In this Click & Learn, students explore mathematical models that describe how populations change over time and apply these models to the invasive lionfish population in the Bahamas. They also use data from other species to learn how density-dependent factors limit population size.
The Click & Learn includes realistic and actual data from lionfish and other case studies. It provides opportunities to use the logistic growth model, graph data, and interpret figures from published scientific research.
Additional information related to pedagogy and implementation can be found on this resource’s webpage, including suggested audience, estimated time, and curriculum connections.
- Mathematical population models are used to study how populations of organisms, including invasive species, change over time.
- Discrete-time models describe how populations change over specific time periods.
- Continuous-time models describe populations that change instantaneously.
- Logistic models describe population growth that is limited by negative density-dependent factors. In a logistic model, the growth rate changes depending on the population’s density.
- Negative density-dependent factors include competition, predation, disease and parasites, and social behaviors.
Student Learning Targets
- Describe invasive species and their impacts on ecosystems.
- Define carrying capacity and explain how it relates to density-dependent population growth.
- Use discrete-time and continuous-time logistic equations to model population dynamics.
- Describe how the population growth rate varies with population density in a logistic model.
- Compare realistic field data to projections from models.
- Use data from case studies to explain how various negative density-dependent factors regulate population size.
Benkwitt, Cassandra E., Mark A. Albins, Kevin L. Buch, Kurt E. Ingeman, Tye L. Kindinger, Timothy J. Pusack, Christopher D. Stallings, and Mark A. Hixon. “Is the lionfish invasion waning? Evidence from The Bahamas.” Coral Reefs 36, 4 (2017): 1255–1261. https://doi.org/10.1007/s00338-017-1620-7.
Bryan, David R., Jeremiah Blondeau, Ashley Siana, and Jerald S. Ault. “Regional differences in an established population of invasive Indo-Pacific lionfish (Pterois volitans and P. miles) in south Florida.” PeerJ 6 (2018): e5700. https://doi.org/10.7717/peerj.5700.
Côté, I. M., and N. S. Smith. “The lionfish Pterois sp. invasion: Has the worst‐case scenario come to pass?” Journal of Fish Biology 92, 3 (2018): 660–689. https://doi.org/10.1111/jfb.13544.
Dahl, Kristen A., Morgan A. Edwards, and William F. Patterson III. “Density-dependent condition and growth of invasive lionfish in the northern Gulf of Mexico.” Marine Ecology Progress Series 623 (2019): 145–159. https://doi.org/10.3354/meps13028.
Goodbody-Gringley, Gretchen, Corey Eddy, Joanna Michelle Pitt, Alex David Chequer, and Struan Robert Smith. “Ecological drivers of invasive lionfish (Pterois volitans and Pterois miles) distribution across mesophotic reefs in Bermuda.” Frontiers in Marine Science 6 (2019): 258. https://doi.org/10.3389/fmars.2019.00258.
Green, Stephanie J., John L. Akins, Aleksandra Maljković, and Isabelle M. Côté. “Invasive lionfish drive Atlantic coral reef fish declines.” PLoS ONE 7, 3 (2012): e32596. https://doi.org/10.1371/journal.pone.0032596.
Whitfield, Paula E., Roldan C. Muñoz, Christine A. Buckel, Brian P. Degan, D. Wilson Freshwater, and Jonathan A. Hare. “Native fish community structure and Indo-Pacific lionfish Pterois volitans densities along a depth-temperature gradient in Onslow Bay, North Carolina, USA.” Marine Ecology Progress Series 509 (2014): 241–254. https://doi.org/10.3354/meps10882.
Case study 1: Fruit production in paprika peppers
Cavero, J., R. Gil Ortega, and M. Gutierrez. “Plant density affects yield, yield components, and color of direct-seeded paprika pepper.” HortScience 36, 1 (2001): 76–79. https://doi.org/10.21273/hortsci.36.1.76.
Case study 2: Population growth rates of protozoa
Holdridge, Erica M., Catalina Cuellar-Gempeler, and Casey P. terHorst. “A shift from exploitation to interference competition with increasing density affects population and community dynamics.” Ecology and Evolution 6, 15 (2016): 5333–5341. https://doi.org/10.1002/ece3.2284.
Case study 3: Parasites on fish farms
Jansen, Peder A., Anja B. Kristoffersen, Hildegunn Viljugrein, Daniel Jimenez, Magne Aldrin, and Audun Stien. “Sea lice as a density-dependent constraint to salmonid farming.” Proceedings of the Royal Society B: Biological Sciences 279, 1737 (2012): 2330–2338. https://doi.org/10.1098/rspb.2012.0084.
Case study 4: Cannibalism in shore crabs
Moksnes, Per-Olav. “Self‐regulating mechanisms in cannibalistic populations of juvenile shore crabs Carcinus maenas.” Ecology 85, 5 (2004): 1343–1354. https://doi.org/10.1890/02-0750.
Case study 5: Predation of mosquito larvae
Bickerton, Matthew W., Joseph Corleto, Thomas N. Verna, Eric Williges, and Deepak Matadha. “Comparative efficacy of Pimephales promelas , Fundulus diaphanus, and Gambusia affinis and influence of prey density for biological control of Culex pipiens molestus larvae.” Journal of the American Mosquito Control Association 34, 2 (2018): 99–106. https://doi.org/10.2987/17-6718.1.