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POPULATION ECOLOGY. Density and Dispersion. Density - The number of individuals per unit area What are the three patterns of dispersion?. Patterns of Dispersion Within a Population’s Geographic Range. Clumped. Random. Uniform. Estimating Population Size. Mark re-capture method.

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## POPULATION ECOLOGY

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**Density and Dispersion**• Density - The number of individuals per unit area • What are the three patterns of dispersion?**Patterns of Dispersion Within a Population’s Geographic**Range Clumped Random Uniform**Estimating Population Size**• Mark re-capture method. • You capture 200 grasshoppers, mark them all and then release them back into the wild. A few days later you capture 100 grasshoppers and 50 of them were marked. How many grasshoppers do you estimate are in this population?**N = # marked x # recaptured**number marked & recaptured 200 x 100/50 = 400 Original Population is approx. 400**You capture 50 rabbits, mark all them**and release them back into the wild. The following week you capture 30 rabbits and 15 are marked. How many rabbits do you estimate in the population?**50 rabbits marked X 30 recaptured**15 marked recaptured Original Population is approx 100.**Demography**• Study of vital statistics that affect population size • Life Tables are age-specific summaries of the survival pattern of a population**Life Table for Belding Ground Squirrels (Spermophilus**beldini) at Tioga Pass, in the Sierra Nevada Mountains of California**Age Structure – the relative number**of individuals at each age commonly represented in pyramids. It shows present and future growth trends.**Survivorship Curves**• Plot of the numbers of a cohort that are alive at each age. • Survivorship curves are generally classified into three types:**Life Histories**• Traits that affect time of reproduction and death including: 1. Clutch size 2. Number of reproductive episodes per lifetime 3. Age at first reproduction**Figure 52.6**• Species that exhibit semelparity, or “big-bang” reproduction • reproduce once and die**Species that exhibit iteroparity, or repeated reproduction**• Produce offspring repeatedly over time**Birds with high probability of dying have larger clutch**sizes**Large clutch sizes mean one reproductive episode per life.**• Small clutch sizes means more than one reproductive episode • Age at first reproduction is younger in large clutch size reproducers; they invest less energy in their own growth and development.**Models of Population Growth**• r = reproductive rate, r = b-d/N • b = births, d = deaths, N = population size • multiply both sides of the equation by N, we get: rN = b-d , rN = change in population during a given time interval: DN/ Dt = b - d**Models of Population Growth**• r max = the maximum rate of increase in growth of a species; intrinsic/maximum rate of increase • The equation for exponential population growth is: dN/ dt= rmaxN**r max = 1**r max = .5**Population Density is the number of**• individuals per unit area. • Three factors affect a population’s size: • number of births • number of deaths • number of individuals who immigrate • and emigrate**Exponential Growthoccurs when**the individuals in a population reproduce at a constant rate. At first, the number of individuals in an exponentially growing population increases slowly, but over time the population becomes larger and larger. (J shaped curve)**Logistic Growth occurs when a**population’s growth slows or stops following a period of exponential growth. (S shaped curve)**Exponential**Growth Curve Carrying Capacity Logistic Growth Curve**(K N)**dN rmax N dt K • The logistic growth equation • Includes K, the carryingcapacity, the largest number of individuals of a population that an environment can support**If N is less than K, then the population growth is positive**and population increases ? What is occurring here?**A limiting factor causes**population growth to decrease.**Density Dependent Factors**become limiting only when the per unit area – reaches a certain level Examples: competition, predation, parasitism, and disease.**Density Independent Factors**affect all populations in similar ways, regardless of the population size. Examplesinclude unusual weather, natural disasters, seasonal cycles, and certain human activities (such as damming rivers or cutting forests)**K selection (density dependent**• selection) • long maturation time • long lifespan • low death rate • few offspring/reproduction • several reproductive episodes • reproduces later in life • large sized offspring • parental care for young**r selection (density independent selection)**short maturation time short life-span high death rate many offspring/reproduction one reproductive event reproduces early in life small sized offspring no parental care

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