Narrow Results

The paper describes the slow evolution of two adaptive traits that regulate the interactions between two mutualistic populations (e.g. a flowering plant and its insect pollinator). For frozen values of the traits, the two populations can either coexist or go extinct. The values of the traits for which populations extinction is guaranteed are therefore of no interest from an evolutionary point of view. In other words, the evolutionary dynamics must be studied only in a viable subset of trait space, which is bounded due to the physiological cost of extreme trait values. Thus, evolutionary dynamics experience so-called border collision bifurcations, when a system invariant in trait space hits the border of the viable subset. The unfolding of standard and border collision bifurcations with respect to two parameters of biological interest is presented. The algebraic and boundary-value problems characterizing the border collision bifurcations are described together with some details concerning their computation.

A mutualism is an interaction where the involved species benefit from each other. We study a two-dimensional hexagonal three-state cellular automaton model of a two-species mutualistic system. The simple model is characterized by four parameters of propagation and survival dependencies between the species. We map the parametric set onto the basic types of space-time structures that emerge in the mutualistic population dynamic. The structures discovered include propagating quasi-one-dimensional patterns, very slowly growing clusters, still and oscillatory stationary localizations. Although we hardly find such idealized patterns in nature, due to inreased complexity of interaction phenomena, we recognize our findings as basic spatial patterns of mutualistic systems, which can be used as baseline to build up more complex models.

The generally accepted Moolgavkar's theory of carcinogenesis assumes that all cancers are clonal, i.e. that they arise from progressive genetic deregulation in a cell pedigree originating from a single ancestral cell.¹⁸ However, recently the clonal theory has been challenged by the field theory of carcinogenesis, which admits the possibility of simultaneous changes in tissue subject to carcinogenic agents, such as tobacco smoke in lung cancer. Axelrod et al.¹ formulated a more detailed framework, in which partially transformed cells depend in a mutualistic way on growth factors they produce, in this way enabling these cells to proliferate and undergo further transformations. On the other hand, the field theory assumes spatial distribution of precancerous cells and indeed there exists evidence that early-stage precancerous lesions in lung cancer progress along linear, tubular, or irregular surface structures. This seems to be the case for the atypical adenomatous hyperplasia (AAH),¹⁰ a likely precursor of adenocarcinoma of the lung. In this paper we explore the consequences of linking the model of spatial growth of precancerous cells,¹² with the mutualistic hypothesis. We investigate the solutions of the model using analytical and computational techniques. The picture emerging from our modelling indicates that production of growth factors by cells considered may lead to diffusion-driven instability, which in turn may lead either to decay of both population, or to emergence of local growth foci, represented by spike-like solutions. Mutualism may, in some situations, increase the stability of solutions. One important conclusion is that models of field carcinogenesis, which include spatial effects, generally have very different behaviour compared to ODE models.

In this paper we present a mathematical model describing the interaction of two species, a plant population and an insect population, the latter being divided in two subgroups: novice and expert pollinators. We analyze the system and show the existence of a single nontrivial equilibrium, which is stable and represents a state of mutual benefit for all species involved. We show some numerical simulations of the global stability.

In this paper, we investigate two predator–prey models which take into consideration hunting cooperation (i.e., mutualism) between two different predators and within one predator species, respectively. Local and global dynamics are obtained for the model systems. By a detailed bifurcation analysis, we investigate the dependence of predation dynamics on mutualism (cooperative predation). From our study, we prove that mutualism may enhance the survival of mutualist predators in a severe condition and break the competitive exclusion principle. We further provide quantitative information about how the cooperative predation (mutualism) may (i) establish multiple stability switches on the positive equilibrium; (ii) generate backward bifurcation on equilibria; (iii) induce supercritical or subcritical Hopf bifurcations; and (iv) establish bi-stability phenomenon between the predator-free equilibrium and a positive equilibrium (or a limit cycle).

In this paper, a three-species system consisting of two predators which are in mutualism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey–predator system are considered. So the biological parameters are not precise in reality. This paper presents a different approach to study the prey–predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under impreciseness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin’s maximum principle. Numerical examples are provided to support the proposed approach.

In this paper, we propose a model describing the interaction between two species: a plant population that gets pollinated by an insect population. We assume the plant population is divided into two groups: the first group in mutualistic relationship with the insect and the second group attracting the insects while deceiving them and not delivering any reward. In addition, we assume that the insect population reduces the number of visits to the plants after several unsuccessful visits. We are interested in the conditions for the coexistence of both species, especially in the appearance of damped or sustained oscillations. We focus the analysis on the parameters that measure the balance among deceit, the benefit that the insect gets from the plant, and the learning by the pollinators. We are especially interested in analyzing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants.

Business can be a for-profit, not-for-profit or hybrid organization. But all these businesses focus on the satisfaction of their stakeholders. Although many businesses adopt a limited perspective of their stakeholders, focusing primarily on the interests of their investors, customers and, in some cases, their employees, it is a fact that the long-term sustainability of any business will depend on its contributions to the society. The long-term objective of all businesses is to serve and support the society and contribute to the socioeconomic development of their people. Therefore, this chapter presents a comprehensive review of the relationship between business and society, with special reference to the three main types of businesses: commercial businesses, social enterprises and non-governmental organizations. As in the case of biological systems, the relationship between business and society may be characterized predominantly by one of the three types of symbiotic relationships: mutualism, commensalism and parasitism. However, the successful co-existence of business and society, in the long run, would depend on the degree of mutualism in their relationship.

Dipterocarp forests of SE Asia are rich in ant-plant interactions. Many of the characteristic pioneer trees in these forests belong to the genus Macaranga (Euphorbiaceae) of which a high percentage lives in close association with ants. The genus Macaranga is very diverse and comprises the full range of species from those not regularly inhabited by ants over intermediate forms to obligate ant-plants. Macaranga is the only plant genus in the Oriental and Australian region with a substantial radiation of myrmecophytes (with at least 23 known myrmecophytic species in the Malay Archipelago).

This myrmecophytic system is very complex in regard to life types and species diversity. Three main types of association are described. The non-myrmecophytic species are not inhabited by ants but visited by a variety of ant species which are attracted by extrafloral nectaries and food bodies. Only myrmecophytic Macaranga species offer nesting space for ants and are associated with a specific ant-partner. Species of Crematogaster ants (Subfamiliy Myrmicine) are dominant, but associations with ants of other subfamilies also occur.

The most important ecological function of the ants for the plants is protection against herbivore damage and climbers. Non-specific, facultative associations with ants can be advantageous for Macaranga plants. The outcome of the defence against herbivore damage appears to be rather variable depending on habitat, herbivore pressure and associated ant species. Non-myrmecophytes do not receive protection against plant competition. Although even non-specific ant-plant interactions provide some herbivore protection, the obligate ant-partners in myrmecophytic Macaranga species are much more effective. Most important is the ants' defense against climbers which are abundant in the light-rich habitats of Macaranga. The partner-ants bite off any foreign plant part coming into contact with their host plant, thus allowing Macaranga plants to grow at sites of strongest plant competition. The ants also effectively protect their plants against herbivore damage.

All our studies have demonstrated that these ant-plant interactions are not just a curious example for symbiotic relationships. They are a very important ecological factor for the role that Macaranga trees play in the regeneration of dipterocarp forests.