1 1 Population Growth Chapter 11

2 2 Outline Geometric Growth Exponential Growth Logistic Population Growth Limits to Population Growth  Density Dependent  Density Independent Intrinsic Rates of Increase

3 3 Geometric Growth- pulsed reproduction annual plant or insect When generations do not overlap, growth can be modeled geometrically. N t = N o λ t  N t = Number of individuals at time t.  N o = Initial number of individuals.  λ = Geometric rate of increase (Constant ratio)  t = Number of time intervals or generations.

4 4 Fig. 11.2

5 5 Fig. 11.3

6 6 Exponential Growth Continuous population growth in an unlimited environment can be modeled exponentially. dN / dt = r max N Appropriate for populations with overlapping generations.  As population size (N) increases, rate of population increase (dN/dt) gets larger.

7 7 Assumes a population is growing without limits at its maximal rate  Rate is symbolized r and called the biotic potential The Exponential Growth Model Growth rate = dN/dt = r i N No. of individuals in a population Intrinsic rate of increase Change over time The actual rate of population increase is r = (b – d) + (i – e) BirthrateDeathrateNet immigration Net emigration

8 8 Exponential Growth For an exponentially growing population, size at any time can be calculated as: N t = N o er max t N t = Number individuals at time t. N 0 = Initial number of individuals. e = Base of natural logarithms. r max = Per capita rate of increase (constant) t = Number of time intervals.

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11 Exponential Population Growth

12 Logistic Population Growth 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.

13 Logistic Population Growth

14 Fig. 11.9

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18 dN/dt=rmax N Add element that slows growth as pop size approaches K dN/dt=rmax N(K-N)  K

19 Logistic Population Growth dN/dt = r max N(1-N/K) r max = 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.

20 Limits to Population Growth Environment limits population growth by altering birth and death rates.  Density-dependent factors Disease, Resource competition  Density-independent factors Natural disasters

21 Galapagos Finch Population Growth Boag and Grant - Geospiza fortis was numerically dominant finch (1,200). After drought of 1977, population fell to (180). Food plants failed to produce seed crop x normal rainfall caused population to grow (1,100) due to abundance of seeds and caterpillars.

22 Galapagos Finch Population Growth

23 Fig

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25 Cactus Finches and Cactus Reproduction 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

26 Cactus Finches and Cactus Reproduction 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.

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