Identifying realistic recovery targets and conservation actions for tigers in a human dominated landscape using spatially-explicit densities of wild prey and their determinants

Aim Setting realistic population targets and identifying actions for site and landscape-level recovery plans are critical for achieving the global target of doubling wild tiger numbers by 2022. Here, we estimate the spatially explicit densities of wild ungulate prey across a gradient of disturbances in two disjunct tiger habitat blocks (THBs) covering 5212 km2, to evaluate landscape-wide conditions for tigers and identify opportunities and specific actions for recovery. Location Western Terai Arc Landscape, India. Methods Data generated from 96 line transects in 15 systematically selected geographical cells (166.5 km2) were used to estimate spatially explicit densities of six wild ungulate prey species at a fine scale (1 km2). Employing distance-based density surface models, we derived species-specific estimates within three major forest land management categories (inviolate protected areas (PA), PAs with settlements and multiple-use forests). By scaling estimated prey densities using an established relationship, we predicted the carrying capacity for tigers within each THB. Results Species-specific responses of the six wild ungulates to natural-habitat and anthropogenic covariates indicated the need for targeted prey recovery strategies. Inviolate PAs supported the highest prey densities compared with PAs with settlements and multiple-use forests, and specifically benefited the principal tiger prey species (chital Axis axis and sambar Rusa unicolor). The estimated mean prey density of 35.16 (±5.67) individuals per km2 can potentially support 82 (62–106) and 299 (225–377) tigers across THB I and THB II, which currently support 2 (2–7) and 225 (199–256) tigers, respectively. This suggests a potential c. 68% increase in population size given existing prey abundances. Finally, while THB I represents a potential tiger recovery site given adequate prey, PAs where resettlement of pastoralists is underway represent potential prey recovery sites in THB II. Main conclusions This systematic approach of setting realistic population targets and prioritizing spatially explicit recovery strategies should aid in developing effective landscape conservation plans towards achieving global tiger conservation targets

Solitary waves, periodic and elliptic solutions to the Benjamin, Bona & Mahony (BBM) equation modified by viscosity

In this paper, we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate periodic and solitary wave solutions of the modified Benjamin, Bona & Mahony equation (BBM) to include both dissipative and dispersive effects of viscous boundary layers. Under certain circumstances that depend on the traveling wave velocity, classes of periodic and solitary wave like solutions are obtained in terms of Jacobi elliptic functions. An ad-hoc theory based on the dissipative term is presented, in which we have found a set of solutions in terms of an implicit function. Using dynamical systems theory we prove that the solutions of \eqref{BBMv} experience a transcritical bifurcation for a certain velocity of the traveling wave. Finally, we present qualitative numerical results.Comment: 14 pages, 11 figure

Numerical Simulations of Snake Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation

Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation and (b) a system of three ordinary differential equations resulting from the variational approximation

Weierstrass Traveling Wave Solutions for Dissipative Benjamin, Bona, and Mahoney (BBM) Equation

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified Benjamin, Bona, and Mahony (BBM) equation by viscosity. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in certain regions there still exist bounded traveling wave solutions in the form of solitary waves, periodic, and elliptic functions. By using the canonical form of Abel equation, the polynomial Appell invariant makes the equation integrable in terms of Weierstrass ℘ functions. We will use a general formalism based on Ince\u27s transformation to write the general solution of dissipative BBM in terms of ℘ functions, from which all the other known solutions can be obtained via simplifying assumptions. Using ODE (ordinary differential equations) analysis we show that the traveling wave speed is a bifurcationparameter that makes transition between different classes of waves

Interactions and Focusing of Nonlinear Water Waves

A theoretical and computational study is undertaken for the modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting waves gives rise to localized large-amplitude wavepackets (wave focusing). The coupled cubic nonlinear Schrödinger (CNLS) equations are used to derive a nonlinear dispersion equation which give rise to new class of modulational instabilities and demonstrates the dependence of obliqueness of the interacting waves. The computations, due to nonlinear wave-wave interactions, waves that are separately modulationally stable can give rise to the formation of large-amplitude coherent wave packets with amplitudes several times that of the initial waves. In the case for the original Benjamin-Feir instability, in constrast, waves disintegrate into a wide spectrum

Losing time for the tiger Panthera tigris: delayed action puts a globally threatened species at risk of local extinction

Meeting global and regional environmental targets is challenging, given the multiplicity of stakeholders and their diverse and often competing policy agendas and objectives. Relatively few studies have sought to systematically analyse the progress, or lack thereof, of institutionally complex and diffuse projects. Here we analyse one such project, which aims to protect and restore a critical landscape corridor for tigers Panthera tigris in north-western India, using a temporal–analytic framework that integrates ecological information on species population status and spatial connectivity modelling with a systematic examination of the decision-making process. We find that even with adequate ecological knowledge the tiger population is on the verge of local extinction because of weak institutional support, poor adaptive planning and ineffective leadership in a complex political arena, which has led to delays in conservation action. From the outset the conservation agencies and NGOs that were the primary drivers of the project lacked awareness of the political idiosyncrasies of coordinating the actions of disparate agencies within the decision-making process. To secure better future environmental outcomes we recommend the adoption of an improved project appraisal methodology that explicitly encompasses an evaluation of organizational incentives, to determine political buy-in, including alignment with organizational objectives and funding availability