To specify this distribution, we fit a variety of probability models to the survey data. The model with the smallest sum of squared errors was the Weibull. Fit to the entire data

set, the Weibull had a shape parameter of 0.95 (SE = 0.02) and a scale parameter of 6.85 (SE = 0.27). Given the number of cows in a group, we then drew selleck kinase inhibitor the number of calves from a beta-binomial distribution. We conducted two rounds of simulations. First, because time of day was identified as an important source of variation in the data, we simulated calf:cow ratios using the mean relationship for Solar Time and Solar Time squared. The probability each cow had a calf at solar noon was fixed to 0.05, 0.1, 0.15, or 0.2 and covered the range of values observed during surveys. We examined three values of overdispersion, θ  =  4, 10, or 20, as RG7204 order these covered the range observed in most study years (Table 4). Because future surveys may occur under different circumstances, such as at a different time of year, we repeated the simulations assuming that there was no relationship between the calf:cow ratio and time of day. When time of day must be accounted for, attaining 20% relative

precision generally required sampling >300 groups with cows for ratios ≥0.15 and θ  =  10 or 20 (i.e., higher calf:cow ratios and lower overdispersion). With higher overdispersion, θ  =  4, or lower calf:cow ratios, r = 0.05 or 0.1, >400 groups must be sampled to attain 20% relative precision (Fig. 5A). Sampling 200 groups was sufficient to attain 30% relative precision at all calf:cow ratios and all levels of overdispersion, except r = 0.05. If the effect of time of day need not be estimated, 20% relative precision can be attained by sampling 200 groups with cows for all calf:cow ratios except 0.05 (Fig. 5B). Age ratios, such as calf:cow ratios, are typically used to estimate recruitment and to infer population status. The utility of age ratios for inferring population status has been widely criticized, because increasing

and decreasing populations may have similar age distributions and, therefore, have similar age ratios D-malate dehydrogenase (Caughley 1974, McCullough 1994). Because of this, numerous authors (e.g., Caughley 1974, McCullough 1994, Harris et al. 2008) suggest that independent estimates of population growth or abundance are necessary to verify that inferences based on age ratios are correct. However, it is premature to conclude that age ratio data are not useful. The utility of age ratios to reflect changes in population growth or to estimate survival is primarily dependent upon the stability of the ratio’s denominator (McCullough 1994, Harris et al. 2008). The denominator is stable when the number of adults does not change over time and this requires that recruitment into the adult age classes be balanced by adult mortality.