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Chapter 11

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Chapter 10 (Part 1)

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Why must species very high reproductive rates have a Type III survivorship curve ?

If these species didn’t have a Type III survivor-ship curve the Earth would be covered with their bodies.

Why must species low reproductive rates have a Type I survivorship curve ?

If these species didn’t have a Type I survivor-ship curve they would be extinct.

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What is the expected relationship b/t reproductive rate and patterns of survival ?

The greater the number offspring produced, the less energy / care the parent can invest in each offspring, the lower the survivorship of juveniles.

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AgeAge ddxx nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 180180 660660 1.0001.000 00 00 00

11 240240 480480 0.7270.727 11 0.7270.727 0.7270.727

22 120120 240240 0.3640.364 22 0.7280.728 1.4561.456

33 6060 120120 0.1820.182 22 0.3640.364 1.0921.092

44 6060 6060 0.0910.091 00 00 00

TotalTotal 660660 RR00 = = 1.8191.819 3.2753.275

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Generation Time ( T )T = Sum (X Lx mx) / R0 T = 3.275 / 1.819T = 1.80

Per Capita Rate of Increase ( r )r = Ln (R0) / Tr = Ln (1.819) / 1.80r = 0.332

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AgeAge nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 660660 1.0001.000 00

11 480480 0.7270.727 22

22 240240 0.3640.364 22

33 120120 0.1820.182 11

44 6060 0.0910.091 00

TotalTotal RR00 = =

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AgeAge nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 660660 1.0001.000 00 00 00

11 480480 0.7270.727 22 1.4541.454 1.4541.454

22 240240 0.3640.364 22 0.7280.728 1.4561.456

33 120120 0.1820.182 11 0.1820.182 0.5460.546

44 6060 0.0910.091 00 00 00

TotalTotal RR00 = = 2.3642.364 3.4563.456

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Generation Time ( T )T = Sum (X Lx mx) / R0 T = 3.456 / 2.364T = 1.46

Per Capita Rate of Increase ( r )r = Ln (R0) / Tr = Ln (2.364) / 1.46r = 0.589

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Effect of shifting reproduction to younger age classes?

Increased R0 1.819 vs. 2.364 (30% increase)

Decreased T 1.800 vs. 1.46 (19% decrease)

Increased r 0.332 vs. 0.589 (77% increase)

Should natural selection favor early reproduction ?

If r = “fitness”, this analysis suggests YES.

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Any disadvantages to earlier reproduction?

Smaller mothers produce fewer, smaller, and(or) less vigorous young.

Smaller mothers at a disadvantage in competition for resources, less able to provide for young.

Survivorship of small mothers and young lower.

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Effect of increased prey density (food) on life history traits of predator?

Lx:

mx:

R0:

T:

r:

Increase ( ↑ vigor, better defenses)

Increase ( ↑ eggs, ↓ abortion)

Increase (given Lx and mx increase)

Decrease (rapid growth accelerates maturation)

Increase ( given ↓T & ↑R0 )

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AgeAge ddxx nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 800800 850850 1.0001.000 00 00 00

11 2525 5050 0.0590.059 200200 11.811.8 11.811.8

22 1515 2525 0.0290.029 250250 7.257.25 14.514.5

33 55 1010 0.0120.012 300300 3.63.6 10.810.8

44 55 55 0.0060.006 350350 2.12.1 8.48.4

TotalTotal 850850 RR00 = = 24.7524.75 45.545.5

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Generation Time ( T )T = Sum (X Lx mx) / R0 T = 45.5 / 24.75T = 1.84

Per Capita Rate of Increase ( r )r = Ln (24.75) / 1.85r = 1.74

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Type of Survivorship Curve ?Type III Most individuals die at a very young age. Those that get past juvenile period have lower mortality rate.

Type of Life History Pattern ?r−selected: Life table indicates

short life span, low juvenile survivorship, and high birth rates.

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AgeAge nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 850850 1.0001.000 00 00 00

11 800800 0.9410.941 00 00 00

22 750750 0.8820.882 00 00 00

33 700700 0.8240.824 11 0.8240.824 2.472.47

44 650650 0.7650.765 33 2.2952.295 9.189.18

55 600600 0.7060.706 33 2.1182.118 10.5910.59

66 500500 0.5880.588 33 1.7641.764 10.5810.58

77 200200 0.2350.235 33 0.7050.705 4.944.94

88 5050 0.0590.059 33 0.1770.177 1.421.42

R0 = 7.88 39.17

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Generation Time ( T )T = Sum (X Lx mx) / R0 T = 39.17 / 7.88T = 4.97

Per Capita Rate of Increase ( r )r = Ln (7.88) / 4.97r = 0.415

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Type of Survivorship Curve ?Type I Most individuals survive juvenile age. Most mortality is in oldest age classes.

Type of Life History Pattern ?K−selected: Life table indicates

longer life span, high juvenile survivorship, and low birth rates.

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Geometric Growth Exponential Growth Logistic Population Growth Limits to Population Growth

Density Dependent Density Independent

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When generations do not overlap, growth can be modeled geometrically.

Nt = Noλt

Nt = Number of individuals at time t.

No = Initial number of individuals. λ = Geometric rate of increase. t = Number of time intervals or generations.

21Molles: Ecology 2nd Ed.

Currently 100 individuals Population rate, = 2

Nt = No t

After 5 years, pop has 3200100 x 25

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Continuous population growth in an unlimited environment can be modeled exponentially.

dN / dt = rmax N

Appropriate for populations with overlapping generations. As population size (N) increases, rate of

population increase (dN/dt) gets larger.

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For an exponentially growing population, size at any time can be calculated as:

Nt = Noermaxt

Nt = Number individuals at time t. N0 = Initial number of individuals. e = Base of natural logarithms. rmax = Per capita rate of increase. t = Number of time intervals.

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As resources are depleted, population growth rate slows and eventually stops: logistic population growth. Sigmoid (S-shaped) population growth curve. Carrying capacity (K) is the number of individuals

of a population the environment can support. Finite amount of resources can only support a finite

number of individuals.

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dN/dt = rmaxN(1-N/K)

rmax = Maximum per capita rate of increase under ideal conditions.

When N nears K, the right side of the equation nears zero. As population size increases, logistic growth rate

becomes a small fraction of growth rate. Highest when N=K/2. N/K = Environmental resistance.

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Environment limits population growth by altering birth and death rates. Density-dependent factors

Disease, Resource competition Density-independent factors

Natural disasters, Weather

30Molles: Ecology 2nd Ed.

Boag and Grant - Geospiza fortis was numerically dominant finch (1,200)

After drought of 1977, pop. fell to (180)

Food plants failed to produce seed crop. 1983 - 10x normal rainfall caused population to grow

(1,100) due to abundance of seeds and caterpillars.

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Grant and Grant documented several ways finches utilized cacti: Open flower buds in dry season to eat pollen Consume nectar and pollen from mature

flowers Eat seed coating (aril) Eat seeds Eat insects from rotting cactus pads

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Finches tend to destroy stigmas, thus flowers cannot be fertilized. Wet season activity may reduce seeds

available to finches during the dry season. Opuntia helleri main source for cactus finches.

Negatively impacted by El Nino (1983). Stigma snapping delayed recovery.

Interplay of biotic and abiotic factors.

34Molles: Ecology 2nd Ed.

Fig 11.20

35Molles: Ecology 2nd Ed.

On average, small organisms have higher rates of per capita increase and more variable populations than large organisms

Fig 11.21

36Molles: Ecology 2nd Ed.

Populations of marine pelagic tunicate (Thalia democratica) grow at exponential rates in response to phytoplankton plumes

Filter feeders

37Molles: Ecology 2nd Ed.

Algae bloom in spring off Australian coast Numerical response can increase pop. size

dramatically due to extremely high reproductive rates

Figure 11.22

38Molles: Ecology 2nd Ed.

Pacific Gray Whale (Eschrichtius robustus) divided into Western and Eastern Pacific subpopulations

Summer here

Winter here

39Molles: Ecology 2nd Ed.

Examined whales killed by whalers Estimated avg. annual mortality rate of

0.089 and calculated annual birth rate of 0.13 r = 0.13 - 0.089 = 0.041

Gray Whale pop. growing at 4.1% per yr

40Molles: Ecology 2nd Ed.

Reilly et.al. used annual migration counts from 1967-1980 to obtain growth rate

Thus from 1967-1980, pattern of growth in California Gray Whale pop fit exponential model:

Nt = No e0.025t

Figure 11.22

41Molles: Ecology 2nd Ed.

What type of growth curve?

Figure 11.27

42Molles: Ecology 2nd Ed.

Are we at carrying capacity?

Will resources become limited for humans?Figure 11.27

43Molles: Ecology 2nd Ed.

Distribution of the Human Population

44Molles: Ecology 2nd Ed.

Variation in Human Population Density

45Molles: Ecology 2nd Ed.

Age Distributions for Human Populations:

Predictors of Future Population Growth

Population SizeWill be Stable

Population SizeWill Decline

Population SizeWill IncreaseRapidly

Ag

e C

las

s

% of Population

46Molles: Ecology 2nd Ed.

Historical and Projected Human Populations

Figure 11.26

47Molles: Ecology 2nd Ed.

Can the current growth rate of the global human population be sustained ?

If not, what will slow or reverse human population growth ?

What Will the Future Bring ?

48Molles: Ecology 2nd Ed.

Trend of decreasing per capita availability of farmland and freshwater.

Trend of decreasing total crop land, range land, and forest

13 of 15 major marine fisheries are in a state of near or total collapse.

Humans already consume 40% of global primary productivity.

49Molles: Ecology 2nd Ed.

Death Rate Solution: Decrease Lx Malnutrition Disease Warfare Pollution

Chemical Radiation

Birth Rate Solution: Decrease mx

Increase age of first reproduction (T) Education/employment

for girls/women

Decrease R0

Universal availability of contraceptives

Decrease infant mortality Increase standard of

living

50Molles: Ecology 2nd Ed.

Green Revolution (Part 2) ???

Renewable and clean energy sources (solar, wind, hydro)

Medical research to combat new and resistant diseases

Warp Drive ???

51Molles: Ecology 2nd Ed.

Or maybe we should be doing something NOW ?

52Molles: Ecology 2nd Ed.

With abundant resources, pop’s can grow at geometric or exponential rates

As resources depleted, pop growth rate slows, eventually stops: logistic population growth

Environment limits population growth by changing birth and death rates

On avg., small organisms have higher (r) and more variable pops. – while large organisms have lower (r) and less variable pops

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