Search

Finite population sampling theory is useful in estimating total population size (abundance) from abundance estimates of each sampled unit (quadrat). We develop estimators that allow correlated quadrat abundance estimates, even for quadrats in different sampling strata. Correlated quadrat abundance estimates based on mark–recapture or distance sampling methods occur when data are pooled across quadrats to estimate, for example, capture probability parameters or sighting functions. When only minimal information is available from each quadrat, pooling of data across quadrats may be necessary to efficiently estimate capture probabilities or sighting functions. We further include information from a quadrat-based auxiliary variable to more precisely estimate total population size via a ratio estimator. We also provide variance estimators for the difference between or the ratio of 2 abundance estimates, taken at different times. We present an example based on estimating the number of Mexican spotted owls (Strix occidentalis lucida) in the Upper Gila Mountains Recovery Unit, Arizona and New Mexico, USA. Owl abundance for each quadrat was estimated with a Huggins 4-pass mark–resight population estimator, but with initial capture and resighting probabilities modeled in common across all sample quadrats. Pooling mark–resight data across quadrats was necessary because few owls were marked on individual quadrats to estimate quadrat-specific capture probabilities. Model-based estimates of owl abundance for each quadrat necessitated variance estimation procedures that take into account correlated quadrat estimates. An auxiliary variable relating to topographic roughness of sampled quadrats provided a useful covariate for a ratio estimator.

We studied population subdivision and density-dependent and independent factors influencing population processes between 1965 and 2001 for elk (Cervus elaphus) inhabiting Rocky Mountain National Park (park) and the adjacent Estes Valley (town), Colorado, USA. Elk numbers within the park were held relatively constant by management controls until 1967, after which time they were allowed to increase without human interference. Radiotelemetry of 73 elk indicated limited exchange between the subpopulations; combined with clear distinctions in population dynamics, this suggests that these subpopulations are relatively independent despite the absence of physical barriers between them. The elk subpopulation within the park initially increased at 6.5%/year between 1968 and 1970, then growth gradually slowed-exhibiting density-dependent reductions both in calf survival and recruitment with increasing population size-and approached an estimated carrying capacity of 1,069 ± 55 (?±SE). Since 1991, this subpopulation has remained within ±5% of this equilibrium. The adjacent Estes Valley subpopulation grew at an estimated maximum 5-year average rate of 11.0% from 1979 to 1983 and is still increasing at 5.2%/year (1991-2001 average). Estimated town population currently is about 70% of our projected carrying capacity of 2,869 ±415 elk based on projection of observed calf recruitment decline with increasing population. Both carrying-capacity estimates are consistent with independent estimates based on forage biomass and energy considerations. Adult cow survival rate was not found to differ between park and town, and we estimated a constant rate of 0.913 [95% CI = 0.911, 0.915]. Bull survival rates increased in the park from 0.52 to 0.79 between 1965 and 2001, but remained constant at 0.42 [0.35, 0.47] in the Estes Valley. Colder winter temperatures were correlated with reduced calf recruitment (calves:cow at age 0.5 yr) and with reduced calf survival (between age 0.5 and 1.5 yr) in town. Recruitment of town elk also increased with warmer summer temperatures and greater summer precipitation. No weather covariates were significantly correlated with calf recruitment or survival in the park. Declining calf recruitment has been nearly linear and similar in both the park and town. In the park, calf survival responded little to density when the population was well below carrying capacity, but responded at an increasing rate as the population neared carrying capacity. This pattern may explain why calf survival response to density has not yet been detected in town. We estimated current combined population size of 3,049 [2759, 3369] elk in 2001. Elk in the town sector currently outnumber elk in the adjacent national park by almost 2:1 and are projected to increase by 46% before being nutritionally limited, suggesting that human-elk conflicts likely will increase in the absence of active management intervention.

Management of an ungulate population to maintain it at a desired level requires monitoring population size and vital rates to be able to harvest the population wisely. We present equations for the optimal allocation of resources for estimating total population size, recruitment rate of juveniles into the adult population, and juvenile and adult survival to minimize the variance of the adult female population size and the adult female population rate of change. These equations require information on the variance of the population growth process (process variance), expected sampling variance, and per unit costs for each of the 4 sampling procedures.

Regulating the abundance of ungulate populations using hunting can prevent populations from reaching levels that cause harm to natural and human dominated systems. However, there are an increasing number of cases where hunting is infeasible, and in such cases, fertility control has been widely advocated as an alternative means for controlling populations. Here, we develop simple analytical models offering general insight into the feasibility of using fertility control to regulate the abundance of ungulates. The models are structured in stages to represent variation in the duration of effect of fertility control agents. Analysis of these models offers several predictions, amenable to testing in field studies. (1) More than 50% of fertile females will need to be maintained infertile to achieve meaningful reductions in ungulate numbers even when fertility rates are low. (2) The relationship between the proportion of females maintained infertile and the steady state density is highly nonlinear. This means that small errors in estimating levels of infertility can lead to large errors in achieved density. It also means that managers should expect to see little change in steady-state density across a broad range of delivery rates. (3) The efficacy of fertility control as a management technique depends strongly on the persistence of the effect of the fertility control agent and the ability of managers to recognize previously treated animals. (4) Fertility control using long-lived agents can be more efficient than culling in regulating ungulate numbers. (5) Treating small populations with irreversible agents magnifies the likelihood of population extinction relative to treatment by culling. As with all techniques, managing population fertility must extend from a sound understanding of the influence of management actions on the state and dynamics of the population.

We conducted a 4-year management experiment to examine the annual effects of alternative management treatments, including anthelmintic administration, on lamb survival in Rocky Mountain bighorn sheep (Ovis canadensis canadensis) herds in southcentral Colorado. Beginning in December 1991, 4 bighorn herds were managed under alternative treatment regimes: baiting with alfalfa hay and apple pulp treated with fenbendazole (BT), baiting with alfalfa hay and apple pulp without fenbendazole (B), placing fenbendazole-treated salt blocks on winter ranges (T), and both withholding bait and fenbendazole (control; C). Treatments were rotated annually under a predetermined, randomly-selected schedule. Mean lamb production, survival, and recruitment rates did not differ among herds or years. None of the management treatments produced demonstrable improvements in lamb production, survival, or recruitment. Estimated effects (±SE) of treatments on lamb production and survival were small (≤0.09 ± 0.18). Annual recruitment rates (lambs/marked ewe) through October ranged from 0.13 to 0.88, but overall recruitment rates (mean; 95% CI) for B (0.72; 0.55-0.90), T (0.71; 0.47-0.95), and BT (0.52; 0.08-0.97) were indistinguishable from C (0.62; 0.19-1.0). Sick and coughing lambs were observed every summer in 1 herd and 1 summer in a second. Our results demonstrate that annual parasite treatment is not prerequisite for acceptable lamb survival among southcentral Colorado's wild bighorn populations, and that annual parasite treatment may not prevent catastrophic losses of lamb cohorts. Based on these data, we question the need for annual baiting and parasite treatment in the herds studied here and recommend such practices be reevaluated elsewhere.

A new procedure for constructing confidence interval estimates of population size in mark-sight experiments is presented. The method of selecting animals for marking must be equivalent to a simple random sample without replacement. Marked animals are required to be individually identifiable. The number of times animals are sighted must be independent of their mark status. The sighting process does not need to be composed of independent sighting trials or even decomposable into separate trials. Sighting probabilities can vary among individuals and can depend on such factors as group size and vegetational cover. Other methods of constructing confidence intervals in mark-sight experiments given these latter conditions have failed to achieve their stated nominal confidence level. Our confidence interval procedures are shown by simulation to have actual confidence levels close to nominal under conditions encountered in an application to a Colorado moose (Alces alces shirasi) population. For this population with 29 radio-collared moose and 5 helicopter sighting flights, the 90% confidence interval for the moose population size on the 1,400-km 2 area was 382-505.

Unbiased and precise estimates of pronghorn (Antilocapra americana) density and herd structure are necessary for proper management. We applied sample-based survey methods in Colorado sagebrush (Artemisia spp.) steppe (SBS) and shortgrass prairie (SGP) habitats to estimate pronghorn density and herd structure concurrently during late summer surveys with random quadrat (2.59 km 2 ) and random strip transect (1.6 km wide) sample units. Density estimates were lower (P = 0.015) for strips than for quadrats (2.24 pronghorn/km 2 ± 1.05) in SBS, but not for SGP (P = 0.122, 0.25 pronghorn/km 2 ± 0.27). Strip transect survey estimates of buck:doe ratios were lower than quadrat survey estimates in sagebrush (P = 0.014) and shortgrass (P = 0.003) habitats, which we attribute to observer bias in detecting bucks while searching strip transects. The mean difference in buck:doe ratios between strips and quadrats was 12.8 ± 5.87 in sagebrush and 20.0 ± 5.35 in shortgrass. Fawn:doe ratios did not differ by method in either sagebrush (P = 0.149, 5.2 fawns:100 does ± 6,40) or shortgrass (P = 0.849, 1.3 fawns:100 does ± 14.16). Double sample tests for bias failed to detect a bias in quadrat-based estimates of population size. On average, the population estimate on strips was about 50 and 70% of the estimate on SBS and SGP quadrats, respectively. We conclude there is undercounting bias in wide strip surveys. Population estimates from narrow strip transects (200 m wide) in both areas were consistent with line transect estimates. Line and narrow strip transect estimates were numerically (10-27%) but not statistically (P > 0.05) larger than quadrat estimates, leaving open possibilities that quadrats produce underestimate bias, lines and narrow strips produce overestimate bias, or the numerical differences represent sampling error. Quadrats offer acceptable precision and may be the least biased of any method tested for estimating population size and herd structure concurrently during the same aerial survey in late summer

Valid use of kidney fat index to track the annual fat cycle assumes that kidney mass is a constant proportion of bled carcass mass, and assumption not met for some cervids. Among 51 mature male and 89 mature female Rocky Mountain mule deer (Odoloileus hemionus hemionus) shot a approximately weekly intervals, curves of the annual cycle of kidney fat index and kidney fat mass coincided, but curves of the annual cycles of kidney mass and bled carcass mass did not. We recommended the more easily measured and less ambiguous kidney fat mass (KGM) as the best index of the annual fat cycle. A regression model approach indicated that mean transformed ln(KFM) can be estimated with high precision at a fixed point in time with small sample sizes. Fluctuations in the annual kidney fat mass cycle and daily rates of percent change were sex-specific and were associated with a nutritional cycle−reproductive cycle interaction

porary unmarked plots for surveys of ungulate fecal pellet-group densities (Neff 1968). Here we report on estimating densities of mule deer (Odocoileus hemionus) pellet groups using both permanent and temporary plots in an area of juniper-pinyon (Juniperus osteosperma-Pinus edulis) woodland. Temporary plots have been considered to have several inherent problems. Errors in determining numbers of new pellet groups could be significant as subjective differentiation of new from old groups not previously cleared from plots would be necessary (Neff 1968). However, Ferguson (1955), Robinette et al. (1958), and Rogers et al. (1958) concluded that new groups could be subjectively distinguished from old groups provided surveys were conducted during spring. Temporary plots varying annually in location may introduce an important source of variability in estimating pellet-group densities and they could also be placed with bias if established by pacing (Robinette et al. 1958). In spite of these concerns, use of temporary and permanent plots to estimate pellet-group densities has not been directly compared. Temporary plots are attractive because of their low cost. They would also facilitate changes in sampling systems that might otherwise be precluded if permanent plots were established. Our objective was to compare estimates of mule deer pellet-group densities on 10cadastral mi2 (2.59-km2) sample units (SU) using equal numbers of permanent (PERM) and temporary (TEMP) plots. The study was conducted from 1977 through 1980 in the Piceance Basin of northwestern Colorado.

Validity of models for sample observations from each of two sampling plans for estimating fawn: doe and buck : doe ratios of Rocky Mountain mule deer (Odocoileus hemionus hemionus) are examined. Standard-error formulas useful for bionomial random variables can give misleading results when applied to fawn : doe ratios. Standard-ratio estimators with route and quadrat sampling plans yielded nearly identical estimates of buck:doe and fawn:doe ratios. However, for equivalent levels of precision, route counts were more efficient. J. WILDL. MANAGE. 48(2):500-509 Management of mule deer is routinely dependent on sample ratios of sex and age to: (1) estimate the proportion of bucks, does, and fawns to assess the effects of sport hunting regulations on a population (Connolly 1981b:261), and (2) provide an index of fawn production and survival (Connolly 1981a:294-298). Sex and age ratios are also the basic data for the change-in-ratio method of estimating the abundance of many vertebrate populations, including deer (Hanson 1963, Paulik and Robson 1969, Seber 1982). Based on computer simulations, Caughley (1974:562) concluded that age ratios of wildlife populations "cannot be interpreted without a knowledge of rate of increase, and if we have an estimate of this rate we do not need age ratios." He conceded (p. 562), however, that a "sudden change in an age ratio ... indicates that something has happened-but more information is needed to find out what has happened." Since an estimate of the rate of increase requires annual population estimates (Connolly 1981a:301) and most wildlife management agencies do not invest in such estimates, the more easily obtained age (fawn: doe) ratios, cautiously interpreted, provide a useful index of the dynamics of mule deer populations. Despite widespread use of sex and age ratios in the management of mule deer, the associated sampling variation, sample s ze requirements, and statistical measures of reliability have received little specific study. Published exceptions include estimates of sample size requirements (Leop ld et al. 1951:108, Robinette et al. 1977: 79) and procedures for calculating approximate confidence limits (Riney 1956). Random sampling plans for estimating sex and age ratios of North American deer have not been published. The objectives of our study were to: (1) present an example of sex and age ratio estimates with relevant standard errors for a mule deer population, (2) examine assumptions or models for sample observations which permit development of measures of reliability of estimates of sex and age ratios, and (3) present implementable random sampling plans for sex and age ratio estimates of deer populations. We thank D. L. Baker, T. H. Pojar, L. H. Stelter, and particularly C. Wallmo and E. MacConnell-Yount for field assistance. E. G. Johnson examined probability models describing field counts of mule ' Present address: 206 South 5th, Montrose, CO 81401. 500 J. Wildl. Manage. 48(2):1984 This content downloaded from 157.55.39.223 on Wed, 24 Aug 2016 05:51:30 UTC All use subject to http://about.jstor.org/terms SEX AND AGE RATIOS OF MULE DEER * Bowden et al. 501 deer, and E. E. Remmenga provided initial advice. This is a contribution from Colorado Fed. Aid Proj. W-105-R and W38-R. ENVIRONMENT AND SAMPLE POPULATION Fieldwork was done on a 647.5-km2 portion of mule deer winter range within the Cache la Poudre River drainage, Roosevelt National Forest, on the east slope of the Front Range in north-central Colorado. The Cache la Poudre River flows easterly through the Front Range, a generally rugged, often precipitous region characterized by massive granitic outcrops and dendritic drainage patterns. That portion of winter range sampled extended from the eastern edge of the Front Range from about 1,646 to 2,896 m elevation. Mountain shrub and ponderosa pineDouglas-fir (Pinus ponderosa-Pseudotsuga menziesii) plant communities characterize the lower and upper elevational limits, respectively, of the Cache la Poudre winter range (Costello 1954). Mountain park, quaking aspen (Populus tremuloides), and big sagebrush (Artemisia tridentata) communities occur at higher elevations within the ponderosa pineDouglas-fir vegetation zone. Selected abiotic and biotic factors of the Cache la Poudre winter range and apparent responses of mule deer to those factors have been characterized by Loveless (1967) and Anderson et al. (1972a,b,c). The mule deer population is largely migratory. No estimates of the total population of wintering deer are available, but average deer pellet group-derived densities on three representative portions of the Cache la Poudre winter range varied from 10.8 to 23.9 deer/km2, 1962-65 (Anderson et al. 1972c). METHODS

This paper is primarily concerned with estimation of the parameters 1, al2 /-2 a22 and p in the mixture of two normal distributions when independent sample information is available from one of the populations. The solution to the maximum likelihood (ML) equations was obtained using Newton's iterative method. Some interesting results for the moment estimates were obtained for the case when independent sample observations are available from one population. Extensive Monte Carlo simulation was employed to obtain the sample variances of the estimates as well as the estimated asymptotic variances. The variances of the estimates are influenced by the separation of the two means with respect to the variances, the mixture proportion (p), and, of course, the size of the sample. When the number of observations is small and the means are not well separated, the sample variance of the estimates can be as much as three times greater than the estimated asymptotic variances.

Suivi par radiopistage de 27 femelles adultes de Odocoileus hemionus dans les collines du piemont des Rocheuses au colorado de 1982 a 1985 afin de determiner leurs deplacements saisonniers et les aires de deplacement hivernales

Hunting is a fundamentally important tool for wildlife managers. We examined the null hypothesis that hunting does not influence deer movement and their use of habitat types. Seventeen radio-collared, adult, female Rocky Mountain mule deer (Odocoileus hemionus hemionus) were located 1 day before the 1983 first Colorado deer season, and during day 2 of the first and day 3 of the second deer seasons in the foothills west of Fort Collins, Colorado. Distance from the preseason location to each location during hunting seasons were calculated for each deer. There were no differences between mean distance from pre-hunting season location to hunting season location for 10 deer that had all 3 locations in the area closed to hunting, and 4 deer that had 3 locations in the area open to hunting (P = 0.34 and 0.52). All 17 deer had all 3 locations in the interior of their minimum convex polygon home ranges. Those home ranges had a mean size of 226 ha and range of 117 to 323 ha. However, deer in the section open to hunting generally moved to vegetation types with increasingly better escape cover as the hunting seasons progressed. We conclude that hunting pressure did not cause deer movement in terms of distance or cause them to leave their normal home ranges, but did cause deer to move into more adequate cover.

Mule deer (Odocoileus hemionus) were censused by 2 observers in a helicopter during 3 consecutive winters on 193 0.6475-km2 quadrats distributed, in a stratified random sampling design, throughout 1,688 km2 of pinyon-juniper (Pinus edulis-Juniperus osteosperma) winter range on the Uncompahgre Plateau, in southwestern Colorado. Quadrats were plotted on maps and aerial photos, and the 4 corners were permanently marked on the ground. Estimates of total deer population and 90% confidence limits for the 3 years were 11,401 + 2,205, 17,884 + 4,042, and 17,085 ? 2,951, respectively. During the 2nd and 3rd years the sample was sufficient to permit estimation of the population within 22.6 and 17.3% of the mean number of deer per 2.59 km2, respectively, with 90% confidence. Stratified random sampling reduced variance of the mean number of deer seen per 2.59 km2 by 42, 21, and 37%, respectively, relative to simple random sampling during the 3 years of the census. Procedures for conducting a census of this type and methods for minimizing observer error are detailed. J. WILDL. MANAGE. 44(3):632-639 This study was initiated as a result of widespread concern among wildlife managers and the public that Colorado mule deer populations had suffered recent declines. These declines could not be documented, however, due to lack of deer census systems that had been implemented and tested on a large scale (Gill 1976, Wallmo et al. 1976). The need for such a census sytem was, therefore, clearly recognized. Mountainous terrain and relative inaccessibility of many areas in the West compound problems of censusing deer. A technique employing a helicopter to survey randomly located quadrats was selected for assessment of feasibility because it appeared to offer a reasonable solution to those problems. Numerous studies have evaluated aerial census systems for large ungulates. Many of these have involved counting African animals along transects (Goddard 1967, Bell et al. 1973, Norton-Griffiths 1973). Bergerud (1963) used the transect method to count caribou (Rangifer tarand s) in Newfoundland and Labrador, and Caughley et al. (1976) used it in Australia to count kangaroos (Megaleia rufa, Macropus giganteus and fuliginosus) and domestic sheep. The transect system is suited only to use in relatively flat terrain, however, because counting errors occur in mountainous terrain due to variations in altitude and banking the aircraft, which affect definition of the transect strip (Pennycuick 1969). Big game animals on quadrats can be censused using a helicopter in the steepest mountain

Twenty-two adult, female mule deer (Odocoileus hemionus hemionus) were radio-collared with activity sensors and monitored with ground triangulation from mid-November through March, for 3 years (1982-1985) in the foothills west of Fort Collins, Colorado, to test 4 general hypotheses about habitat selection and activity: (1) The proportion of time deer spend feeding and resting varies with time of day. (2) Deer alter their activity patterns in response to environmental influences. (3) Selection of specific vegetation types for feeding and resting varies with time of day. (4) Ecotones are preferred habitats. Deer were monitored during 6-hr sampling periods: sunrise, daytime, sunset, and night. Deer fed most during sunset, night, and sunrise periods and least during the day. Feeding occupied similar proportions of an average deer's time during sunset, night, and sunrise periods. They preferred the grassland type for feeding and resting at night and the mountain mahogany (Cercocarpus montanus) type for both activities during all other periods. Preference deer showed for the ponderosa pine (Pinusponderosa) type for feeding activity was inversely related to canopy cover. Deer rested most during daytime and night periods. During periods of daylight, deer using the grassland type showed preference for ecotones with certain types offering escape cover. No such preference was observed at night. Deer fed less and rested more when snow depth exceeded 36 cm. No significant differences (P>0.05) in the proportion of time deer devoted to feeding were found in the following comparisons: clear versus cloudy full-moon nights (-50 vs. + 50% cloud cover), full-moon versus new-moon, low versus high wind speeds (0-32 vs. 32-56 km/hr), and warm versus cold temperatures (+18 to -15 vs. -15 to -23? C). No significant relationships were found for the same comparisons in proportion of time devoted to resting.

Counts of mule deer (Odocoileus hemionus) fecal groups on 960, 100-ft2 circular plots located on three north-central Colorado winter range study areas of about 500 acres each, were related to mean forage yields in pounds (ovendry) per acre and mean utilization per plot (percentage weight) of true mountain mahogany (Cercocarpus montanus), antelope bitterbrush (Purshia tridentata), and big sagebrush (Artemisia tridentata) sampled on those plots from 1962 to 196S. Scatter diagrams and regression analysis revealed no significant ( P > O.OS ) correlations between the indices of deer numbers and mean yield or utilization of true mountain mahogany and antelope bitterbrush. Mean yield and mean utilization were significantly (P

Measurements of 32 site factors on 931, 100 ft2, circular plots systematically distributed among lower, middle and upper Cache la Poudre, Colorado winter range study areas of about 500 surface acres each, were related to cumulative mule deer (Odocoileus her&onus) fecal groups counted on those plots (1963-65). Single and multiple linear regression and C&i-square analyses indicated that vegetative measurements, particularly antelope bitterbrush (Purshia trident&u) parameters, were the site factors most closely related to fecal group counts. These site factors accounted for about lo-13 percent in single linear regressions, and 8-20 percent in multiple linear regressions of the significant variation (R2) in fecal group counts.

Ages estimated from (1) molar tooth ratios (Robinette et al. 1957), (2) visual evaluation of molariform tooth wear at a check station, and (3) regression of eye lens weight (Y) on age (X), were compared to assumed known ages obtained from counts of cementum annuli in the first permanent incisor of mule deer (Odocoileus hemionus). Ages of 62 of 100 mule deer about 26 months and older were not correct when estimated to the nearest year from the molar tooth ratios. Ages of 43 of 116 (37 percent) were not correct when estimated from visual evaluations of permanent molariform tooth wear at a check station and assigned to one of 5 age groups (2, 3+4, 5+6, 7+8, and 9+ years). A regression of eye lens weight (Y) on age (X) for 177 mule deer of both sexes was fitted with the equation loge Y = 0.3585710.94080 1/X with a correlation coefficient of -0.98. A deer whose lens weight exceeded about 0.9 g, corresponding to an estimated age of 16 months from birth, had a confidence interval greater than 12 months in width and could not be assigned to a single-year age-class with 95 percent confidence. None of the three methods examined was found satisfactory for accurate individual age estimation. Reliable interpretations of population dynamics of deer require that age structures be estimated with minimal error. Various techniques have been developed for age estimation of Odocoileus deer. These include: (1) tooth replacement and wear criteria (based on known-age deer) given in qualitative form (Severinghaus 1949, Ryel et al. 1961), and quantitative form (Severinghaus 1949, Ryel et al. 1961, Robinette et al. 1957, Brown 1961); (2) eye lens weight (Lord 1962, Lueth 1963, Longhurst 1964, Larsen 1964, Hoffman and Robinson 1966, Connolly et al. 1969); and (3) cementum annuli counts for Odocoileus and other cervids (Sergeant and Pimlott 1959, Mitchell 1963, Low and Cowan 1963, McEwan 1963, Gilbert 1966, Ransom 1966, 1A contribution from Colorado Federal Aid Project W-105-R, and based, in part on J. A. Erickson's M. S. Thesis, Colorado State University, Fort Collins. 2Present address: U. S. Forest Service, Intermountain Forest and Range Experiment Station, Boise, Idaho. Reimers and Nordby 1968, Erickson and Seliger 1969). Little has been published on the magnitudes of error involved in either qualitative or quantitative methods of estimating mule deer age from wear of permanent molariform teeth. Among qualitative estimates made to the nearest year, Brown's (1961: 22) data show a 60 percent error in a sample of 47 known-age deer (0. h. columbianus) 2.5-7.5 years of age, and Ryel et al. (1961:312) show a 43 percent error in a sample of 39 known-age deer (O. virginianus) 2.5-5.5 years of age. An indication of the error involved in quantitative estimates is found in Robinette et al. (1957) and Brown (1961) who used wearreflecting measurements of molariform teeth of known-age deer. Both works show considerable overlap in the 95-percent confidence intervals about the mean measurement ratios for successive year classes. Estimation of deer age from eye-lens weight has yielded conflicting results. Lueth (1963) judged the technique inac

The Poisson, Neyman type A, negative binomial, and the Thomas distributions were fitted to the frequency distributions of the number of fecal groups per plot for mule deer (Odocoileus hemianus) counted on a systematic sample of 960, 100 ft2, and 1,687, 43.6 ft2, circular plots on two diverse Colorado habitats sampled over two seasons. The three latter distributions represented fecal-group data equally well. However, there was a consistent appearance of one or two high frequencies with very small probability of occurrence under the three distributions regardless of plot size, sampling intensity, habitat, or season of fecal-group deposition. Fecal-group densities were too low to distinguish between the three distributions, but the negative binomial offered the simplest explanaffon of ie data, and appropriate standard errors and confidence limits may be readily computed. The two following modes of deer behavior (or a combination of the two) could give rise to any of the three distributions: (1) deer wandering at random over the sampled area in groups of various sizes, and (2) single deer wandering at random within homogeneous blocks of land but a different mean rate for each bloek. Since Bennett English, and McCain (1940) first applied the method to deer (Odocoileus spp.), fecal drol?ping counts have been successfully used as a census method on a statewide basis in Michigan ( Michigan Department of Conservation 1966), on a herd basis in California (McCain 1948), on small study areas in western Texas (Wallmo 1958), and in western Washington ( Brown 1961 ) . Its validity as a census method has been experimentally confirmed with small, known, penned populations of white-tailed deer (O. virginianus) on natural habitat in Michigan (Eberhardt and Van Etten 1956, Ryel 1959); with small, approximately known, free-ranging populations of mule deer in Colorado ( Harris 1959 ) and Montana ( White 1960 ); and for black-tailed deer (O. hemionus columbianus) in California (Dasmann and Taber l9SS). Other uses, not experimentally confirmed) are as indices to the relative intensity of use 1 Contribution from Colorado Federal Aid Projects W-105-R and W-114-R. 2Present address: U. S. Forest Service, Intermountain Forest and Range Experiment Station, Boise, Idaho. and the relative distribution of deer within adjacent habitats ( Wallmo 1958 White 1960) disjunct habitats (Brown 1961)) and portions of fairly homogeneous habitats ( Reynolds 1964 ) . Julander ( 1955 ) used sample counts of deer and cattle fecal droppings as an index to their relative distribution within a diverse habitat in Utah. Neff (1968) presented a detailed review of the literature on the technique and concluded that the method is valid in obtaining reliable big game population data. Few authors have attempted to test the fit of appropriate mathematical models to frequency distributions of fecal group counts. However, lmowledge of an appropriate model is essential for reliable confidence-interval estimates of deer use except perhaps, for very large sample sizes. Knowledge of the model may point to the necessity for transfolming data for further regression and analysis of variance interpretations. Also, appropriate models may offer clues on behavioral patterns. Loveless ( 1967:82) sampled about 150 acres of precipitous winter range with 100ft2 circular plots and concluded that mule

Weights of paired, fresh adrenals were sampled yearlong from 145 to 176 Cache la Poudre mule deer (Odocoileus hemionus), 1961-65. Annual population densities of this migratory herd xvere unknown within the S28-mile2 area of deer collections. Mean (+ SD) absolute adrenal weights svere 6.08 + 1.64 grams for 46 mature, male deer and S.15 + 1.40 grams for 80 mature, female deer. This difference was significant (P < 0.01). Significant (P < 0.05) annual changes in the mean absolute adrenal weight did not occur in either sex. A significant (P < O.OS) regression of absolute adrenal xveight on a polynomial in the day of collection, which consisted of peaks (high stress) in late January and early August and lows (low stress ) during April and mid-December, accounted for about 35 percent of the variation (R2) in absolute adrenal weight of mature males. The regression of absolute adrenal ereight of mature females on a polynomial in the day of collection was not significant (P < 0.05). Simple correlation coefficients and stepwise multiple regression analyses showed that age and age-related variables svere important sources of variation in absolute adrenal weights and that environmental variables were unimportant. LOge absolute adrenal weight could be predicted ( R2 = 0.84) in male mule deer from lOge estimated age, eviscerated carcass weight, and date of collection. Absolute adrenal weight could be predicted ( R2 = 0.75 ) in female mule deer from lOge estimated age, eviscerated carcass xveight, date of collection, and elevation of collection site. Adrenals of females had proportionately more variation associated with eviscerated carcass weight, season, and elevation at a given age than did adrenals of males. Mean relative adrenal weight did not differ significantly (P < 0.05) between sexes, ageclasses, or years. Significant seasonal changes in the mean relative adrenal zZeights of each sex appeared to be a function of variation in fat reserves. By extending Selye's ( 1946) ieory of the general adaptation syndrome, Christian (1950) hypothesized a density-dependent, behavioral endocrine feedback system that regulates populaltions of some kinds of mammals. Christian and Davis (1964:1580) reviewed and defended ffie hypothesis and concluded that the system "is important in the regulation of populations of rodents, lagomorphs, deer, and possibly ather nzammals.'' The vcxluminous literature on endocrine-population relationships has been reviewed by Christian et al. ( 1965 ) . Much of this research has utilized such indices of adrenocortical activity as cholesterol content of the adrenal glanld, urine metabelites, lymphocytes or eosinophil counts of the 1 A contribution from Colorado Federal Aid Project W-105-R. 9 Present address: U. S. Forest Service, Intermountain Forest and Range Experiment Station, Boise, Idaho. blood, histologic study of ffie adrenal gland, ascorbic acid ccontent of the adrenal gland, and the absolute or relative weight of the paired adrenals to either deteot or assess the effects of various stressors on confinecl laboratol:y mammals. Several authors have analyzed adrenal sveights of free-ranging and captive deer. Browman and Sears (1956) and Taber et al. (1960) studied mule deer, Hughes and Mall (1958) blacktailed deer ( Odocoi1zas 7xem?onus columbianus), NVelch ( 1962) and Hoffman and Robinson (1966) rvhite-tailed deer (Odocoileus virginulnus ), Wandeler ( 1966 ) and Bubenik an!d Bubenik ( 1967 ) roe deer (Capreolus capreolus), Christian (3t al. (1960) sika deer (Cerous nippon), and Flook (1970) wapiti (Certuscanadensis). Welch ( 1962 :100 ) suggested that annual trends ill mean adrenal sveights, presumably as sampled during the hunting season, rnay furnish a useful supplementary index of condition

Growth curve models and analyses have received considerable attention from a number of authors. Recent papers which reference earlier work are Potthoff and Roy [1964], Elston [1964], Rao [1965], and Krishniaiah [1967]. The main concern of these and earlier papers was to establish a model for growth curves and then to perform tests of hypotheses on the population mean growth curve or to construct confidence intervals or bands for the population mean growth curve. In this paper the model of Rao [1965] is used to construct tolerance bands for a population of individual growth curves. In the model employed each individual in the population has a growth curve whose expectation can be expressed as a polynomial in time. The tolerance bands desired are bands such that a given proportion, 7r, of the individuals in the population have their expected growth curves entirely within the bands. In the case where the parameters of the expected growth curves are unknown, a solution is given which contains a proportion ir of the expected growth curves with confidence level approximately (1 a). These bands would be useful, for example, in determining when to move fish from one hatchery pond to another for larger fish. At any time with any set confidence, limits can be found for the size of 90%, say, of the population. Given a set of tolerance bands based on a large number of fish growth curves, the manager can decide at what time any given run of fish can be expected to have a proportion ir of their numbers in a particular size range. In section 5 a numerical example is presented for a sample of fish with approximate linear growth for the time-span of interest. Consider the model for polynomial growth curves