Ecology Laboratory - Kennesaw State University



Demography and Life Tables

Part 1

Introduction

A summary of mortality, survivorship, and life expectancy by age is called a life table. Such tables are useful in population studies (and in life insurance actuarial work). It is best to construct a life table for populations in which one can determine the ages of individuals with some precision. Many temperate zone insects, for example, synchronize their emergence in spring from their over- wintering form (eggs or pupae), and survivorship of this single cohort can be monitored through time. In other species, the individual’s age at death can be determined from some physical characteristic (skull sizes, growth rings of trees or mollusks, for example) so that survivorship can be monitored more or less instantaneously. Alternatively, the age and number of individuals in each age class can be used to estimate survivorship.

Simulating Life Table Data

In this week’s lab, we will use a simulation to explore the calculations needed to develop a life table. We will use an organism known as Envelopa interofficis, actually interoffice mail envelopes, as our “population” and the number of times that they have been used as our estimate of “age”. The number of individual “mailings” can be determined by counting the number of names that appear on the envelope. You can use the attached table for your calculations.

Life tables can be constructed by knowing either the number dying in each age class, or the number surviving in each age class. For the later type of data, we must assume that population has a stable age distribution (resulting from birth and death rates which have remained constant over time). So in our population of envelopes, the envelopes might have been collected from people’s trashcans (i.e. envelops that have reached the end of their life and have therefore died). Alternatively, the envelops could have been collected from peoples desks, drawers and mailboxes (i.e. envelops that are still in circulation and therefore still alive). Your calculations will depend on whether the envelopes represent dead individuals or living individuals. In other words, you must figure out into which column (in each of the two following tables) to place the raw data collected (i.e. the number of envelopes in each age class).

The terms that appear in the table are defined below.

a = the age intervals (or expressed as x in some textbooks)

La = survivors at the beginning of interval a

Da = number that died in interval a

qa = mortality rate

la = survivorship

The calculations for each of the terms are as follows:

La+1 = La - Da

Da = La - La+1

la = La / L1

1000La = La*(1000/L1) = la * 1000

qa = Da / La

To facilitate your initial data gathering, use the table below:

|Number of signatures |Number of envelopes |

|0-3 | |

|4-6 | |

|7-9 | |

|10-12 | |

|13-15 | |

|16-18 | |

|19-21 | |

|22-24 | |

|25-27 | |

|28-30 | |

|>30 | |

The first step will be to determine into which column you should place the raw date in each type of life tables on the following page. This depends on whether the envelopes represent living individuals or dead individuals. Then, based on that column, calculate the values for the other columns in each table. You will create survivorship curves based on each of the two senerios.

Names:

Life table for envelops if they represent living individuals:

|Interval |a |La |Da |la |1000La |qa |

|0-3 |1 | | | * |* | |

|4-6 |2 | | | | | |

|7-9 |3 | | | | | |

|10-12 |4 | | | | | |

|13-15 |5 | | | | | |

|16-18 |6 | | | | | |

|19-21 |7 | | | | | |

|22-24 |8 | | | | | |

|25-27 |9 | | | | | |

|28-30 |10 | | | | | |

|>30 |11 | | | | | |

Life table for envelops if they represent dead individuals:

|Interval |a |La |Da |la |1000La |qa |

|0-3 |1 |** | | * |* | |

|4-6 |2 | | | | | |

|7-9 |3 | | | | | |

|10-12 |4 | | | | | |

|13-15 |5 | | | | | |

|16-18 |6 | | | | | |

|19-21 |7 | | | | | |

|22-24 |8 | | | | | |

|25-27 |9 | | | | | |

|28-30 |10 | | | | | |

|>30 |11 | | | | | |

* Note that l1 is calculated as 1.0 and thus 1000L1 is 1000 so we can determine survivorship from that age class on (in actuality, some mortality has probably occurred from birth to the end of this age class).

** You cannot use the equation to determine L1 , but instead must determine it from the number of individuals that have died assuming birth rates and death rates have been constant.

Plot two survivorship curves (1000La as a function of a), one for each set of calculations (based on dead individuals and on living individuals). Use the graph provided on the next page or plot in Excel (make sure the y-axis is set on logarithmic scale). A logarithmic function transforms processes undergoing a proportional change into a linear relationship (e.g. in type II survival, death rate is constant, meaning a certain constant proportion is lost in each age class and when log transformed this survivorship 'curve' is a straight line).

Envelope mortality

age interval

Name_________________________

Pine Life Table Worksheet Part 1

Each student should individually turn in a hard copy of your graphs and answers to following questions for the survivorship curve based on dead individuals:

How would you describe the survivorship curve of mailing envelopes. In other words, is the proportion of individuals dying over each age interval greater for younger, middle or older age classes, or about the same?

What would the survivorship curve that you produced tell an office manager about how people in the office decide when to discard envelopes? i.e. Are people using them in the most cost efficient way?

Formulate, based on one of the techniques used this week, a way to construct survivorship curves for pine trees on campus. Unlike our envelope population, recruitment of seed (i.e. births) is essentially a one-time event occurring over a few short years. This means that within an area where the forest is of equal age, all individuals are essentially within the same age class. In your description of your methodology, describe the parameters you will measure and how these will be measured. Also, state and explain any assumption that must be true in order for your estimate of survivorship to be accurate.

Extra Credit: Life expectancy (i.e. future life expectancy for individuals reaching age a.) can also be calculated for each age class and can vary with age class. What type of pattern in survivorship with age would produce a population where life expectancy (probable length of life from that age on) was shorter for the youngest age classes, then longer for middle age classes. Explain.

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Mortality rate

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