Carrying capacity and demographics lab

Investigation Manual

Carrying Capacity and Demographics

BIOLOGY

Dry Lab

CARRYING CAPACITY AND DEMOGRAPHICS

Overview Modeling population growth is an important aspect of environ- mental and social sciences. In the first two activities, students simulate the population growth of an asexually reproducing organism without a carrying capacity and then of a bird popula- tion on an island with a set carrying capacity. In the third activity, they use birth and death dates to examine human demographics and survivorship curves. For the final activity, students use census data to visualize the age structure of world populations and gain insight into major historic events.

Outcomes • Compare logistic and exponential growth. • Examine the interactions between birth and death rates, and

how they affect population growth. • Apply the concept of carrying capacity. • Use demographics to make predictions about the growth of

national populations.

Time Requirements Preparation ....................................................................... 5 minutes Activity 1: Simulation without Carrying Capacity ........... 15 minutes Activity 2: Simulation with Carrying Capacity ................ 45 minutes Activity 3: Cohort Analysis ...................................................2 hours Activity 4: Population Pyramids ..................................... 30 minutes

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Table of Contents

2 Overview 2 Outcomes 2 Time Requirements 3 Background 6 Materials 6 Safety 6 Preparation 7 Activity 1 7 Activity 2 9 Activity 3 10 Activity 4 11 Disposal and Cleanup 13 Observations

Background Examining changes in populations over time is essential in many fields. Wildlife and fisheries managers need to make predictions about future population sizes to set acceptable hunting/catch limits. Economists want to know about human populations in different regions so they can make predictions about economic conditions. Demography is the study of factors that affect the rate at which populations, including human populations, grow.

Growth Rate Growth rate describes how a population is changing. It is affected by four main factors: birth, death, immigration (individuals moving into a population), and emigration (individuals moving out of a population). Mathematically, the growth rate (r) of a population can be represented as:

r = (births + immigration) – (deaths + emigration)

If increases due to births and immigration are greater than losses from death and emigration, then the growth rate is positive and the popula- tion is increasing. If the decreases from deaths and emigration are greater than increases from births and immigration, then the growth rate is negative and the population is shrinking. When the growth rate is zero, the population is holding steady.

Population Growth and Carrying Capacity In 1798, Thomas R. Malthus published a mathematical description of unlimited popu- lation growth. He argued that human popula- tions continue to grow until limited by famine, disease, poverty, or war. In mathematical terms, the current size of a population is equal to the

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previous size of the population multiplied by the growth rate:

N(t + 1) = Ntr where

N t = the number in the population at time t r = the growth rate constant

This formula reflects unlimited exponential growth if the value of r is greater than 1. If r is equal to 1, there is no change in the population size. If it is less than 1, the population declines to extinction. The formula depends on discrete intervals of time. To calculate growth over a continuous period, calculus is required.

In response to Malthus’s formula, other popu- lation scientists argued that wild populations frequently stay steady over time. They attributed a slowing of a population’s growth rate to a limitation of resources in the environment and suggested that population sustainability is due to a carrying capacity dependent on resources. Carrying capacity is the maximum sustainable size a population can reach within its environ- ment. Pierre Verhulst first based a formula on the presumption that, as a population approaches the carrying capacity of its environment, the rate of growth is slowed. That formula is now gener- ally presented as follows:

N(t + 1) = Ntr [(K – Nt)] where

N t = the number in the population at time t K = the carrying capacity

r = the growth rate constant

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K

CARRYING CAPACITY AND DEMOGRAPHICS

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This type of growth is called logistic growth. The factors that contribute to this type of growth rate can be summarized as birth, death, immigration, and emigration. Individuals can enter a population only by being born into it or moving into it. Likewise, they exit only by dying or moving out.

Population-limiting factors may be density dependent or density independent for carrying capacity. Among the density- dependent factors are decreased resource availability (e.g., food, water, and space), competition with similar species, disease and parasitism, and buildup of waste. The most frequent density-independent factors are natural disasters or extreme weather.

Population Demographics Like all organisms, humans are affected by resource quality and availability. A human population will grow until the carrying capacity of its environment is met. For instance, archeological evidence indicates that drought conditions contributed to the collapse of the ancient Ancestral Pueblo (Anasazi) empire in the 12th and 13th centuries. Similarly, disease, drought, and exhaustion of soil nutrients are commonly cited as explanations for the rapid decline in population that marked the end of the Classic Maya civilization in the 8th and 9th centuries. Today, scientists examine a wide range of characteristics, or demographics, to study population trends. Demographics are shaped in part by resources. Demographic data includes numbers of births and deaths, age, rates of emigration and immigration, and many other statistics.

Background continued

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One way that demographers evaluate a population is to generate a graph called a population pyramid. This analytical tool shows how the total population is subdivided into age brackets. A population pyramid can be used to predict future growth. Three population pyramids for 2016 are demonstrated in Figure 1, illustrating populations that are undergoing negative growth, rapid growth, and slow growth, respectively.

The population pyramid is a period analysis that works from a snapshot of the population at one time. This can be useful for understanding a current situation but does not allow for particularly accurate projections of the future population.

The alternative is cohort analysis, in which the population is broken into cohorts that are then followed over time. This allows for greater accuracy, because parameters such as birth, death, and migration rates can be age specific. The effects of any variations, such as a baby boom, can be tracked over time.

A cohort is a group of individuals who do something (e.g., are born) in the same time period. The researcher decides on age groupings that can be split enough to reflect important life stages but are not so numerous as to overwhelm the computational capacity. A cohort of individuals moves together through various age groups over time and is often subdivided by sex.

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The death rate is the number of individuals who die within the set time period divided by the number of individuals who belonged to the cohort at the beginning of the time period.

crude death rate = number of deaths total population

Likewise, the birth rate is the number of live births divided by the number of individuals. It can be hard to track marriages, divorces, deaths, and remarriages, so to keep from counting one child twice (for each parent), the birth rate is generally given as the number of births per each woman in the population.

crude birth rate = number of births total population

Survivorship curves (see Figure 2) show the attrition of a single cohort over the entire time that any members survive. The curves are generally set up as the number or percentage of surviving individuals versus age or time. Different organisms have different strategies for ensuring the next generation.

Figure 1.

–20,000,000 –10,000,000 0 10,000,000 20,000,000

–20,000,000 –10,000,000 0 10,000,000 20,000,000

–20,000,000 –10,000,000 0 10,000,000 20,000,000

Figure 2.

CARRYING CAPACITY AND DEMOGRAPHICS

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Materials Needed but not supplied: • Paper, 6 sheets • Graph paper • Printer • Computer with internet access • Cup of 160 counters, such as dried beans, dry

rice grains, or pennies

Safety There are no safety concerns for this investigation.

Preparation Read through the activities completely.

K-strategists (named for the K in the carrying capacity equation) typically have fewer offspring but invest more energy in caring for the young. Elephants are an example of this strategy. Elephants give birth to only one calf at a time, and most have five years between calves. Calves stay under the protection of the mother and her herd until maturity at 10 to 15 years of age. Organisms of this strategy exhibit a Type I survivorship curve, having a slow decline at the beginning and middle of the curve (a low early mortality) followed by a rapid decline (most mortality among older individuals).

In the r strategy, organisms invest energy in producing many offspring in the hope that some will survive. Little energy is invested in the care for the offspring. Oysters, for example, spawn millions of eggs and sperm into a water column. Most of the eggs fail to be fertilized much less settle to grow into adult oysters. But the sheer number of offspring produced ensures the continuation of the species. Organisms that are r strategists usually have a rapid decline in their survivorship curve (a high mortality among the young) followed by a leveling off (a lower mortality for mature individuals). A Type III survivorship curve results from this kind of strategy.

Type II curves lie between these two extremes.

Background continued

8. Return all the counters to the cup. 9. Graph your results for all four values of

r. Put all four lines on the same graph for comparison. Be sure to label both axes and title your graph.

ACTIVITY 2

A Simulation with Carrying Capacity In this activity, you will model and document the changes in a population of birds over time. This population does not meet the assumptions made in Activity 1, so this investigation takes into account several additional factors. Birth Rate This model examines the bird population on a small island. Each nesting pair defends a number of territories. The more territories a pair can control, the more resources it has access to and the more chicks the pair can raise to adulthood. There are 32 territories on this island, each of which has the minimum space required to raise a single chick to adulthood. A given pair of birds can occupy from 1 to 4 of these territories and will have a corresponding number of offspring (1, 2, 3, or 4) each breeding season. As the population increases, competition will cause the ranges of the breeding pairs to shrink to the minimum size of 1 territory. Death Rate Initially, assume a constant death rate of 0.1. Then repeat the calculations using a death rate of 0.5. Immigration and Emigration Strong prevailing winds prevent immigration to the island. However, adults that cannot find a

ACTIVITY 1

A Simulation without Carrying Capacity

This activity simulates the growth of an asexually reproducing organism, such as yeast or bacteria. The growth rate can be thought of as the number of individuals dividing in a given time period.