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Models of population growth • This is the simplest model of population growth for species with discrete breeding seasons. • In this model, there is no competition, and population dynamics are governed solely by the net reproductive rate, R. • If R > 1, the population increases indefinitely and exponentially. Nt+1 = NtR Or Nt = N0Rt
Models of population growth: incorporating competition • Graphically, we can see that the population increases exponentially when Nt is very low. • But the rate of increase declines as population size rises. • At carrying capacity, the growth rate is zero. • Above carrying capacity, the population will decline. • K is therefore a stable equilibrium.
Reindeer on St. Matthew Island, Alaska • In 1944, 29 reindeer introduced to St. Matthew Island (300 km2) • Approximate initial density 0.1/km2 • 24 females, 5 males, all 2 years old
Reindeer on St. Matthew Island, Alaska • R. Rausch visited the island in 1954, and on the basis of counts, estimated the population size at 400-500. • C.J. Rhode visited the island in 1955, and estimated the population size at 700-900.
Reindeer on St. Matthew Island, Alaska • David Klein visited the island in 1957, and made a total count of 1,350 animals. • This implies an average annual growth rate of 34 percent. • Klein assumed that the population growth rate earlier in the explosion must have been near the theoretical maximum for the species.
Reindeer on St. Matthew Island, Alaska • Population growth during this period looks like unlimited growth. • Klein recognized the potential importance of this study during his 1957 visit.
At a density of 4.5 inds./km2, the animals were in excellent condition • Noticeable, extensive fat deposition, especially on large males • Weights of all reindeer collected exceeded the average weight range for other Alaskan reindeer • No external parasites noted • Very large and uniform antler growth on males and females
What contributed to the unlimited growth and excellent condition of reindeer on St. Matthew Island? • Abundant winter and summer forage • No competitors • No large predators • No large herbivores had been there previously • But Klein sensed there was trouble on the horizon
Signs that limits to population growth were imminent in 1957 • Lichen beds were showing signs of fracturing due to overgrazing and trampling (winter range) • Prostrate willows were also showing signs of heavy browsing (summer range) • Calf percentage of 26% was “below the indicated level of previous years” • Klein concluded/warned that “the population decline may be rapid after the peak is reached”.
What happened next: • Klein revisited the island in 1963 and surveyed it with 2 Coast Guard helicopters. • “As their boots hit the shore, they saw reindeer tracks, reindeer droppings, bent-over willows, and reindeer after reindeer.” – Ned Rozell, Alaska Science Forum • The survey revealed the population had increased to 6000 • Calf percentage was lower than in 1957 • Recruitment was down from 29% in 1957 to 17% in 1963 • “There was ample evidence of overpopulation, and the stage was apparently set for wholesale die-off.”
What happened next: • May 1964: an aerial survey of the island located no reindeer. “We were unaware, of course, that a die-off had already taken place.”
The introduction, increase, and crash of reindeer on St. Matthew Island Klein, D.R. 1968. J. Wildl. Manage. 32:350-367. • Upon returning in 1966, Klein found only 42 reindeer; • Of these, 1 male; the rest were females 2yrs old and older • No calves or yearlings, indicating the crash die-off probably occurred in late winter 1964.
What caused the crash die-off? • Extremely high density (20/km2) • Unusually harsh winter in 1963-64 (exceptionally cold, with unusually deep snow) • Long bones of examined skeletons contained no marrow fat, indicating starvation • Many skeletal remains were found in groups, suggesting the animals died over a very short period. • By the mid 1980s, there were 0 reindeer on the island.
Physical characteristics of the animals in 1957 and 1963: • Avg body weight declined by 38% for adult females and by 43% for adult males • Not only were they smaller just before the crash, regressions between body weight and skeletal parameters indicated growth rates were lower in 1963 • Lichens had been completely eliminated as a significant component of the winter diet
Carrying capacity • Klein (1968) suggested that forage quantity primarily governs population size, while quality determines the size of the individual. • The winter component governs the upper limit of the population, and the summer component determines the stature of the individual.
Klein (1968) attributed the large-scale die-off to the following factors: • Overgrazing of lichens, with no possibility of the reindeer expanding into alternative range; • Excessive density of reindeer competing for a very restricted winter resource; • Relatively poor condition of reindeer going into the winter of 1963, resulting from intense competition; • Extreme weather conditions, primarily deep snow, during the winter of 1963-64.
Intraspecific competition and carrying capacity • Competition may be defined as (Begon et al. 1984): An interaction between individuals, brought about by a shared requirement for a resource in limited supply, and leading to a reduction in the survivorship, growth, and/or reproduction of the competing individuals.
Effects of competition on individuals • Increased energy expenditure (searching for the unexploited resource), increased risk of mortality, and decreased rate of food intake may all decrease individual’s chances of survival
Effects of competition on individuals • Increased energy expenditure and decreased food intake may leave less energy available for development and less available for reproduction. • Increases in density will therefore decrease the contribution made by each individual to the next generation.
Common features of intraspecific competition • The ultimate effect of competition is a decreased contribution to the next generation; • Intraspecific competition leads to decreased rates of resource intake per individual, decreased rates of individual growth or development, or to decreases in the amounts of stored reserves; • These may lead to decreases in survival and/or fecundity. • Evidence from St. Matthew Island?
Common features of intraspecific competition • The resource for which individuals compete must be in limited supply • Competing individuals might or might not interact directly; • Exploitation competition occurs when individuals remove an item needed by others; • Interference competition occurs when individuals interact directly and prevent others from occupying a portion of habitat and exploiting its resources; • Which type presumably occurred on St. Matthew Island?
Common features of intraspecific competition • The competing individuals are in essence equivalent, but in practice they are not • “One-sided reciprocity” or “Asymmetric competition”; • The effects of competition are not the same on all individuals in the population; • Evidence of asymmetry on St. Matthew Island?
Common features of intraspecific competition • The likely effect of competition on any individual is greater the more competitors there are. • The effects of intraspecific competition are thus said to be density dependent.