Setting up Simulations

Displaying Population Characteristics

The population characteristics that influence population growth are birth rates and death rates, immigration rates and emigration rates. Birth rates (or fertility rates) and death rates (mortality rates) generally depend on age (and sex). Demography displays fertility and mortality graphically as functions of age (e.g., Figure 1). These graphs can be changed at any time, even when the simulation is running (see Manipulating Population Characteristics).

Figure 1. Fertility as a function of age. The current position of the cursor is displayed in the box in the lower left side of the graph. Other features are explained in the text.

In this instance, fertility values are the average number of female offspring per female in a given age class. In this example, fertility values are displayed for five-unit intervals. If this represented a human population, the units would be years, and females between 35 and 40 would be expected to have 1 female offspring on average during the five-year interval.

The values displayed in the Mortality vs. Age report the probability that an individual in a given age interval will die before reaching the next interval. This can be used to determine the population size of the next age interval in the subsequent time interval. For instance, if the mortality rate of age interval 30-35 is 25%, and the number of individuals in the 30-35 age group at time 10 is 200, then the number of individuals in the age interval 35-40 at time 15 will be 150.

The Current Age Distribution displays the percentage of the total population in each age interval in the form of an "age pyramid". For instance, the lowest bar on the pyramid represent the percentage of individuals in the youngest age interval (e.g., 0-5), the next higher bar represents 5-10 years old, etc. In each age class, females are shown (in red on a color monitor) to the right of the center vertical axis , males on the left (in blue).

Three other options (Summary Statistics, Survivorship vs. Age, and Stable Age Distribution) display data that is directly derived from the fertility and mortality graphs. You cannot directly change these displays. You can, however, investigate a number of important questions in population biology by studying how the values they display are influenced by changes in the fertility, mortality, or current age distribution graphs. Demography immediately updates the data in the Summary Statistics, Survivorship vs. Age, and Stable Age Distribution displays whenever you change the fertility, mortality, or current age distribution graphs.

For a more complete description of the meaning of the statistics or graphs, refer to the Glossary, or to a relevant textbook.

Manipulating Population Characteristics

The mortality graphs, the fertility graphs, and the current age distribution can be edited by users. There are three ways to change the graphs: by using the mouse to move points to desired locations, by typing in values in a spreadsheet format, or (in the case of mortality and fertility) by clicking on the buttons on the tool bar at the top-right of the window to manipulate the whole graph (e.g., shifting all values to the right or left, or multiplying all y-values by a constant).

To edit a graph directly, place the cursor in the graphing area. Note that the cursor changes from an arrow to cross-hairs whenever it is in this region. Practice clicking and dragging the mouse in the graphing region. Notice how the points (or bars) move to the position of the cursor. You may use the mouse to reshape the graphs or bar charts in any way you wish. To help you to position points on the graph with precision, note that the current position of the cursor appears in the box to the lower left of the graph.

If you wish to be even more precise, you may display the data in table format and edit it like you would a ìspreadsheetî. To change from a graph to a table, choose the particular graphing region and click on the display type in the title bar at the top of the viewing area. If you simply click, the viewing area will cycle through the possible display types for a particular data set. For example, if you wish to view the fertility vs. age data set as a table, find the fertility vs. age graph, and click in the region the title region at the top of the graph, where it says "Fertility vs. Age". Keep clicking as the display cycles through the display options until a table appears.

If none of the current display areas is showing the data set that you want to view, you have two choices. First, you can create a new display area, and second, you can change the data set being displayed in any of the current display areas.

If you hold the mouse button down momentarily over the title area, a menu will appear with options showing the types of data that can be displayed (e.g., "Fertility vs. Age, Morta;ity vs. Age...)(Figure 2). The ways in which the data can be displayed are shown in a submenu (e.g., "Graph, Bar Plot, Table"). Choose the appropriate display type.

Figure 2. The display-type menu allows you to choose which data to display, and the form in which to display it.

Click in the cell(s) that you want to change, and type in the desired value(s). To return to the graphical display, make the appropriate choice from the menu of display choices. Note that unlike previous versions of Demography for the Macintosh, JAVA Demography allows you to have the same data displayed in different (or even the same!) ways simultaneously.

Figure 3. The table view of the Fertility vs. Age data.

Model Settings

Some of Demography's settings are under user control. By choosing the "Age Intervals..." command from the Settings menu, for example, the user can alter a population's maximum age and the length of each age interval. The default settings are useful for human populations. By altering these settings as needed, users of Demography can study the dynamics of a large variety of animal and plant populations. Warning: changing these parameters during the run will cause the run to start over from the beginning time interval, so only change these parameters before you begin a simulation, or when you are ready to start a new one.

Figure 3. The ìAge Intervalsî dialog box allows you to edit the length of each age interval and the maximum age in the population.

Length of each age interval is the number of years of age between groups of the population. It is initially set to 5 years of age, which means that the first group will be individuals between birth and 5 years old, the second group will be individuals between 5 and 10 years old, etc., up to the age interval between 95 and 100 years.

Maximum age is the oldest age an individual in the population will reach. It is initially set to 100 years old.

Simple vs. Sex-Differentiated Models

Users may also choose between four different types of population models available in Demography. The first, which we refer to as the simple model, assumes that either the organisms are asexual, that both sexes are equally abundant and have identical fertility curves and mortality curves, or that information about only one sex (females) is sufficient to determine population dynamics. The other two models allow for differences between sexes in age-specific fertility, mortality and abundance. They differ in the way male and female fertility values are combined to determine actual births (see discussion below). Unless you are investigating questions that deal specifically with differences between sexes, we recommend that you use the simple model. It is faster, you are less likely to make mistakes manipulating the graphs, and the results are easier to interpret.

In the simple model, there is only one mortality curve and one fertility curve, and the age distribution is always symmetric. In the sex-differentiated models there are two curves for fertility and mortality, one for males and one for females. This is also indicated in the legend on each graph. To make sure that you are editing the right curve, first click on either the M or F in the legend, and then use the mouse to move individual data points or to reshape the curve. In the sex-differentiated models, the current age distribution may also be asymmetrical. Modifying the values for one sex does not automatically affect the other.

The two sex-differentiated models differ in the way that fertility values are used to calculate the number of births. The female-limited and male-limited models assume that births can be calculated directly from the fertility values of the limiting sex. For instance, if it is generally safe to assume that adding more males to a population would have little affect on births, then a female-limited model would be appropriate.

In earlier versions of Demography for the Macintosh a fourth, "harmonic-mean", model was also available. Rather than assuming that the same sex is always limiting, it takes the harmonic mean of the total fertility values for males and females, weighted by their relative abundance. In this model, the number of births in a given time interval will be influenced most heavily by the rarer sex. Look for the harmonic mean model in future versions of Java Demogrpahy.

To pick a model type, select "Model Type..." from the Settings menu, and choose the appropriate model from the hierarchical menu

Immigration/Emigration

JAVA Demography incorporates age-specific immigration and emigration into and out of a population. If you want to enable immigration and/or emigration, check the appropriate boxes in the ìModel Settingsî dialog box. Immigration and/or emigration can be incorporated into either the simple or sex-differentiated models.

Figure 5. The Age vs.Immigration and Age vs. Emigration graphs. These windows are only accessible if they have been enabled by checking the appropriate box in the ìModel Settingsî dialog box.

Immigration is specified as the numbers of individuals per age range who immigrate into the population during a time interval. Emigration is specified as the percentage of each age group leaving the population during each time interval. The emigration rates shown in the graph in Figure 5 would be very high, since more than 20% of each age group would be leaving during each time interval.

The model adds the number of individuals immigrating into each age group before birth and death calculations are made. The number of individuals emigrating from each age group are subtracted from the population after immigration is added, but before birth and death calculations are made.

The statistics presented in the ìSummary Statisticsî table and the calculation of the stable age distribution assume no immigration or emigration, even when these features are enabled. Consequently, the stable age distribution actually achieved in a simulation allowing immigration and emigration may differ significantly from the pyramid presented in the ìStable Age Distributionî display. The differences can be used as an estimate of the effects of dispersal on the population.

Density-Dependence

Density dependence is not yet an option in Java Demography. If this feature is of interest to you, make sure that you join our email update list, and we'll let you know when we've got it working.

Variable Settings

By choosing the "Initial Time..." or "Population Size..." commands from the Settings menu, users can modify the values for the initial time and for the current population size, respectively. For example, if you wanted to model the growth of the U. S. population since the turn of the century, you might want to set initial time to 1900 and the population size to 76 (million).

In the sex-differentiated models you can also set the primary sex ratio. This relates to the ratio of the number of male offspring produced per female offspring. In the simple model, the primary sex ratio is fixed at 0.5.

In addition to the primary sex ratio, which you set, there is an additional parameter, current sex ratio, which is calculated. This relates the number of male and female individuals within the population. It is reported in the Summary Statistics table. You can modify this value indirectly by manipulating the graph of the current age distribution.

Display Settings

The "Summary Statistics" table displays the values of a number of composite variables, calculated from fertility values, mortality values and the population age distribution, that summarize key characteristics of a population. For example, "Doubling Time", the number of time units that it would take for the population to double, given current fertility and mortality values, is often a useful indicator of how rapidly a population is growing. Click here for a more complete description of your options.

The "Summary Statistics" table is updated immediately whenever the fertility, mortality , or current age distribution data are changed.

The meaning and/or usefulness of each of these statistics will depend on the particular problem that you are investigating. By choosing the "Summary Statistics..." command from the Settings menu, you can select the appropriate set of statistics to display.

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