WLF 448: Fish & Wildlife Population Ecology

Fall 2006

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IX. POPULATION GROWTH IN LIMITED ENVIRONMENTS (Limitgro.cpl, Sustainable Harvest of Sage-grouse.ppt, Himalayn.cpl)

A. Introduction

1. General features of logistic growth

• In the beginning, population growth in nearly exponential, with increases close to r_max

• Population growth begins to slow and the growth rate decelerates.

• Population size plateaus (asymptotic to K) and fluctuates around some mean.

2. Cause or mechanism

• As N increases, resources become limited (which theoretically can lead to intraspecific competition).

• Density-dependent effects on population processes: as N increases, death rates increase and/or birth rates decrease until at some point b - d = 0. In mathematical terms, there is a constant linear decrease in r (or lambda) as N increases.

3. Examples

• Flour beetles (Tribolium confusum) -- figure

• Pheasants on Protection Island -- figure

• Tasmanian sheep population -- figure

• Mice -- figure

4. Overview by Peterson (1977)

B. Logistic Growth Equation

• dN / dt = r_max N (1 - N/K)

where N/K expresses the unutilized capacity for increase

• N_t = K / (1 + e^a-rt)

where a = ln [(K - N₀) / N₀]

• Relationship between dN/dt, r, N, and K

C. Estimating Parameters

• Dennis and Taper (1994)

D. Assumptions

1. Population starts with a stable-age distribution

2. Density is measured in appropriate units.

3. There is a real attribute of the population corresponding to r_max

4. The relationship between density and rate of increase per individual is linear (which is probably violated in many growing populations).

5. No time lags (i.e., the relationship between density and the rate of increase operates instantaneously).

6. K (carrying capacity) is constant.

7. The population is large.

8. Continuous growth with overlapping generations (birth-flow populations).

E. Applications / Utility

1. Simple model that introduces the concepts of density-dependence and mean-population level.

2. Explore theoretical harvest strategies, e.g., MSY, OSY, Richer Curves, potential effects of overharvest, etc.

F. Density-Dependence and Intraspecific Competition

1. Evidence of density dependence in mammals

2. Density dependence in reproductive rates (examples)

• Copora lutea per doe in relation to deer density

• Nest success in relation to catbird-nest density

• Components of the Great Tit's reproductive rate in relation to density

3. Density dependence in mortality rates (examples)

• Mortality of adult ruffed grouse in relation to density

• Mortality of Russian partridge in the next breeding season in relation to number of young immediately after hatch

4. Density dependence in rates of spring-to-fall increase

• Bobwhites and pheasants

• Hungarian partridge

5. Case Study: Himalayan Thar

• Riney's model of eruption after liberation

• Changes in fecundity, mortality, and fat reserves

• Winter food: snow tussocks

G. Stochastic Logistic Growth

H. Population Growth - Limited Environments with Time Lags

I. Student Responsibilities

• Be able to discuss the logistic growth equation. What does the equation say?

• What are the assumptions of the logistic equation?

• What is the value of the logistic equation?

• How is sustained yield related to population density?

• OTHER?

J. References

Begon, M., and M. Mortimer. 1986. Population ecology: A unified study of animals and plants. Blackwell Scientific Publ., Boston, Mass. 220pp.

Dennis et al. ...

Elseth, G. D., and K. D. Baumgardner. 1981. Population biology. D. Van Nostrand Co., New York. 623pp.

Johnson, D. H. 1994. Population analysis. Pages 419-444 in T. A. Bookhout, ed. Research and management techniques for wildlife and habitats. Fifth ed. The Wildlife Society, Bethesda, Md.

Krebs, C. J. 1972. Ecology: the experimental analysis of distribution and abundance. Harper & Row, Publ., New York. 694pp.

Peterson, R. J. 1977. Source?

Wilson, E. O., and W. H. Bossert. 1971. A primer of population biology. Sinauer Assoc., Inc., Sunderland, Mass. 192pp.

Updated 06 August 1996