Exponential pattern of cell age distribution in dividing cells of plant meristems

In order to determine the pattern of cell age distribution in proliferating cells of Allium cepa roots we have measured by cytophotometry two cell size parameters, protein content and surface area projection, in cells that correspond to the entire proliferating population or only to the ana-telophase subpopulation. The size values of ana-telophase cells have been employed to construct theoretical size distributions for the entire proliferating cell population of the root meristem by assuming either a uniform or an exponential cell age distribution. Statistical comparison of theoretical distributions with the experimental one rules out a uniform cell age distribution and strongly favours an exponential age distribution similar to that found in bacteria.     

Analysing spatial correlation of weeds and harvester ants in cereal fields using point processes

The interaction between the spatial distribution of weed richness and weed cover and the spatial location of harvester ant nets was investigated in cereal fields. The understanding of such interdependencies can be relevant to understand weed population dynamics in dryland cereal fields and may enhance management strategies for weed control. We used spatial statistical tools derived from point process theory. In particular, we compared the two spatial configurations by assuming two different point patterns. We did so by replacing the random weed fields by a related point pattern and comparing it with the point pattern of harvester ants. Our results suggest that areas with a high density of ant nests are, in this case study, in areas with low weed richness and that large nests have a greater impact than small nests. Considering that only one field was analysed, preserving and enhancing regular ant nest distributions, especially of large nests, might have an impact on depleting weeds and consequently enhancing weed control.     

Hierarchical multivariate mixture generalized linear models for the analysis of spatial data: An application to disease mapping

Disease mapping of a single disease has been widely studied in the public health setup. Simultaneous modeling of related diseases can also be a valuable tool both from the epidemiological and from the statistical point of view. In particular, when we have several measurements recorded at each spatial location, we need to consider multivariate models in order to handle the dependence among the multivariate components as well as the spatial dependence between locations. It is then customary to use multivariate spatial models assuming the same distribution through the entire population density. However, in many circumstances, it is a very strong assumption to have the same distribution for all the areas of population density. To overcome this issue, we propose a hierarchical multivariate mixture generalized linear model to simultaneously analyze spatial Normal and non‐Normal outcomes. As an application of our proposed approach, esophageal and lung cancer deaths in Minnesota are used to show the outperformance of assuming different distributions for different counties of Minnesota rather than assuming a single distribution for the population density. Performance of the proposed approach is also evaluated through a simulation study.     

Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.     

The natural variability of vital rates and associated statistics

The first concern of this work is the development of approximations to the distributions of crude mortality rates, age-specific mortality rates, age-standardized rates, standardized mortality ratios, and the like for the case of a closed population or period study. It is found that assuming Poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate Poisson distribution. The Lexis diagram is seen to make direct use of the result. It is suggested that in a variety of cases, it will be satisfactory to approximate the distribution of the number of deaths given the population size, by a Poisson with mean proportional to the population size. It is further suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic Poisson distribution for the number of deaths, with mean proportional to the population size and an exponential function of a linear combination of the explanatories. Such a model is fit to mortality data for Canadian females classified by age and year. A dynamic variant of the model is further fit to the time series of total female deaths alone by year. The models with extra-Poisson variation are found to lead to substantially improved fits.     

A host-parasite model yielding heterogeneous parasite loads

Many models of parasitic infections lead to an approximately Poisson distribution of parasites among hosts, in stark contrast to the highly over-dispersed distributions that are usually encountered in practice. In this paper, a model is analyzed which, while assuming all individuals to be alike, can still lead to a very heterogeneous distribution of parasites among the host population. The model can be viewed as a very simple mean field interacting particle system, with the particles corresponding to the individual hosts, which behaves like an associated deterministic system when the number of hosts is large. The deterministic system describes the evolution over time of the proportions of the population with different parasite loads, and its equilibria are interpreted as typical distributions of parasites among hosts. Despite its simplicity, the model is complicated enough mathematically to leave a number of open problems.This work was supported in part by Schweiz. Nationalfonds Grants Nos 21-25579.88 and 20-31262.91, and by NSF Grant DMS 90-05833     

Comparison of VNTR allele frequencies and inclusion probabilities over six populations

There is considerable debate about the methodologies used to estimate VNTR (Variable Number of Tandem Repeats) multi-locus genotype frequencies or odds of inclusion in forensic cases. To compare two of the methods in use, allele frequency distributions among six populations were compared and the effect of population heterogeneity on VNTR multi-locus genotype frequency estimation was examined. Genotype frequencies estimated from single population data were one or two orders of magnitude smaller than those estimated by picking the highest allele frequency in a group of subpopulations to estimate genotype frequencies using a ceiling principle. The average change does not appear to be very sensitive to the set of subpopulations used; four locus frequencies still give inclusion odds of one in a million or less. We think that use of the ceiling principle solves both the statistical problem engendered by subpopulation heterogeneity and the legal problem of assuming that the prepetrator and suspect belong to the same subpopulation. The counterintuitive fact of human genetic polymorphism is that it is easier to identify an individual than it is to identify the subpopulation, ethnic group or race to which that individual belongs.     

Search and navigation in dynamic environments – from individual behaviors to population distributions

Animal movement receives widespread attention within ecology and behavior. However, much research is restricted within isolated sub-disciplines focusing on single phenomena such as navigation (e.g. homing behavior), search strategies (e.g. Levy flights) or theoretical considerations of optimal population dispersion (e.g. ideal free distribution). To help synthesize existing research, we outline a unifying conceptual framework that integrates individual-level behaviors and population-level spatial distributions with respect to spatio-temporal resource dynamics. We distinguish among (1) non-oriented movements based on diffusion and kinesis in response to proximate stimuli, (2) oriented movements utilizing perceptual cues of distant targets, and (3) memory mechanisms that assume prior knowledge of a target's location. Species' use of these mechanisms depends on life-history traits and resource dynamics, which together shape population-level patterns. Resources with little spatial variability should facilitate sedentary ranges, whereas resources with predictable seasonal variation in spatial distributions should generate migratory patterns. A third pattern, 'nomadism', should emerge when resource distributions are unpredictable in both space and time. We summarize recent advances in analyses of animal trajectories and outline three major components on which future studies should focus: (1) integration across alternative movement mechanisms involving links between state variables and specific mechanisms, (2) consideration of dynamics in resource landscapes or environments that include resource gradients in predictability, variability, scale, and abundance, and finally (3) quantitative methods to distinguish among population distributions. We suggest that combining techniques such as evolutionary programming and pattern oriented modeling will help to build strong links between underlying movement mechanisms and broad-scale population distributions.     

Modeling species distributions by breaking the assumption of self-similarity

Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte's bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.     

Inherent high correlation of individual motility enhances population dispersal in a heterotrophic, planktonic protist

Quantitative linkages between individual organism movements and the resulting population distributions are fundamental to understanding a wide range of ecological processes, including rates of reproduction, consumption, and mortality, as well as the spread of diseases and invasions. Typically, quantitative data are collected on either movement behaviors or population distributions, rarely both. This study combines empirical observations and model simulations to gain a mechanistic understanding and predictive ability of the linkages between both individual movement behaviors and population distributions of a single-celled planktonic herbivore. In the laboratory, microscopic 3D movements and macroscopic population distributions were simultaneously quantified in a 1L tank, using automated video- and image-analysis routines. The vertical velocity component of cell movements was extracted from the empirical data and used to motivate a series of correlated random walk models that predicted population distributions. Validation of the model predictions with empirical data was essential to distinguish amongst a number of theoretically plausible model formulations. All model predictions captured the essence of the population redistribution (mean upward drift) but only models assuming long correlation times (minute), captured the variance in population distribution. Models assuming correlation times of 8 minutes predicted the least deviation from the empirical observations. Autocorrelation analysis of the empirical data failed to identify a de-correlation time in the up to 30-second-long swimming trajectories. These minute-scale estimates are considerably greater than previous estimates of second-scale correlation times. Considerable cell-to-cell variation and behavioral heterogeneity were critical to these results. Strongly correlated random walkers were predicted to have significantly greater dispersal distances and more rapid encounters with remote targets (e.g. resource patches, predators) than weakly correlated random walkers. The tendency to disperse rapidly in the absence of aggregative stimuli has important ramifications for the ecology and biogeography of planktonic organisms that perform this kind of random walk.     

The dynamics of finite haploid populations with overlapping generations. I. Moments, fixation probabilities and stationary distributions

Much of the work on finite populations with overlapping generations has been limited to deriving effective population numbers with the tacit assumption that the dynamics of the population will be similar to a population with nonoverlapping generations and the appropriate population number. In this paper, some exact and approximate results will be presented on the behavior of the first two moments of the gene frequencies. The probability of fixation of a neutral gene is found equal to the initial average reproductive value of the gene, and the means and covariances of the stable distribution with mutation in both directions are found by a simple extension of the values found by assuming nonoverlapping generations.     

Critical notes on a proposed method to estimate production

To estimate annual production, Hamilton (1969) initially calculated mean losses/sample, as did Hynes (1961) and Hynes & Coleman (1968). While the latter failed to convert these means to annual production, Hamilton has overcome this problem by assuming a population at equilibrium. Then, production may be calculated by multiplying mean losses with the number of classes through which specimens can grow. The method was claimed to be suitable for unidentified material and not to depend strongly on growth patterns; both claims are refuted here. The main objection is that for calculations, populations must be divided into fractions. While equilibrium might be acceptable for an entire population, it is not for any of its fractions. The particular conversion factor therefore has no justification and the method becomes inapplicable.     

Employing relative entropy techniques for assessing modifications in animal behavior

In order to make quantitative statements regarding behavior patterns in animals, it is important to establish whether new observations are statistically consistent with the animal's equilibrium behavior. For example, traumatic stress from the presence of a telemetry transmitter may modify the baseline behavior of an animal, which in turn can lead to a bias in results. From the perspective of information theory such a bias can be interpreted as the amount of information gained from a new measurement, relative to an existing equilibrium distribution. One important concept in information theory is the relative entropy, from which we develop a framework for quantifying time-dependent differences between new observations and equilibrium. We demonstrate the utility of the relative entropy by analyzing observed speed distributions of Pacific bluefin tuna, recorded within a 48-hour time span after capture and release. When the observed and equilibrium distributions are gaussian, we show that the tuna's behavior is modified by traumatic stress, and that the resulting modification is dominated by the difference in central tendencies of the two distributions. Within a 95% confidence level, we find that the tuna's behavior is significantly altered for approximately 5 hours after release. Our analysis reveals a periodic fluctuation in speed corresponding to the moment just before sunrise on each day, a phenomenon related to the tuna's daily diving pattern that occurs in response to changes in ambient light.     

Diffusion analysis and stationary distribution of the two-species lottery competition model

The lottery model is a stochastic population model in which juveniles compete for space. Examples include sedentary organisms such as trees in a forest and members of marine benthic communities. The behavior of this model appears to be characteristic of that found in other sorts of stochastic competition models. In a community with two species, it was previously demonstrated that coexistence of the species is possible if adult death rates are small and environmental variation is large. Environmental variation is incorporated by assuming that the birth rates and death rates are random variables. Complicated conditions for coexistence and competitive exclusion have been derived elsewhere. In this paper, simple and easily interpreted conditions are found by using the technique of diffusion approximation. Formulae are given for the stationary distribution and means and variances of population fluctuations. The shape of the stationary distribution allows the stability of the coexistence to be evaluated.     

The effect of travel loss on evolutionarily stable distributions of populations in space

A key assumption of the ideal free distribution (IFD) is that there are no costs in moving between habitat patches. However, because many populations exhibit more or less continuous population movement between patches and traveling cost is a frequent factor, it is important to determine the effects of costs on expected population movement patterns and spatial distributions. We consider a food chain (tritrophic or bitrophic) in which one species moves between patches, with energy cost or mortality risk in movement. In the two-patch case, assuming forced movement in one direction, an evolutionarily stable strategy requires bidirectional movement, even if costs during movement are high. In the N-patch case, assuming that at least one patch is linked bidirectionally to all other patches, optimal movement rates can lead to source-sink dynamics where patches with negative growth rates are maintained by other patches with positive growth rates. As well, dispersal between patches is not balanced (even in the two-patch case), leading to a deviation from the IFD. Our results indicate that cost-associated forced movement can have important consequences for spatial metapopulation dynamics. Relevance to marine reserve design and the study of stream communities subject to drift is discussed.     

Could the tree diversity pattern in Europe be generated by postglacial dispersal limitation?

The relative importance of contemporary climate and history as controls of geographical diversity patterns is intensely debated. A key example is the controversy over the extent to which temperate tree distributions and diversity patterns reflect postglacial dispersal limitation. Here, we focus on Central and Northern Europe, and show that recent estimates of tree migration rates < 100 m year⁻¹ imply that many species have probably not reached equilibrium with climate in this region. We then demonstrate that geographical accessibility from glacial refuges explains 78% of the geographical variation in the region's tree diversity and is a much stronger diversity predictor than climate. Finally, we show that realistic estimates of migration rates can be derived from the observed tree diversity pattern by assuming it to be purely dispersal driven. In conclusion, the tree diversity pattern in Central and Northern Europe could, to a large extent, be a result of postglacial dispersal limitation.     

A theoretical approach for zone-based management of the deer population on Yakushima Island

The biological balance of Yakushima Island is currently being compromised by overpopulation of sika deer (Cervus nippon yakushimae). We predicted that the island's deer population would continue to grow unless control efforts are raised threefold from their 2012 levels. To identify the best management practice for future implementation, we evaluated and compared the performances of three different zone-based management strategies. Under the current management scenario, the median population size of the sika deer on the island would temporarily decrease, but it would subsequently rebound. Under a scenario that allows management zones to be prioritized according to the occurrence of threatened plant species and deer population size, model simulations suggested that the scenario focusing on the central zone would show the best performance based on the probability of achievement of the management goal (assuming that there is no dispersal between zones). This course of action would lead to a decrease in the median deer population size and would further ensure a high probability of achieving the 2022 target population size across most zones (up to 85 %), even if catch levels were not increased. In a future study, we would need to conduct a more detailed analysis of plants and deer density distributions.     

The effect of structural behavior change on the spread of HIV in a one-sex population.

Within a preferred mixing type of model for the spread of HIV in a one-sex population, the effects of structural behavior change, that is movements of individuals from one activity class to another, with accompanying changes of contact pattern are investigated. It is concluded that such behavior change makes it more difficult for an epidemic to arise if the contact pattern is of the restricted type, whereas the effect is indeterminate in the proportional mixing case. Some of the problems in analyzing sexual activity data from a population within which this behavior change mechanism is at work are also commented upon.