Unlimited growth, carrying capacity, and limited growth

1. Unlimited growth, carrying capacity, and limited growth

2. 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

3. 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.

4. St. Matthew Island, Alaska

5. 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

6. 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.

7. 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.

8. 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.

9. Natural mortality was assessed from skeletons

10. Physical condition was assessed from animals shot during fieldwork

11. Physical condition was assessed from animals shot during fieldwork

12. Physical condition was assessed from animals shot during fieldwork

13. 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

14. 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

15. 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”.

16. 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.”

17. 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.”

18. 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.

19. 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.

20. Sex and age composition of the die-off

21. Compare natural mortality (1957) with crash die-off (1966)

22. 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

23. 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.

24. 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.

25. 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.

26. 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

27. 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.

28. 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?

29. 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?

30. 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?

31. 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.