The pattern of species turnover resulting from stochastic population dynamics: The model and field data

The model of random population dynamics in a sampling site returns geometric distribution of longevities of continuous presence (=persistence) and Poisson distribution of the presence–absence transitions. This discrete-time stochastic process describes the presence–absence pattern observed in the beetles surveyed 6 years on Mount Carmel, Israel. Homogeneous pools of species mostly on the Families rank, exhibit the predicted by the model patterns. Conformity to an ergodic hypothesis is the criterion of ecological homogeneity. This criterion assumes the equivalence of short-term behavior of entire pool and long-term behavior of any species from this pool. The pool of all 801 species of Order Coleoptera does not match the model. Thus a taxon of an arbitrary rank may not be considered a priory as a unit of ecological study. Determined from field data parameters of the model are biased and magnitude of the bias depends on longevity of the survey. Parameter of distribution depends also on species tolerance, which is the level adaptation of given species to given environment in given time interval. Random process of species turnover may be considered as a game of species to gain their presence against deteriorative fluctuations of environmental conditions.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

Clustering species using a model of population dynamics and aggregation theory

The high species diversity of some ecosystems like tropical rainforests goes in pair with the scarcity of data for most species. This hinders the development of models that require enough data for fitting. The solution commonly adopted by modellers consists in grouping species to form more sizeable data sets. Classical methods for grouping species such as hierarchical cluster analysis do not take account of the variability of the species characteristics used for clustering. In this study a clustering method based on aggregation theory is presented. It takes account of the variability of species characteristics by searching for the grouping that minimizes the quadratic error (square bias plus variance) of some model’s prediction. This method allows one to check whether the gain in variance brought by data pooling compensate for the bias that it introduces. This method was applied to a data set on 94 tree species in a tropical rainforest in French Guiana, using a Usher matrix model to predict species dynamics. An optimal trade-off between bias and variance was found when grouping species. Grouping species appeared to decrease the quadratic error, except when the number of groups was very small. This clustering method yielded species groups similar to those of the hierarchical cluster analysis using Ward’s method when variance was small, that is when the number of groups was small.     

A model approach to evaluate the effect of temperature and food concentration on individual life-history and population dynamics of Daphnia

We present a model framework for the simulation of growth and reproduction of Daphnia at varying conditions of food concentration and temperature. The core of our framework consists of an individual level model that simulates allocation of assimilated carbon into somatic growth, maintenance costs, and reproduction on the basis of a closed carbon budget. A fixed percentage of assimilated carbon is allocated into somatic growth and maintenance costs. Special physiological adaptations in energy acquisition and usage allow realistic model performance even at very low food concentrations close to minimal food requirements. All model parameters are based on physiological measures taken from the literature. Model outputs were thoroughly validated on data from a life-table experiment with Daphnia galeata. For the first time, a successful model validation was performed at such low food concentrations. The escalator boxcar train (EBT) was used to integrate this individual level model into a stage-structured population model. In advance to previous applications of the EBT to Daphnia we included an additional clutch compartment into the model structure that accounts for the characteristic time delay between egg deposition and hatching in cladocerans. By linking two levels of biological organisation, this model approach represents a comprehensive framework for studying Daphnia both at laboratory conditions and in the field. We compared outputs of our stage-structured model with predictions by two other models having analogous parameterisation: (i) another individual level Daphnia model (Kooijman–Metz model) and (ii) a classical unstructured population model. In contrast to our Daphnia model, the Kooijman–Metz model lacks the structure to account for the optimisation of energy acquisition and maintenance requirements by individual daphnids. The unstructured population model showed different patterns of population dynamics that were not in concordance with typical patterns observed in the field. Thus, we conclude our model provides a comprehensive tool for the simulation of growth and reproduction of Daphnia and corresponding population dynamics.     

SPAnDX: a process-based population dynamics model to explore management and climate change impacts on an invasive alien plant,Acacia nilotica

This paper describes a process-based metapopulation dynamics and phenology model of prickly acacia, Acacia nilotica, an invasive alien species in Australia. The model, SPAnDX, describes the interactions between riparian and upland sub-populations of A. nilotica within livestock paddocks, including the effects of extrinsic factors such as temperature, soil moisture availability and atmospheric concentrations of carbon dioxide. The model includes the effects of management events such as changing the livestock species or stocking rate, applying fire, and herbicide application. The predicted population behaviour of A. nilotica was sensitive to climate. Using 35 years daily weather datasets for five representative sites spanning the range of conditions that A. nilotica is found in Australia, the model predicted biomass levels that closely accord with expected values at each site. SPAnDX can be used as a decision-support tool in integrated weed management, and to explore the sensitivity of cultural management practices to climate change throughout the range of A. nilotica. The cohort-based DYMEX modelling package used to build and run SPAnDX provided several advantages over more traditional population modelling approaches (e.g. an appropriate specific formalism (discrete time, cohort-based, process-oriented), user-friendly graphical environment, extensible library of reusable components, and useful and flexible input/output support framework).     

Modelling crayfish population dynamics using catch data: A size-structured model

In this study we explore a rather unique time series (1979–2002) of catch data of the crayfish Astacus astacus in Lake Steinsfjorden (SE Norway) in combination with temperature data and data on Canadian pondweed Elodea canadensis coverage. In 1977, E. canadensis was for the first time observed in the lake. Over the following years, the plant established dense covers over large parts of the shallow areas, excluding the crayfish from these areas and causing a sudden drop in population size. A size-structured model with bi-stability including a range of observed stage-specific life-cycle attributes (e.g. growth, fecundity, fertility, sex-ratio), population specific parameters and density-dependant (shelters, cannibalism, unspecified predators, competition between individuals, catch, number of traps) as well as density independent factors (temperature and Elodea coverage) were constructed to evaluate the various drivers for the population dynamics, and as a predictive tool for assessing the effects of future changes. Our model revealed that the decline primarily was due to density-dependant effect of the Elodea expansion with reduced number of hides and thus increased risk for predation and cannibalism, but also that temperature played an important role related to recruitment. The model should be relevant for crayfish stock management in general, and by demonstrating the major role of temperature, it is also relevant for predicting population responses under a changing climate. The model should also be applicable to other crustaceans and species with discrete growth and late maturation.     

Coupling soil water and shoot dynamics in three grass species: A spatial stochastic model on water competition in Neotropical savanna

Savannas are ecosystems known for their high environmental and economic value. They cover at least 20% of the global land surface and, in some cases, can act as a boundary between tropical rainforest and deserts. Water is an important determinant of savanna ecosystems.In this paper, we present a theoretical stochastic model of root competition for water, which couples, soil water availability, phenology, and root and shoot architecture applied to three Neotropical savanna grasses. Soil moisture was simulated using a daily balance, as proposed by Rodriguez-Iturbe et al. [Rodriguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., Cox, D.R., 1999. Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Proc. R. Soc. London, Ser. A 455, 3789–3805.]. To simulate rainfall stochasticity, we used daily precipitation data from the airport weather station in the State of Barinas, Venezuela, for the period 1991–2007. Competition among neighbouring plants took into account the spatial distribution of the individuals. As a final step, the model allowed us to calculate the shoot dynamic of the species as a function of soil water availability.Using these data, we compared the behaviour of isolated plants, pairs and trios, and we found below-ground competition to be a fundamental component of global (shoot + root) competition. Finally, our model suggests various circumstances that allow poor competitor plants to coexist in competition for water with more successful competitors. Apparently, this is not only due to transpiration rates, but also to differences in shoot emergence and shoot growth.     

A hydrologically driven model of swamp water mosquito population dynamics

We develop a swamp water mosquito population model that is forced solely by environmental variability. Measured temperature and land surface wetness conditions are used to simulate Anopheles walkeri population dynamics in a northern New Jersey habitat. Land surface wetness conditions, which represent oviposition habitat availability, are derived from simulations using a dynamic hydrology model. Using only these two density-independent effects, population model simulations of biting Anoph. walkeri correlate significantly with light trap collections. These results suggest that prediction of mosquito populations and the diseases they transmit could be better constrained by inclusion of environmental variability.     

A mathematical model for dispersal of an annual plant population with a seed bank

In order to describe the spatial dispersion of a population of annual plants with a seed bank, we have formulated a delay integrodifference equation model. The plant population growth is considered as being dependent on the density of seedlings that spring from seeds of the two previous years. We have analyzed the effects of the seed bank on the total population size, on the population spatial distribution as well as on the population velocity of invasion. It is showed that the seed bank can significantly alter the dynamics of annual plants, since it can have both a stabilizing and a destabilizing effect on the total population and can also homogenize the spatial distribution of the plants.     

A finite element method to solve a population dynamics stage-structured model of intertidal barnacles

Many marine organisms are fixed or highly sedentary as adults but the adult population may be strongly dependent on the oceanic transport of planktonic larvae. In order to assess interactions between oceanographic and biological processes that determine the population dynamics of marine organisms with a sessile adult phase restricted to the coastline and a planktonic larval phase, we present a stage-structured finite element model for the barnacle Balanus glandula that inhabits the rocky intertidal zone of central California, USA.     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

A Voronoi diagram based population model for social species of wildlife

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.     

Seed terminal velocity, wind turbulence, and demography drive the spread of an invasive tree in an analytical model

Little is known about the relative importance of mechanistic drivers of plant spread, particularly when long-distance dispersal (LDD) events occur. Most methods to date approach LDD phenomenologically, and all mechanistic models, with one exception, have been implemented through simulation. Furthermore, the few recent mechanistically derived spread models have examined the relative role of different dispersal parameters using simulations, and a formal analytical approach has not yet been implemented. Here we incorporate an analytical mechanistic wind dispersal model (WALD) into a demographic matrix model within an analytical integrodifference equation spread model. We carry out analytical perturbation analysis on the combined model to determine the relative effects of dispersal and demographic traits and wind statistics on the spread of an invasive tree. Models are parameterized using data collected in situ and tested using independent data on historical spread. Predicted spread rates and direction match well the two historical phases of observed spread. Seed terminal velocity has the greatest potential influence on spread rate, and three wind properties (turbulence coefficient, mean horizontal wind speed, and standard deviation of vertical wind speed) are also important. Fecundity has marginal importance for spread rate, but juvenile survival and establishment are consistently important. This coupled empirical/theoretical framework enables prediction of plant spread rate and direction using fundamental dispersal and demographic parameters and identifies the traits and environmental conditions that facilitate spread. The development of an analytical perturbation analysis for a mechanistic spread model will enable multispecies comparative studies to be easily implemented in the future.     

Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations

Many biological populations are subject to periodically changing environments such as years with or without fire, or rotation of crop types. The dynamics and management options for such populations are frequently investigated using periodic matrix models. However the analysis is usually limited to long-term results (asymptotic population growth rate and its sensitivity to perturbations of vital rates). In non-periodic matrix models it has been shown that long-term results may be misleading as populations are rarely in their stable structure. We therefore develop methods to analyze transient dynamics of periodic matrix models. In particular, we show how to calculate the effects of perturbations on population size within and at the end of environmental cycles. Using a model of a weed population subject to a crop rotation, we show that different cyclic permutations produce different patterns of sensitivity of population size and different population sizes. By examining how the starting environment interacts with the initial conditions, we explain how different patterns arise. Such understanding is critical to developing effective management and monitoring strategies for populations subject to periodically recurring environments.     

Risk aversion and adaptive management: Insights from a multi-armed bandit model of invasive species risk

This article explores adaptive management (AM) for decision-making under environmental uncertainty. In the context of targeting invasive species inspections of agricultural imports, I find that risk aversion increases the relative value of AM and can increase the rate of exploratory action. While calls for AM in natural resource management are common, many analyses have identified modest gains from this approach. I analytically and numerically examine the distribution of outcomes from AM under risk neutrality and risk aversion. The inspection decision is framed as a multi-armed bandit problem and solved using the Lagrangian decomposition method. Results show that even when expected gains are modest, asymmetry in the distribution of outcomes has important implications. Notably, AM can serve to buffer against large losses, even if the most likely outcome is a small loss.     

Importance of individual and environmental variation for invasive species spread: a spatial integral projection model

Plant survival, growth, and flowering are size dependent in many plant populations but also vary among individuals of the same size. This individual variation, along with variation in dispersal caused by differences in, e.g., seed release height, seed characteristics, and wind speed, is a key determinant of the spread rate of species through homogeneous landscapes. Here we develop spatial integral projection models (SIPMs) that include both demography and dispersal with continuous state variables. The advantage of this novel approach over discrete-stage spread models is that the effect of variation in plant size and size-dependent vital rates can be studied at much higher resolution. Comparing Neubert-Caswell matrix models to SIPMs allowed us to assess the importance of including individual variation in the models. As a test case we parameterized a SIPM with previously published data on the invasive monocarpic thistle Carduus nutans in New Zealand. Spread rate (c*) estimates were 34% lower than for standard spatial matrix models and stabilized with as few as seven evenly distributed size classes. The SIPM allowed us to calculate spread rate elasticities over the range of plant sizes, showing the size range of seedlings that contributed most to c* through their survival, growth and reproduction. The annual transitions of these seedlings were also the most important ones for local population growth (lambda). However, seedlings that reproduced within a year contributed relatively more to c* than to lambda. In contrast, plants that grow over several years to reach a large size and produce many more seeds, contributed relatively more to lambda than to c*. We show that matrix models pick up some of these details, while other details disappear within wide size classes. Our results show that SIPMs integrate various sources of variation much better than discrete-stage matrix models. Simpler, heuristic models, however, remain very valuable in studies where the main goal is to investigate the general impact of a life history stage on population dynamics. We conclude with a discussion of future extensions of SIPMs, including incorporation of continuous time and environmental drivers.     

Life cycle and population dynamics of Pycnogonum litorale (Pycnogonida) in a natural habitat

A natural population of Pycnogonum litorale Ström was examined every 4 weeks over a period of 15 months and thereafter at yearly intervals for 15 years. Adult pycnogonids – mating couples and males carrying egg batches – and freshly hatched protonymphon larvae within these egg batches were found throughout the year. The second, third, and fourth instar larvae were only found from April to July, during the vegetation period of their hydroid host Clava multicornis. After metamorphosis to the fifth instar (first juvenile instar) the pycnogonids have a significantly larger proboscis than during the larval period, and they feed on the sea anemone Metridium senile. First juvenile instars were found on M. senile from May to August. Older and larger juvenile stages were found over longer time spans throughout the year, and the maximum number of successive instars shifted slowly from June to December. Freshly moulted adults occurred throughout the year. Males, which on the average are smaller, usually reach the adult stage during late autumn of the first year and females, at the end of the following spring. We conclude that in nature the development from egg to adult stage is completed within one year. Continuous reproduction and asynchronous embryonic development provide offspring throughout most of the year. The annual cycle is synchronized by the vegetation period of C. multicornis, the only host of these pycnogonid larvae in the investigated habitat, and by the arrest of growth during low winter temperatures. The low level of locomotory activity of P. litorale probably requires an environment in which both host species coexist. The abundance of C. multicornis, M. senile, and juvenile pycnogonids decreased from 1990 to 1996, maybe due to hydrographic conditions.     

A process-based population dynamics model to explore target and non-target impacts of a biological control agent

The risks and benefits associated with efforts to control invasive alien species using classical biological control are being subjected to increasing scrutiny. A process-based population dynamics model was developed to explore the interactions between a folivorous biological control agent, Cleopus japonicus, and its plant host Buddleja davidii. The model revealed that climate could have a significant impact upon the interactions between B. davidii and C. japonicus. At the coolest sites, the impact of C. japonicus on B. davidii was slowed, but it was still eventually capable of controlling populations of B. davidii. At the warmer sites where both B. davidii and C. japonicus grew faster, B. davidii succumbed rapidly to weevil damage. We hypothesise that barring an encounter with a natural enemy, C. japonicus will eventually be able to provide sustained control B. davidii throughout the North Island of New Zealand. The model scenarios illustrate the potential for the C. japonicus population to attain high densities rapidly, and to defoliate patches of B. davidii, creating the potential for spill-over feeding on non-target plants. The potential magnitude of this threat will depend partly on the climate suitability for C. japonicus, the pattern by which it migrates in response to a reduction in the available leaf resource, and the suitability of non-target plants as hosts. In all migration scenarios considered, the pattern of population growth and resource consumption by C. japonicus was exponential, with a strong tendency toward complete utilisation of resource patches more quickly at the warmer compared to colder sites. In addition to providing some useful hypotheses about the effects of climate on the biological control system, and the non-target risks, it also provides some insight into the mechanisms by which climate affects the system.     

A simulation model to evaluate the impacts of invasive earthworms on soil carbon dynamics

Recent studies have reported that earthworm invasions alter native communities and impact nutrient cycling in terrestrial ecosystems. We developed a simulation model to evaluate the potential impacts of earthworm invasions on carbon dynamics, taking into consideration earthworm feeding strategies and priming effects on the microorganisms through their casting activities. Responses of carbon stocks (forest litter, soil organic matter, microbial biomass and earthworm populations) and carbon fluxes (litter decomposition, earthworm consumption, and microbial respiration) were used to evaluate an earthworm invasion of a forest ecosystem. Data from a northern temperate forest (Arnot Forest, New York) were adapted for model calibration and evaluation. Simulation results suggest that the impact and outcome of earthworm invasions are affected by pre-invasion resource availability (litter and soil organic matter), invasive earthworm assemblages (particularly feeding strategy), and invasion history (associated with earthworm population dynamics). The abovementioned factors may also determine invasion progress of earthworm species. The accuracy of the model could be improved by the addition of environmental modules (e.g., soil water regimes), precise parameters accounting for individual species attributes under different environmental conditions (e.g. utilization ability of different types of food resources), as well as earthworm population dynamics (size and structure) and interactions with predators and other invasive/indigenous species during the invasion progress. Such an earthworm invasion model could provide valuable evaluation of the complicated responses of carbon dynamics to earthworm invasions in a range of forest ecosystems, particularly under global change scenarios.     

A hierarchical Bayesian non-linear spatio-temporal model for the spread of invasive species with application to the Eurasian Collared-Dove

The spread of invasive species is a long studied subject that garners much interest in the ecological research community. Historically the phenomenon has been approached using a purely deterministic mathematical framework (usually involving differential equations of some form). These methods, while scientifically meaningful, are generally highly simplified and fail to account for uncertainty in the data and process, of which our knowledge could not possibly exist without error. We propose a hierarchical Bayesian model for population spread that accommodates data sources with errors, dependence structures between population dynamics parameters, and takes into account prior scientific understanding via non-linear relationships between model parameters and space-time response variables. We model the process (i.e., the bird population in this case) as a Poisson response with spatially varying diffusion coefficients as well as a logistic population growth term using a common reaction-diffusion equation that realistically mimics the ecological process. We focus the application on the ongoing invasion of the Eurasian Collared-Dove.