Traveling wave solutions for a predator-prey system with Sigmoidal response function

We study the existence of traveling wave solutions for a diffusive predator-prey system. The system considered in this paper is governed by a Sigmoidal response function which is more general than those studied previously. Our method is an improvement to the original method introduced in the work of Dunbar \cite{Dunbar1,Dunbar2}. A bounded Wazewski set is used in this work while unbounded Wazewski sets were used in \cite{Dunbar1,Dunbar2}. The existence of traveling wave solutions connecting two equilibria is established by using the original Wazewski's theorem which is much simpler than the extended version in Dunbar's work

TRY plant trait database – enhanced coverage and open access

Plant traits—the morphological, anatomical, physiological, biochemical and phenological characteristics of plants—determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits—almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Mathematical model of Zika virus with vertical transmission

Zika is a flavivirus transmitted to humans through either the bites of infected Aedes mosquitoes or sexual transmission. Zika has been linked to congenital anomalies such as microcephaly. In this paper, we analyze a new system of ordinary differential equations which incorporates human vertical transmission of Zika virus, the birth of babies with microcephaly and asymptomatically infected individuals. The Zika model is locally and globally asymptotically stable when the basic reproduction number is less than unity. Our model shows that asymptomatic individuals amplify the disease burden in the community, and the most important parameters for ZIKV spread are the death rate of mosquitoes, the mosquito biting rate, the mosquito recruitment rate, and the transmission per contact to mosquitoes and to adult humans. Scenario exploration indicates that personal-protection is a more effective control strategy than mosquito-reduction strategy. It also shows that delaying conception reduces the number of microcephaly cases, although this does little to prevent Zika transmission in the broader community. However, by coupling aggressive vector control and personal protection use, it is possible to reduce both microcephaly and Zika transmission. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15. Keywords: Zika virus, Vertical transmission, Microcephaly, Stability, Contro

A sampling theory for dispersal-limited, niche-structured communities

We introduce the first analytical model of a dispersal-limited, niche-structured community to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Dynamics of the multivariate species abundance distribution (SAD) for an asymmetric local community are modeled explicitly as a dispersal-limited sampling of the surrounding metacommunity. Coexistence may arise either from approximate functional equivalence or a competition-colonization tradeoff. At equilibrium, these symmetric and asymmetric mechanisms both generate unimodal SADs. Multiple modes only arise in asymmetric communities and provide a strong indication of non-neutral dynamics. Although these stationary distributions must be calculated numerically in the general theory, we derive the first analytical sampling distribution for a nearly neutral community where symmetry is broken by a single species distinct in ecological fitness and dispersal ability. Novel asymptotic expansions of hypergeometric functions are developed to make evaluations of this distribution tractable for large communities