Turing Instability in an Economic-Demographic Dynamical System Can Lead to Pattern Formation on Geographical Scale

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the emergence of the densely populated areas at their present locations is widely believed to be linked to more favourable environmental and climatic conditions. In this paper, we challenge this point of view. We first identify a few areas at different parts of the world where the environmental conditions (quantified by the temperature, precipitation and elevation) are approximately uniform over thousands of miles. We then examine the population distribution across those areas to show that, in spite of the homogeneity of the environment, it exhibits a clear nearly-periodic spatial pattern. Based on this apparent disagreement, we hypothesize that there exists an inherent mechanism that can lead to pattern formation even in a uniform environment. We consider a mathematical model of the coupled demographic-economic dynamics and show that its spatially uniform, locally stable steady state can give rise to a periodic spatial pattern due to the Turing instability. Using computer simulations, we show that, interestingly, the emergence of the Turing patterns eventually leads to the system collapse.Comment: 26 pages, 14 figure

Attractors and long transients in a spatio-temporal slow-fast Bazykin's model

Spatio-temporal complexity of ecological dynamics has been a major focus of research for a few decades. Pattern formation, chaos, regime shifts and long transients are frequently observed in field data but specific factors and mechanisms responsible for the complex dynamics often remain obscure. An elementary building block of ecological population dynamics is a prey-predator system. In spite of its apparent simplicity, it has been demonstrated that a considerable part of ecological dynamical complexity may originate in this elementary system. A considerable progress in understanding of the prey-predator system's potential complexity has been made over the last few years; however, there are yet many questions remaining. In this paper, we focus on the effect of intraspecific competition in the predator population. In mathematical terms, such competition can be described by an additional quadratic term in the equation for the predator population, hence resulting in the variant of prey-predator system that is often referred to as Bazykin's model. We pay a particular attention to the case (often observed in real population communities) where the inherent prey and predator timescales are significantly different: the property known as a `slow-fast' dynamics. Using an array of analytical methods along with numerical simulations, we provide comprehensive investigation into the spatio-temporal dynamics of this system. In doing that, we apply a novel approach to quantify the system solution by calculating its norm in two different metrics such as $C^0$ and $L^2$. We show that the slow-fast Bazykin's system exhibits a rich spatio-temporal dynamics, including a variety of long exotic transient regimes that can last for hundreds and thousands of generations

An Exact Solution of a Diffusive Predator-Prey System

We consider a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey community where the prey per capita growth rate is damped by the Allee effect. Using an appropriate change of variables, we obtain an exact solution of the system, which appears to be related to the issue of biological invasion. In the large-time limit, or for appropriate parameter values, this solution describes the propagation of a travelling population front. We show that the properties of the solution exhibit biologically reasonable dependence on the parameter values; in particular, it predicts that the travelling front of invasive species can be stopped or reversed owing to the impact of predation

BLOOD MEAL TAKING OF SOME HORSE FLIES SPECIES (DIPTERA, TABANIDAE) ON HORSES (EQUUS CABALLUS)

Istraživanje mjesta uzimanja krvnih obroka obada na konjima, obavljeno je tijekom 1993. godine na pašnjaku u Petrijevcima CR 05. Lovnom mrežicom na konjima uhvaćeno je 2010 jedinki. Sve uhvaćene jedinke su ženke. U sakupljenom uzorku utvrđeno je 26 vrsta obada od kojih su Haematopota bigoti i Hybomitra ucrainica nove u fauni Hrvatske. Obadi su svrstani u potporodice Chrysopsinae i Tabaninae, te rodove Chrysops, Arylotus, Hybomitra, Tabanus, Heptatoma i Haematopota. Dokazano je X² (Hi - kvadrat) testom da vrste Haematopota subcylindrica, Haematoppota pluvialis, Chrysops parallelogrammus, Hybomitra ciureai, Tabanus bromius i Tabanus autumnalis signifikantno razlikuju pojedine dijelove tijela konja pri uzimanju krvnih obroka, jer se na taj način smanjuje kompeticija među vrstama.The research of the horse flies blood meal taking location, the pasture in the village Petrijevci CR 05, took place in 1993. With the help of the net there were collected 2010 specimens, all of which were female. In the collected sample we established 26 species two of which Haematopota bigoti and Hybomitra ucrainica were new for Croatia. Horse flies to belong subfamily Chrysopsinae and Tabanidae, and genera Chrysops, Atylotus, Hybomitra, Tabanus, Heptatoma and Haematopota. X² test demonstrated that species Haematopota subcylindrica, Hameatopota pluvialis, Chrysops parallelogrammus, Hybomitra ciureai, Tabanus bromius and Tabanus autumnalis significantly distinguish between certain parts of the horse while taking their blood meal. In that way is diminished the competitive relationship between some species

Using a multi-lens framework for landscape decisions

1. Landscape decisions are multi-faceted. Framing landscape decision-making as a governance process that requires a collective approach can encourage key stakeholders to come together to co-inform a discussion about their priorities and what constitutes good governance, leading to more holistic landscape decisions. 2. In this paper, we recognise that a suite of complementary and multi-dimensional approaches are in practice used to inform and evaluate land use decisions. We have called these approaches ‘lenses’ because they each provide a different perspective on the same problem. The four lenses are: i) Power and Market Gain, ii) Ecosystem Services, iii), Place based Identity and iv) Ecocentric. Each brings a different set of evidence and viewpoints (narrative, qualitative and experiential, as well as quantitative metrics such as monetary) to the decision-making process and can potentially reveal problems and solutions that others do not. 3. Considering all lenses together allows dialogue to take place which can reveal the true complexities of landscape decision-making and can facilitate more effective and more holistic decisions. Employing the lenses requires governance structures that give equal weight to all lenses, enable dialogue and coexistence between top down and bottom up approaches, and permit adaptation to local and granular place specifics rather than developing “one-size-fits-all” solutions. 4. We propose that formalising the process of balancing all the lenses requires public participation, and that a lens approach should be used to support landscape decisions alongside a checklist that facilitates transparency in the conversation, showing how all evidence has been considered and critically assessed

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called “activity-density” problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth

Managing biological invasions: the cost of inaction

Ecological and socioeconomic impacts from biological invasions are rapidly escalating worldwide. While effective management underpins impact mitigation, such actions are often delayed, insufficient or entirely absent. Presently, management delays emanate from a lack of monetary rationale to invest at early invasion stages, which precludes effective prevention and eradication. Here, we provide such rationale by developing a conceptual model to quantify the cost of inaction, i.e., the additional expenditure due to delayed management, under varying time delays and management efficiencies. Further, we apply the model to management and damage cost data from a relatively data-rich genus (Aedes mosquitoes). Our model demonstrates that rapid management interventions following invasion drastically minimise costs. We also identify key points in time that differentiate among scenarios of timely, delayed and severely delayed management intervention. Any management action during the severely delayed phase results in substantial losses (>50% of the potential maximum loss). For Aedes spp., we estimate that the existing management delay of 55 years led to an additional total cost of approximately $4.57 billion (14$ 32.31 billion, or more than seven times the observed inaction cost. These results highlight the need for more timely management of invasive alien species—either pre-invasion, or as soon as possible after detection—by demonstrating how early investments rapidly reduce long-term economic impacts

On time scale invariance of random walks in confined space

Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is non-conservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour