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Population Dynamics

Population Dynamics. Lecture 9. TWO TERMS. Population Growth – refers to the increase or decrease in size, density,or number of individuals in a population through time. Growth = (B-D)+(I-E)

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Population Dynamics

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  1. Population Dynamics Lecture 9

  2. TWO TERMS • Population Growth – refers to the increase or decrease in size, density,or number of individuals in a population through time. Growth = (B-D)+(I-E) • Biotic Potential – maximum reproductive power of a population or the ability of the population to reproduce under optimum environmental conditions.

  3. POPULATION GROWTH PATTERNS • Exponential Growth Pattern • Logistic Growth Pattern

  4. Expression of the Biotic Potential • dN/dt = rN where r = intrinsic rate of increase = innate capacity of increase = Malthusian parameter = mathematical expression of the biotic potential N = existing population size t = unit of time

  5. Growth rate is higher when? dN/dt = rN 1. _________________________ e.g. Popn A Popn B No = 100 No = 100 rA = 0.5 rB = 0.1 dN/dt = (100)(0.5) dN/dt = (100)(0.1) = 50 = 10 2. ________________________ e.g. Popn A Popn B No = 10 No = 1000 rA = 0.5 rB = 0.5 dN/dt = (10)(0.5) dN/dt = (1000)(0.5) = 5 = 50

  6. r • The index “r” is basically the difference between birth and death rates r = b-d dn/dt = (b-d)N = rN

  7. Exponential Growth Pattern • dN/dt = rN  Nt = Noert where Nt = population size at time t No = initial population size e = base of natural log (2.71828) r = rate of increase t = unit of time “ the population size at time t (Nt) is equal to the product of the initial population size (No) and the natural log of the product of the intrinsic rate of increase (r) and the time (t)

  8. Example: • A growing insect population with an initial population size of 100 shows an instantaneous birth rate of 0.65 and death rate of 0.10. Compute for the population size after 10 years. Solution: r = b-d = 0.65 – 0.10 = 0.55 e = 2.71828 N10 = Noert = (100) (2.71828) (0.55) (10) = 24,469 Doubling time = how long it takes for population to double? Nt/No = 2 = ert ln2= rt t = ln2/r = 0.693/r = 0.693/0.55 = 1.26 years Humans t = 0.693/0.02 = 35 years

  9. How to get “r”. For Whooping Cranes, we can estimate r from winter census counts at Aransas. Opposite is a table which summarizes counts for the ten-year period 1942 to 1952. Since there is considerable annual variation, we have used the ten year period.Recall that r is the average number of individuals added to the population per individual per time unit. The rate of increase can be calculated as the change in population size (final N – initial N) divided by initial population size per time period, or:(21 – 18) / 18 per 10 years= 0.167 / 10 = 0.0167 per year

  10. Exponential Growth (dN/dt=rN) • Number of individuals added to a population at the beginning of exponential growth is relatively small. But numbers increase quickly as the population, and thus the given percentage of that population, grows. • J-shaped curve “the larger the population becomes, the faster it grows”

  11. J-shaped curve

  12. Logistic Growth Pattern • dN/dt = rN (K-N) (Verhulst Pearl Equation) K • K – carrying capacity or the maximum population size allowed by the environment • (K-N)/K – “nearness to carrying capacity equation” • (1) If N is small in comparison to K, e.g. when N=5 K= 100 dN/dt = 1 x 5 (100 -5) = 5 x 0.95 = 4.75 100 (2) If N is close to K e.g. when N= 98 K = 100 dN/dt = 1 x 5 (100-50) = 2.5 100 (3) At carrying capacity, when N=K e.g. when N = 100 K= 100 dN/dt = 1 x 100 (100-100) = 0 (ZPG) – “zero population growth” 100 “A population following logistic growth grows at slower and slower rate as it nears the carrying capacity”  S-shaped curve!

  13. S-shaped Curve

  14. Inflection Point

  15. Carrying Capacity • For most populations, four factors interact to set the carrying capacity, K. • Availability of raw materials • The availability of energy • The accumulation of waste products and their means of disposal • Interactions among organisms • All factors above act together to limit population size and they are collectively called as environmental resistance factors

  16. Examples • 1. Grass populations limited by a. availability of nutrients (N2 and Mg) and water b. number of insects feeding on them c. competition with one another

  17. 2. Intraspecific competition within a population as manifested by crowding: causes breakdown in normal social behavior which leads to fewer birth rates and increased death rates a. shrinkage of reproductive organs b. abnormal mating behavior c. decreased litter size d. fewer litters per year e. lack of maternal care f. increased aggression in some rats

  18. Logistic Growth • Logistic Growth - Growth rates regulated by internal and external factors until it comes into equilibrium with environmental resources. • Growth rate slows as population approaches carrying capacity. • S-Shaped curve • Environmental Resistance - Any environmental factor that reduces population growth.

  19. Population Oscillations • Overshoot - Measure of extent to which population exceeds carrying capacity of its environment. • Dieback - Negative growth curve. • Severity of dieback generally related to the extent of overshoot.

  20. Malthusian Growth • Malthusian Growth (Irruptive Growth) - Population explosions followed by population crashes. • Malthus concluded human populations tend to grow until they exhaust their resources and then crash.

  21. REGULATING POPULATION GROWTH • Intrinsic factors - Operate within or between individual organisms in the same species. e.g. crowding, behavior, dispersal • Extrinsic factors - Imposed from outside the population. e.g. weather, human activity, resource availability, diseases and parasites, predation • Biotic factors - Caused by living organisms. • Abiotic factors - Caused by non-living environmental components.

  22. Density Dependent Factors • Factors whose effects intensify as the density of the population increases. • Tend to reduce population size by decreasing natality or increasing mortality as population size increases. • e.g. resource availability diseases predation rate

  23. Density Independent Factors • Factors whose effects do not vary regardless of population density. • Tend to be abiotic components. • Do not directly regulate population size. e.g. weather and climate volcanic eruptions storms, fires, hurricanes

  24. REPRODUCTIVE STRATEGIES • Populations can be divided into two broad categories based on their reproductive strategies (1) K-strategists -individuals allocate more energy for non-reproductive activities - occurs in stable or predictable environment where mortality is density-dependent - usually large organisms that have relatively long lives - produce few offspring - provide care for the young

  25. REPRODUCTIVE STRATEGIES (2) r-strategists ( “Big Bang” reproducers) - individuals allocate more energy to reproduction and less to growth, maintenance and ability to compete - occurs in harsh or unpredictable environment where mortality is density- independent - usually small organisms that have relatively short life span - produce many offspring - but little parental care e.g. insects, annual plants, Pacific salmon, microorganisms

  26. END OF LECTURE

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