Using a nonrecursive formula to determine cladogram probabilities

Three properties of bifurcating branching diagrams that are used for representing a specific number of taxa are (1) the number of possible arrangements, (2) the number of possible topologies, and (3) the probabilities of formation according to particular models of cladogenesis. Of these, the probabilities have received the least attention in the literature. Indeed, many biologists would be astonished by the observation that the probability of a commonly cited cladogram containing 35 phyla of the animal kingdom is < 0.0072% of the value of the average probability taken over all possible cladograms! We reviewed works on cladogram arrangements and topologies and developed a computer-generated table of enumerations that extends and corrects such tables in the literature. We also developed a nonrecursive formula for the determination of cladogram probabilities. This formula facilitates calculation and thereby should promote use of cladogram probabilities, which might provide more accurate null hypotheses for tests of cladogenic events than do considerations of cladogram arrangements or topologies.     

Risikoberechnungen beim autosomal-rezessiven Erbgang

Genetic risk calculations are demonstrated for autosomal recessive diseases using Bayesian calculation tables. The Hardy-Weinberg law forms an important basis for the determination of a priori probabilities. We demonstrate how healthy relatives, molecular test results and complex genetic models affect the risk. Examples of autosomal recessive inheritance with cystic fibrosis (CF) and infantile spinal muscular atrophy (SMA) have been selected.     

North Atlantic climate variation influences survival in adult fulmars

There is increasing evidence that large scale climate variation influences reproductive parameters of seabirds, but fewer studies have investigated possible effects on adult survival. Previous work has shown that climate variation reflected by the winter North Atlantic oscillation (WNAO) influences reproductive success in northern fulmars. Here, we use a 34 year long (1962–1995) individual‐based data set to investigate inter‐annual and inter‐individual variation in adult survival in this species. Breeding success in the previous and current seasons, and both the WNAO and one‐year lagged WNAO indexes, were considered as potential sources of inter‐annual variation in survival and recapture probabilities. Sex and an index of body size were considered as potential sources of inter‐individual variation in survival and recapture probabilities. Body size effects were not significant, but males and females differed in both their survival and recapture probabilities. Probability of recapture of females was positively correlated with breeding success in both the current and previous breeding seasons, whereas male recapture probabilities were correlated only with previous breeding success. Male and female survival decreased over the study period, suggesting that there had been a degradation of environmental conditions. This hypothesis was supported by the detection of a negative correlation between survival and the WNAO, which, in turn, showed a positive increase over this period. The negative correlation between female adult survival and WNAO did not result only from the long term behaviour of the two time series, but persisted for higher frequency fluctuations. In contrast, the correlation between male survival and WNAO seemed to result only from the long term behaviour of the two time series. Despite uncertainties over causal mechanisms, these findings add to the body of evidence that large scale climate variation could dramatically affect seabird population dynamics. Furthermore our results suggest that climate variation can differentially influence individuals with distinct phenotypic characteristics.     

Probability of success of breeding strategies for improving pro-vitamin A content in maize

Biofortification for pro-vitamin A content (pVAC) of modern maize inbreds and hybrids is a feasible way to deal with vitamin A deficiency in rural areas in developing countries. The objective of this study was to evaluate the probability of success of breeding strategies when transferring the high pVAC present in donors to elite modern-adapted lines. For this purpose, a genetic model was built based on previous genetic studies, and different selection schemes including phenotypic selection (PS) and marker-assisted selection (MAS) were simulated and compared. MAS for simultaneously selecting all pVAC genes and a combined scheme for selecting two major pVAC genes by MAS followed by ultra performance liquid chromatography screening for the remaining genetic variation on pVAC were identified as being most effective and cost-efficient. The two schemes have 83.7 and 84.8% probabilities of achieving a predefined breeding target on pVAC and adaptation in one breeding cycle under the current breeding scale. When the breeding scale is increased by making 50% more crosses, the probability values could reach 94.8 and 95.1% for the two schemes. Under fixed resources, larger early generation populations with fewer crosses had similar breeding efficiency to smaller early generation populations with more crosses. Breeding on a larger scale was more efficient both genetically and economically. The approach presented in this study could be used as a general way in quantifying probability of success and comparing different breeding schemes in other breeding programs.     

Factors influencing territorial occupancy and reproductive output in the Booted Eagle Hieraaetus pennatus

During a 7-year research project in a forested area of southeastern Spain, we studied territorial occupancy and reproductive success in a Booted Eagle Hieraaetus pennatus population. We monitored 65 territories, gathering information on 406 occupancy events and 229 breeding attempts, including those of two potential competitors, the Northern Goshawk Accipiter gentilis and the Common Buzzard Buteo buteo . Generalized linear mixed models were used to explain occupancy and productivity, by evaluating the relative contribution of three different types of variables (habitat, competition and past events) and considering territory as a random effect. We examined a set of a priori hypothesized models, together with a number of additional models, and selected the best models following an information-theoretic approach. Our best models related territorial occupancy and productivity to previous breeding success (the fledging of one or two young), which appeared to be the most important factor determining the probability of reoccupation and the reproductive output in the subsequent year. The best occupation model revealed that the probabilities of occupancy were also conditioned by a competition variable (intraspecific nearest-neighbour distance) and two habitat variables (the location of the nest on the valley slope and the distance to the nearest forest track). Unlike the best occupation model, however, the selected model for reproductive output did not incorporate any competition variable besides previous breeding success, but included another two habitat variables (the effects of trunk height and NNE orientation).     

A complete enumeration and classification of two-locus disease models

There are 512 two-locus, two-allele, two-phenotype, fully penetrant disease models. Using the permutation between two alleles, between two loci, and between being affected and unaffected, one model can be considered to be equivalent to another model under the corresponding permutation. These permutations greatly reduce the number of two-locus models in the analysis of complex diseases. This paper determines the number of nonredundant two-locus models (which can be 102, 100, 96, 51, 50, or 58, depending on which permutations are used, and depending on whether zero-locus and single-locus models are excluded). Whenever possible, these nonredundant two-locus models are classified by their property. Besides the familiar features of multiplicative models (logical AND), heterogeneity models (logical OR), and threshold models, new classifications are added or expanded: modifying-effect models, logical XOR models, interference and negative interference models (neither dominant nor recessive), conditionally dominant/recessive models, missing lethal genotype models, and highly symmetric models. The following aspects of two-locus models are studied: the marginal penetrance tables at both loci, the expected joint identity-by-descent (IBD) probabilities, and the correlation between marginal IBD probabilities at the two loci. These studies are useful for linkage analyses using single-locus models while the underlying disease model is two-locus, and for correlation analyses using the linkage signals at different locations obtained by a single-locus model.     

Influence of maternal characteristics and oceanographic conditions on survival and recruitment probabilities of Weddell seals

For long‐lived animals, maternal age and breeding experience can vary widely and affect offspring survival and recruitment probabilities. In addition, these vital rates may be influenced by annual variation in environmental conditions. We evaluated various hypotheses regarding how offspring survival and recruitment probabilities vary as functions of maternal characteristics and oceanographic conditions, using 25 years of data from a study of individually‐marked Weddell seals in Erebus Bay, Antarctica. We predicted that survival and recruitment would be positively related to maternal age and experience up to some threshold value and considered three hypothesized shapes for the relationship beyond the threshold age (steadily increasing, pseudo‐threshold, or decreasing). We predicted an inverse relationship between maternal age at first reproduction and offspring survival and recruitment probabilities. We predicted that sea‐ice extent, which positively influences primary productivity, would be positively related to annual recruitment probabilities. Results revealed contrasting influences of maternal age on probabilities of survival and recruitment of young. Survival rate was best modeled by a pseudo‐threshold relationship with maternal age, e.g. in 1999, survival rate was estimated as 0.61, 0.69 and 0.72, respectively, for seals born to 6‐, 14‐ and 22‐yr‐old mothers. In contrast, estimated recruitment probability was highest for seals born to young mothers, e.g. recruitment probability for a 7‐yr‐old who had not yet had a pup was estimated as 0.51 vs 0.30, respectively, if she was born to a 6‐ versus a 14‐yr‐old mother. The combined results for offspring survival and recruitment suggest countervailing selection where genotypes favored for reproductive success are generally selected against as juveniles, resulting in high recruitment probabilities for individuals that had low juvenile survival rates. Finally, we found support for our prediction that oceanographic conditions affected annual recruitment rates, but not survival rates. Specifically, annual recruitment probability was positively related to the sea‐ice extent in September of the previous year.     

The influence of variable rates of inbreeding on fitness,environmental responsiveness,and evolutionary potential

We manipulated experimental populations of the housefly (Musca domestica L.) under three inbreeding schemes (fast, slow, and punctuated) to partition out the influences of different means and variances in the rate of inbreeding, per generation, while controlling for the final level of inbreeding as a constant. One treatment used constant fast inbreeding (11% per generation; Ne = 4 for 4 generations), for a comparison to one that was consistently slow (3% per generation; Ne = 16 for 14 generations). The third followed a model for serial founder-flush events. Each founder-flush episode involved a one-generation pulse of fast inbreeding (Ne = 4) followed by two generations of very low (or no) inbreeding, yielding high intergenerational variation (i.e., for an average inbreeding rate of 4% per generation). Allozyme assays showed that we achieved the intended final inbreeding coefficient of about 37%. All inbreeding schemes decreased fitness levels in terms of egg-to-adult viability, development time, and male mating success relative to the outbred control. The consistently fast inbreeding protocol had more pronounced reductions in fitness, relative to the other two inbreeding schemes. In comparison to the fast and punctuated regimes, the consistently slow protocol preserved evolutionary potential (as assayed by the genetic divergence of subpopulations exposed to different environments) in egg-to-adult viability, and (albeit anecdotally) reduced the extinction probabilities, especially in a novel environment. The punctuated treatment did not optimize the potential for purge as predicted, but instead reduced fitness, evolutionary potential, and environmental responsiveness (as measured by genotype-by-environment interactions). This founder-flush treatment also had the highest extinction probabilities. Longer periods of population flush might be necessary to purge effectively in a punctuated scheme. We conclude that the rate of inbreeding, independent from the final level, can have important effects on population fitness, environmental responsiveness, and evolutionary potential.     

Obtaining meaningful comparisons of nest success: data from New Zealand robin (

Nest success, the proportion of clutches resulting in one or more fledglings, is a key indicator for assessing the effect of management on bird populations. However, the figures reported for New Zealand populations are usually "apparent nest success", the number of successful nests divided by the total number found. Apparent nest success invariably overestimates the true success rate, and the degree of bias depends on the population and monitoring regime. Consequently, apparent nest success rates cannot be reliably compared. We used Stanley?s (2000) method for estimating stage-specific daily survival probabilities for New Zealand robin (Petroica australis) nests at Tiritiri Matangi, Paengaroa, Boundary Stream and Pureora. We show how Stanley?s method can be used to eliminate biases, to calculate point estimates and confidence intervals for nest success, and to model the factors affecting nest success. At Pureora, where monitoring was extremely intensive, the apparent overall nest success (39%) was close to that estimated from daily survival probabilities (37%). Apparent nest success rates were extremely biased for the other populations due to less intensive monitoring, with the bias exacerbated by changes in survival probabilities with season and/or stage of the nesting cycle. Modelling the data showed that failure rates were: (1) higher early in the breeding season for at least some mainland populations, (2) different for incubation and nestling stages, with the pattern depending on the season (early or late) and type of predator, and (3) substantially lowered by predator control at Pureora, with the impact varying between sites and stages. Taking these factors into account, the estimated nest success (and 95% confidence limits) was 60% (44- 74) at Pureora after predator control, 47% (23-73) at Boundary Stream, 37% (26-49) at Tiritiri Matangi, 25% (11- 48) at Paengaroa, and 25% (17-35) at Pureora without predator control.     

Competing risks analysis in mountain pine beetle dynamics

This paper presents an application and evaluation of competing risks analysis (Chiang , 1968) of mountain pine beetle life tables. Three known and one group of unknown risks are used. Interpretation of the results imply that only the crude probability of death from a specific cause is applicable to this situation; net and partial crude probabilities are yet incomplete. None of the risks (factors of mortality) exerted sufficient influence upon the population to be considered factors of regulation or reduction. Evidence remains that the mountain pine beetle is food-regulated at optimum temperature conditions and temperature-regulated at optimum food conditions.     

Tables and Procedures for the Determination of Power and Sample Sizes in Univariate and Multivariate Analyses of Variance and Regression

The available power tables for use in experimental design only serve for limited practical purposes, since they are restricted to very few levels of significance such as .01, .05, and .10. With these values, however, usually no correction for cumulating error probabilities, for example, by the Dunn-Bonferroni method, can be achieved, because (very) low values of a and sometimes even of α are necessary. Therefore, power tables are presented that encompass a wide range of different values for a (.0005 to .40), for power (.50 to .9995), and for 45 different values of the degrees of freedom for the numerator of the F ratio (u = 1 to 150). Four of the 16 tables are printed. Their use is demonstrated for some paradigmatic problems in univariate and multivariate analyses of variance and regression.     

Environmental heterogeneity generates fluctuating selection on a secondary sexual trait

In any population in which resources are limiting, the allocation of resources toward increased reproductive success may generate costs to survival [1-8]. The relationship between a sexually selected trait and fitness will therefore represent a balance between its relative associations with fecundity versus viability [3, 6, 7]. Because the risk of mortality in a population is likely to be heavily determined by ecological conditions, survival costs may vary as a function of the prevailing environment [7]. As a result, for populations experiencing heterogeneous ecological conditions, there may not be a single optimal level of allocation toward reproduction versus survival [9]. Here, we show that early viability and fecundity selection act in opposing directions on a secondary sexual trait and that their relative magnitude depends upon ecological conditions, generating fluctuating selection. In a wild population of Soay sheep (Ovis aries), phenotypic and genetic associations between male horn growth and lifetime reproductive success were positive under good environmental conditions (because of increased breeding success) and negative under poor environmental conditions (because of reduced survival). In an unpredictable environment, high allocation to early horn growth is a gamble that will only pay off if ensuing conditions are favorable. Such fluctuating selection may play an important role in preventing the erosion of genetic variance in secondary sexual traits.     

Correlations in the utilization of carbon sources in the range of griseus species of the genus Streptomyces

The author proposes a new scheme for arranging the data about the assimilation of carbon sources in tables; this is illustrated with the Griseus species belonging to the Streptomyces genus and with the information about them presented by Bergey [2]. In the scheme, carbon sources in the tables are arranged in the order of their diminishing availability for streptomycetes, and the lists of species within the morphological groups are constructed according to the property of a carbon source not being assimilated. Such an arrangement of data in the tables is very clear and convenient to use; it allows one to make optimal schemes for determining the assimilation of carbon sources by actinomycetes, and makes it easy to divide any large number of cultures into groups according to a similar assimilation of carbon sources. The scheme has been used to analyse the data available in science and to establish correlations in the assimilation of carbon sources by species of the Griseus series belonging to the Streptomyces genus.     

Allocation Variable-Based Probabilistic Algorithm to Deal with Label Switching Problem in Bayesian Mixture Models

The label switching problem occurs as a result of the nonidentifiability of posterior distribution over various permutations of component labels when using Bayesian approach to estimate parameters in mixture models. In the cases where the number of components is fixed and known, we propose a relabelling algorithm, an allocation variable-based (denoted by AVP) probabilistic relabelling approach, to deal with label switching problem. We establish a model for the posterior distribution of allocation variables with label switching phenomenon. The AVP algorithm stochastically relabel the posterior samples according to the posterior probabilities of the established model. Some existing deterministic and other probabilistic algorithms are compared with AVP algorithm in simulation studies, and the success of the proposed approach is demonstrated in simulation studies and a real dataset.     

Impact of two follow-up schemes on morbidity management and disability prevention (MMDP) programme for filarial lymphedema in Matara,Sri Lanka

Alleviating morbidity due to lymphatic filariasis (LF)—especially in elderly patients who are rather ignorant—is presently the biggest challenge for the national filariasis campaign. We introduced two follow-up schemes and compared each other to address three key programmatic issues (1) locating patients, (2) educating patients, family members on practice of lymphoedema self-care (3) well sustained daily self-care. Hundred and seven lymphoedema patients were introduced to the new Community Home Based Care (CHBC) programme as a part of MMDP programme at their homes. Twenty seven of 107 patients were selected by purposive sampling and followed-up under two schemes, 14 in Daily follow-up (DFU) scheme and 13 in Monthly follow-up (MFU) scheme. Impact was assessed using a KAP score, number of entry lesions (EL) and number of ADL episodes, limb volume, its appearance, changes in the quality of life and gained benefits. Visiting patients in their homes to introduce lymphoedema care programme was a success. KAP scores of the more important activities on lymphoedema care were significantly higher in DFU scheme. Number of patients (51.9%; 14/27) who had EL/s at baseline reduced significantly to 18.5% (5/27) at one year follow-up. The mean numbers of ADL episodes/year reduced significantly in both schemes. Six photographs of 27 showed obvious improvement in lymphoedema and its grade. Mean volume of lymphoedema reduced significantly in both schemes at one year no significant difference between schemes. Benefit score at one year revealed that the patients in DFU scheme received significantly higher amount of benefits compared to MFU scheme. In conclusion daily instruction has significantly motivated the patient and his/her family bringing a new hope.     

Effects of genotyping errors on parentage exclusion analysis

Genetic markers are widely used to determine the parentage of individuals in studies of mating systems, reproductive success, dispersals, quantitative genetic parameters and in the management of conservation populations. These markers are, however, imperfect for parentage analyses because of the presence of genotyping errors and undetectable alleles, which may cause incompatible genotypes (mismatches) between parents and offspring and thus result in false exclusions of true parentage. Highly polymorphic markers widely used in parentage analyses, such as microsatellites, are especially prone to genotyping errors. In this investigation, I derived the probabilities of excluding a random (related) individual from parentage and the probabilities of Mendelian-inconsistent errors (mismatches) and Mendelian-consistent errors (which do not cause mismatches) in parent-offspring dyads, when a marker having null alleles, allelic dropouts and false alleles is used in a parentage analysis. These probabilities are useful in evaluating the impact of various types of genotyping errors on the information content of a set of markers in and thus the power of a parentage analysis, in determining the threshold number of genetic mismatches that is appropriate for a parentage exclusion analysis and in estimating the rates of genotyping errors and frequencies of null alleles from observed mismatches between known parent-offspring dyads. These applications are demonstrated by numerical examples using both hypothetical and empirical data sets and discussed in the context of practical parentage exclusion analyses.     

Stream amphibians as metrics of critical biological thresholds in the Pacific Northwest, U.S.A.: a response to Kroll et al.

1. Kroll, Hayes & MacCracken (in press) Concerns regarding the use of amphibians as metrics of critical biological thresholds: a comment on Welsh and Hodgson 2008 . Freshwater Biology, criticised our paper [ Welsh & Hodgson (2008) Amphibians as metrics of critical biological thresholds in forested headwater streams of the Pacific Northwest. Freshwater Biology, 53 , 1470–1488] proposing the use of headwater stream amphibians as metrics of stream status in the Pacific Northwest (PNW). They argued that our analysis of previously published data reflected circular reasoning because we reached the same conclusions as the earlier studies. In fact, we conducted a meta‐analysis to address new questions about the optimum values and thresholds (based on animal densities) for abiotic stream attributes that were found to be important to these amphibians in earlier studies. This is analogous to determining blood pressure thresholds or fat‐to‐weight ratios that facilitate predicting human health based on meta‐analyses of earlier data from studies that found significant correlations between these variables and relative health. 2. Kroll et al. argued that we should not make inference to environmental conditions across the PNW from data collected in California. We collected data from northern California and southern Oregon, the southern extent of the PNW. We made inference to the Klamath‐Siskiyou and North Coast bioregions, and argued that available research on these headwater species indicates that our results have the potential to be applied throughout the PNW with minimal regional adjustments. 3. Kroll et al. contended that we need reproductive success, survival estimates and density estimates, corrected for detection probabilities, to establish relationships between animal density and stream attributes. Reproductive success and survival estimates are important for demographic modelling and life tables, but they are not necessary to demonstrate meaningful relationships with abiotic conditions. Both corrected occupancy estimates and individual detection probabilities are unnecessary, and take multiple sampling efforts per site, or onerous mark release and re‐capture studies, respectively, to determine accurately. 4. Kroll et al. questioned the use of stream amphibians as a surrogate for measuring physical parameters, such as water temperature, claiming that measuring the physical parameters directly is more efficient. Here they misinterpreted the main point of our paper: stream organisms are integrators of what happens in a catchment, and carefully selected species can serve as surrogates for the biotic community and the relative condition of the network environment. 5. Kroll et al. claimed that we demonstrated weak inferences regarding ecosystem processes. We argue that by relating densities of stream amphibians with changes along abiotic environmental gradients that are commonly affected by anthropogenic activities, we are establishing biological links to gradients that represent important ecosystem processes and identifying biometrics that can be used to quantify the status (health) of these gradients.     

Using probability of persistence to identify important areas for biodiversity conservation

Most attempts to identify important areas for biodiversity have sought to represent valued features from what is known of their current distribution, and have treated all included records as equivalent. We develop the idea that a more direct way of planning for conservation success is to consider the probability of persistence for the valued features. Probabilities also provide a consistent basis for integrating the many pattern and process factors affecting conservation success. To apply the approach, we describe a method for seeking networks of conservation areas that maximize probabilities of persistence across species. With data for European trees, this method requires less than half as many areas as an earlier method to represent all species with a probability of at least 0.95 (where possible). Alternatively, for trials choosing any number of areas between one and 50, the method increases the mean probability among species by more than 10%. This improvement benefits the least-widespread species the most and results in greater connectivity among selected areas. The proposed method can accommodate local differences in viability, vulnerability, threats, costs, or other social and political constraints, and is applicable in principle to any surrogate measure for biodiversity value.     

Using fledged brood counts of hedgerow birds to assess the effect of summer agri-environment scheme options

A key aim of many European agri-environment schemes (AES) is to improve biodiversity on farmland. In recent years, several countries have been looking at long term trends in the spring adult population size of a target group of farmland birds as an indicator of this. The overall trend in these indicators is however not upwards. While this might suggest we need to look at the design and deployment of habitat management options within schemes, there is an increasing view that we also need to refine and improve our indicators, or the way we monitor them.Relating spring adult bird population size to AES options is problematic not least because of the time lag between the deployment of those designed to enhance bird breeding success in summer, and the spring surveys the following year. At the other end of the scale detailed studies of breeding success in farmland birds have practical/cost restraints. We argue that to understand the impact on farmland birds of particular summer options within AESs we need to be able to estimate the breeding success of local bird populations quickly and cheaply. This would enable us to relate particular AES options to the breeding performance of the birds actually using them.Complementing a previous study of woodland birds, we assess the likelihood of encountering fledged broods of hedgerow nesting bird species during transect surveys without finding nests, and then apply a simple mark-recapture analysis technique to provide an index of breeding success for those species. Following spring adult assessments, counts of fledged broods were undertaken four times a week during April, May, June and July, in four 2.5 km hedgerow transects, at four sites in southern England in 2010. Mean daily detection probabilities of fledged broods of 16 common hedgerow birds were calculated from these counts using the software Presence. For 15 out of these 16 species these detection probabilities were sufficiently high for a programme of fledged brood surveys, involving just two or three visits per week from mid-May to mid-July, to provide a useful estimate of breeding success.The survey technique and associated analyses make certain assumptions when providing estimates of breeding success and these are discussed. Little is known about initial dispersal in passerine fledglings and a study in hedgerows may be useful here. However our pilot study suggests that the method could have application as a relatively easily derived productivity index for hedgerow birds, and hence an additional method available to study the impact of certain AES options on indicator species, or for research studies.     

Quasi-likelihood estimation for relative risk regression models

For a prospective randomized clinical trial with two groups, the relative risk can be used as a measure of treatment effect and is directly interpretable as the ratio of success probabilities in the new treatment group versus the placebo group. For a prospective study with many covariates and a binary outcome (success or failure), relative risk regression may be of interest. If we model the log of the success probability as a linear function of covariates, the regression coefficients are log-relative risks. However, using such a log-linear model with a Bernoulli likelihood can lead to convergence problems in the Newton-Raphson algorithm. This is likely to occur when the success probabilities are close to one. A constrained likelihood method proposed by Wacholder (1986, American Journal of Epidemiology 123, 174-184), also has convergence problems. We propose a quasi-likelihood method of moments technique in which we naively assume the Bernoulli outcome is Poisson, with the mean (success probability) following a log-linear model. We use the Poisson maximum likelihood equations to estimate the regression coefficients without constraints. Using method of moment ideas, one can show that the estimates using the Poisson likelihood will be consistent and asymptotically normal. We apply these methods to a double-blinded randomized trial in primary biliary cirrhosis of the liver (Markus et al., 1989, New England Journal of Medicine 320, 1709-1713).