|J. L. Boone, Ph.D., Ecology|
|Boone, J. L., and R. G. Wiegert. 1994. Modeling deer herd management: sterilization is a viable option. Ecological Modeling, 72:175-186.|
Modeling deer herd management: Sterilization is a viable option
James L. Boone
Richard G. Wiegert
A closed-population demographic model was developed to examine population consequences of hunting, predation, and sterilization as methods of deer herd (Odocoileus sp.) reduction strategies. Sterilization appears attractive where legislation or public pressure prevent hunting or other forms of culling. Sterilizing a fixed number of animals annually during the initial phase of a control program, and then reducing the number of annual sterilizations as herd size declines, will probably not be effective, as our model predicts only two outcomes: no reduction in herd size, or extinction. The number of annual sterilizations must be calculated based on the number of fertile females remaining in the herd, not on total herd size, and the number of annual sterilizations must be greatly reduced before total herd size decreases significantly. For Cumberland Island National Seashore, GA, the model predicts that the herd of 1500 deer can be controlled at 750. Over three years, an initial rate of 200 sterilizations per year is reduced to a constant rate of 42 per year. If the current levels of hunting and predation continue, the initial number of sterilizations is reduced from 200 to 81, but the constant annual rate increases to 58.
When deer (Odocoileus sp.) numbers are near or above carrying capacity, wildlife managers may want to reduce herd size to prevent starvation, improve trophy hunts, or reduce crop and environmental damage (Schemnitz, 1980; Shaw, 1985). Hunting or other forms of culling are the usual methods of herd reduction because the results are economical and immediate (Leopold, 1963). However, hunting and culling are often prohibited or problematic in urban areas, secured government installations, and National Parks, and public pressure may prevent hunting (Leopold, 1963; Harder and Peterle, 1974). For example, the management hunt at Fire Island National Seashore, New York, was suspended in 1988 due to a court order obtained by animal rights activists. Non-lethal techniques of herd reduction such as trapping and relocation are expensive and places to release deer are limited; therefore, these techniques are generally not practical substitutes for hunting and culling (Harder and Peterle, 1974).
An alternate management technique, sterilization using oral and/or injected drugs, has been implemented in zoos with big cats (Felidae; Seal et al., 1976), in captive wildlife such as red foxes (Vulpes fulva; Linhart and Enders, 1964), red-winged blackbirds (Agelaius phoenicus; Vandenbergh and Davis, 1962), rock doves (Columba livia ; Elder, 1964), white-tailed deer (O. virginianus; Harder and Peterle, 1974), and Norway rats (Rattus norvegicus; Brooks and Bowerman, 1971), and in free-ranging species such as elk (Cervus canadensis; Greer et al., 1968), coyotes (Canis latrans; Balser, 1964), horses (Equus cabilus; Kilpatrick et al., 1982), and Norway rats (Rattus norvegicus; Marsh and Howard, 1969). Kilpatrick and Turner (1985) present an historical review and other examples. Sterilization removes animals from the reproductive pool as does hunting, but it differs by leaving animals in place to use resources, contribute to crowding, and participate in social interactions, thus preventing the increase in reproductive output that may be exhibited when density is reduced (Ricklefs, 1979). Previous sterilization efforts have, however, all faced similar problems: they are expensive, animals tend to develop aversions to bait treated with oral drugs, and only short-term control has been achieved.
Two new techniques have been proposed for sterilizing wild female deer. The first is to capture and surgically implant long-lasting, effectively permanent, chemical sterilants (Plotka and Seal, 1989). Capturing deer is difficult and expensive (Hawkins et al., 1970; Harder and Peterle, 1974), but sterile animals can be marked, and managers can use mark-recapture methods to estimate the number of fertile females remaining in the herd. The second technique is to ballistically implant the chemical by shooting the animal with a sterilant capsule, as has been done with horses on Cumberland Island, Georgia (Goodloe, 1991) and Assateague Island, Virginia (Holden, 1992). This technique is less costly, but sterilized female deer cannot be permanently marked. Managers would hunt more or less randomly and sterilize any female deer encountered. As the number of sterile females increases, repeat sterilizations occur, and effective effort decreases.
Robert J. Warren (personal communication, 1990), working with Goodloe, has suggested that sterilization might be used to reduce the deer herd on Cumberland Island to reduce habitat damage resulting from the relatively high density of deer. We modeled this situation to determine its feasibility. Our specific objective was to use a simulation model to determine how many female deer must be sterilized each year to reduce the deer herd on Cumberland Island, Georgia to half its present size in five to eight years, given that the sterilization technique is feasible.
We initially assumed that deer could be ballistically sterilized at a constant number of annual sterilizations (e.g. 50 or 100) until herd size decreased, at which time the number of annual sterilizations would be decreased. We assumed that as the percentages of sterile females and repeat sterilizations increased, an equilibrium herd size would be reached. However, early versions of the model showed that, depending on the number of annual sterilizations, such a method will either exterminate the herd or be ineffective. The initial number of sterilizations can vary, but this number must rapidly decrease before herd size decreases significantly. For a program to be successful, it is crucial to estimate the number of fertile females, not the total herd size. The model estimates the proper number of animals to sterilize for the ballistic implantation technique, allowing managers to develop an effective, remotely administered sterilization program.
Population to be Simulated
There are about 1,500 white-tailed deer on Cumberland Island, and the herd is believed to be at carrying capacity. Survey data from 1986 and 1987 on Cumberland Island (Miller, 1988) were used to derive reproductive rates, fetal sex ratios, survival rates, and initial herd sizes per age class. There is light hunting of both sexes, but hunters take more males than females. Bobcats (Felis rufus) have recently been reintroduced (R. J. Warren, personal communication, 1990) and should feed on fawns and an occasional adult. Currently, the fetal sex ratio is approximately 2 males: 1 female.
In the model, the herd is divided into four groups: fertile females, sterile females, males, and fawns (Fig. 1). The effects (hunting males, hunting females, fawn predation, female sterilization, or any combination of these) are simulated by removing animals or by transferring them from one group to another. The manager specifies the maximum number to manipulate, and this number is converted to the actual number under the control of various functions. For example, managers may wish to remove 750 of 1500 deer from an island in a given year, but as herd size decreases, it would become increasingly difficult to find and remove deer; resulting perhaps in only 650 being removed that year. Additional mortality results from all other causes at age-specific rates. Herd structure, with a maximum of 12 age classes, is maintained using Leslie Matrix techniques (Pielou, 1969; Caswell, 1989) and constant age-specific reproductive and survival rates. All input parameters, including the number of age classes to use, are controlled by the user. Stochastic processes are not included in the model because this would confound interpretation of the results.
Age-specific maximum reproductive rates are set by the user, and controls are applied to reduce the maximum rates based on current herd size relative to carrying capacity (K). Below K/2, reproductive rates are maximum; above K/2, rates decrease linearly until K is reached, when they are zero. Although the deer on Cumberland Island are part of a complex trophic structure, and ignoring this fact is unrealistic, we assume that K is constant and defined by the sum of all factors limiting the herd. Herd size can, of course, temporarily exceed K. White-tailed deer typically do not exhibit a 1:1 fetal sex ratio. Under conditions of low density and high resource availability, the ratio is typically 54 males to 46 females. Under opposite conditions, the ratio shifts to 66:34. Fetal sex ratio is determined using a linear relationship based on density. At K, offspring are produced at a 66:34 ratio, and at K/2, the ratio is 54:46. This relationship was obtained from an expert (L. Marchinton, personal communication, 1990) and confirmed in principle by Verme (1983).
Constant, age-specific survival rates are used in the simulation (Table 1). Because sterile females do not divert energy to reproduction, sterile females are given higher winter survival rates than fertile females. In this simulation, sterile females in one age class (n) were given the same survival probability as fertile females in the previous age class (n-1), but the user may implement any survival rates.
Sterilization is simulated by converting fertile females to sterile females under the control of two functions. First, if fertile females can be identified and counted or estimated, the specified number of fertile females are sterilized (#Ster) until the number of fertile females falls below an upper limit (FK). When females are not marked and counted, the specified number of females are sterilized (#Ster) until herd size falls below an upper limit (K). Between the upper limit and a lower limit (FRef or Refug), a linear function controls the total number to sterilize (Fig. 2). Below the lower limit, none are sterilized. Second, a different function is used to sample each age class proportional to its size, the expectation if deer are randomly distributed and randomly encountered in the field.
Hunting and predation are simulated using the same methods as sterilization: the user defines a maximum number of males hunted (MHun), females hunted (FHun), or fawns taken by predators (FPred); this number is reduced based on herd size relative to upper and lower limits, and the number in each age class is removed by sampling proportional to age class size. Female (F) and male (M) removal rates are controlled by FK, FRef, MK, and MRef; fawn (Fa) predation is controlled by FaK and FaRef, where _K and _Ref operate as described for sterilization. Hunting does not discriminate between fertile and sterile females or select for older (trophy) males, and predation only affects fawns (although predation on adults can be simulated using the hunting parameters). The user may ignore these simulation options by specifying that no animals are hunted or lost to predation.
All input values used in this simulation are shown in Table 1. Note that figures begin at year five; the first four iterations of the model stabilize herd size based on input values and are not displayed. All treatments begin at year 10, and all ratios are male: female. A copy of the program, which runs on Macintosh computers, is available from the authors.
RESULTS AND DISCUSSION
Without hunting, predation, or sterilization, the model yields predictable results: the population stabilizes near carrying capacity (1491), the number of each sex remains constant at 814 males and 677 females, recruitment (offspring per reproductive female) is low (0.34), and sex ratio is maximally skewed to males (Fig 3A).
Prior data from Cumberland Island show that hunting at current levels (about 100 animals per year, 7:3 sex ratio) results in virtually no change in herd size. The number of males decreases slightly, the number of females increase slightly, recruitment increases compensating for mortality (0.44), and the sex ratio remains unchanged. Heavy hunting pressure (initially 300 per year) affects herd size differently depending on the ratio of males to females taken. At 2:1, there is no significant effect on herd size; recruitment simply increases (0.78). At 1:1, herd size falls to refuge levels (the minimum herd size based on FRef and MRef), the sex ratio shifts (54:46), and recruitment increases (1.37, Fig. 3B). This agrees with expert opinion (L. Marchinton, personal communication, 1990) that removing 300 animals per year should suppress the herd.
When bobcats were first recommended for reintroduction on Cumberland Island, it was suggested that increased fawn mortality due to predation could reduce the herd. Later discussions, however, indicated that this was unlikely. The model agrees with these opinions: unless predation is extremely high (>330 fawns per year), there is no significant effect on herd size. For predation pressure below and above 330, the graphs of herd size are similar to Figs. 3A and 3B, respectively, except recruitment rates are higher (1.40 and 2.00, respectively).
The results of sterilization depend on whether total herd size is used to determine when to decrease the number of annual sterilizations, or if the number of fertile females is used. Using total herd size, if 100 unmarked females are initially sterilized per year, herd size oscillates but is not reduced to desired levels (Fig. 3C). This observation leads to increasing the number of sterilizations. If 150 are initially sterilized, herd size fluctuates until the herd is functionally extinct after 26 years because all females are sterilized. The numbers of fertile females, sterile females, and males fluctuate out of phase, and in the final years herd size is high due to the presence of many sterile females, and sterilization occurs at a high rate (Fig. 3D). If 200 are initially sterilized, the herd is functionally extinct in 6 years. These results are due to a time-lag between the time when fertile females decline in number (early) and the total herd size declines (late). Fertile females simply switch to a different category; they do not immediately leave the herd.
Using female herd size, if females are captured, marked, and counted, sterilization reduces herd size, even at relatively low annual sterilization rates. At an initial rate of 100 per year, the cumulative percentage of sterilized females reaches 60% in 10-12 years, and herd size stabilizes at K/2. With an initial number of 200 sterilizations, herd size reaches K/2 in 7-8 years (Fig. 3E). At 400 sterilizations per year, K/2 is reached in 5 years. In each case, after the herd is reduced to K/2, 41 annual sterilizations maintains the desired herd size. The sterilization schedule used in this simulation for marked females is presented in Table 2.
Assuming random sampling with ballistic sterilization and censusing females, the number of fertile females in the herd can be estimated. This estimate is used to determine the number of annual sterilizations (compensating for repeats); therefore it is not necessary to mark females to obtain desired results. The initial number of sterilizations (e.g. the number a field crew can do in a year) is divided between the two female classes based on the number of each in the herd; thus, some of the effort is spent on repeat sterilizations. If 100 animals are initially sterilized, the herd can be controlled, but the time increases from 10-12 to 16-18 years. The maintenance sterilization level rises from 41 to 67, but the number newly sterilized is still 41. The difference, 26, is a tax on the system compensating for repeat sterilizations. Sterilization at an initial rate of 200 results in control of herd size in 9-10 years, up from 7-8 years. The maintenance level is 70, of which 42 are new, and the graph is virtually identical to Fig. 3E. With an initial rate of 400, control is achieved in 7-8 years, up from 5 years, and the maintenance level is 71, of which 43 are new. The sterilization schedule used in this simulation for unmarked, but estimated female numbers, is presented in Table 2.
Equilibrium herd size is sensitive to changes in _K and _Ref, parameters that determine the magnitude of control functions. For example, in sterilization simulations with female herd size above FK, the control function is turned off and the maximum number of females are sterilized; below FRef, none are sterilized. If the number of fertile females is between FRef and FK, equilibrium herd size is defined by the interaction of these two parameters. The minimum female herd size (therefore equilibrium herd size) depends on FRef, and population stability at lower herd sizes depends on FK (Fig. 3F). Assuming that a manager has the personnel to exceed these limits, the control functions operate as settings on a machine. Changing these values changes the equilibrium outcome; they are controls on the model that managers can manipulate to generate sterilization schedules to meet their needs.
The model is also sensitive to changes in reproductive and survival rates when herd size is between K and the refuge levels. A 25% reduction in reproductive rates added to the scenario in Fig. 3E (sterilize and mark 200 animals) reduces the equilibrium herd size from 745 to 645. A reduction of 10% in survival rates reduces the herd size to 507. A 25% reduction in reproduction and 10% reduction in survival reduces the herd to 439. These changes suggest that fairly accurate estimates of these parameters are needed to arrive at a particular equilibrium herd size. However, when the number of fertile females is known or estimated, it never falls below the refuge level, regardless of the magnitude of other parameters (within biologically reasonable limits). Thus, the decrease in herd size resulting from lower reproductive and survival rates is entirely at the expense of the males and sterile females, and if the number of fertile females is known, there is no fear of exterminating the herd, regardless of errors in input parameters.
Management generally involves minimizing cost/benefit ratios. The number of annual recruits is maximum at K/2 (Shaw, 1985), so it may be better to maintain a herd at less than K/2. With essentially the same effort of 200 annual sterilizations for 3 years, herd size can be reduced from 745 to 353 by lowering FRef from 120 to 50. At the lower herd size, the maintenance level is reduced from 41 to 20. If the minimum annual cost is important, the second option would be better. Managers also need to address cost/benefit ratios when deciding whether to remotely sterilize animals and accept a tax on the system, or capture and mark sterile animals. If a degree of uncertainty in the actual number of fertile females can be tolerated, then remote sterilizations would be better because ballistically implanting 70 animals would probably be less expensive than capturing and marking 41.
The current level of hunting and expected level of predation could continue under a sterilization program on Cumberland Island (using immunosterilants), and would reduce the initial number of sterilizations needed to maintain the herd at K/2. Comparing with Fig. 3E, if hunting and predation are included in the sterilization simulation, the number of sterilizations required to maintain the herd at K/2 is reduced from the initial number of 200 to an initial number of 81, although the maintenance level rises from 41 to 53 (Fig. 4). If females are remotely sterilized and their numbers estimated, the number is reduced from 200 to 94, and the maintenance level rises to 61. If FRef and FK are manipulated, the time required to reach K/2 can be made comparable with that in Fig. 3E. Thus, for the situation on Cumberland Island, sterilization at reasonable annual rates appears to be an effective management alternative.
The results of this model mimic reality for hunting and predation. The results probably also mimic reality for sterilization, but there are no data to which these results can be compared. Assuming that sterilization predictions are accurate, herd size in closed populations can be regulated in the field relatively quickly if fertile and sterile animals can be identified, or alternatively if the number in each group is estimated and an appropriate sterilization schedule is generated. However, demonstration of mathematical feasibility and political reality may be two entirely different matters. Sterilization is not a quick fix, and it must be viewed as a long term solution. Sterilization must be implemented every year, and it is unclear whether management agencies will be willing to continue indefinite funding. As stated by D. R. McCullough (Contraception in Wildl. Conf., Philadelphia, 1987), America is well suited to concentrated effort and quick fixes, but our patience is limited and we like to solve problems, not deal with them forever.
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Table 1. All input parameters used in this simulation, any of which may be changed by the user. The figures show parameter values that differ from these. Symbols for the other parameters are defined in the methods.
------------------------------------------------------------------------------------ Age Class 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 Max. Repro Rates 0 1 1 2 2 2 2 2 2 2 2 2 Repro Fem Survival 1 1 0.99 0.99 0.99 0.95 0.91 0.86 0.78 0.66 0.39 0.25 Sterile Fem Survival 1 1 1 0.99 0.99 0.99 0.95 0.91 0.86 0.78 0.66 0.39 Male Survival Rates 1 1 0.81 0.79 0.77 0.74 0.71 0.67 0.63 0.62 0.71 0.99 Repro. Fem Initial Density 71 71 70 70 69 69 66 60 51 41 27 10 Sterile Fem Initial Den 0 0 0 0 0 0 0 0 0 0 0 0 Male Initial Densities 137 137 111 87 67 67 49 34 23 15 9 6 Other parameters FaRef FaK FRef FK MRef MK K Refug MHun FHun #Ste FPred 120 280 120 280 120 280 1500 750 0 0 0 0 ------------------------------------------------------------------------------------
Table 2. Schedules for sterilizing an initial annual maximum of 200 marked or unmarked, but counted, females. Yr = year, HS = total herd size, FS = number of fertile females sterilized; TS is the total number of females remotely sterilized per year.
------------------------------------------- Marked Unmarked, (# est.) --------- ------------------------- Yr HS FS Yr HS FS TS ------------------------------------------- 1 1493 200 1 1493 200 200 2 1446 200 2 1446 157 200 3 1370 200 3 1388 136 200 4 1221 0 4 1299 122 200 5 1100 30 5 1153 13 23 6 1014 31 6 1073 37 65 7 952 45 7 983 32 56 8 886 34 8 926 44 74 9 843 46 9 865 37 63 10 796 37 10 826 44 74 ------------------------------------------
Fig. 1. Flow diagram showing interactions modeled between fertile females, sterile females, males, fawns, predators, and hunters. Arrows represent flow between categories and dotted lines represent feedback controls on the flow rates.
Fig. 2. Relationship between female herd size and the number of females sterilized. Changing the limiting parameters changes the slope of the line, and therefore changes the flow rate and equilibrium herd size.
Fig. 3. Model outputs. Input parameters not shown are given in Table 1. H = herd size, M = male, F = female, S = sterile. Values on the left axis are the ending number of animals in each category. Nominal run with no sterilization, hunting, or predation (A). Effect of hunting 150 males and 150 females (B). Effect of remotely sterilizing 100 females per year. Females are not marked, and their numbers are unknown. Herd size oscillates until stabilizing in about 100 years (C). Effect of remotely sterilizing 150 females per year. Females not marked, numbers not known. Herd size oscillates until functional extinction after 26 years of treatment (D). Effect on herd size of sterilizing 200 females per year. Females not marked, but numbers are estimated. Herd size is reduced to K/2 in 7-8 years at 41 annual sterilizations (E). Effect of sterilization with a lower FK. (F, Compare with E).
Fig. 4. If hunting and predation continue on Cumberland Island at expected rates, the initial number of animals sterilized per year to reach and equilibrium at K/2 is reduced from 200 to 81, but the maintenance number is increased from 42 to 53. Symbols defined in Fig. 3.
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