Island biogeography with ping pong balls

Introduction

One of the first global patterns of diversity that early naturalists observed was the relationship between area and the number of species that a space holds.  This relationship was easy to describe on islands where species richness of multiple groups of animals or plants (taxa) had been described. For example, Figure 1 demonstrates this species-area relationship. For example, Cuba is the largest island in the Caribbean, and Redonda is one of the smallest. If you look at the number of species (amphibians and reptiles, classically studied as a group by herpetologists) found on each island (y-axis), Cuba has far more species than Saba does.  Ecologists noted that species richness did not just increase with size; it tended to increase at a regular rate.   In general, we find that an area that is 10 times larger has about twice as many species. Note this relationship appears linear in the figure due to the use of log scales on both axes!  

While studying patterns of species richness on islands, two ecologists, Robert H. MacArthur and Edward O. Wilson,  noted some exceptions to the rule. For example, some large islands had fewer species than expected due to their size, while some small islands tended to be more species-rich than expected.  To explain these global patterns they proposed the Equilibrium Theory of Island Biogeography.   It focuses on how size and distance from a "mainland", or source of species, influences island richness.  To understand the Island Theory of Biogeography, let's first consider Figure 2.  

Imagine there are two islands  located off the coast of the mainland. Although the two islands are about the same size, the second island is located much farther away than the first island. If you are a bird that lives on the mainland, which island are you most likely to end up on? The answer is generally the first island.  This means immigration (or colonization) is influenced by the distance of an island from the mainland (a source of colonists). Therefore, islands that are closer to the island are more likely to receive immigrants than islands that are further away. 

Once a species manages to reach and colonize an island, the rate of extinction is largely influenced by size of the island. This is because smaller islands tends to hold smaller populations (which are more likely to experience extinction due to stochastic effects like genetic drift!).    Larger habitat size reduces the probability of extinction  of the colonized species due to chance events.  Smaller islands are also likely to holder fewer populations in general because they have less resources and less diversity of resources.  Larger islands have larger and more habitat areas, which typically leads to more differences in habitat, or habitat heterogeneity. Higher heterogeneity means that there are more opportunities for a variety of species to find their suitable niches. Habitat heterogeneity  also helps increase the number of species to successfully colonize after immigration. 

We could plot both immigration and extinction relationships on a single image, like is done in Figure 3. Not the y-axis is the number of species.

This basic graph makes a lot of assumptions but also offer a lot of insight.  In this graph, immigration rates (blue lines) depend on proximity to mainland.  Immigration rates also decline with species richness. That's becasuse its' easiest to immigrate to an island when it is empty because all the resources on the island are available.  As the islands gets more and more full, colonizing the island becomes more difficult.  

Extinction rates (orange lines), as noted above, depend on island size.  We also see that extinction rates tend to increase with the number of species.  This should make sense: If there are no species on an island, extinction is impossible, but as more and more species arrive (and compete!) extinction becomes more likely.  

Figure 3  shows the basic Equilibrium Theory of Island Biogeography. It suggests that islands will reach an equilibrium, or stable, number of species when immigration and extinction rates are equal!  Note this model could be modified in multiple ways. Size of an island, for example, likely also impacts immigration rate (larger islands are easier to hit!), and islands that are close together may also share individuals (the Rescue effect!), but even this simple conceptualization has proven useful for understanding global species richness patterns.  

One interesting point to note is that an equilibrium number of species is reached when immmigration and extinction rates are equal, not when those processes stop! This means islands may consistently be changing species composition but should maintain fairly consistent levels of species richness. As odd as this sounds, early tests of the Equilibrium Theory of Island Biogeography supported these assumptions.  When mangrove islands off the coast of Florida were fully cleared of their invertebrate (insect and arachnid) communities and allowed to recolonize, islands eventually stabilized with communities of about the same richness as they had before disturbance.  

The island biogeography model has crucial applications for wildlife management, because wildlife reserves or patches of habitat can be considered “islands” of habitat in “an ocean” of an inhabitable area. 

In this exercise, we will simulate the island biogeography model using egg cartons and Ping-Pong balls. We use egg cartons as islands, Ping-Pong balls as species, and cups of egg cartons as different niches. Imagine that each species (or a Ping-Pong ball) has unique feature(s) (e.g. species of finch with robust beaks to crack open hard seeds) thus live in a niche where the species find lots of hard seeds that no other birds can consume).  The goal of this exercise is to investigate how island size and the distance between an island and the mainland, influence the equilibrium between immigration and extinction.

Methods

Materials (per group)

• 1 egg carton, size depending on your simulation scenario.

• 1 dozen-sized egg carton – “large island”

• 1 half-sized egg carton – “small island”

• 16 ping-pong balls (species)

• 1 pair of dice, of different colors (e.g. green and red)

• Felt-tip markers to match dice colors (e.g. green and red)

• Labelling tape and meter stick

Protocol

Set-up: 

• 1. Instructors will divide the class into groups to carry out one or more of the following simulations..

     • Large / Close Island (12 egg carton/1m distance)

     • Small / Close Island (6 egg carton/1m distance)

     • Large / Far Island (12 egg carton/2 m distance)

     • Small / Far Island (6 egg carton /2m distance)

 2. For simulations using large egg cartons, label the 6 cups at one side of the large egg carton 1-6 with one color and other half with another color.

3. For simulations using small egg cartons, number the 6 cups of the small egg carton 1-6 (single color).

4. Designate each team member a role 

1)   Colonization simulator

2)   Extinction simulator

3)   Ping-Pong ball catcher

4)   Data recorder

PART 1 - Simulations

Team 1: Simulate colonization of a large close Island:

• 1. Mark the position of your mainland using labelling tape (this is where the colonization simulator will be standing), and place the large egg carton (a large island) one meter away from you. 

  2. The colonization simulator stands on the mainland and tries to bounce 5 Ping-Pong balls into the niche spaces on the “large island.” Ping-Pong balls that do not settle into a “niche” have not become “established” and must be removed.

  3. After the 5-ball colonization trial, the extinction simulator shakes the two dice (e.g. green and red), pick one die out at random, and tosses it. The color and number of the die indicates the side of the large island and the ”niche” (e.g. green & 1). If this niche is occupied, remove the ball (a species) and consider one “extinction event” has occurred. 

  4. The recorder writes down the information in Simulation Data Table: large close island.

     • Column 1: number of species existed at the beginning of the round.

     • Column 2:  number of successful colonization events occurred during that round.

     • Column 3:  number of species present on the island after the colonization simulation. (Add Column 1 & 2) 

     • Column 4:  number of species went extinct.

Notes: Keep all of the balls colonized the island and move on to the next round, 5 balls throws = 1 Round.

5. Repeat step 2 through 4 for 30 rounds.

Team 2 : Simulate colonization of a small close Island:

• 1. Follow the simulation instruction for Team 1, EXCEPT, replace the large egg carton with the half-dozen-sized egg carton. Use one die instead of two dice. Each number of the one die indicates one ”niche” of the island.

  2. Repeat step 2 through 4 in the Team 1 simulation instruction for 30 rounds (Simulation Data Table: small close island)

Team 3: Simulate colonization of large distant island:

• 1. Follow the simulation instruction for Team 1, EXCEPT, place the large egg carton (a large island) two meter away from your marked location (main island).

  2. Repeat step 2 through 4 in the Team 1 simulation instruction for 30 rounds (Simulation Data Table: large distant island)

Team 4: Simulate colonization of small distant island:

• 1. Follow the simulation instruction for Team 1, EXCEPT, place the half-dozen-sized egg carton two meter away from your marked location (main island). Use a die instead of two dice. For example, a number of the die indicates one ”niche”.

  2. Repeat step 2 through 4 for 30 rounds (Simulation Data Table: small distant island) 

PART II - Data analysis

 Calculate Colonization Rate

• 1.  Each team will pool data from their own simulation(s) and fill out the DATA TABLE COLONIZATION (one table for each simulation!). Find all cases in which the initial species number is 0 from the column 1 of your Simulation Data Table. Multiply the number of cases by 5 to determine the “# of colonization attempts by your group” for column 5 in DATA TABLE COLONIZATION. Add up rows of column 2 in Simulation Data Table for the cases that the initial species were 0. 

  2. Repeat the step 1 above for cases in which the initial number of resident species is 1 through 12 for the teams used large cartons (TEAM 1 & 3), and 1 through 6 for the teams used small cartons (TEAM 2 & 4).

  3. Divide (total successes:  col. 6) / (total attempts :  col. 5) to calculate the rate of immigration in column 7.

DATA TABLE COLONIZATION (LARGE ISLAND- TEAM 1 & 3)

DATA TABLE COLONIZATION (SMALL ISLAND- TEAM 2 & 4)

Calculate Extinction Rate

• 1. Now you will calculate extinction rate of your simulation(s).  For each simulation, the numbers in column 3 in Simulation Data Table are the numbers present after colonization event. We assume that the extinction rate is zero when no species are present on the island.  Look through Column 3 in your Simulation Data Table and find all cases in which 1 species is present. Write the total number of cases in Column 8 “# of extinction trials” in Data Table Extinction. Then add up the number of extinction events that actually occurred in these cases from Column 4 in your Simulation Data Table, and write down the sum in Column 9 in Data Table Extinction.

  2. For the teams that used large egg-cartons (TEAM 1 & 3), repeat step 1 above for cases with 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 species present at the beginning of the extinction trial. For the teams that used small egg-cartons (TEAM 2 & 4), repeat step 1 above for cases with 2, 3, 4, and 5 species present at the beginning of the extinction trial.

  3. Divide (# extinction events : col. 9) / (# of extinction trials :  col. 8) to calculate the rate of extinction in column 10 in DATA TABLE EXTINCTION. We will assume that the extinction rate for an island with maximum number of species present is 1.0 (100%), since the die will indicate the removal of one of the 12 balls no matter what whenever all of the niches are completely occupied.

      DATA TABLE EXTINCTION (LARGE ISLAND - TEAM 1 & 3)

      DATA TABLE EXTINCTION (SMALL ISLAND - TEAM 2 & 4)

PART 3 -Plot immigration and extinction rates on the graph:

• 1. Share the colonization and extinction rates from your simulation with your class (e.g. write on the white board) so that each team can have all of the simulation results (large/close, small/close, large/far, small /far). 

  2. Plot graphs for each case (large/close, small/close, large/far, small /far) by following the instruction. Your team can divided the tasks to draw the graphs.

     • Plot the class immigration rates (using software or provided graph)

X-axis : initial species # 

Y-Axis : rate of immigration (Data Table Extinction: Column 7)

• • • Plot the class extinction rates on the same graph.

X-axis : initial species # 

Y-Axis : rate of extinction (Data Table Extinction: Column 10)

IMMIGRATION AND EXTINCTION CURVES 

3. Compare the graphs of 4 scenarios and make sure you can answer the following questions:

• • • Why is island size an important factor in terms of number of species present on an island?

    • Why is island distance from the mainland an important factor in terms of number of species present on an island?

    • Explain the species-area relationship

    • Which size/distance of island has the highest colonization rate?

    • Which size/distance of island has the lowest colonization rate?

    • Which size/distance of island has the highest extinction rate?

    • Which size/distance of island has the lowest extinction rate?

    • Why do extinction rates increase with increasing number of species on the island?

    • Why does the colonization rate decrease with increasing number of species on the island?

    • How can the theory of Island Biogeography be useful for conservation preserves?

This lab module is adapted from:

https://www.hartnell.edu/sites/default/files/u136/Wheat/is_biogeography_lab.doc

http://amnhconbio.blogspot.com/p/session-9.html​

Still interested?