Ecology is essentially the study of organisms and how they interact with each other and their environment. Ecology can include factors as specific as nitrate concentration in the soil to the effects of climate change. In AP Biology, we will be investigating ecology at three levels (populations, communities, and ecosystems), but there are many others (including behavioral ecology).
Before discussing the intricacies of populations, it is important to clarify that a population is a group of individual of the same species that share resources. While the populations consist only of that species, they, of course, rely on resources from their environment and other organisms in order to survive and grow.
Thus, you cannot investigate a population effectively without also considering its environment. Within that environment, there will be relevant abiotic factors, which are nonliving, as well as relevant biotic factors which are living. These factors can impact whether a population survives, thrives, dies out, or even dictate what resources is limiting.
https://byjus.com/biology/biotic-and-abiotic/
https://blogs.scientificamerican.com/guest-blog/does-living-in-crowded-places-drive-people-crazy/
When describing populations, it can be crucial to note their densities. A population's density is how many individuals are present in a given area. Consider humans, as those are most familiar to us.
According to the 2020 census data, New York City has a populations of over 29,303 people per square mile whereas Gary, Indiana has a density of 1,388 in that same area.
So imagine yourself in a square whose sides each measure one mile. If you live in New York City, you need to share that square with about 29,000 other people. However, living in Gary, Indiana means you only have to share that square with 1,387 others.
Now obviously density is not the only factor to consider when choosing where to live, but consider some of the things that are relevant to your survival: food, disease, weather conditions. Some of these factors depend on your density. For instance, if a communicable disease were to be introduced to each city, you'd be much less likely to catch it in Gary, Indiana than in New York City. Diseases such as these will spread more quickly in denser populations. Thus, disease is an example of a density-dependent factor - one whose impact depends on the population's density.
Some resources or factors, however, do not depend on a population's density, and, thus are considered density-independent factors. Most examples of these will come from climate and weather because they are so broad-reaching. For instance, a hurricane does not travel faster or slower if more or fewer people are present.
These are all examples of limiting factors which may limit a population's growth. This will be discussed further later.
https://sciencestruck.com/comparison-of-density-dependent-density-independent-factors
Often equally important to its density is a population's dispersion, or how those individuals distribute themselves. The following figure, from your textbook, represents the primary three dispersion patterns to be aware of: clumping, uniformity, and random.
Organisms group together, usually around a resource such as food, leading to some areas of high density. Competition may occur.
Organisms space themselves out in regular, repeating patterns. Territoriality and competition may occur.
Organisms align themselves randomly, leading to areas of higher and areas of lower density by chance.
Living in different populations can involve varying experiences. Some organisms are born one at a time while some organisms have thousands of offspring at a given time. The wide array of survivorship can be displayed with a simplified curve, as shown. Essentially, we break this idea up into three ideals: Types I, II, and III. No organism fits perfect on any one curve, but these are general categorizations.
Type I organisms have low mortality (or death rate) early in life, often due to parental care. These organisms invest a lot into their offspring to ensure survival, and so most mortality occurs late in life. Humans fall into this category in areas of established healthcare systems, in particular.
Type II organisms have a steady mortality rate throughout their entire life span.
Type III organisms have high mortality early in life, usually because parents will maximize how many offspring they have. As a result, not all individuals will survive into adulthood, most dying quite young.
Urry, L., Cain, M., Wasserman, S., Orr, R., & Minorsky, P. (2020). Campbell Biology in Focus, AP Edition (3rd ed.). Pearson Education.
Different taxa can have wildly different survivorship or reproductive rates, meaning that different populations can change in size in drastically different fashion. For example, rabbits are well-known for reproducing quickly, thus they have a high birth rate. This means the population size should increase rapidly> However, they also often have high death rates, which works to bring down the population size.
Birth and death are not the only ways to enter or leave a population, however. Organisms might also enter or leave geographically via immigration or emigration respectively.
A population's growth rate, or the change in its size per unit time, is thus simply a summation of all the inputs and the outputs.
https://sites.google.com/a/mcs.k12.in.us/mrs-birch-science/science/populations?tmpl=%2Fsystem%2Fapp%2Ftemplates%2Fprint%2F&showPrintDialog=1
change in population size = (inputs - outputs) = (births + immigration) - (deaths + emigration)
Often, however, we use mathematical symbols to represent these quantities. B represents birth rate and D represents death rate, I and E represent immigration and emigration, and dN (the d stands for delta, or change) represents the change in population size (N). Thus, the change in population size can be represented by the following equation, often dubbed the BIDE model.
dN = B + I - D - E
Generally, populations will tend to increase in size when resources are abundant. That is because birth rates will be higher and death rates lower when resources are plentiful. If left unchecked, a population will grow exponentially, and a graph of population size over time (or generations) will look like this, sometimes called a J-curve.
Even a population that starts very low in size (as long as it's got enough individuals to reproduce) will increase. As the population size (N) increases, the rate of population increase per generation will also increase. This is because there are more individuals that are reproducing. This is what results in that exponential growth rather than linear growth.
Urry, L., Cain, M., Wasserman, S., Orr, R., & Minorsky, P. (2020). Campbell Biology in Focus, AP Edition (3rd ed.). Pearson Education.
That rate of increase (or slope) on the graph is known as the intrinsic rate of increase (r), or the per capita rate at which an exponentially growing population increases at each instant in time.
Different organisms have different intrinsic rates of increase depending on their ecology (i.e. generation length, reproductive age). Thus, two different populations may both show exponential growth, but have steeper or shallower slopes on average.
In the above example, the blue line increased more rapidly with r = 1.0 whereas the red line's population had r = 0.5.
The population's slope (dN/dt) on the graph, therefore, is constantly changing and is dependent on the population's size (N) and its intrinsic growth rate (r). Thus, to calculate the slope of an exponential growth curve, use the equation dN/dt = rN
Exponential growth curves are simple and make sense until you apply them to more realistic scenarios. No population has limitless resources and so exponential growth cannot continue indefinitely. In reality, every population has limiting factors, which inhibit its growth beyond a certain point.
Every population is different, so the relevant limiting factors can be any resource - space, food, water, etc. Eventually, there isn't enough of something to go around, competition for that thing gets high, and birth rates decrease as death rates increase in that deficit.
These limiting factors cause there to be a carrying capacity (K), a maximum number of individuals in a population that can be sustainably supported. This carrying capacity can change as limiting factors change (during a drought, for instance).
As a population approaches its carrying capacity, its growth rate will slow, and so its slope will decrease. This results in the logistic growth curve with its distinctive S-shape.
Urry, L., Cain, M., Wasserman, S., Orr, R., & Minorsky, P. (2020). Campbell Biology in Focus, AP Edition (3rd ed.). Pearson Education.
The slope (dN/dt) of this curve at any given point can be calculated by this equation. Initially this equation resembles the exponential growth equation, however, the latter half includes the term (K-N)/K. This portion of the equation essentially takes into account how close the population is to the carrying capacity at any given time, and adjust the slope accordingly.
As N approaches the carrying capacity (K), the slope will decrease. So what happens if a population exceeds carrying capacity? In other words, what if N > K? If N > K, dN/dt, or the slope, will be negative.
Negative growth? That just means shrinking, or decreasing in size. so if the population exceeds the carrying capacity, you can expect it to decrease in size thereafter. If it then goes below the carrying capacity, the calculated growth rate will be positive.
Thus, a population can show logistic growth and never be at the carrying capacity for long. It can oscillate up and down near that carrying capacity, as shown here.
http://www.uwyo.edu/dbmcd/popecol/janlects/lect05.html
These models are very useful when discussing population growth over time, but it is important to keep in mind that these, like all models, are imperfect. Real data can approximate these curves, but often there are slight discrepancies. Plotting a line of best fit over these data reveals the J- and S-curves. Below are some examples of real data showing these growth patterns.
Urry, L., Cain, M., Wasserman, S., Orr, R., & Minorsky, P. (2020). Campbell Biology in Focus, AP Edition (3rd ed.). Pearson Education.
Urry, L., Cain, M., Wasserman, S., Orr, R., & Minorsky, P. (2020). Campbell Biology in Focus, AP Edition (3rd ed.). Pearson Education.