11 Population Growth Chapter 11 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

22 Geometric Growth 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 (lambda) = Geometric rate of increase. – t = Number of time intervals or generations.

33 Exponential Growth Continuous population growth in an unlimited environment can be modeled exponentially. dN / dt = r max N  dN = change in number  dt = change in time  r max = per capita rate increase  N = Population size Rate of population growth

44 Exponential Growth dN / dt = r max N Appropriate for populations with overlapping generations. – As population size (N) increases, rate of population increase (dN/dt) gets larger. Which variable above would best represent the “Intrinsic rate of increase”?

55 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. t = Number of time intervals.

66 Exponential Population Growth

77 Logistic Population Growth

88 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.

99 Logistic Population Growth

10 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.

11 Limits to Population Growth Environment limits population growth by altering birth and death rates. – Density-dependent factors?!? – – Density-independent factors?!? –

12 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.

13 Galapagos Finch Population Growth

14 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

15 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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