The Sterile Insect Release Method - A Simulation Exercise

Phil A. Arneson
Department of Plant Pathology
Cornell University
Ithaca, NY 14853

The sterile insect release method (SIRM) of pest population suppression was first conceived by E. F. Knipling (1955). It sometimes goes by the names "sterile male technique" and "autocidal control". The method consists of releasing large numbers of sterilized insects into the environment to reduce the probability that members of a natural population of the same species will successfully reproduce. The method has been associated almost exclusively with efforts to eradicate particular species from well-defined and limited geographic areas. Simple mathematical models devised by Knipling (1979) demonstrate that, in theory, the method can bring about the total eradication of a defined population in a small number of generations. Its practical feasibility has been demonstrated by the eradication of the screwworm, Cochliomyia hominivorax, from the Caribbean island of Curaçao and peninsular Florida, and the elimination of isolated infestations of the Mediterranean fruit fly, Ceratitis capitata, other fruit flies, and the gypsy moth, Lymantria dispar. It has also been applied in regional suppressional programs against the cotton boll weevil, Antonomus grandis, mosquitoes and the codling moth, Cydia pomonella.

The method works as follows: large numbers of insects are produced in a rearing facility and are sterilized by radiation or chemical means. The sterilized insects are released into the natural population in numbers sufficient to ensure that most wild individuals will mate with a sterile insect, resulting in failure to produce viable offspring. Additional releases of the same number of sterile insects are made in subsequent generations, so that the ratio of sterile to fertile insects increases dramatically over time. Within a few generations, no fertile matings are likely to occur, and the wild population is eliminated. The method is unique among insect control tactics in that it operates in an inverse density-dependent, or destabilizing, way. As the size of the target population becomes smaller and smaller, the effectiveness of a given number of released, sterile insects increases. This feature is what makes eradication theoretically possible. The method works best in conjunction with other approaches that first reduce the size of the target population so that fewer sterile insects need be reared and released.

Success of the method depends on a number of assumptions that must hold true. Some of the more important are:

Insects can be reared and sterilized in large quantities.
Methods exist for distributing the sterile insects throughout the target area so they thoroughly mix with the wild population.
The release is timed to coincide with the reproductive period of the target insect.
The released, sterile insects compete successfully for mates in the natural environment.
The release ratio (sterile insects to native, fertile insects) is large enough to overcome the natural rate of increase of the population, so that the trend in population size is downward after the first release.
The target population is closed; i.e., there is no immigration of fertile insects from outside the release zone.

Calculating the required release ratio for a particular situation is difficult. This requires an accurate estimate of the size of the natural population and its spatial distribution. It also requires knowledge of the natural rate of increase of the population. For a number of reasons, it may be desirable to release only sterile males. This requires a way of separating the sexes in the rearing facility and knowledge of the sex ratio of the wild population.

In this laboratory exercise you will use a simulation model of the SIRM to investigate the effect of several variables on the effectiveness of the method and what happens when some of the basic assumptions of the model are relaxed or violated in some way. You should gain some understanding of the sorts of things that complicate the application of the technique in situations that are more realistic than those assumed by Knipling in his simple analyses.

The Model

This simulation is a version of the original model by A. J. Sawyer (1987), which has now been adapted to run under Microsoft Windows. It was written to illustrate the effects of changes in the assumptions of the simple mathematical models of Knipling (1979). We have given it the name "Curaçao" after the Caribbean island on which Knipling first demonstrated the feasibility of sterile insect release by eradicating the screwworm fly.

Assumptions of the basic model. The basic model (using the default parameters in the setup file) uses the original assumptions of Knipling (1979). It is assumed that the target population exists in a well-defined zone. Its initial size is 1,000,000 individuals, half male and half female. The population will increase 5X each generation (up to a point) (200 eggs/female x 0.05 survival rate to the adult stage x 0.5 female = 5). There is no dispersal. Sterile males are released in a ratio of 9:1 (sterile to fertile males). The population is distributed uniformly throughout the zone, and the released insects are well mixed with the indigenous population. Sterile males are completely competitive with wild males in mating with females. The model is deterministic, in that the mean sex ratio, survival of immatures, proportion of females mating with fertile males, and fecundity all apply exactly, even in extremely small populations (those near extinction). Thus, random, or stochastic, events do not alter the outcome of a release program.

Variations on the basic model: Countless variations of the basic simulation can be made by changing parameter values or even the structure and underlying assumptions of the model. One of the more interesting variations is to introduce space into the problem. Three different levels of spatial resolution are possible: low, medium and high. In the low resolution case, the central target zone is surrounded by a second zone that is divided into 6 cells. This second zone may or may not have an initial population, as you wish. When a zone consists of more than one cell, the population may or may not be heterogeneous in that zone all cells need not have the same population density). Rates of survival and reproduction can be different in the second zone, to represent habitat of different suitability. Most importantly, now that there is space, you can have movement. You can specify emigration probabilities for each zone. This is the fraction of the population that will leave each cell during the dispersal phase of each generation. For example, if you specify an emigration rate of 0.01, one insect in a hundred will leave the cell in which it developed and enter a neighboring cell during the dispersal period. Individuals leaving a cell have an equal probability of moving to each of the six neighboring cells. If a cell is on the boundary of the outermost zone, dispersing individuals leave the modelled area and disappear into the sea. (They can't return.)

Order of events. The order in which events occur assumes that you timed your release of sterile insects to occur just before the mating and dispersal of the native population. The order of events, therefore is: Release (of sterile males), Mating, Dispersal (if any). This can be changed to represent different life histories or release strategies.

Stochastic simulation. The model can be changed to a stochastic one in which random events play a role, especially in small populations. Because the SIRM is concerned with what happens to a very small population, this is an important feature. For example, when the remaining population is less than 100 or so, the sex ratio, survival of immatures, outcome of mating and fecundity may depart from expected values just by chance. That last female may just happen to mate with a fertile male even though it is unlikely. A fertile female might disperse to a neighboring cell outside of the release zone and initiate a new infestation, even though the chances of this happening are small. The stochastic version takes much more computation time because random events must be generated for each individual, with probabilities drawn from appropriate distributions having the expected values as in the deterministic version.

Competitiveness. The competitiveness of released sterile males can be set to some value less than 1.0. This parameter represents the relative value of the released males in competing for mates on an equal basis with native males. For example, a release of 100,000 sterile males whose mean competitiveness is 0.8 is equivalent to a release of 80,000 fully competitive sterile males. In competition with 100,000 indigenous males, 40% of the mating will be with sterile males (80,000/200,000). As in Knipling's basic model, we assume that all females mate (except at very low densities, when some may fail to find mates), and females mate only once. Incidentally, this last assumption is not a necessary one for the application of the SIRM. With other mating systems, the mathematics used to calculate the expected outcome of a release are different, but the technique still works. Its efficiency depends on the reproductive details of each species.

Estimation of native population size. The release of sterile males can be based on the actual size of the target population, or on an estimate of that population size. The latter is more realistic, since in practice a sampling survey must be conducted to determine the population size prior to a release. Of course, sampling is subject to error. In this model, the standard error of an estimate of population density is assumed to be 40% of the mean, and an estimate is drawn from the appropriate normal distribution. As noted before, the initial population can be made homogeneous within a zone, or can vary from cell to cell (with the correct overall mean). To achieve heterogeneity, an aggregation index can be specified from each zone. This parameter is actually the coefficient of variation (S. D./mean) for individual cell densities. It may be given a value ranging from 0.30 (somewhat clumped) to 1.00 (very clumped). Use 0.0 for a uniformly distributed population. The cell densities are drawn from a gamma distribution with the appropriate mean and variance. Sterile insects can be released on a zone basis or on a cell-by-cell basis. That is, the desired release ratio may apply to the (actual or estimated) population of an entire zone, in which case the same number of insects is released in each cell of the zone, or the ratio may apply to the (actual or estimated) population in each individual cell. In this case, different numbers of sterile insects may be released in each cell. In a real field program, this would require greater sampling effort and a more highly refined distribution system, but it would assure more efficient matching of the actual release ratio to that which is intended (particularly for a patchily-distributed target population).

Number of sterile insects released. Finally, you can specify a total number of sterile insects to release in each zone, without regard to the ratio of sterile to fertile males. This is useful if a buffer zone, in which sterile insects are released outside of the area of infestation, is needed.

Installing and Running the Simulation

Note: To run this simulation, you will need the program installed on your computer. (it runs under Windows 3.x or Windows 95, occupying 230 kB on your hard drive and requiring a minimum of 8 MB of RAM.) If you want to install the program and have not already done so, download the zip file: curacao.zip

In this exercise, you will need to have both the simulation program and your Web browser ("Netscape", "Microsoft Internet Explorer", etc.) running simultaneously so that you can toggle back and forth between the two using the [Alt]-[Tab] keys. In these instructions, the symbol will signal you to toggle from this document, complete the given instructions on the simulator and toggle back. (You may prefer to resize your browser window and run it and the simulator side-by-side on the screen, or you may find it easiest to print a copy of these instructions to follow as you execute the simulations.) Minimize your Web browser now (Click on the minus button in the upper right corner.) and then double click on the Curaçao icon to start the program. Use the the [Alt]-[Tab] key combination to toggle back to this Web page.

General instructions:

To select a menu item, move the cursor to either File, Insects, or View, and click. Clicking outside the menu will make the menu disappear, and clicking outside the Curaçao window will make the Curaçao window disappear. Clicking on another menu item will bring up that menu.
We will not use the View menu in this exercise. Explore the Insects menu by clicking on each menu item in turn and then clicking on "Cancel" in the dialog box that appears.
Details of the various items that you will use in the File menu will be explained as you proceed through the assignment. You may want to create a text log of your session to help you remember what you did. Click on File, Log to Disk..., that is, click on File, and when the menu appears, move the cursor down to Log to Disk... and click again. When the dialog box appears, you can see that the default name is CURACAO.TXT. It would be helpful for you to identify your file with your own unique file name. Just type in your 8-character name followed by .TXT, and click OK

The Simulation Exercise

Knipling's example. Recreate Knipling's example by executing the model without changing any of the parameters. Select the File menu and click on Run. A diagrammatic representation of the island of Curaçao will appear with a shaded square in the center representing the population of screwworm flies. Click on the& Generation button in the lower right corner of the window to advance the simulation one generation at a time. Observe the numerical summary in the window on the right. In how many generations is eradication achieved? How many sterile males had to be released in total?
Minimum initial release ratio. Under the assumptions that Knipling used, eradication could have been achieved with a lower ratio of released sterile males to native, fertile males. (Remember the "normal trend", that is, the population increase with each generation, and think about what proportion of the matings must be sterile to offset this increase.)

Select the File menu again, and this time click on New. When it asks "Repeat the same problem?", click on No. Select the Insects menu, and click on Release by Zone. Change the initial release ratio in Zone 1 by moving the cursor to the left end of the box for "Release ratio: Zone 1:". Inside the box, the cursor changes from an arrow to a vertical bar. Position the vertical bar just to the left of the number that you want to change. Press down the mouse button and roll the cursor to the right until all the digits that you want to change are shaded, then release the button. (Alternatively, you can double click on the number, and the entire number will become shaded.) Now type in at the keyboard the numbers that you want. When you are satisfied with all of the numbers in the window, click OK. Select the File menu again, click on Run, and step through the generations as before. At the end of each run, you must click on File, New and click on No in response to "Repeat the problem?". Decrease the initial release ratio until you find the smallest initial release ratio (to the nearest tenth) that will result in eradication. What is the minimum effective initial ratio of sterile to fertile males that results in eradication? In how many generations is eradication achieved at this ratio, and how many total sterile males must be released? How does this compare with the results of the original Knipling example? (Explain.)
Sterile male competitiveness. Click on File, New and No. Then click on File, Open, and No in response to "Save Current Problem?". In the "Open File Name" dialog box, double click on startup.sir to reset the default parameters. In the Insects menu, click again on Release by Zone, and change the competitiveness from 1.0 to 0.5. How many generations and how many total sterile males are required for extinction at an initial release ratio of 9.0 to 1? Now what is the minimum effective initial release ratio (to the nearest tenth), and how does this relate to the normal trend? How many sterile males (total) must be released to achieve extinction? How do your results compare with the original Knipling model? (Explain.)
Fecundity of females. Return to the default setup with File, New and File, Open startup.sir as before. Click on Insects, Native. Increase the fecundity of females (eggs per female) from 200 to 300. Now how many generations and how many sterile males are required for extinction? What is the normal trend in this situation, and what is the minimum effective initial release ratio? How does this compare with the original Knipling example? (Explain.)
Survival to adult. Return to the default setup again. Bring up the Insects, Native dialog box and increase the rate of survival to adult from 0.05 to 0.08. What is the normal trend, and what is the minimum effective initial release ratio? How many generations and how many sterile males are required for extinction? How do these result compare with the original Knipling model? (Explain.)
Initial release ratio based on population estimate. Base a release on an estimate of the native insect population in Zone 1, rather than its exact size (which you wouldn't know). To do this, return to the default setup again, and bring up the Insects, Release by Zone dialog box. Click on the button that says Ratio (estimated pop.). This time your estimates of the native population (and therefore your actual release ratios) will be different each time you run the model, varying about the mean according to a normal distribution. Run the simulation as before, noting the number of generations and the total sterile males required for extinction. This time, however, after clicking on File, New and getting the dialog box, "Repeat the same problem?", click on Yes. Run the model 10 times using the original initial release ratio of 9.0 and another 10 times using the minimum initial release that you determined in Step 2. How many times out of ten were you successful in eradicating the population in each case? Why do you suppose Knipling used 9:1 as the initial release ratio in his example?
Spatial aggregation. Return to the default setup, and click on File, Options. Click on the first set of options until High Spatial Resolution appears, then click OK. Next click on Insects, Native, and set the Aggregation Index (coefficient of variation) to 0.4. (Note that we are back to an exact estimate of the ratios, but this time the spatial aggregation of the insects will be different for each run.) Repeat this problem 10 times with an initial release ratio of 9.0. Note the number of generations and the total number of sterile males released each time. How many times were you successful in eradicating the native population? (Explain the reason for any failures.) Set the Aggregation Index to 0.5 and repeat this problem 5 times. What effect does the tighter aggregation have on the success of the sterile insect release method? (Remember you are releasing the same initial population in Zone 1 in each case.)
Emigration. Now add the element of pest mobility to the spatial aspects just considered. Return to the default setup. Select File, Options... and select the High Spatial Resolution as before. Select File, Save As... and save these startup options as startup2.sir. Select Insects, Native, and set the Aggregation Index (coefficient of variation) to 0.4 and the Probability of Emigration to 0.01 (1 insect in a 100 will leave each cell for one of the adjacent ones in each generation). Run the same problem 5 times, and note the movement of the population each time. (Once the population trend turns upward in Zone 2, there is no point in continuing with further generations.) Check the populations in a few selected cells in Zone 2 in each generation by moving the cursor to the desired cell and double clicking. A dialog box will tell you the populations of native and sterile males in that cell. Why is extinction of the population not possible?
Border zone. To see the importance of establishing a border zone in attempting to eradicate a mobile pest, return to the same problem in the previous step by clicking on File, New, and No. Open the startup file that you just created by selecting File, Open... and double clicking on "startup2.sir". Keep the same native insect population parameters as before (Total Population, Zone 1: 1000000; Aggregation Index: 0.4; and Probability of Emigration: 0.01), but for the Release by Zone, change the Release by: from ratio (exact population) to numbers. Now release 4,500,000 sterile males in Zone 1 (which gives the same 9:1 ratio), but this time also add 4,500,000 sterile males to Zone 2. (Remember, the native, target insects initially are found only in Zone 1.) Repeat this same problem 10 times. Did you have any unsuccessful eradication attempts? If so, what was the spatial nature of the population development?
Hot spots. Generally it is not enough simply to adjust release ratios based upon the initial assessment of the native population, particularly where the populations are highly aggregated. It is necessary to monitor the populations each generation and to increase the numbers of sterile males released in those areas where the population trend is not downward. Return to the same problem in the previous step by clicking on File, New, and No, and increase the Aggregation Index to 0.5 to increase the chance of developing a "hot spot". Run the simulation, and at each generation look for the development of cells with high population densities. Move the cursor to one of these cells, and double click. A dialog box will tell you the populations of native and sterile males in that cell. If the population of native males gives you a release ratio in the current generation of less than about 5:1, release more sterile males by typing in a value that corresponds to a release ratio of about 10:1 for that cell, then clicking OK. Repeat this same problem 5 times without any release ratio adjustments and 5 times with increases in release ratios in the hot spots. How did the outcomes of these two approaches compare? What is the importance of detailed monitoring of the population?
Nonuniform release. With the exception of the "hot spot" releases just completed, the simulations that we have done so far have assumed uniform distribution of the released sterile males (as they might be dispersed by a release from an aircraft). Let us now look at what might happen with a cell-by-cell release (as if we had to place caged insects in specific sites). To avoid having to mark too many cells, let us first reduce the spatial resolution by clicking on File, Options... and selecting Medium Spatial Resolution. To increase our chances of success, we will do this with an insect that has a dispersal phase before mating, and we will time our release to occur just before this dispersal phase, so while in the "MODEL OPTIONS" dialog box, select the Release-Disperse-Mate order of events. Then click on Insects, Native.... For this exercise we will put 1,000,000 insects in each of the 3 zones, with an Aggregation Index of 0.4 and a Probability of Emigration of 0.1. (Note: you might find it easier to shift the focus from box to box with the tab key rather than the mouse.) Next click on Insects, Release by Cell.... Select Release by: numbers and Release in: marked cells only, and for No. released per cell put 4,500,000. Since we might want to come back to this set of start-up parameters again, let us save it by clicking on File, Save As... and entering the file name, nonunifm.sir.

Now click on File, Run. Note the message that reminds us that we have to mark the release points. Click on Insects, Mark Cells, and note that the cursor has now changed to cross-hairs. To better see the cells, click on View, Show Grid. Press the mouse button down to see the coordinates of the cell under the cross-hairs. Starting in the upper left corner of the island (Cell No. 1,3) and progressing diagonally downward to the left, double click on each cell to make a line of four marked cells. Go back up to row 1 and move to the right, skipping a cell to mark Cell No. 1,5. Again progress diagonally downward to the left to mark a line of 6 cells parallel to the first but displaced 2 cells to the right. Now mark the last cell in the second row (Cell No. 2,7) and progress downward as before, marking a line of 6 cells parallel to the other two. Finally, mark the line of 4 cells along the lower right margin of the island, beginning with Cell No. 4,8. When the desired cells have been marked, click on Insects, Quit Marking. Now progress through the simulation by clicking on Generation. Repeat this same problem 5 times to see how many times you successfully eradicate the native population. (Note you will have to mark the cells again for each new simulation.) Record the number of generations and the total number of sterile males required for each successful eradication. Note the pattern of extinctions with each successive generation.

Now let us see what would happen if the insects mated before they dispersed. Start a new problem with all the same conditions except the order of events. Click on File, Options... and select Release-Mate-Disperse. Run it 5 times just as before, marking the same cells. How many successful eradications did you have? What characteristics of the life cycle are important to consider when you release insects from cages, and how does this affect the timing of the release?

Let us try it again, this time with a reduced mobility of the insects. To facilitate setting up your original starting conditions, open the file that you saved earlier by clicking on File, Open..., and double click on nonunifm.sir Insects, Native... and set the Probability of Emigration to 0.01. Run this problem 5 times also, marking the same cells as before. Were you successful in eradicating the native population? Where did the population develop? If you have to release from cages, what is the importance of having highly mobile insects?

References

Knipling, E. F. 1955. Possibilities of insect control or eradication through the use of sexually sterile males. J. Econ. Entomol. 48:459-62.
Knipling, E. F. 1979. The basic principles of insect population suppression management. U.S.D.A. Agric. Handbook No. 512. 659 pp.
Sawyer, A. J. Z. Feng, C. W. Hoy, R. L. James, S. E. Naranjo, S. E. Webb, and C. Welty. 1987. Instructional Simulation: Sterile Insect Release Method with Spatial and Random Effects.