Genotypes are frequently used to identify parentage. Such analysis is notoriously vulnerable to genotyping error, and there is ongoing debate regarding how to solve this problem. Many scientists have used the computer program CERVUS to estimate parentage, and have taken advantage of its option to allow for genotyping error. In this study, we show that the likelihood equations used by versions 1.0 and 2.0 of CERVUS to accommodate genotyping error miscalculate the probability of observing an erroneous genotype. Computer simulation and reanalysis of paternity in Rum red deer show that correcting this error increases success in paternity assignment, and that there is a clear benefit to accommodating genotyping errors when errors are present. A new version of CERVUS (3.0) implementing the corrected likelihood equations is available at http://www.fieldgenetics.com.

We describe a discrete-time, stochastic population model with density dependence, environmental-type process noise, and lognormal observation or sampling error. The model, a stochastic version of the Gompertz model, can be transformed into a linear Gaussian state-space model (Kalman filter) for convenient fitting to time series data. The model has a multivariate normal likelihood function and is simple enough for a variety of uses ranging from theoretical study of parameter estimation issues to routine data analyses in population monitoring. A special case of the model is the discrete-time, stochastic exponential growth model (density independence) with environmental-type process error and lognormal observation error.We describe two methods for estimating parameters in the Gompertz state-space model, and we compare the statistical qualities of the methods with computer simulations. The methods are maximum likelihood based on observations and restricted maximum likelihood based on first differences. Both offer adequate statistical properties. Because the likelihood function is identical to a repeated-measures analysis of variance model with a random time effect, parameter estimates can be calculated using PROC MIXED of SAS.We use the model to analyze a data set from the Breeding Bird Survey. The fitted model suggests that over 70% of the noise in the population's growth rate is due to observation error. The model describes the autocovariance properties of the data especially well.While observation error and process noise variance parameters can both be estimated from one time series, multimodal likelihood functions can and do occur. For data arising from the model, the statistically consistent parameter estimates do not necessarily correspond to the global maximum in the likelihood function. Maximization, simulation, and bootstrapping programs must accommodate the phenomenon of multimodal likelihood functions to produce statistically valid results.

We report on a new statistical test for detecting density dependence in univariate time series observations of population abundances. The test is a likelihood ratio test based on a discrete time stochastic logistic model. The null hypothesis is that the population is undergoing stochastic exponential growth, stochastic exponential decline, or random walk. The distribution of the test statistic under both the null and alternate hypotheses is obtained through parametric bootstrapping. We document the power of the test with extensive simulations and show how some previous tests in the literature for density dependence suffer from either excessive Type I or excessive Type II error. The new test appears robust against sampling or measurement error in the observations. In fact, under certain types of error the power of the new test is actually increased. Example analyses of elk ( Cervus elaphus) and grizzly bear ( Ursus arctos horribilis) data sets are provided. The model implies that density-dependent populations do not have a point equilibrium, but rather reach a stochastic equilibrium (stationary distribution of population abundance). The model and associated statistical methods have potentially important applications in conservation biology.

Genetic data are useful for estimating the genealogical relationship or relatedness between individuals of unknown ancestry. We present a computer program, ml‐relate that calculates maximum likelihood estimates of relatedness and relationship. ml‐relate is designed for microsatellite data and can accommodate null alleles. It uses simulation to determine which relationships are consistent with genotype data and to compare putative relationships with alternatives. ml‐relate runs on the Microsoft Windows operating system and is available from http://www.montana.edu/kalinowski.

We develop a general model for the effect of body size on fitness. We define fitness as reproductive power, the rate of conversion of energy into offspring. Reproductive power is assumed to be limited by a two-step process: first, the rate of acquisition of energy from the environment, which scales allometrically as body mass raised to approximately the 0.75 power, and then the rate of conversion of energy into offspring, which scales as mass to approximately the -0.25 power. The model predicts (1) the distinctive right-skewed shape of the frequency distribution of logarithms of body sizes among species that is observed in a wide variety of organisms from bacteria to mammals; (2) a taxon-specific optimal body size, which for mammals is approximately 100 g and is supported by data on the body sizes of mammals on islands; and (3) that in each taxon the relationships between such life-history and ecological characteristics as longevity, clutch size, home range size, and population density will change both slope and sign on either side of the optimal size. An energetic definition of fitness has the potential to unify areas of ecology and evolutionary biology that have previously used models based on different currencies.