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Section 5 Professor Donald McFarlane Lecture 18 Ecology: Population Growth.

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Presentation on theme: "Section 5 Professor Donald McFarlane Lecture 18 Ecology: Population Growth."— Presentation transcript:

1 Section 5 Professor Donald McFarlane Lecture 18 Ecology: Population Growth

2 2 Population – group of interbreeding individuals occupying the same habitat at the same time  Water lilies in a particular lake  Humans in New York City Population ecology – study of what factors affect population size and how these factors change over space and time

3 3 How populations grow Life tables can provide accurate information about how populations grow from generation to generation Simpler models can give insight to shorter time periods  Exponential growth – resources not limiting, prodigious growth  Logistic growth – resources limiting, limits to growth

4 4 Per capita growth rate  Change in population size over any time period  Often births and deaths expressed per individual  100 births to 1000 deer = 0.10  50 deaths in 1000 deer = 0.05 Net Reproductive Rate, R 0, is approximately birth rate – death rate R 0 ~ (b – d) ~ (0.1 – 0.05) = 0.05

5 5 r = “intrinsic rate of increase” = -ln R 0 T gen The differential growth equation: dN = rN dt

6 6 R 0 for deer was 0.05 T gen is 4 years Therefore r = - ln(0.05)/4 = dN = rN dt Starting with 10 deer (N 0 = 10) N 0 = 10 N 1 = 17 N 2 = 31 `N 3 = 53 N 4 = 94 N 5 = 163

7 7 Exponential growth  When r>0, population increase is rapid  Characteristic J-shaped curve  Occurs when population growth is UNREGULATED by the environment  e.g., growth of introduced exotic species, yeast in brewing medium, and global human population

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9 9 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display Population size (a) Tule elk Year (b) Black-footed ferrets Number of animals Survey year Predicted abundance Actual abundance

10 10 Logistic growth  Eventually, resources become limiting as populations grow  Carrying capacity (K) or upper boundary for population  Logistic equation dN = rN ( K – N ) dt K

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13 13 Not all individuals in a population are the same with respect to births and deaths….. We can account for differences with a LIFE TABLE

14 14 Age-specific fertility rate, m x  Proportion of female offspring born to females of reproductive age  100 females produce 75 female offspring m x =0.75 Age-specific survivorship rate, l x  Use survivorship data to find proportion of individuals alive at the start of any given age class l x m x = contribution of each age class to overall population growth

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16 16 Density-dependent factors  Mortality factor whose influence varies with the density of the population  Parasitism, predation, and competition  Predators kill few prey when the prey population is low, they kill more prey when the population is higher  Detected by plotting mortality against population density and finding positive slope Density-independent factor  Mortality factor whose influence is not affected by changes in population size or density  Generally physical factors – weather, drought, flood, fire

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18 18 Life history strategies  Continuum  r-selected species – high rate of per capita population growth, r, high mortality rates  K-selected species – more or less stable populations adapted to exist at or near carrying capacity, K Lower reproductive rate but lower mortality rates

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20 20 Survivorship curve – plots numbers of surviving individuals at each age  Use log scale to make it easier to examine wide range of population sizes  Beavers have a fairly uniform rate of death over the life span

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22 22 3 patterns of survivorship curves  Type I – rate of loss of juveniles low and most individuals lost later in life  Type II – fairly uniform death rate Beaver example  Type III – rate of loss for juveniles high and then loss low for survivors

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24 24 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Population (billions) B.C.E B.C.E 5000 B.C.E 4000 B.C.E 3000 B.C.E 2000 B.C.E 1000 B.C.E 1 C.E 1000 C.E 2000 C.E


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