Adding energy gradients and long‐distance dispersal to a neutral model improves predictions of Madagascan bird diversity

Macroecological patterns are likely the result of both stochastically neutral mechanisms and deterministic differences between species. In Madagascar, the simplest stochastically neutral hypothesis – the mid‐domain effects (MDE) hypothesis – has already been rejected. However, rejecting the MDE hypothesis does not necessarily refute the existence of all other neutral mechanisms. Here, we test whether adding complexity to a basic neutral model improves predictions of biodiversity patterns. The simplest MDE model assumes that: (1) species' ranges are continuous and unfragmented, (2) are randomly located throughout the landscape, and (3) can be stacked independently and indefinitely. We designed a simulation based on neutral theory that allowed us to weaken each of these assumptions incrementally by adjusting the habitat capacity as well as the likelihood of short‐ and long‐distance dispersal. Simulated outputs were compared to four empirical patterns of bird diversity: the frequency distributions of species richness and range size, the within‐island latitudinal diversity gradient, and the distance‐decay of species compositional similarity. Neutral models emulated empirical diversity patterns for Madagascan birds accurately. The frequency distribution of range size, latitudinal diversity gradient, and the distance‐decay of species compositional similarity could be attributed to stochastic long‐distance migration events and zero‐sum population dynamics. However, heterogenous environmental gradients improved predictions of the frequency distribution of species richness. Patterns of bird diversity in Madagascar can broadly be attributed to stochastic long‐distance migration events and zero‐sum population dynamics. This implies that rejecting simple hypotheses, such as MDE, does not serve as evidence against stochastic processes in general. However, environmental gradients were necessary to explain patterns of species richness and deterministic differences between species are probably important for explaining the distributions of narrow‐range and endemic species.     

Using mean first passage times to quantify equilibrium resilience in perturbed intraguild predation systems

Regime shift inducibility depends on equilibrium resilience, which depends on species interactions. When species interactions include intraguild predation (IGP), integrated pest management may induce regime shifts because enhancing the abundance of intraguild predators simultaneously increases competition with, and predation on, invasive prey. To explore the dynamical consequences of such manipulations, we use a bistable, deterministic IGP model with stochastic removals that perturb invader density from the high-density equilibrium. We quantify the combined effects of IGP and such perturbations in terms of mean first passage times (MFPTs) to target invader densities such as thresholds between regimes. Analytical MFPTs compare favorably with those generated by Monte Carlo numerical solutions of the stochastically perturbed IGP model. MFPTs can therefore usefully quantify equilibrium resilience in terms of perturbation schedules. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Stochastic and deterministic processes jointly structure tropical arthropod communities

The question of whether ecological assemblages are structured by stochastic and deterministic (e.g. interspecific competition) processes is controversial, but it is difficult to design sampling regimes and experiments that can dissect the relative importance of stochastic and deterministic processes in natural assemblages. Using null models, we tested communities of arthropod decomposers in tropical epiphytes for patterns of species co-occurrence, while controlling for habitat gradients, seasonal variations and ecological succession. When environmental conditions were controlled, our analysis showed that the communities were structured stochastically. However, analysing mixed sets of communities that were deliberately created either from two distinct heights or two successional stages revealed that communities were structured deterministically. These results confirm that habitat gradients and dispersal/competition trade-offs are capable of generating non-random patterns within decomposer arthropod communities, but reveal that when such effects are accounted for, species co-occurrence is fundamentally random.     

Alternatives to the Wright-Fisher model: The robustness of mitochondrial Eve dating

Methods of calculating the distributions of the time to coalescence depend on the underlying model of population demography. In particular, the models assuming deterministic evolution of population size may not be applicable to populations evolving stochastically. Therefore the study of coalescence models involving stochastic demography is important for applications. One interesting approach which includes stochasticity is the O’Connell limit theory of genealogy in branching processes. Our paper explores how many generations are needed for the limiting distributions of O’Connell to become adequate approximations of exact distributions. We perform extensive simulations of slightly supercritical branching processes and compare the results to the O’Connell limits. Coalescent computations under the Wright-Fisher model are compared with limiting O’Connell results and with full genealogy-based predictions. These results are used to estimate the age of the so-called mitochondrial Eve, i.e., the root of the mitochondrial polymorphisms of the modern humans based on the DNA from humans and Neanderthal fossils.     

Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles

This paper develops a deterministic model of frequency distributions for energy imparted (total energy deposition) in small volumes similar to DNA molecules from high-energy ions of interest for space radiation protection and cancer therapy. Frequency distributions for energy imparted are useful for considering radiation quality and for modeling biological damage produced by ionizing radiation. For high-energy ions, secondary electron (delta-ray) tracks originating from a primary ion track make dominant contributions to energy deposition events in small volumes. Our method uses the distribution of electrons produced about an ion's path and incorporates results from Monte Carlo simulation of electron tracks to predict frequency distributions for ions, including their dependence on radial distance. The contribution from primary ion events is treated using an impact parameter formalism of spatially restricted linear energy transfer (LET) and energy-transfer straggling. We validate our model by comparing it directly to results from Monte Carlo simulations for proton and alpha-particle tracks. We show for the first time frequency distributions of energy imparted in DNA structures by several high-energy ions such as cosmic-ray iron ions. Our comparison with results from Monte Carlo simulations at low energies indicates the accuracy of the method.     

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors ( < 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.     

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors (< 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.     

Manipulation of habitat isolation and area implicates deterministic factors and limited neutrality in community assembly

Theory predicts deterministic and stochastic factors will contribute to community assembly in different ways: Environmental filters should regulate those species that establish in a particular area resulting in the ecological requirements of species being the primary driver of species distributions, while chance and dispersal limitation should dictate the likelihood of species reaching certain areas with the ecology of species being largely neutral. These factors are specifically relevant for understanding how the area and isolation of different habitats or islands interact to affect community composition. Our review of the literature found few experimental studies have examined the interactive effect of habitat area and isolation on community assembly, and the results of those experiments have been mixed. We manipulated the area and isolation of rock “islands” created de novo in a grassland matrix to experimentally test how deterministic and stochastic factors shape colonizing animal communities. Over 64 weeks, the experiment revealed the primacy of deterministic factors in community assembly, with habitat islands of the same size exhibiting remarkable consistency in community composition and diversity, irrespective of isolation. Nevertheless, tangible differences still existed in abundance inequality among taxa: Large, near islands had consistently higher numbers of common taxa compared to all other island types. Dispersal limitation is often assumed to be negligible at small spatial scales, but our data shows this not to be the case. Furthermore, the dispersal limitation of a subset of species has potentially complex flow‐on effects for dictating the type of deterministic factors affecting other colonizing species.     

Deterministic model for the transport of energetic particles: Application in the electron radiotherapy

A new deterministic method for calculating the dose distribution in the electron radiotherapy field is presented. The aim of this work was to validate our model by comparing it with the Monte Carlo simulation toolkit, GEANT4. A comparison of the longitudinal and transverse dose deposition profiles and electron distributions in homogeneous water phantoms showed a good accuracy of our model for electron transport, while reducing the calculation time by a factor of 50. Although the Bremsstrahlung effect is not yet implemented in our model, we propose here a method that solves the Boltzmann kinetic equation and provides a viable and efficient alternative to the expensive Monte Carlo modeling.     

Shot noise perturbations and mean first passage times between stable states

Predicting crossings between stable states is a central issue in population biology. Crossings from low-density to high-density equilibria are often associated with pest outbreaks, while the opposite crossings are often associated with population collapse of harvested species. Here I use a simple, bistable model to demonstrate a technique for estimating mean first passage times (MFPT) of thresholds, including boundaries between stable equilibria. The approach is based on stochastic "shot-noise" perturbations to the population and the MFPTs compare favorably with mean crossing times from Monte Carlo numerical solutions of the stochastically perturbed model. This agreement suggests that MFPT approximations can be used to quantify expected effects of species manipulations, whether the goal is pest control or sustainable harvest.     

A stochastic approach to predator-prey models

A deterministic investigation of a linear differential equation system which describes predator vs prey behavior as a function of equilibrium densities and reproductive rates is given. A more realistic structure of this model in a stochastic framework is presented. The reproductive rates and initial population sizes are considered to be random variables and their probabilistic behavior characterized by various joint probability distributions. The deterministic behaviors of the prey and predator species as functions of time are compared with the mean behaviors in the stochastic model.     

Strong plant-soil associations in a heterogeneous subtropical broad-leaved forest

The relative importance of deterministic and neutral processes on community assembly is currently a topic of much debate among ecologists. Analyzing species-environment associations is an effective way to assess the importance of deterministic process such as niche differentiation, but both habitat association and dispersal limitation can produce similar patterns of spatial aggregation in species. Therefore, it is crucial to control for the impact of dispersal limitation on species distributions when analyzing species-environment associations. We sampled soil with high resolutions in a 24 ha stem-mapped subtropical forest and tested plant-soil associations. We controlled for the influence of dispersal limitation by employing the homogeneous Thomas process to simulate the effect of dispersal limitation on the aggregation of tree species. After controlling for the effect of dispersal limitation, we found that the spatial heterogeneity of soil properties was associated with distributions of 88.2% (90 of 102 species) of tree species in this subtropical forest. Furthermore, not only did soil properties influence the distribution of tree species, but also tree species tended to affect properties of the soil around them. The soil factors most strongly influencing species distributions were TC, TN, TP, K, Mg, Si, soil moisture, and bulk density. We found the spatial heterogeneity of soil properties to be strongly associated with tree species distributions. Niche partitioning of soil gradients contributed substantially to species coexistence in this subtropical forest.     

Noise-induced neural impulses

The firing pattern of neural pulses often show the following features: the shapes of individual pulses are nearly identical and frequency independent; the firing frequency can vary over a broad range; the time period between pulses shows a stochastic scatter. This behaviour cannot be understood on the basis of a deterministic non-linear dynamic process, e.g. the Bonhoeffer-van der Pol model. We demonstrate in this paper that a noise term added to the Bonhoeffer-van der Pol model can reproduce the firing patterns of neurons very well. For this purpose we have considered the Fokker-Planck equation corresponding to the stochastic Bonhoeffer-van der Pol model. This equation has been solved by a new Monte Carlo algorithm. We demonstrate that the ensuing distribution functions represent only the global characteristics of the underlying force field: lines of zero slope which attract nearby trajectories prove to be the regions of phase space where the distributions concentrate their amplitude. Since there are two such lines the distributions are bimodal representing repeated fluctuations between two lines of zero slope. Even in cases where the deterministic Bonhoeffer-van der Pol model does not show limit cycle behaviour the stochastic system produces a limit cycle. This cycle can be identified with the firing of neural pulses.     

Variable effort fishing models in random environments

We study the growth of populations in a random environment subjected to variable effort fishing policies. The models used are stochastic differential equations and the environmental fluctuations may either affect an intrinsic growth parameter or be of the additive noise type. Density-dependent natural growth and fishing policies are of very general form so that our results will be model independent. We obtain conditions on the fishing policies for non-extinction and for non-fixation at the carrying capacity that are very similar to the conditions obtained for the corresponding deterministic model. We also obtain conditions for the existence of stationary distributions (as well as expressions for such distributions) very similar to conditions for the existence of an equilibrium in the corresponding deterministic model. The results obtained provide minimal requirements for the choice of a wise density-dependent fishing policy.     

Waiting times to appearance and dominance of advantageous mutants: estimation based on the likelihood

The germinal center reaction (GCR) of vertebrate immunity provides a remarkable example of evolutionary succession, in which an advantageous phenotype arises as a spontaneous mutation from the parental type and eventually displaces the parental type altogether. In the case of the immune response to the hapten (4-hydroxy-3-nitrophenyl)acetyl (NP), as with several other designed immunogens, the process is dominated by a single key mutation, which greatly simplifies the modeling of and analysis of data. We developed a two-stage model of this process in which the primary stage represents the appearance and establishment of the mutant population as a stochastic process while the second stage represents the growth and dominance of the clone as a deterministic process, conditional on its time of establishment from stage one. We applied this model to the analysis of population samples from several germinal center (GC) reactions and used maximum-likelihood methods to estimate the waiting times to arrival and to dominance of the mutant clone. We determined the sampling properties of the maximum-likelihood estimates using Monte Carlo methods and compared them to their asymptotic distributions. The methods we present here are well-suited for use in the analysis of other systems, such as tumor growth and the experimental evolution of bacteria.     

Variation within and between cyanobacterial species and strains affects competition: Implications for phytoplankton modelling

Cyanobacteria Microcystis aeruginosa and Cylindrospermopsis raciborskii are two harmful species which co-occur and successively dominate in freshwaters globally. Within-species strain variability affects cyanobacterial population responses to environmental conditions, and it is unclear which species/strain would dominate under different environmental conditions. This study applied a Monte Carlo approach to a phytoplankton dynamic growth model to identify how growth variability of multiple strains of these two species affects their competition.Pairwise competition between four M. aeruginosa and eight C. raciborskii strains was simulated using a deterministic model, parameterized with laboratory measurements of growth and light attenuation for all strains, and run at two temperatures and light intensities. 17 000 runs were simulated for each pair using a statistical distribution with Monte Carlo approach.The model results showed that cyanobacterial competition was highly variable, depending on strains present, light and temperature conditions. There was no absolute ‘winner’ under all conditions as there were always strains predicted to coexist with the dominant strains, which were M. aeruginosa strains at 20 °C and C. raciborskii strains at 28 °C. The uncertainty in prediction of species competition outcomes was due to the substantial variability of growth responses within and between strains. Overall, this study demonstrates that within-species strain variability has a potentially large effect on cyanobacterial population dynamics, and therefore this variability may substantially reduce confidence in predicting outcomes of phytoplankton competition in deterministic models, that are based on only one set of parameters for each species or strain.     

The roles of ecological and evolutionary influences in providing structure to parasite species assemblages.

Parasite species assemblages currently are thought to range from isolationist to interactive, their dynamic properties being related to the number of species and types of hosts involved. The literature contains few experimental tests of this concept, however, and many of the host/parasite systems studied to date are not amenable to experimental manipulation. In this review, the presence of a parasite species, in a sample of host individuals, is considered to be an evolutionary phenomenon, but the parasite's population structure is considered to be an ecological one. Studies that allow evaluation of these 2 influences are comparative in nature and include data from a series of homogeneous samples of host populations. A lottery model is presented, in which hosts acquire their assemblages of parasites by Monte Carlo type sampling from multiple kind arrays; the major structuring influence is the relative probability of becoming infected by various parasite species. Claims of parasite species interaction need to be supported by studies showing departures from the predictions of this model. The species density and infraassemblage diversity index distributions are recommended as quantitative tools useful in such work.     

Seidel–Herzel model of human baroreflex in cardiorespiratory system with stochastic delays

The stochastic versus deterministic solution of the Seidel–Herzel model describing the baroreceptor control loop (which regulates the short-time heart rate) are compared with the aim of exploring the heart rate variability. The deterministic model solutions are known to bifurcate from the stable to sustained oscillatory solutions if time delays in transfer of signals by sympathetic nervous system to the heart and vasculature are changed. Oscillations in the heart rate and blood pressure are physiologically crucial since they are recognized as Mayer waves. We test the role of delays of the sympathetic stimulation in reconstruction of the known features of the heart rate. It appears that realistic histograms and return plots are attainable if sympathetic time delays are stochastically perturbed, namely, we consider a perturbation by a white noise. Moreover, in the case of stochastic model the bifurcation points vanish and Mayer oscillations in heart period and blood pressure are observed for whole considered space of sympathetic time delays.      

Dynamic population epidemic models.

Most multipopulation epidemic models are of the contact distribution type, in which the locations of successive contacts are chosen independently from appropriate contact distributions. This paper is concerned with an alternative class of models, termed dynamic population epidemic models, in which infectives move among the populations and can infect only within their current population. Both the stochastic and deterministic versions of such models are considered. Their threshold behavior is analyzed in some depth, as are their final outcomes. Velocities of spread of infection are considered when the populations have a spatial structure. A criterion for finding the equivalent contact distribution epidemic for any given dynamic population epidemic is provided, enabling comparisons to be made for the velocities and final outcomes displayed by the two classes of models. The relationship between deterministic and stochastic epidemic models is also discussed briefly.     

Fish distributions along depth gradients of a sea mountain range conform to the mid‐domain effect

Species richness often peaks in the middle of bounded geographic domains (e.g. latitude, altitude or depth). Hump‐shaped richness distributions may be due to deterministic processes, such as adaptations to environmental variation. Alternatively, such distributions might also be due to stochastic process. The mid‐domain effect (MDE) posits that hump‐shaped richness distributions arise when species ranges are randomly arranged within the limits of the domain. We tested whether the MDE could account for the richness of bottom‐associated (demersal) fishes between 200 and 800 m on the Chatham Rise, New Zealand. We quantified the depth distributions of 59 fish species from 1891 research trawl catches made between 1991 and 2007. Results showed a broad plateau of high species richness near the centre of the domain (between 300 and 700 m), which was consistent with expectations of the MDE. Further, empirical species richness was better explained statistically by predictions of the MDE than models incorporating additional abiotic predictor variables. Our results deviated from previous studies that identified a greater richness of fishes in warmer, shallower depths with higher primary production. However, our study was conducted entirely below the euphotic zone, at depths where gradients are relatively weak, suggesting that support for the mid‐domain effect may increase across oceanic domains characterised by weak environmental gradients.