Statistical sensitivity for detection of spatial and temporal patterns in rodent population densities.

A long-term monitoring program begun 1 year after the epidemic of hantavirus pulmonary syndrome in the U.S. Southwest tracked rodent density changes through time and among sites and related these changes to hantavirus infection rates in various small-mammal reservoir species and human disease outbreaks. We assessed the statistical sensitivity of the program's field design and tested for potential biases in population estimates due to unintended deaths of rodents. Analyzing data from two sites in New Mexico from 1994 to 1998, we found that for many species of Peromyscus, Reithrodontomys, Neotoma, Dipodomys, and Perognathus, the monitoring program detected species-specific spatial and temporal differences in rodent densities; trap-related deaths did not significantly affect long-term population estimates. The program also detected a short-term increase in rodent densities in the winter of 1997-98, demonstrating its usefulness in identifying conditions conducive to increased risk for human disease.


Statistical Methods
The overall experimental design and field sampling procedures are described by Mills et al. (this issue, pp. 95-101). The rodent density estimates we analyzed were based on mark-recapture trapping data from three permanently marked trapping webs at each site (1,2). We used monthly trapping data collected from August 1994 to February 1998. Trapping and rodent handling methods were described by Parmenter et al. (3), and safety procedures during animal processing followed Mills et al. (4). Blood samples collected from Peromyscus maniculatus were analyzed by the Centers for Disease Control and Prevention for Sin Nombre virus (SNV). Rodent densities were calculated by the program DISTANCE (2). Each dataset was analyzed by three models (uniform, half-normal, and hazard) A long-term monitoring program begun 1 year after the epidemic of hantavirus pulmonary syndrome in the U.S. Southwest tracked rodent density changes through time and among sites and related these changes to hantavirus infection rates in various small-mammal reservoir species and human disease outbreaks. We assessed the statistical sensitivity of the program's field design and tested for potential biases in population estimates due to unintended deaths of rodents. Analyzing data from two sites in New Mexico from 1994 to 1998, we found that for many species of Peromyscus, Reithrodontomys, Neotoma, Dipodomys, and Perognathus, the monitoring program detected species-specific spatial and temporal differences in rodent densities; traprelated deaths did not significantly affect long-term population estimates. The program also detected a short-term increase in rodent densities in the winter of 1997-98, demonstrating its usefulness in identifying conditions conducive to increased risk for human disease.
Hantavirus with three possible model adjustments (cosine, polynomial, and hermite). Akaikes information criterion was then used to select the model that best fit the particular dataset (2). The three web density estimates for each trapping period were then partitioned into proportional densities representing each species, on the basis of the relative proportion of each in the total web sample. These species-specific densities (in numbers of mice per hectare) were analyzed by a repeated measures analysis of variance (RMANOVA) to test for differences between sites and through time and for site and time interactions. If significant F values were observed, we conducted within-trapping-period tests to detect differences among site means; we used Fishers least-significant-difference method.
The effect of low death rates among rodents on estimates of population size was analyzed by minimum number alive (MNA) methods (5). For this analysis, we calculated the observed MNA values for each species during each sampling period on the basis of actual field data, which included occasional trap deaths of rodents. We then constructed a hypothetical MNA, assuming that no trap deaths occurred in the sampled populations. The hypothetical death-free MNAs were computed by extending the projected life span of each animal that died in the trap. The length of the extensions differed by species and site and was determined by the mean number of trapping periods during which each species would normally have been present on each site (this figure was based on the lifespans of all other mice of that species that did not die in the traps or during handling). For example, if Neotoma albigula at the Sevilleta National Wildlife Refuge site, Web 1, had a mean lifespan of three trapping periods (i.e., its initial capture period [time zero] plus three additional sampling periods), and a mouse died in a trap on its first capture, we would add one mouse to the observed MNA values for three additional trapping periods to arrive at the hypothetical MNA values. If the mouse died during its second trapping period, we would add two trapping periods to the MNA estimates, and so on. In addition, if the dead mouse was pregnant or lactating, we increased the hypothetical MNA by the average number of offspring that would have been produced; mean numbers of offspring for each species were determined from specimen databases at the University of New Mexicos Museum of Southwest-ern Biology. These offspring were included for the duration of the expected lifespan on each study site. Thus, if a pregnant female N. albigula died during the study, we would add two offspring (the mean litter size for this species in New Mexico) to the MNA estimates for the full three trapping periods of their life expectancy. This process created species-specific hypothetical MNA values that were either equal to or greater than the observed MNA values. The two MNA datasets were then compared by RMANOVA.

Spatial Differences in Rodent Densities
RMANOVA successfully distinguished rodent densities between sites for a number of species (Table 1). Ords kangaroo rat and the

Hantavirus
Plains pocket mouse (Heteromyidae) were much more abundant at the Sevilleta National Wildlife Refuge site than at Placitas ( Figure 1A, B) and had greater statistical differences in the RMANOVA results (Table 1). In contrast, other rodent species (Muridae) had no overall differences by site (Table 1) and usually had similar densities, except for occasional episodes (Figures 1C-G). Although we observed no overall effect of site on density for these species, Fishers leastsignificant-difference methods showed significant differences between sites during certain periods ( Figures 1C,D,F,G), demonstrating that within a particular species, intersite differences could be discerned in both long-term sequences and during episodic, site-specific population irruptions.

Temporal Changes in Rodent Densities
The analyses also detected changes in rodent densities through time in all species examined (Table 1). Several species with generally low densities (e.g., the harvest mouse [ Figure 1D], the white-footed mouse [ Figure 1E], and the deer mouse [ Figure 1G]) occasionally became locally extinct but periodically recolonized the sites. Other species (e.g., the pinyon mouse [ Figure 1F] and the white-throated wood rat [ Figure 1C]) were found consistently on both sites, although their densities fluctuated considerably. In all cases, RMANOVA found significant differences in these temporal patterns.

Short-Term Rodent Population Increases
To determine the capability of the analyses to show statistically significant short-term increases in rodent densities (e.g., a rodent population explosion), we selected May 1997 to February 1998, a period characterized by a rodent density increase in some species (Figures 1A-G). We then tested the datasets for this period alone; RMANOVA results indicated significant increases in densities for the Plains pocket mouse, deer mouse, white-footed mouse, pinyon mouse, and Western harvest mouse (Table 2; Figure 1 B,D-G) during the winter of 1997 to 1998. Therefore, the monitoring program was capable of showing sudden, short-term increases in rodent densities that may precede a disease outbreak in humans.
Blood tests to determine the presence of SNV in deer mice showed generally low infection rates (Figure 2), with a maximum of only one mouse testing positive per trapping period at Placitas, and none at Sevilleta. The SNV-positive rodents were detected during periods of moderate abundance in 1994 and 1995 but not in the early stage of the population increase during the winter of 1997-98.

Low Death Rates among Rodents and Population Estimates
Four species had sufficient sample sizes for the MNA analyses, which were based on 28 trapping periods between August 1994 and January 1997 and included 7,024 rodent captures (Table 3). During field sampling, trap death rates were generally lower than 10% (3). A breakdown of the number of new animals, recaptured resident animals, and trap deaths indicated that immigration and reproduction rates were consistently higher than trap death rates ( Figure 3A-D). Species showing territorial behavior (e.g., Merriams kangaroo rat [ Figure  3A] and the white-throated wood rat [ Figure 3C]) had higher ratios of residents to immigrants than species without strongly defended territories.
In constructing the hypothetical MNA values, we used the following mean life expectancy values (number of trapping periods after initial capture): D. merriami = 2.16; P. flavescens = 1.11; P. truei = 0.68; N. albigula = 2.75. For female rodents of reproductive age, the following mean numbers of offspring were used (on the basis of University of New Mexicos     (Table 3). While highly significant temporal differences in MNA values were observed ( Figures 4A-D), no treatment-by-time interactions were produced, which demonstrated that the low death rates during the monitoring program did not affect rodent population estimates.

Conclusions
Our analyses indicated that the field experimental statistical design was sufficiently sensitive to detect a range of differences in densities of rodent species across study sites and through time. Even relatively moderate levels of increases were detectable by our methods, although they were far less dramatic than those observed during the 1993 SNV outbreak (6). While rodent densities of certain species significantly increased during this study (1994 to 1998), the maximum densities were considerably lower than those observed at the Sevilleta National Wildlife Refuge site in 1993 during the SNV outbreak (6). In addition, seroprevalence in deer mice dropped to zero in 1996 ( Figure 1G) and did not return, despite the higher densities observed in this species at these sites. Clearly, the population dynamics observed at this time were not equivalent to the rodent outbreak of 1993. Continued monitoring of these populations will be needed to determine the extent and importance of this apparent trend in rodent population ecology.
The statistical sensitivity demonstrated in this study is critical to the success of field monitoring programs, particularly those that function as early warning systems to alert health-care workers and researchers of impending outbreaks of disease (7,8). In the case of SNV, the monitoring program serves as both an early warning system and as a research database to which numerous environmental variables and the prevalence of SNV infections in rodents can be correlated.
In addition to the need for statistical power in distinguishing spatial and temporal patterns, the monitoring program must provide study site population estimates that can be directly compared. Standardization of techniques used by collaborating research groups ensures such comparability. In these hantavirus studies, the use of trapping webs and distance sampling theory (2) also allows for direct comparisons of rodent densities among species and across widely varying ecosystems. Trapping grids, and their associated population estimators, often produce results that may be suitable for local studies (internally consistent within a single experiment), but cannot be compared across ecosystem types and taxa because of site-specific characteristics or species-specific assumptions of capture probabilities. Trapping webs and distance sampling density estimators, however, have produced reasonably accurate density estimates in both a computer simulation study (9) and a field study (10). The accuracy of trapping webs and grids in estimating rodent densities is being evaluated more fully at the Sevilleta National Wildlife Refuge site.
All these methods require an appropriate sampling design and an understanding of the basic biology of the rodents. For example, the Plains pocket mouse has MNA values of four animals per month for the months of November, 1994 to March 1995 ( Figure 4B). In contrast, its density for the same period is zero ( Figure 1B), which indicates that no animals were captured during field sampling. The species habit of A potential source of estimation bias in rodent monitoring programs is the inadvertent influence of trapping and handling of rodents during field sampling. Capturing, anesthetizing, measuring, and collecting blood and saliva samples traumatizes small animals and may affect future trapping success, which, in turn, could bias the accuracy of the density or population estimators. Previous studies have shown various effects of trapping and handling on rodent body mass, ability to trap rodents in the future, and survival (3,11,(12)(13)(14)(15)(16)(17), but none have addressed the effect of low death rates on long-term population trends. While precautions are taken to ensure survival of sampled animals, occasionally a few die during sampling, especially those with a lower tolerance to the physical, physiologic, and psychologic stress of being captured and handled. Chronic loss of study animals from trapping or handling could underestimate their densities when compared to those of natural or undisturbed populations nearby. Results of our study indicate that death rates from trapping at these sites had no significant effect on long-term rodent population estimates.
The existing network of rodent population study sites seems successful in identifying local species-specific fluctuations in densities. Data from these sites can be used in addressing hypotheses on the relationships among environmental factors, rodent abundance, and SNV infections, as well as in providing an early warning for potential rodent population explosions that may increase the risk for other hantavirus pulmonary syndrome outbreaks in the southwestern United States.