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Ecology Unit Two: Population Growth
Terms in this set (38)
Abiotic literally means "non-biological". Abiotic factors that affect living organisms include physical factors such as weather, soil structure, water availability, light availability, and altitude, as well as chemical factors such as pH and available nutrients and minerals. All species have limited tolerances to abiotic factors. Any living organism is affected by a combination of both abiotic and biotic factors, which determine how and where it can live.
Biotic literally means "living". This term describes either the living components of a system or the environmental influences that result from living organisms' activities. Biotic and abiotic factors combine to form an ecosystem.
Put simply, dispersal is the movement of an organism from its place of birth or activity to another location. In ecology, dispersal usually refers to the movement of individuals away from a group of others of the same species. Organisms usually disperse in search of new resources such as food and space. By dispersing away from a densely populated area, individuals may be able to evade competition for those resources. Dispersal also allows colonization of new areas to increase a species' range.
Demography is the study of population dynamics and characteristics. The growth, density, distribution, age structure, and size of populations are studied through the analysis of birth rates, death rates, life expectancy, survivorship, fertility rates, and migration statistics. Demographers usually gather data via a census of a population or through statistical records.
Geometric Growth Population
Geometric population growth is a growth model for populations with non-overlapping generations and unlimited resources. Successive generations differ in size by a constant ratio.
If the birth rate exceeds the death rate, the population size will obviously ______. Vice versa, if the death rate exceeds the birth rate, the population size will ______.
The finite rate of increase (λ)
The finite rate of increase for a population with non-overlapping generations growing geometically is the ratio of the population size at one time step ( Nt+1 ) to the size of the population at the previous time step ( Nt ).
λ = Nt+1 / Nt
Usually, the time step used is equivalent to the generation time (e.g., a year for an annual plant). The geometric growth model assumes the population's growth is not restricted by limiting resources, predation, etc.
geometic growth equation
The geometic growth equation is a useful population growth model for organisms with non-overlapping generations. (also, non-limited resources)
To calculate lambda (λ), the finite rate of increase:
λ= Nt+1 / Nt
To calculate the population size for geometric growth, if λ is known:
Nt+1 = λ Nt
The generalized form of the geometric growth equation is:
Nt = N0 λ^t
λ is the population's finite rate of increase (per time unit).
t is time.
Nt is the population size at time t
Nt+1 is the population size at time t + 1
N0 is the initial population size, at time 0.
The geometric model...
...works when populations are not limited in their growth, so they can continue increasing at the same rate each unit of time. The model also assumes that there is only one discrete reproduction event per unit of time for all individuals.
The geometric growth model assumes not only that reproduction is discrete but also that resources are unlimited and factors like predation are unimportant.
The geometric growth model applies to organisms that have one distinct bout of reproduction each year, so individuals are added to the population all at once. This is often called _________ __________.
_______ fish are born in fresh water, live some or all of their adult lives in salt water, and then return to freshwater to breed.
Exponential Growth Equation
Exponential growth equation
Exponential population growth occurs when the increase in a population's size is proportional to its current size.
The population size ( N ) as a function of time ( t ) is:
Nt = N0 e^(rt)
Here, r is the per capita growth rate. The relationship between r and λ, the finite rate of increase, is:
r = ln(λ)
The instantaneous rate of change for the population, dN / dt is:
dN / dt = rN
Note that when the population is small, dN / dt will be comparatively small. Conversely, when the population is large, dN / dt will be comparatively large.
When r is ______ than 0, the population is increasing; when r is ______ than 0, the population is decreasing.
Instantaneous Rate of Change
The term dN/dt is the rate of change at any given time point on the graph. It expresses how quickly the line on the graph is going up (positive dN/dt) or down (negative dN/dt). That rate of change is the slope of the curve at that point. The slope can be visualized by drawing a tangent line to the curve at that point.
In more technical terms, dN/dt is the instantaneous rate of change. The "d" in this expression symbolizes change and is related to the greek letter delta, Δ. You can find much more thorough descriptions in any beginning calculus text or online.
Intrinsic Population Growth Rate
The intrinsic population growth rate (or intrinsic rate of increase), symbolized by r, is the population growth rate, per individual, for a population with unlimited resources.
The same symbol, r, is sometimes used to describe the current per capita growth rate for a population. The intrinsic rate of growth is the maximum possible per capita growth rate in a certain environment, with unlimited resources.
As a number (ex: N) gets bigger so does something else (ex: change per unit time)
Maximum Intrinsic Growth Rate
The maximum intrinsic rate of increase for a species is the maximum value at which a population of that species could grow given an ideal environment and unlimited resources.
Per Capita Growth Rate
The per capita growth rate is the rate at which additional individuals are being added to the population, per individual already in the population.
Mathematically, per capita growth rate is (dN/dt) / N. For exponential growth, r, the intrinsic growth rate, also describes per capita growth rate. This equivalency holds when resources are unlimited in a given environment.
When resources are limiting, as with logistic growth, r is usually greater than the actual per capita growth rate.
The per capita growth rate for a population can be estimated by taking the natural log of λ, the finite rate of increase.
If a species exists outside of its environmental tolerance range, r will become ______ and the population size _________
Doubling time is the amount of time required for a population to double in size. To calculate doubling time (td) using the exponential growth equation model:
td = 0.693/ r
where r is the population's per-capita growth rate.
For the population to double, the abundance of aphids will be twice the size at time td as it was at time zero. In other words, the ratio of the population size N at time td to the population size at time zero ( N0 ) is equal to 2.
N(sub td) / N (sub 0) = 2
N (sub td) = N (sub 0) e ^(r * td)
N (sub td) / N (sub 0) = e ^ (r * td)
The replacement level of a population is the rate of reproduction that offsets mortality and maintains a stable population size. In human demography, the replacement level for a couple is considered to be around 2, since two children per couple replaces their two parents in the population after the parents die. If the birth rate of a population is below the replacement level, that population will decline in size through time.
The exponential growth equation describes a population with _______ resources that is expanding at an increasing rate over time
Carrying Capacity, K
A population's carrying capacity is the maximum number of individuals that its environment can sustainably support. The carrying capacity is usually constrained by limiting factors such as space, nutrients, food availability, water, and light.
Logistic growth is a model of population growth in which the per capita growth rate ( r ) declines as the population size increases. As a population approaches its maximum possible size (its carrying capacity, K ), the growth of the population slows towards no growth. A plot of population size versus time for logistic growth produces a sigmoid, or S-shaped, curve.
Logistic Growth Equation
Logistic growth is a model of population growth in which population growth rate (dN/dt) declines as the population size increases and approaches its maximum possible size (its carrying capacity, K). If the population size is larger than K, growth is negative and the population shrinks.
The logistic growth equation models population growth in the presence of a limiting resource. The equation is:
dN/dt = r N ( 1 - (N/K))
where r is the intrinsic growth rate, K is carrying capacity, and N is population size.
The influence of density-dependent factors on the dynamics of a population changes with the size of that population. Normally, the larger the population size, the greater the effect these factors have. Examples include disease, competition for food, parasitism, and predation.
The influence of density-independent factors on the dynamics of a population does not change with the size of that population. These factors have the same relative impact on the population regardless of how many individuals are present. Events such as storms, fires, volcanoes, and floods are examples of density-independent factors that lead to the same proportion of the population being affected whether the population is large or small.
Growth Rate, R
r = b - d
growth rate = birth rate -death rate
r = birth rate - death rate + immigration rate - emigration rate
In common usage, a species becomes extinct when the last living individual of that species dies. In biology, extinction is also applied to populations. If the last living individual in a distinct population dies, then that population becomes extinct.
Source-sink Population Dynamics
In some areas, one population persists stably over a long period of time while nearby populations are not stable and can go extinct.
If emigrants from the stable population (the source) often rescue the other populations (the sinks) from extinction, we call the whole system of populations a source-sink system, and this system has source-sink population dynamics.
A metapopulation is a collection of spatially distinct subpopulations of the same species that are connected via dispersal. It is sometimes referred to as a population of populations. In the strictest definition of a metapopulation, the whole system persists over time, even though individual populations sometimes go extinct.
Patch Occupancy Dynamics of a Metapopulation
dP / dt = c
P (1 - P) - e
refers to seemingly random variability in resource availability, ecological community composition, predation pressure, weather events, etc., which often causes fluctuations in a population's growth rate.
Population growth rate is determined by birth and death rates. By chance, there could be many births in a row, leading to a higher population growth than you would expect. Or by chance, there could be a number of deaths in a row, leading to unexpected extinction. Such a chance sequence of events leading to variation in a population's growth is known as demographic stochasticity.
The Allee effect is a phenomenon in ecology wherein, for very small populations, there is a positive correlation between population size and the per capita population growth rate. That is, the smaller the population size, the lower the birth rate and higher the death rate, regardless of other factors. This effect often challenges attempts made to save populations on the brink of extinction.
"an Allee effect is when the population growth rate at small population sizes is lower than at somewhat higher population sizes"
Discrete Logistic Equation
N(sub t+1) = Nt + (λ - 1) *Nt (1 - (Nt/K)
Here the population size at time t+1 is split into the portion that represents the replacement of the current population (the first term, Nt ) and the portion that represents the increase or decrease in the population during the current time step (the second term, which occurs after the plus sign). That second term says, in words, that the population in the next timestep (t+1) is limited by density effects during this timestep (t)
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