Ecology
the branch of biology that deals with the relations of organisms to one another and to their physical surroundings.
Emigration
movement
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Exponential Growth
Growth pattern in which the individuals in a population reproduce at a constant rate, without the carrying capacity taken into account
geographic range
the area over which a population is spread (reflects in part the climates a population can tolerate)
geometric rate of increase
lambda, populations grow when more than one, stable when equal to one, shrinking when less than 1
immigration
movement into a population
intrinsic rate of increase
the rate of change in population size for continuous growth (r max)
lambda
expresses a population's growth rate over a discrete interval of time (i.e. on day, one year, etc.)
per capita growth rate (r)
equal to the per capita growth rate plus the per capita immigration rate minus the per capita death rate minus the per capita emigration rate
population
A group of individuals that belong to the same species and live in the same area
vital rates b, i, d, and e
birth, immigration, death, emigration
carrying capacity (K)
the limit of how many individuals in a population the environment can sustain
density-independent factor
limiting factor that affects all populations in similar ways, regardless of population size (ex: tornado)
density-dependent factor
factor that limits a population more as population density increases
equilibrium
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limiting factors
Any biotic or abiotic factor that restricts the existence, numbers, reproduction, or distribution of organisms. (biotic factors CAN regulate, abiotic CANNOT)
logistic growth
resource limitation stops exponential growth, so curve starts to flatten close to carrying capacity.
overshoot
populations that are undergoing exponential growth go over the carrying capacity before stabilizing
population density
the population's size divided by the range. Tells how crowded or dispersed the individuals that make up the population are
population size (N)
the number of individuals at all ages alive at a particular time at a particular place
What is ecology? What sorts of problems do ecologists work on?
ecology is the study of how organisms interact with one another and with their physical environment. Ecologists work on applied problems such as invasive species, infectious disease, pollutants, global warming, etc.
What four things can change the size of a population? What are the vital rates?
Birth, immigration, death, and emigration. These are the 4 vital rates of a population
What do changes in population size reflect?
Changes in population size reflect the sum of the four vital signs.
What do B, I, D, and E stand for?
B=number of births, D=number of deaths I=immigration number E-emigration number
What does N represent? What does t represent? What is lambda, λ? What does it mean if lambda is greater than, less than, or equal to 1?
N is the number of individuals, t is time (now), λ is the geometric growth rate. If lambda is: populations grow when more than one, stable when equal to one, shrinking when less than 1
How can we predict population size one time step into the future? How can we predict population size more than one time step into the future? Why should you be careful predicting very far into the future?
If predicting one step into the future, use N t+1=λNt (the equation for geometric population growth. For more than one step into the future, use Nt=λ^tN0
How does lambda relate to the percent increase in the population?
λ=1+c, where c=% increase in decimal form
What is the difference between discrete and continuous growth?
Discrete growth happens over a "discrete" interval of time. This is expressed by lambda. As the time intervals become infinitely smaller, the growth becomes continuous, and the population grows exponentially.
What is dN/dt? What is rmax?
dN/dt is the slope of an exponential time v. population size graph, and shows the rate of change over a very short time interval (in a continuous manner). rmax is the rate of change in population size for continuous growth. (the max rate of change for a population for a set amount/type of resources)
How are λ and rmax related?
λ=e^rmax, and rmax=lnλ (for continuously growing populations)
What is the difference between B, I, D, and E vs. b, i, d, and e?
The capital letters (B, D, I, and E) are all the birth, etc. rates for a population, while the lowercase letters are the rates but per capita (so they are the capital letters divided by the total population size)
What does "per capita" mean?
Per capita means per person (so it is any rate divided by total population)
What is the relationship between r and rmax?
r is the rate of growth per individual, while rmax is the max rate of increase of the population for a given set of abiotic conditions. r is usually smaller than rmax
How can you calculate the change in population size for a population that is growing exponentially?
N(t)=λ^tN(0) OR dN/dt=rmaxNt
If given information on births, deaths, immigration, emigration, and population size — or if given b, i, d, and e — how can you calculate r?
r= b+i-d-e
For what values of r are populations growing? What about for λ? For what values of r are populations shrinking? What about for λ?
Growing when λ>1 or r>0
Stable when λ=1 or r=0
Shrinking when λ<1 or r<0
When a population has a constant rmax or λ, what happens to the number of individuals added to the population per time step?
The number of individuals added are equal to the number taken away when the population is stable.
Can populations grow exponentially indefinitely? Why or why not?
Not usually, since at some point there will be a limitation of resources or some density-independent thing will happen to limit the population. Usually populations hover around their carrying capacity as biotic factors regulate.
As population size increases in an already large population, what changes do you expect to see in birth rate and death rate?
The birth rate will start to lower as resources become more limited. Death rate will increase as there is less food to eat, and parasites and such become more common with a high population.
What is carrying capacity? What is the variable that represents carrying capacity? What sets carrying capacity? How does intraspecific competition relate to carrying capacity?
Carrying capacity is the max number of individuals that a population can support. K represents carrying capacity. it is set by resources, and intraspecific competition (competition within a species) regulates the pop. around K.
How does r change over time in a population as it grows from a very small population relative to carrying capacity to a large population near (and eventually at) carrying capacity?
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When a population is growing logistically, what does the pattern look like if time is on the x-axis and density is on the y-axis? What does the pattern look like if density is on the x-axis and r is on the y-axis? What specific factor causes the pattern shown in both of these
graphs?
The pattern is s-shaped when time is on the x axis. When density is on the x-axis and r is on the y, it looks like a straight, diagonal line. In both of these graphs, the higher the pop. density gets, the lower the r is, and visa versa.
What equation can be used to describe logistic growth? How does this equation differ from the one for exponential growth?
The logistic growth model: dN/dt=rmaxNt(K-Nt/K). This equation considers the carrying capacity, which the exponential equation does not have.
What happens to the term in parentheses in the logistic growth equation as a population moves from a very low density to a density very close to carrying capacity?
The (K-Nt/K) term aka "room to grow" decreases as the population comes close to the carrying capacity.
In a population experiencing logistic growth, how does dN/dt change over time as you move from a very low density to a density very close to carrying capacity?
Decreases?
At which point (relative to density) are exponential and logistic growth most similar?
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Does rmax change over time in logistic growth? If so, how? Does 'real' r change over time in logistic growth? If so, how?
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What happens if the population size exceeds carrying capacity? What happens to dN/dt when N > K? What happens to population size when N > K?
After the population overshoots the carrying capacity dN/dt will be less than 0 as there begin to be more deaths than births, and population begins to shrink.
What is the difference between density dependent and density independent growth?
Density-dependent affects the population in accordance to how dense the pop. is; density-independent does not matter how dense the pop. is
What factors can regulate population size? What factors can influence (but not regulate) population size? In ecology terminology, is there a difference between "influence" and "regulate"?
Biotic factors regulate population size, and abiotic factors can influence pop. size. YES there is a difference, influencing a pop. does not attract a pop. to it's equilibrium density like regulation does.
How is population regulation like a thermostat?
It adjusts and requires negative feedback.
How can you tell if a figure/graph shows density dependence or density independence?
Density dependence will show logistic growth, and be diagonal on a density v r graph. Independence will show exponential growth and be a horizontal line.
Is a population that is growing in a density dependent manner growing exponentially or logistically? Is a population that is growing in a density independent manner growing exponentially or logistically?
Density-dependent=logistic growth, density-independent=exponential growth [Show Less]