Download Measuring and Modelling Potential Change

Austin Brown
Measuring and Modelling Potential Change
Definitions
Carrying Capacity: Maximum population that can be sustained with the resources at a time.
Population Dynamics: changes in the population from births, deaths, immigrations, and
emigrations
Fecundity: potential for species to produce offspring in their life
Open population: pop. # and density are determined by birth, death, immigration, emigration
Closed Population: pop. size/density measured with natality (birth rates) and mortality (death
rates). Only natality and mortality can be measured because the population can’t migrate.
Biotic Potential: Max rate a population can increase in ideal conditions
Geometric Growth: population pattern where organisms reproduce at fixed intervals at constant
rate. Compares population size to population size of previous year at the same time.
e.g.
λ=N(t+1)/N(t)
λ=N(2)/N(1)
λ=2
λ=fixed growth rate, N=pop size in year (t+1) and (t)
Exponential Growth: organisms reproduce continuously at a constant rate
e.g
dN/dt=rN r=per capita growth rate, N= population size, dN/dt=instantaneous growth rate
=(0.03)(2500)
=75 per hour
td=0.69/r td=doubling time
=0.69/0.03
=23 hours
Logistic Growth: model of population growth that describes growth levels as size approaches
carrying capacity
dN/dt=pop. growth rate at given
e.g. dN/dt=rmaxN((K-N)/K)
dN/dt=(0.5)(20)((1000-20)/1000)
dN/dt=9.8
time
rmax=max growth rate
N=pop. size at given time
K=carrying capacity of
environment
Lag Phase: when pop. growth rates slow due to small pop. size (Geometric, exponential, logistic
pop growth)
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Log Phase: when growth rates are very rapid (Geometric, exponential, logistic pop growth)
Environmental Resistance: factor that limits populations biotic potential as it passes or
approaches the carrying capacity
Stationary Phase: population growth decreases and stabilizes as carrying capacity is reached
(logistic pop. growth)
Dynamic Equilibrium: birth rates=death rates (no net change)
Notes
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An ecosystem only has so many resources at any time
Populations can vary in different ecosystems therefore
Factors affecting population growth:
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Populations are always fluctuating
Increase through births and immigration
Decrease through death and emigration
Species with long lives tend to produce less offspring during a cycle to decrease their
fecundity
Long lived species often have a later sexual development
Fertility often lower than fecundity (disease, food availability, and sexual success all
factors)
Calculating changes in population size:
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Population change=((births+immigration)-(deaths+emigration)) *100
Initial population size (n)
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Higher birth/immigration then positive growth
Scientists tend to study closed populations (mark-recapture)
Population Growth Models:
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Most species have constant death rate
Birth only during certain seasons (pop. grows rapidly during breeding season)
This is called geometric growth
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Some species have exponential growth
Exponential growth results in fast growth j shaped growth curve
Geometric/exponential models assume a pop. will grow for ever
This means there are unlimited supplies and the growth rate is a max (rmax)
As pop. grows food, water, light, space all limit size
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Growth rate drops below rmax and reproduction slows
Deaths are close to births and equilibrium achieved
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Logistic growth curves look like a s (sigmoidal curve)
Stationary phase
Log phase
Lag phase
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When pop is small lag phase
Rapid growth log phase
Resources become limited pop experiences environmental resistance leading to stationary
phase
Causing dynamic equilibrium
Use these models to predict the population sizes for later years