Section 5 Professor Donald McFarlane Lecture 18 Ecology:
Population Growth
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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
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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
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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
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5 r = intrinsic rate of increase = -ln R 0 T gen The
differential growth equation: dN = rN dt
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6 R 0 for deer was 0.05 T gen is 4 years Therefore r = -
ln(0.05)/4 = 0.748 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
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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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8
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9 Copyright The McGraw-Hill Companies, Inc. Permission required
for reproduction or display. 1970 0 1980 Population size 19902000
600 500 300 200 100 400 (a) Tule elk Year (b) Black-footed ferrets
400 200 100 0 Number of animals Survey year 2000 2001200320042005
2006 Predicted abundance Actual abundance
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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 Not all individuals in a population are the same with
respect to births and deaths.. We can account for differences with
a LIFE TABLE
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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 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 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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19
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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 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 Copyright The McGraw-Hill Companies, Inc. Permission
required for reproduction or display. Population (billions) 0 1 2 3
4 1975 2000 5 6 7 8 7000 B.C.E 1950 1900 1800 6000 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
