1. 1 William P. Cunningham University of Minnesota Mary Ann Cunningham Vassar College Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. *See PowerPoint Image Slides for all figures and tables pre-inserted into PowerPoint without notes. Chapter 06 Lecture Outline *

2. 2 Population Biology

3. 3 Outline Dynamics of Population Growth Factors affecting Population Growth Survivorship and regulation of population growth Maintaining populations using conservation biology

4. 4 Biotic Potential Biotic potential refers to unrestrained biological reproduction. Biological organisms can produce enormous numbers of offspring if their reproduction is unrestrained. Constraints include:  Scarcity of resources  Competition  Predation  Disease

5. 5 Describing Growth Mathematically (N) Population – total number of all the members of a single species living in a specific area at the same time. (r) Rate—This is the rate of growth; the number of individuals which can be produced per unit, of time under ideal conditions. (t)Time—This is the unit of time upon which the rate is based. Geometric Rate of Increase--The population that size that would occur after a certain amount of time under ideal conditions is described by the formula: N t =N 0 r t Exponential Growth - growth at a constant rate of increase per unit time (geometric) ; has no limit.

6. 6 Geometric Rate of Increase Example If cockroaches can reproduce 10 new roaches for each adult roach per 3 month unit of time, the geometric rate of increase would be as follows: timeNrate (r)r x N t 1 21010 x 2 = 20 t 2 201010 x 20 = 200 t 3 2001010 x 200 = 2000 t 4 20001010 x 2000 =20,000 Conclusion: 1 pair of roaches can produce a population of 20,000 roaches in 1 year!

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8. 8 Exponential Growth Describes Continuous Change The previous example projects growth at specific time periods, but in reality, growth in cockroaches under ideal conditions occurs continuously. Such change can be described by modifying our previous formula to: dN/dt=rN The d is for delta which represents change. This is a simple mathematical model of population showing Exponential Growth.

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10. 10 Exponential Growth Always Has Limits Exponential growth only can be maintained in a population as long as nothing limits the growth. In the real world there are limits to growth that each population will encounter. Eventually, shortages of food or other resources lead to a reduction in the population size.

11. 11 Population Terminology Defined Carrying capacity – the population of a species that can be supported in a specific area without depleting the available resources. Overshoot – when a population exceeds the carrying capacity of the environment and deaths result from a scarcity of resources. Population crash – a rapid dieback in the population to a level below the carrying capacity. Boom and bust – when a population undergoes repeated cycles of overshoots followed by crashes.

12. 12 Boom and bust – when a population undergoes repeated cycles of overshoots followed by crashes

13. 13 Resource Scarcity Slows Exponential Growth Population growth can slow down as resources become scarce. This slowing rate of growth results in an “s-shaped” or sigmoidal growth curve. Such growth is also sometimes referred to as logistic growth and can be represented mathematically as: dN/dt = r N (1 - N/K)

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15. 15 S-Curve or Logistic Growth

16. 16 Factors Affecting Population Growth Logistic Growth is density-dependent which means that the growth rate depends on the population density. Many density-dependent factors can influence a population including: disease, physiological stress and predation. Density-dependent factors intensify as population size increases. Density independent factors may also affect populations. These may include drought, fire, or other habitat destruction that affects an ecosystem.

17. 17 r and K Selected Species r-selected species rely upon a high reproductive rate to overcome the high mortality of offspring with little or no parental care. Example: A clam releases a million eggs in a lifetime. K-selected species have few offspring, slower growth as they near carrying capacity and exercise more parental care. Example: An elephant only reproduces every 4 or 5 years.

18. 18 Reproductive Strategies

19. 19 Factors That Affect Growth Rates 4 factors affect growth rate: Births, Immigration, Deaths and Emigration. (r=B+I-D-E) Births –the number of births that occur in the population at any give time; rate of births vary by species and also with stress and food availability. Immigration – the number of organisms that move into the population from another population. Deaths—mortality, or the number of deaths that occur in the population at any given time, vary by species and with environmental factors. Emigration—the number of organisms that move out of the population to another population.

20. 20 Life Span Vary by Species Maximum Life span - the longest period of life reached by a given type of organism  Bristlecone pine live up to 4,600 years.  Humans may live up to 120 years.  Microbes may live only a few hours. Differences in relative longevity among species are shown as survivorship curves.

21. 21 Survivorship Curve Vary by Species Three general patterns:  Full physiological life span if organism survives childhood - Example: elephants  Probability of death unrelated to age - Example: Sea gull  Mortality peaks early in life. - Example: Redwood Trees

22. 22 Survivorship Curves

23. 23 Factors that Regulate Population Growth Intrinsic factors - operate within or between individual organisms in the same species Extrinsic factors - imposed from outside the population Biotic factors - Caused by living organisms. Tend to be density dependent. Abiotic factors - Caused by non-living environmental components. Tend to be density independent. Example: Rainfall, storms

24. 24 Density Dependent Factors Reduce population size by decreasing natality or increasing mortality. Interspecific Interactions (between species) - Predator-Prey oscillations

25. 25 Density Dependent Factors Continued Intraspecific Interactions - competition for resources by individuals within a population  As population density approaches the carrying capacity, one or more resources becomes limiting. Control of access to resources by territoriality; owners of territory defend it and its resources against rivals. Stress-related diseases occur in some species when conditions become overcrowded.

26. 26 Conservation Biology Critical question in conservation biology is the minimum population size of a species required for long term viability. Special case of islands  Island biogeography - small islands far from a mainland have fewer terrestrial species than larger, closer islands  MacArthur and Wilson proposed that species diversity is a balance between colonization and extinction rates.

27. 27 Conservation Genetics In a large population, genetic diversity tends to be preserved. A loss/gain of a few individuals has little effect on the total gene pool. However, in small populations small events can have large effects on the gene pool. Genetic Drift  Change in gene frequency due to a random event Founder Effect  Few individuals start a new population.

28. 28 Conservation Genetics Demographic bottleneck - just a few members of a species survive a catastrophic event such as a natural disaster Founder effects and demographic bottlenecks reduce genetic diversity. There also may be inbreeding due to small population size. Inbreeding may lead to the expression of recessive genes that have a deleterious effect on the population.

29. 29 Genetic Drift

30. 30 Population Viability Analysis Minimum Viable Population is the minimum population size required for long-term survival of a species.  The number of grizzly bears in North America dropped from 100,000 in 1800 to 1,200 now. The animal’s range is just 1% of what is once was and the population is fragmented into 6 separate groups.  Biologists need to know how small the bear groups can be and still be viable in order to save the grizzly.

31. 31 Metapopulations are connected populations Metapopulation - a collection of populations that have regular or intermittent gene flow between geographically separate units  Source habitat - Birth rates are higher than death rates. Surplus individuals can migrate to new locations.  Sink habitat - Birth rates are less than death rates and the species would disappear if not replenished from a source.

32. 32 Metapopulation

33. 33 The Rule of 70 The Rule of 70 is useful for financial as well as demographic analysis. It states that to find the doubling time of a quantity growing at a given annual percentage rate, divide the percentage number into 70 to obtain the approximate number of years required to double. For example, at a 10% annual growth rate, doubling time is 70 / 10 = 7 years. Similarly, to get the annual growth rate, divide 70 by the doubling time. For example, 70 / 14 years doubling time = 5, or a 5% annual growth rate. Growth Rate (% per Year) Doubling Time in Years 0.1700 0.5140 170 235 323 418 514 612 710 7 The Rule of 70 The Rule of 70 is useful for financial as well as demographic analysis. It states that to find the doubling time of a quantity growing at a given annual percentage rate, divide the percentage number into 70 to obtain the approximate number of years required to double. For example, at a 10% annual growth rate, doubling time is 70 / 10 = 7 years. Similarly, to get the annual growth rate, divide 70 by the doubling time. For example, 70 / 14 years doubling time = 5, or a 5% annual growth rate. The following table shows some common doubling times:

34. 34 Population Growth Equations Practice Simple growth rate of a population N 1 = N 0 + B - D+ I – E Intrinsic Rate (r) of increase for population growth r = B - D Rate of change of population size dN = rN dN = N 1 - N 0 dt Net growth rate of a population (R 0 ) R 0 = N 1 N 0 Doubling time for a population (rule of 70) Dt=70/ R 0 Annual % rate of natural population change % = (B – D) x 100% 1,000

35. 35 1 In 1950, the population of a small suburb in Los Angeles, California, was 20,000. The birth rate was measured at 25 per 1000 population per year, while the death rate was measured at 7 per 1000 population per year. Immigration was measured at 600 per year while emigration was measured at 200 per year. Calculate the population size in 1951. N 0 = 20,000 B= 25/1000 D= 7/1000 I= 600/yearE= 200/year N 1 = N 0 + B - D+ I – E N 1 = 20,000 + 500 -140 + 600 -200 = 20,760

36. 36 2 Calculate the rate of increase for population growth for the preceding problem. B= 25/1000 D= 7/1000 r = B – D r = 18/1000 (or 360/20,000) r = 1.8 %

37. 37 3 Calculate the rate of change for the population in the first example. N 0 = 20,000 N 1 = 20,760 dN = N 1 - N 0 dN = 20,760 – 20,000 dN = 760/year

38. 38 4 Calculate the net growth rate of the population described in the first example. A population that was not growing would have a net growth rate of 1. A population that was doubling would have a net growth rate of 2, and so on. N 0 = 20,000 N 1 = 20,760 R 0 = N 1 N 0 R 0 = 20,760 = 1.038 20,000

39. 39 5 A population had a growth rate of 1.7 in 1995. In what year would the population be double its current value? Assume all other factors are constant. 1995 = 1.7 R 0 = 1.7 Dt =70/ R 0 Dt = 70/ 1.7 = 41.1 or in 2036

40. 40 6 In 2,000, the world birth rate was 22 births per 1000 people. The world death rate was 9 deaths per 1000 people. Calculate the percent world growth rate. B= 22/1000 D= 9/1000 % = (B – D) x 100% 1,000 % = (22-9) x 100% = 1.3% 1,000

41. 41 7 Uganda has a crude birth rate of 48 and a crude death rate of 18.4. Calculate the percent population growth rate for Uganda. B = 48 D= 18.4 % = (B – D) x 100% 1,000 % = (29.6) x 100% = 2.96% 1,000