Mark L. Taper

Revising how the computer program cervus accommodates genotyping error increases success in paternity assignment

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.

EVOLUTION OF BODY SIZE: CONSEQUENCES OF AN ENERGETIC DEFINITION OF FITNESS

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.

DENSITY DEPENDENCE IN TIME SERIES OBSERVATIONS OF NATURAL POPULATIONS: ESTIMATION AND TESTING'

We report on a new statistical test for detecting density dependence in uni- variate 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 hy- potheses 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.

ESTIMATING DENSITY DEPENDENCE, PROCESS NOISE, AND OBSERVATION ERROR

We describe a discrete-time, stochastic population model with density depend ence, 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 (Kaiman 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 populations 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.

Maximum likelihood estimation of the frequency of null alleles at microsatellite loci

We review three methods for estimating the frequency of null alleles at codominant loci (such as microsatellite loci) and present a new maximum likelihood approach. Computer simulations show that the maximum likelihood estimator has a smaller root mean squared error than previous estimators.

Models of character displacement and the theoretical robustness of taxon cycles

The appropriateness of the techniques used in modeling character displacement has been the focus of vigorous debate. In this paper, the three competing methods (the coevolutionarily stable community (CSC), the evolutionarily stable strategy (ESS), and quantitative genetic recursion (QGR)) are compared in models using a common ecological setting. Specific predictions of the CSC model have been used to understand features of character displacement among Cnemidophorous lizards on islands off Mexico, Anolis lizards in the Lesser Antilles and Galápagos finches. Nonetheless, the validity of the approach has been repeatedly questioned. Conceptually the three formalisms vary in the degree to which within species variability is allowed in the models. The predictions of the CSC are found not to be robust to even small violation of its fundamental assumption of absolute species monomorphy. We show by simulation and analytical observations that the CSC is not valid under frequency dependent selection, and that the ESS is the limiting case of QGR as intraspecific phenotypic variation goes to zero. Thus the ESS and the QGR models agree closely when the between‐phenotype component (BPC) of the niche width is small. However, as the BPC increases, quantitative discrepancies between ESS and QGR predictions increase, although model behavior remains qualitatively similar. A fourth approach, termed “Quantitative Genetic Optimization” (QGO) analysis, is suggested, combining advantages of both the ESS and QGR. Although all approaches support the possibility of taxon cycles, the cycle patterns predicted are qualitatively different and strongly model dependent.

Hybridization rapidly reduces fitness of a native trout in the wild

Human-mediated hybridization is a leading cause of biodiversity loss worldwide. How hybridization affects fitness and what level of hybridization is permissible pose difficult conservation questions with little empirical information to guide policy and management decisions. This is particularly true for salmonids, where widespread introgression among non-native and native taxa has often created hybrid swarms over extensive geographical areas resulting in genomic extinction. Here, we used parentage analysis with multilocus microsatellite markers to measure how varying levels of genetic introgression with non-native rainbow trout (Oncorhynchus mykiss) affect reproductive success (number of offspring per adult) of native westslope cutthroat trout (Oncorhynchus clarkii lewisi) in the wild. Small amounts of hybridization markedly reduced fitness of male and female trout, with reproductive success sharply declining by approximately 50 per cent, with only 20 per cent admixture. Despite apparent fitness costs, our data suggest that hybridization may spread due to relatively high reproductive success of first-generation hybrids and high reproductive success of a few males with high levels of admixture. This outbreeding depression suggests that even low levels of admixture may have negative effects on fitness in the wild and that policies protecting hybridized populations may need reconsideration.

DUCK NEST SURVIVAL IN THE MISSOURI COTEAU OF NORTH DAKOTA: LANDSCAPE EFFECTS AT MULTIPLE SPATIAL SCALES

Nest survival is one of the most important parameters in the population dynamics of grassland-nesting ducks (Anas and Aythya spp.) that breed in the Prairie Pothole Region of North America. Grassland habitats used by these species are increasingly threatened by habitat loss and the coincident fragmentation, which may indirectly alter nest survival through effects on predators. Although predators are the dominant cause of nest loss, they are difficult to monitor directly. Thus, indirect analyses of habitat variables are required. Many studies have attempted to address the relationship between fragmentation and nest survival; however, few studies have examined the influence of fragmentation at multiple spatial scales. Understanding how landscape characteristics at multiple spatial scales explain variation in nest survival is important, because no single correct scale is likely to exist for a diversity of landscape metrics. We examined the relationships between habitat variables and duck nest survival (n ≈ 4...

Migration within Metapopulations: The Impact upon Local Population Dynamics

Publisher Summary This chapter examines the impact of migration within metapopulations upon local population dynamics. A central issue in the analysis of metapopulations is the frequency of migration, or demographic connectivity, among component populations. For most analyses, the actual number of migrants that successfully move between two populations per breeding season or generation is the most important measure of the level of connectivity between them. Migration frequency will be a continuous variable, and may range from zero—where populations are completely isolated from one another—to a value that may be nearly equal to the number of individuals in each unit, in which case the two units function as a single population. This chapter focuses on the more general “rescue effect” metapopulation system, in which migration can prevent local population extinctions, but where there may be stochastic variation in both the rate and the direction of migration. Thus, the identities of the “source” and “sink” populations can change unpredictably through time. The studies discussed in this chapter suggest that metapopulations with strong rescue effects may be more common than currently supposed, and the best way to look for metapopulations with strong rescue effects may be to examine habitat types, rather than particular taxa.

On size and area: Patterns of mammalian body size extremes across landmasses

We describe a biogeographic pattern in which mammalian body size extremes scale with landmass area. The relationship between the largest and the smallest mammal species found on different landbridge islands, mountaintops and continents shows that the size of the largest species increases, while that of the smallest species decreases, with increase in the area of the landmass. We offer two possible explanations: (1) that the pattern is the result of sampling artefacts, which we call the ‘statistical artefact hypothesis’, or (2) that the pattern is the result of processes related to the way body size affects the number of individuals that a particular species can pack in a given area, which we call the ‘area-scaling hypothesis’. Our results point out that the pattern is not a statistical artefact resulting from random sampling, but can be explained by considering the scaling of individual space requirements and its effect on population survival on landmasses of different area.