# BIO313: Population Ecology

Unit 2: Population Fundamentals: Describing and Quantifying Populations   In this unit, we will learn mathematical models to describe basic, single-species, density-independent population dynamics.  We will look at how population growth is measured and then will examine the different ways population growth can be predicted.  Birth rates, death rates, and age structuring of a population will be discussed and integrated into our predictive models.  We will also discuss how a population reaches equilibrium and how population size might cycle across time, and we will identify two important measures of population size: minimum viable population and effective population size.

This unit should take you approximately 7½ hours to complete.

☐    Subunit 2.1: 0.5 hours

☐    Subunit 2.2: 1.5 hours

☐    Subunit 2.3: 1.5 hours

☐    Subunit 2.4: 1.5 hours

☐    Subunit 2.5: 0.25 hours

☐    Subunit 2.6: 0.5 hours

☐    Subunit 2.7: 1.5 hours

☐    Subunit 2.8: 0.25 hours

Unit2 Learning Outcomes
Upon successful completion of this unit, students will be able to: - Use mathematical models to estimate population growth and calculate the intrinsic rate of natural increase (r) and carrying capacity (K) for a population. - Construct and explain general, static, and cohort life history tables for a population. - Describe the factors that result in stable population size (equilibrium) and population cycling. - Describe the difference between minimum viable population (MVP) and effective population size (EPS) and explain the importance of these calculations in population conservation.

2.1 Population Growth   - Reading: Utah State University: Dr. Michelle Baker: “Population Growth” Link: Utah State University: Dr. Michelle Baker: “Population Growth” (HTML)

Instructions: Please read this entire webpage, which describes factors that are considered in mathematical models that determine population growth.  All mathematical models provide only an estimate of population size.  Even if members of the population are trapped and counted, one can never be certain that all individuals have been trapped and countedbecause some organisms are trap-shy.  For every individual trapped and counted, scientists usually estimate that two additional individuals have not been counted.  Therefore,estimates of population size are usually underestimates.This material also covers subunits 2.3 through 2.3.2.

2.2 Growth Curves   - Reading: National Institute on Aging: Dr. Alexei Sharov: “Exponential and Logistic Growth” and “Discrete-Time Analogs of the Exponential and Logistic Growth Models” Links: National Institute on Aging: Dr. Alexei Sharov: “Exponential and Logistic Growth” (HTML) and “Discrete-Time Analogs of the Exponential and Logistic Models” (HTML)

Instructions: Please read these entire webpages, which describe the fundamental models of population growth.

2.2.1 Unlimited Growth: Exponential Growth   - Reading: National Institute on Aging: Dr. Alexei Sharov: “Exponential Model” Link: National Institute on Aging: Dr. Alexei Sharov: “Exponential Model” (HTML)

Instructions: Please read this entire webpage.  The exponential growth model describes growth for a population with unlimited resources and no checks on reproduction or survival.  From this basic model, all other population growth models are derived.

2.2.2 Limited Growth: Logistic Growth   - Reading: National Institute on Aging: Dr. Alexei Sharov: “Logistic Model” Link: National Institute on Aging: Dr. Alexei Sharov: “Logistic Model” (HTML)

Instructions: Please read this entire webpage.  The logistic growth model is derived from the exponential growth model but with limitations on population growth added.  This model depicts real population growth more accurately.

2.3 Generational Patterns   2.3.1 Distinct Generations   2.3.2 Overlapping Generations   2.3.3 Life Tables   - Reading: National Institute on Aging: Dr. Alexei Sharov: “Life-Tables and K-Values,” “Age-Dependent Life-Tables,” and “Stage-Dependent Life-Table” Links: National Institute on Aging: Dr. Alexei Sharov: “Life-Tables and K-Values,” (HTML) “Age-Dependent Life-Tables,” (HTML) and “Stage-Dependent Life-Tables” (HTML)

Instructions: Please read these entire webpages.  Life tables describe populations in terms of age, sex, life stage, or cohort and are used for making decision about the population.  For example, life tables for humans are used by life insurance companies to set premiums for their policies.

• Reading: Utah State University: Dr. Michelle Baker: “Population Ecology 2” Link: Utah State University: Dr. Michelle Baker: “Population Ecology 2” (HTML)

Instructions: Please read this entire webpage, which further compares the various life tables.  This material also covers subunits 2.3.3.1 through 2.3.3.3.

2.3.3.1 General Life Table   2.3.3.2 Cohort Life Table   2.3.3.3 Static Life Table   2.4 Leslie Matrix   - Reading: National Institute on Aging: Dr. Alexei Sharov: “Model of Leslie,” “Model Structure,” and “Model Behavior” Links: National Institute on Aging: Dr. Alexei Sharov: “Model of Leslie,” (HTML) “Model Structure,” (HTML) and “Model Behavior” (HTML)

Instructions: Please read these entire webpages.  This material also covers subunit 2.4.1.  The Leslie matrix is used to study age-specific population growth.  This matrix can help a scientist understand how population growth affects age structure in a population as well as how age structure in a population affects population growth.

webpages above.

2.4.1 The Leslie Matrix Setup   2.4.2 Example of the Leslie Matrix   - Reading: National Institute on Aging: Dr. Alexei Sharov: “Model of Leslie” Link: National Institute on Aging: Dr. Alexei Sharov: “Model of Leslie” (HTML)

2.5 Equilibrium   - Reading: The Saylor Foundation: “Equilibrium” Link: The Saylor Foundation: “Equilibrium” (PDF)

Instructions: Please read this entire PDF to understand how population growth arrives at an equilibrium size.

2.6 Population Cycles   - Reading: The Saylor Foundation's “Population Cycles” Link: The Saylor Foundation's “Population Cycles” (PDF)

Instructions: Please read this entire PDF.  Real populations fluctuate in size regularly, as the population is affected by environmental factors or intrinsic life history factors.  In some cases, these fluctuations are cycles that recur regularly at a specific time interval.

2.7 Minimum Viable Population   - Reading: University of Idaho College of Natural Resources: Amy Campbell and Bethany Eckroth: “Minimum Viable Population for the Bay Checkerspot Butterfly” Link: University of Idaho College of Natural Resources: Amy Campbell and Bethany Eckroth: “Minimum Viable Population for the Bay Checkerspot Butterfly” (HTML)

`````` Instructions: Please scroll down to the bottom of this webpage,
describes a field study on the Checkerspot butterfly aimed at
determining the MVP for the population and designing a conservation
program for the species.

displayed on the webpage above.
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• Reading: The Encyclopedia of Earth: Dr. Lochlan W. Traill et al.: “Minimum Viable Population Size” Link: The Encyclopedia of Earth: Dr. Lochran W. Traillet al.: “Minimum Viable Population Size” (HTML)

Instructions: Please read this entire webpage, which describes minimum viable population (MVP): the minimum number of individuals necessary for the population to survive.  This critical value is used extensively in conservation decisions.