Graphs and ecology - they go together like predator and prey. Episode 77 recAPs the four equations discussed in Unit 8.
Graphs and ecology - they go together like predator and prey. Episode 77 recAPs the four equations discussed in Unit 8 - population growth (1:11), exponential growth (2:42), logistic growth (5:00) and Simpson’s Diversity Index (6:26). Get your calculator ready for some practice examples!
The Question of the Day asks (9:01) Autotrophic organisms that capture energy from small inorganic compounds are classified as these.
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Hi and welcome to the APsolute Recap: Biology Edition. Today’s episode will recap Ecology Equations
Zoom out:
Unit 8 - Ecology
Topic 8.3, 8.4, 8.5
Big idea - Energetics & Information Storage and Transmission
Graphs and ecology - they go together like predator and prey. Or like things you need to know on the AP Exam and calculators. Don’t forget that the AP Biology Equations and Formulas sheet is included as a reference during the test. No memorization required. All you need to do is grab your numbers from the questions, plug them into the right equation and get your answer. However, we know that the interpretation and application of these numbers is where understanding comes in.
Let’s Zoom in:
Section 8.3 is titled Population Ecology includes the equations for population growth and exponential growth. Population growth dynamics depend on a number of factors. And growth is a bit deceiving. What we really mean is population size change over time. If your growth is negative, well then the population is shrinking. Let me explain. The population growth equation is very simple, and can likely be solved in your head for most problems. Capital N is always going to represent population size in all of our equations. The change in population (delta N) over change in time (delta t) is equal to the birth rate (capital B) minus the death rate(Capital D). So if you have more births than deaths in a population, your answer would be positive indicating an increase in population size over time. If more individuals are dying than are born, the rate is negative. For example, if the growth rate for a sample of bacteria is 5,000 cells/mL per hour and you started with a population size of 6,000, how many bacteria would you have in 3 hours? 21,000! Bacteria reproduce very quickly by binary fission, so even this estimate is likely low.
Next is the equation for exponential growth - the “kumbaya” of it all - when there's little, if any, restrictions on population size. Resources are plentiful! There's space to stretch out and no predators in sight! Exponential growth is a model which increases quickly and by increasingly large amounts. Graphically, it would look like a J shaped curve. To calculate the exponential growth rate of a population you multiply the population size by r max - which is the maximum per capita growth rate of a population. This value might be given to you directly, or interpreted from a data set. For example, if a population grows from 10 to 15 in a given time frame, then the growth rate is 0.5. If r is greater than zero, the population is going to have fast, exponential growth. If an ecosystem stays relatively stable, we can expect the growth rate to also stay the same. This makes it easier to predict population growth. The r value changes over time for a population as other factors (abiotic like floods and biotic like new predators) enter the equation (figuratively, not literally).
Section 8.4 is titled Effect of Density on Populations and includes the equation for the Logistic growth model. This is the more common scenario for populations, where overcrowding and increased competition for resources set limits on how large a population can get. There just isn’t enough to go around for everybody. The population cannot increase indefinitely, but will instead have a carrying capacity (Capital K in our equation). K is the maximum population size that can be sustained by the resources available. And so, we have the growth rate (change in population N over change in time) is equal to r max times N multiplied by parentheses (K - N over K). So, if r max is 0.5, the carrying capacity is 100 and our population size is 80, what is the logistic growth rate? 8 individuals per unit of time. As your population increases, density increases and you continually run up against limiting factors which slow your growth. If you observe a population graph that is at carrying capacity, there will still be small ups and downs in size, but the average population is consistent and levels off.
Section 8.5 is titled Community ecology and includes the equation for Simpson’s Diversity Index. Essentially, this equation compares the number for one species to the entire sample. Don’t be scared, but sigma is back (the Greek E looking letter that means summation). Small n is the number of organisms of one species and capital N is the number of organisms of all species. And so we have the diversity index equal to 1 minus the sum of parentheses small n over capital N, close parenthesis, squared. Adding some numbers will bring this to light. Imagine you have a parking lot with 100 cars. Let’s say it's a Target Parking lot. 20 are trucks, 60 are SUVs and 20 are vans. What is the diversity index of the parking lot community? Let’s start with the trucks. 20 divided by 100 is 0.2. 0.2 squared is 0.04. Repeat with SUVs and get 0.36. Vans is also 0.04. Add this all up to equal 0.44 and subtract this value from 1. The diversity index of the parking lot is 0.66. If I were to compare this car population to another - say at a Whole Foods - that has a diversity index of 0.75 - which one is more diverse? Whole Foods! the closer the value is to 1, the more diverse the population.
Time for unit connections. Somewhat of a giveaway here. It's all Unit 8 material. However, other factors, like immigration and emigration can also influence population size. This correlates back to Unit 7 with genetic drift and Hardy-Weinberg equilibrium. Alright - what about the exam? Many applications of these equations will involve experimental data and extracting information from graphs. Get cozy with axis labels and don’t forget to check the units!
To recap……
Organisms can be monitored in growth models and diversity. Growth rate is calculated considering births and deaths. Exponential growth occurs with unlimited resources whereas logistic growth models consider carrying capacities. Communities have varying species diversity.
Coming up next on the Apsolute RecAP Biology Edition: Community Ecology
Today’s question of the day is about energy
Question of the day: Autotrophic organisms that capture energy from small inorganic compounds are classified as these.