An R package for simulating metapopulation dynamics and range expansion under environmental change

The metapopulation paradigm is central in ecology and conservation biology to understand the dynamics of spatially-structured populations in fragmented landscapes. Metapopulations are often studied using simulation modelling, and there is an increasing demand of user-friendly software tools to simulate metapopulation responses to environmental change. Here we describe the MetaLandSim R package, mwhich integrates ideas from metapopulation and graph theories to simulate the dynamics of real and virtual metapopulations. The package offers tools to (i) estimate metapopulation parameters from empirical data, (ii) to predict variation in patch occupancy over time in static and dynamic landscapes, either real or virtual, and (iii) to quantify the patterns and speed of metapopulation expansion into empty landscapes. MetaLandSim thus provides detailed information on metapopulation processes, which can be easily combined with land use and climate change scenarios to predict metapopulation dynamics and range expansion for a variety of taxa and ecological systems.

Evolution in subdivided plant populations: concepts, recent advances and future directions.

SUMMARY: Research into the evolution of subdivided plant populations has long involved the study of phenotypic variation across plant geographic ranges and the genetic details underlying that variation. Genetic polymorphism at different marker loci has also allowed us to infer the long- and short-term histories of gene flow within and among populations, including range expansions and colonization-extinction dynamics. However, the advent of affordable genome-wide sequences for large numbers of individuals is opening up new possibilities for the study of subdivided populations. In this review, we consider what the new tools and technologies may allow us to do. In particular, we encourage researchers to look beyond the description of variation and to use genomic tools to address new hypotheses, or old ones afresh. Because subdivided plant populations are complex structures, we caution researchers away from adopting simplistic interpretations of their data, and to consider the patterns they observe in terms of the population genetic processes that have given rise to them; here, the genealogical framework of the coalescent will continue to be conceptually and analytically useful.

Controls on fish distribution and abundance in temporary wetlands

Our main goal was to determine if fish distribution and adundance in temporary wetlands were shaped primarily by large-scale (landscape) or small-scale (local) characteristics and to investigate the influence of cattle ranching on fish assemblages. A total of 24 temporary ponds were selected at the Kissimmee Prairie Sanctuary and the Mac- Arthur Agro-Ecology Research Center. Each wetland was sampled for fish using throw traps and dip nets during 1999. Landscape processes (connectivity to permanent water bodies) predominately influenced fish assemblages, although local processes (depth–hydroperiod) were also important. Furthermore, no colonizing species went locally extinct before wetlands began to dry. Our findings suggest that large-scale processes that influence colonization dynamics are of more importance than small-scale processes that influence extinction dynamics. Finally, hydrological changes (ditching) associated with agriculture (cattle ranching) have adversely affected temporary wetland fish assemblages by reducing wetland hydroperiods and connectivity.

Patch dynamics and metapopulation theory: the case of successional species

We present a mathematical framework that combines extinction-colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied-suitable, empty-suitable, occupied-unsuitable and empty-unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate? extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction-colonization dynamics influences long-term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required far viable management of such species in the Florida scrub ecosystem. (C) 2001 Academic Press.

Dynamics of extinction in coupled populations of the flour beetle Tribolium castaneum

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Unusual dynamics of extinction in a simple ecological model.

Studies on natural populations and harvesting biological resources have led to the view, commonly held, that (i) populations exhibiting chaotic oscillations run a high risk of extinction; and (ii) a decrease in emigration/exploitation may reduce the risk of extinction. Here we describe a simple ecological model with emigration/depletion that shows behavior in contrast to this. This model displays unusual dynamics of extinction and survival, where populations growing beyond a critical rate can persist within a band of high depletion rates, whereas extinction occurs for lower depletion rates. Though prior to extinction at lower depletion rates the population exhibits chaotic dynamics with large amplitudes of variation and very low minima, at higher depletion rates the population persists at chaos but with reduced variation and increased minima. For still higher values, within the band of persistence, the dynamics show period reversal leading to stability. These results illustrate that chaos does not necessarily lead to population extinction. In addition, the persistence of populations at high depletion rates has important implications in the considerations of strategies for the management of biological resources.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

Colonization and extinction of land planarians (Platyhelminthes, Tricladida) in a Brazilian Atlantic Forest regrowth remnant

Long-term assessments of species assemblages are valuable tools for detecting species ecological preferences and their dispersal tracks, as well as for assessing the possible effects of alien species on native communities. Here we report a 50-year-long study on population dynamics of the four species of land flatworms (Platyhelminthes, Tricladida, Terricola) that have colonized or become extinct in a 70-year-old Atlantic Forest regrowth remnant through the period 1955-2006. On the one hand, the two initially most abundant species, which are native to the study site, Notogynaphallia ernesti and Geoplana multicolor have declined over decades and at present do not exist in the forest remnant. The extinction of these species is most likely related with their preference for open vegetation areas, which presently do not exist in the forest remnant. On the other hand, the neotropical Geoplaninae 1 and the exotic Endeavouria septemlineata were detected in the forest only very recently. The long-term study allowed us to conclude that Geoplaninae 1 was introduced into the study area, although it is only known from the study site. Endeavouria septemlineata, an active predator of the exotic giant African snail, is originally known from Hawaii. This land flatworm species was observed repeatedly in Brazilian anthropogenic areas, and this is the first report of the species in relatively well preserved native forest, which may be evidence of an ongoing adaptive process. Monitoring of its geographic spread and its ecological role would be a good practice for preventing potential damaging effects, since it also feeds on native mollusk fauna, as we observed in lab conditions.

Comparing predictions of extinction risk using models and subjective judgement

Models of population dynamics are commonly used to predict risks in ecology, particularly risks of population decline. There is often considerable uncertainty associated with these predictions. However, alternatives to predictions based on population models have not been assessed. We used simulation models of hypothetical species to generate the kinds of data that might typically be available to ecologists and then invited other researchers to predict risks of population declines using these data. The accuracy of the predictions was assessed by comparison with the forecasts of the original model. The researchers used either population models or subjective judgement to make their predictions. Predictions made using models were only slightly more accurate than subjective judgements of risk. However, predictions using models tended to be unbiased, while subjective judgements were biased towards over-estimation. Psychology literature suggests that the bias of subjective judgements is likely to vary somewhat unpredictably among people, depending on their stake in the outcome. This will make subjective predictions more uncertain and less transparent than those based on models. (C) 2004 Elsevier SAS. All rights reserved.

Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement

We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.