BISC 111/113:Lab 11: Population Growth 2

Objectives

1. To finish the Tribolium experiment by conducting final counts and start processing data
2. To explore computer simulation programs that model population growth and interactions

Lab 11 Overview

I. Completing the Triboliumn population growth experiment

II. Modeling beetle population changes using Excel

III. Building beetle population models in Stella

IV. Assignment

Completing the Tribolium population growth experiment

Today you will complete the final counts of your Tribolium populations. Your samples have been placed in the freezer for at least 48 hours prior to the lab. You can isolate the beetles/pupae by sifting some of the culture through the screen over the brown paper on your bench. Try to keep all the flour away from the computers. As you isolate the beetles, put them in a labeled petri dish. There are tools available on your lab bench to help with the counting.

• Enter your data on the class spreadsheet.

• Refer to your lab instructor for information about the oral presentations next week. Sign up for a topic before leaving lab today.

Population Growth and Interactions: Background

Population Structure:
A population is a group of individuals of the same species in a given area with the potential to interbreed. Each population has a structure that includes features such as density, spacing, and movement of individuals over time and space.

Spatial structure addresses the dispersal of individuals in space and can be classified as evenly spaced, clumped or totally random. Genetic structure of a population describes the distribution of genetic variation within that group. There is genetic variation among individuals as well as within the entire population. This variation is the basis of the population’s ability to respond to environmental changes through evolution.

The study of population dynamics examines the ways that populations grow or shrink over time. Reproduction and immigration account for population increases, and death and emigration account for decreases. While some populations may reproduce continually, others experience discrete periods of reproductive growth. Because some populations (human) have no distinct reproductive season, the population grows more or less continuously.

Population growth:
A population that increases continuously under ideal conditions (without limitations) exhibits what is known as exponential growth. During exponential growth, the population growth rate (dN/dt) is proportional to the size of the population (N):

dN/dt = rN

Where: N = population size
r = the “intrinsic rate” of population growth. r is related to the population’s net reproductive rate R₀ and mean generation time T by the expression r = ln(R₀)/T.

You can also see that r = (dN/dt)*1/N, and during exponential growth is the theoretical maximum rate of increase of a population per individual. r under such unlimited conditions is termed r_m, or “r_max”.

Exponential population growth displays as a J-shaped curve of N over time.

The exponential model is also expressed by the equation:

Nt = N₀e^rt

Where: N₀ = the initial (starting) population size at time t = 0 N_t = population size you are trying to predict at some time “t” e = “exponent” = the base of Naperian logarithms; e ≈ 2.718 r = the “intrinsic rate” of (exponential) population growth (usually termed rm under exponential growth) t = time elapsed from time = 0 to time = t

Compare exponential growth to a simple linear model described by the equation:

N_t = N₀ + bt

Where: N₀ = the initial (starting) population size at time t = 0
t = time elapsed from time = 0 to time = t
b = the population linear growth rate, and is a constant that is not proportional to N; it is the slope of the N vs. t linear relationship. Here, dN/dt = b. (You will see that this relationship is described by a linear regression of N on time.)

While exponential growth models are more realistic than the linear models, neither reflects the dynamics of natural populations over the long term.