult coyote weighs about 30 to 35 pounds and can be anywhere from brown to light gray to reddish in color. Jones said her resident coyotes are a kind of buff color, with long, bushy tails tipped in black.

The howl, the bushy tail and pointed ears -- along with piercing yellow eyes -- are ways to tell a coyote from a fox or a stray dog, wildlife officials say.

As on the Jones farm, both parents help to raise the young. Litters vary in size from about five pups to as many as 18. The size of the litter and the frequency of mating often has to do with the availability of food. Like wolves, coyotes usually mate for life, and it isn't unusual for the young from one litter to see their younger brothers and sisters grow up.

Coyotes are adaptive to almost any environment, said Martin Lowney, state director of the USDA department of wildlife services.
"They're good survivors because they will eat anything," Lowney said. "Grasshoppers, blueberries, fruits and vegetables, garbage, watermelon and cantaloupe.
"They could become a problem for melon growers. They'll bite each one until they find one that's ripe. People will just have to adapt."
Cousin to the wolf and domestic dog, coyotes are wary and intelligent, with a keen sense of smell and an insatiable curiosity.
They're likely in Suffolk, especially in the southern end of the city, near the North Carolina line, Whaleyville residents say. Although the coyote population is not one that's counted in the Great Dismal Swamp, dead coyotes have been found on the outskirts of the swamp, a spokesperson for the wildlife refuge said.
In attacks, coyotes typically bite the throat just behind the jaw.
Mike Poston, a member of the Gates County Hunt Club, killed one two years ago while deer hunting and had the pelt made into a rug.

"Every time we see them, we try to kill them," Poston said. "They're considered a nuisance animal. They're tough on livestock down here."Coyotes are not protected by game regulations in either Virginia or North Carolina. And coyotes aren't necessarily a threat to humans. Rabies isn't a prominent disease in the breed, wildlife officials say."As far as personal health and safety, they're nothing to worry about," Lowney said. "But people who own cats might want to be a little cautious. Coyotes eat them. Cats and small dogs. If you start to see chewed up ears and bitten off tails, it could be coyotes."

Copyright 1998, Norfolk Virginian-Pilot