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17 Cards in this Set
- Front
- Back
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Logistic Growth Model
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- Density Dependant
- assumes resources are limited |
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Density Dependent
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- Increased crowding reduces birth rate- less food
- birth, death or both can be density dependent |
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Carrying Capacity (K)
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- Maximum population size an environment can support
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dN/dt = rN[1-(N/K)]
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- Logistic Growth Equation
- describes pop growth in resource limited enviro |
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N(t)=K/(1+[K-N)/N]e^-rt
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- Pop size as a function of time
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Assumption of constant carrying capacity
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- LGM assumption
- resource availability doesn't vary through time |
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Assumption of linear density dependance
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- Assumes that each individual added to the population causes an incremental decrease in per capita rate of population growth
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Time lag
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- Time delay in density Dependent responses
- represented by tau |
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Delayed differential logistic growth equation
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dN/dt=rN[1-(N*t-tau/K)]
- depends on length of lag (tau) and response time of pop (1/r) |
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Amplitude
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- Difference between max and average pop
- if too large pop can hit 0 |
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Period
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- Always 4(tau)
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Damped Oscillation
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-If r(tau) is medium pop overshoots than undershoot
- oscillations diminish until K is reached |
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Stable Limit Cycle
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- If r(tau) is large
- periodically rising and falling about L but never settling |
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Assumptions of Logistic Growth Model
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- No time lags
- no migration - no genetic variation - no age structure - constant carrying capacity - linear density dependence |
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Fig 2.1 & 2.2
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Empirical Ex of density dependence and logistic growth
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- Song sparrows of Mandarte Island. Makes defend territories to reproduce and space is limited. Floaters increase in density Dependant fashion. Density Dependance also seen in surviving young and juveniles
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Continuous exponential growth equation vs. logistical growth equation
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