The fixation probability of a beneficial allele in a population dividing by binary fission

We derive formulae for the fixation probability, P, of a rare benefical allele segregating in a population of fixed size which reproduces by binary fission, in terms of the selection coefficient for the beneficial allele, s. We find that an earlier result P 4s does not depend on the assumption of binary fission, but depends on an assumption about the ordering of events in the life cycle. We find that P 2s for mutations occurring during chromosome replication and P 2.8s for mutations occurring at random times between replication events.     

The distribution of the ancestral haplotype in finite stepping-stone models with population expansion

Recent extensive analyses of human DNA polymorphism reveal that the ancestral haplotype at various genetic loci occurs almost exclusively in African samples. We develop a coalescence-based simulation method in stepping-stone models with population expansion and examine the probability (P(A)) that the ancestral haplotype is found in African samples and the probability (Q(A)) that the most recent common ancestor of sampled genes occurs in Africa. These probabilities and other summary statistics are used to infer the human demographic history. It is shown that the high observed P(A) value cannot be explained simply by sampling bias. Rather, it suggests that the African population has been more strongly subdivided and isolated from each other than the non-African population and that there must have been some African populations which were not directly involved in the Out-of-Africa expansion in the late Pleistocene.     

A symbolic framework for the description of tree architecture models

The system of tree architecture proposed by Hallé and Oldeman consists of 23 models named after botanists playing leading roles in elucidating tree architecture. This system gives no indication why other models do not occur. A symbolism is presented here which can serve as a shorthand in recording tree architectures without assumptions about models. and immediately interpretable. Using this symbolism to represent the models proposed by Hallé and Oldeman permits creation of general rules of tree architecture. some of which raise interesting theoretical questions. Two further tree models that might well be expected to exist and several which would not be expected. are described.     

On the survival probability of a slightly advantageous mutant gene in a multitype population: A multidimensional branching process model

The estimated survival probability of a slightly supercritical Galton-Watson process is generalized to a multitype branching process. The result is used to estimate the probability of initial success of a mutant gene whose effect on the individual carrier depends on the carrier's sex, class, etc. The probability of initial success is also estimated in a case where the effect of the mutation is manifested in terms of the distribution of types within one's progeny, e.g. in a case of a change in the sex ratio.     

A framework for studying transient dynamics of population projection matrix models

Empirical models are central to effective conservation and population management, and should be predictive of real-world dynamics. Available modelling methods are diverse, but analysis usually focuses on long-term dynamics that are unable to describe the complicated short-term time series that can arise even from simple models following ecological disturbances or perturbations. Recent interest in such transient dynamics has led to diverse methodologies for their quantification in density-independent, time-invariant population projection matrix (PPM) models, but the fragmented nature of this literature has stifled the widespread analysis of transients. We review the literature on transient analyses of linear PPM models and synthesise a coherent framework. We promote the use of standardised indices, and categorise indices according to their focus on either convergence times or transient population density, and on either transient bounds or case-specific transient dynamics. We use a large database of empirical PPM models to explore relationships between indices of transient dynamics. This analysis promotes the use of population inertia as a simple, versatile and informative predictor of transient population density, but criticises the utility of established indices of convergence times. Our findings should guide further development of analyses of transient population dynamics using PPMs or other empirical modelling techniques.     

A framework for estimating the sensitivity of eDNA surveys

Imperfect sensitivity, or imperfect detection, is a feature of all survey methods that needs to be accounted for when interpreting survey results. Detection of environmental DNA (eDNA) is increasingly being used to infer species distributions, yet the sensitivity of the technique has not been fully evaluated. Sensitivity, or the probability of detecting target DNA given it is present at a site, will depend on both the survey method and the concentration and dispersion of target DNA molecules at a site. We present a model to estimate target DNA concentration and dispersion at survey sites and to estimate the sensitivity of an eDNA survey method. We fitted this model to data from a species‐specific eDNA survey for Oriental weatherloach, Misgurnus anguillicaudatus, at three sites sampled in both autumn and spring. The concentration of target DNA molecules was similar at all three sites in autumn but much higher at two sites in spring. Our analysis showed the survey method had ≥95% sensitivity at sites where target DNA concentrations were ≥11 molecules per litre. We show how these data can be used to compare sampling schemes that differ in the number of field samples collected per site and number of PCR replicates per sample to achieve ≥95% sensitivity at a given target DNA concentration. These models allow researchers to quantify the sensitivity of eDNA survey methods to optimize the probability of detecting target species, and to compare DNA concentrations spatially and temporarily.     

An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.     

A niche for biology in species distribution models

Why species are found where they are is a central question in biogeography. The most widely used tool for understanding the controls on distribution is species distribution modelling. Species distribution modelling is now a well‐established method in both the theoretical and applied ecological literature. In this special issue we examine the current state of the art in species distribution modelling and explore avenues for including more biological processes in such models. In particular we focus on physiological, demographic, dispersal, competitive and ecological‐modulation processes. This overview highlights opportunities for new species distribution model concepts and developments, as well as a statistical agenda for implementing such models.     

Moments of physiological transit time distributions and the time course of drug disposition in the body

Characterizing the tissue distribution kinetics of drugs by physiological and physico-chemical parameters and using a circulatory model the time course of blood concentration after intravenous injection is predicted for linear pharmacokinetic systems. The interrelationships between the first three (zero to second) moments of the distribution functions of organ transfer times, circulation times and residence times of drug molecules in the body are described. Utilizing literature data the model is applied to the analysis of lidocain kinetics in humans.     

Fixation of Strategies for an Evolutionary Game in Finite Populations

A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.     

A tale of North and South America: time and mode of dispersal of the amphitropical genus Munroa (Poaceae,Chloridoideae)

Plant disjunctions have provided some of the most intriguing distribution patterns historically addressed by biogeographers. We evaluated the three hypotheses that have been postulated to explain these patterns [vicariance, stepping‐stone dispersal and long‐distance dispersal (LDD)] using Munroa, an American genus of grasses with six species and a disjunct distribution between the desert regions of North and South America. The ages of clades, cytology, ancestral characters and areas of distribution were investigated in order to establish relationships among species, to determine the time of divergence of the genus and its main lineages, and to understand further the biogeographical and evolutionary history of this genus. Bayesian inference recovered the North American M. pulchella as sister species to the rest. Molecular dating and ancestral area analyses suggest that Munroa originated in North America in the late Miocene–Pliocene (7.2 Mya; 8.2–6.5 Mya). Based on these results, we postulate that two dispersal events modelled the current distribution patterns of Munroa: the first from North to South America (7.2 Mya; 8.2–6.5 Mya) and the second (1.8 Mya; 2–0.8 Mya) from South to North America. Arid conditions of the late Miocene–Pliocene in the Neogene and Quaternary climatic oscillations in North America and South America were probably advantageous for the establishment of populations of Munroa. We did not find any relationship between ploidy and dispersal events, and our ancestral character analyses suggest that shifts associated with dispersal and seedling establishment, such as habit, reproductive system, disarticulation of rachilla, and shape and texture of the glume, have been important in these species reaching new areas. © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2015, 179 , 110–125.     

A compact result for the time-dependent probability of fixation at a neutral locus

A result is derived, in the form of a sum, for the time-dependent probability of fixation of an unlinked neutral locus. The result captures many of the key features of the probability of fixation in a highly compact form. For ‘small’ times (t?4N_e) a single term of the sum accurately determines the time-dependent probability of fixation. This is in contrast to the well-known result of Kimura, which requires the contribution of many terms in a different sum, for ‘small’ times. Going beyond small times, an approximation is derived for the time-dependent probability of fixation which applies for all times when the initial relative allele frequency is small.     

Zones of influence for soil organic matter dynamics: A conceptual framework for data and models

Soil organic matter (SOM) is an indicator of sustainable land management as stated in the global indicator framework of the United Nations Sustainable Development Goals (SDG Indicator 15.3.1). Improved forecasting of future changes in SOM is needed to support the development of more sustainable land management under a changing climate. Current models fail to reproduce historical trends in SOM both within and during transition between ecosystems. More realistic spatio‐temporal SOM dynamics require inclusion of the recent paradigm shift from SOM recalcitrance as an ‘intrinsic property’ to SOM persistence as an ‘ecosystem interaction’. We present a soil profile, or pedon‐explicit, ecosystem‐scale framework for data and models of SOM distribution and dynamics which can better represent land use transitions. Ecosystem‐scale drivers are integrated with pedon‐scale processes in two zones of influence. In the upper vegetation zone, SOM is affected primarily by plant inputs (above‐ and belowground), climate, microbial activity and physical aggregation and is prone to destabilization. In the lower mineral matrix zone, SOM inputs from the vegetation zone are controlled primarily by mineral phase and chemical interactions, resulting in more favourable conditions for SOM persistence. Vegetation zone boundary conditions vary spatially at landscape scales (vegetation cover) and temporally at decadal scales (climate). Mineral matrix zone boundary conditions vary spatially at landscape scales (geology, topography) but change only slowly. The thicknesses of the two zones and their transport connectivity are dynamic and affected by plant cover, land use practices, climate and feedbacks from current SOM stock in each layer. Using this framework, we identify several areas where greater knowledge is needed to advance the emerging paradigm of SOM dynamics—improved representation of plant‐derived carbon inputs, contributions of soil biota to SOM storage and effect of dynamic soil structure on SOM storage—and how this can be combined with robust and efficient soil monitoring.     

A sequential stratification method for estimating the effect of a time-dependent experimental treatment in observational studies

Survival analysis is often used to compare experimental and conventional treatments. In observational studies, the therapy may change during follow-up and such crossovers can be summarized by time-dependent covariates. Given the ever-increasing donor organ shortage, higher-risk kidneys from expanded criterion donors (ECD) are being transplanted. Transplant candidates can choose whether to accept an ECD organ (experimental therapy), or to remain on dialysis and wait for a possible non-ECD transplant later (conventional therapy). A three-group time-dependent analysis of such data involves estimating parameters corresponding to two time-dependent indicator covariates representing ECD transplant and non-ECD transplant, each compared to remaining on dialysis on the waitlist. However, the ECD hazard ratio estimated by this time-dependent analysis fails to account for the fact that patients who forego an ECD transplant are not destined to remain on dialysis forever, but could subsequently receive a non-ECD transplant. We propose a novel method of estimating the survival benefit of ECD transplantation relative to conventional therapy (waitlist with possible subsequent non-ECD transplant). Compared to the time-dependent analysis, the proposed method more accurately characterizes the data structure and yields a more direct estimate of the relative outcome with an ECD transplant.     

Misconceptions and practical problems in the use of 15N soil enrichment techniques for estimating N2 fixation

The ¹⁵N methods are potentially accurate for measuring N₂ fixation in plants. The only problem with those methods is, how to ensure that the ¹⁵N/¹⁴N ratio in the plant accurately reflects the integrated ¹⁵N/¹⁴N ratio (R) in soil which is variable in time and with soil depth. However, the consequences of using an inappropriate reference plant vary with the level of N₂ fixation and the conditions under which the study was made. For example, the errors introduced into the values of N₂ fixation are higher at low levels of fixation, and decrease with increasing rates of fixation. At very high N₂ fixation rates, the errors are often insignificant. Also, the magnitude of error is proportional to the rate of decline of the ¹⁵N/¹⁴N ratio with time. Since N₂ fixation in most plants would be expected to below 60%, the question of how to select a good reference plant is still pertinent. In this paper, we have discussed some of the criteria to adopt in selecting reference plants, e.g. how to ensure that the reference plant is not fixing N₂, is absorbing most of its N from the same zone as the fixing plant, and in the same pattern with time, etc. In addition, we have discussed ¹⁵N labelling materials and methods that are likely to minimize any errors even when the fixing and reference plants don't match well in certain important criteria. The use of slow release ¹⁵N fertilizer or ¹⁵N labelled plant materials results in slow changes in the ¹⁵N/¹⁴N ratio of soil, and is strongly recommended. Where ¹⁵N inorganic fertilizers are used, the application of the fertilizer in small splits at various intervals is recommended over a one-time application. The problem with the reference crop, which has sometimes discouraged potential users of the ¹⁵N methods, is surmountable, as discussed in this paper.