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The accumulation of knowledge that explains universities’ contributions to innovation and entrepreneurship’s regional eco-systems has mainly adopted a perspective based on technology transfer processes from academia to markets. Alternatively, in this study, we assume the notion of mutualism, based on the biomimetic rationale of eco-system studies that involve bidirectional flows of resources and capabilities to generate interactions and value co-creation among agents. This study theorizes about the interrelation between universities and eco-system actors in two directions: (a) universities fostering and improving eco-systems through their core activities; and (b) eco-system actors shaping capabilities and access to resources for universities. Based on the analysis of five eco-systems in the state of Sao Paulo, Brazil, our results underscore the existence of mutualism in the relationships established between universities and eco-system agents. The findings also highlighted implications related to the coordination of policies and the need for strategic management practices in mutualistic interactions.

This paper is concerned with the stationary problem for a diffusive Lotka-Volterra predator-prey-mutualist model with a protection zone under homogeneous Neumann boundary conditions. Compared with the case where the mutualist is absent in [12] , this paper aims to reveal the effects of mutualism coefficients α and β on the existence, number and stability of steady states. It turns out that when α is large, the model has at most one steady state and it is stable (if it exists); however existence of multiple steady states is examined for large β, moreover asymptotic profiles of steady states are established as β tends to infinity.

We perform a stability analysis on a discrete analogue of a known, continuous model of mutualism. We illustrate how the introduction of delays affects the asymptotic stability of the system's positive nontrivial equilibrium point. In the second part of the paper we explore the insights that the model can provide when it is used in relation to interacting financial markets. We also note the limitations of such an approach.

A three-species population system under a facultative mutualistic relationship of one of the species is studied. The considered interactions are as follows: facultative between the first species and the second species, obligatory mutualism between the second species and the first one, and the third species is a predator of the first species. For this purpose, we extend the model proposed by Morozov et al., originally used to describe obligatory mutualism, to consider obligatory and facultative mutualism and prove that under adequately selected parameters this system produces a spatial patchy spread of populations or continuous wave fronts. Since the analytical treatment of a three-species model is often prohibitive, we first analyze the interaction between two mutualist species without diffusion and without the presence of the predator. Some parameters are fixed in the bistable regime of the mutualistic species to further consider the influence of the third species. The remaining parameters are then selected to produce patchy patterns under different mortality rates. Finally, the equations of the final three-species system are numerically solved to test the influence of different initial conditions in the formation of patchy populations. It is confirmed that the velocity and the profile of a traveling front are independent on the initial conditions. Our approach opens the way to study more general biological situations.

This paper studies global dynamics of a class of plant–pollinator–robber systems, in which plant is the resource while the pollinator and nectar robber are two competing consumers. The nectar robber is a parasite of plant while the pollinator is the mutualist. Based on the competition–parasitism–mutualism interactions, we established a plant–pollinator–robber model by nectar-mediated consumer–resource theory. By complete analysis on the model, we demonstrate necessary and sufficient conditions for the principle of competitive exclusion to hold and give the global dynamical behavior of the three species in the first octant, in which a three-dimensional saddle–node bifurcation is exhibited. It is shown that pollination–mutualisms promote survival of the nectar robber, the invasion of nectar robber would mean extinction of both the pollinator and the nectar robber itself, while the pollinator (resp. robber) can drive the robber (resp. pollinator) into extinction. Initial population densities of the species are exhibited to play a role in persistence of the systems. This analysis demonstrates mechanisms by which the pollinator and nectar robber can stably coexist, which is observed in real situations.

Plant roots are associated with a diverse microbial community that consists of antagonistic, commensal and mutualistic organisms. While beneficial plant-microbe interactions are important for plant performance, direct evidence for the evolution of rhizosphere mutualism remains elusive. Here we experimentally show that initially plant-antagonistic Pseudomonas protegens bacterium can rapidly evolve into a mutualist in the rhizosphere of Arabidopsis thaliana only within six plant growth cycles (6 months). Using an in vivo experimental evolution system, we observed that P. protegens rapidly diversified into distinct phenotypes, with some having clearly positive effects on the plant performance. Crucially, this evolution of plant facilitation was also accompanied with increased bacterial fitness indicative of a mutualistic interaction. At the genetic level, P. protegens mutualism was associated with mutations in the GacS/GacA two-component global regulator system, which is known to affect several aspects of bacterial physiology including carbon metabolism, host-microbe signalling, and downregulation of phytotoxic secondary metabolites. At the phenotypic level, the evolution of mutualism could be explained via two mechanisms: improved competition for root exudates and enhanced capacity for activating the root-specific transcription factor gene MYB72, which is essential for the production and excretion of the antimicrobial scopoletin for which the mutualists evolved enhanced tolerance. Together, these results show that plant-bacteria mutualism can rapidly evolve at an agriculturally relevant evolutionary timescale in the rhizosphere.

Explaining the evolution of cooperation represents one of the greatest challenges in both evolutionary biology and social science. However, asymmetrical interaction, as one typical characteristic of cooperative system, has not been sufficiently considered in the existing literature for the evolution of cooperation. Incorporating the asymmetry in the strategy sets, we here construct an asymmetric game model with the so-called carrot-stick strategy, which is a mixed strategy of reward and punishment. Based on mathematical analyses, it is unveiled that this asymmetric interaction can lower the dilemma of cooperation: the dominant players and recipient players might coexist through cycle frequency. Further analysis shows that the multi-equilibria are possible, which depend on the payoff parameters and the initial conditions. That is to say, by setting up different values of the cost-to-benefit, the punishment-to-benefit, and the reward-to-benefit, we can recover three basic evolutionary dynamics of systems: dominance; bistability and coexistence. These theoretical observations are consistent with existing empirical outcomes that asymmetric sanction or reward of host species might solve the conflicts between the actors in the fig-fig wasp mutualism or in the cleaner fish-client mutualism. It is thus suggested that this asymmetric strategy setup may shed new light into the solution of social dilemmas.

Due to poor technology and lack of proper skills in mineral processing techniques, a greater percentage (about 70%) of gold is lost to the tailings stream in artisanal and small-scale gold mining (ASGM). These tailings, in the last decade, have become a major source of revenue for some large-scale mining (LSM) companies in Ghana because they have advanced technologies to optimize recovery. This paper examines the tailings trade between ASGM and LSM companies in Ghana and determines their associated relationships. It also informs policy decisions regarding gold mining in Ghana. Field visits were made to licensed ASGM sites in the Tarkwa Mining District where the trade is mostly practiced to obtain first-hand information and conduct interviews with diggers. Results indicate that both ASGM operators and LSM companies derive revenue from the tailings trade, exhibiting a relationship that could be described as mutualistic. Based on the tailings price determination, the symbiotic relationship is described as parasitic because the tailings pricing process is largely controlled by the LSM companies to the detriment of the ASGM operators. As a result of the environmental dangers posed by the tailings trade, the interdependency could equally be described as parasitic since both the ASGM operators and the LSM companies benefit to the detriment of the natural ecosystem. It was also observed that while some stakeholders attempt to criminalize the tailings trade, there is presently no law or regulation that prohibits such trade in the Ghanaian mining industry.

Mutualism describes the biological phenomenon where two or more species are reciprocally beneficial, regardless of their ecological intimacy or evolutionary history. Classic theory shows that mutualistic benefit must be relatively weak, or else it overpowers the stabilizing influence of intraspecific competition and leads to unrealistic, unbounded population growth. Interestingly, the conclusion that strong positive interactions lead to runaway population growth is strongly grounded in the behavior of a single model. This model—the Lotka–Volterra competition model with a sign change to generate mutualism rather than competition between species—assumes logistic growth of each species plus a linear interaction term to represent the mutualism. While it is commonly held that the linear interaction term is to blame for the model's unrealistic behavior, we show here that a linear mutualism added to a θ-logistic model of population growth can prevent unbounded growth. We find that when density dependence is decelerating, the benefit of mutualism at equilibrium is greater than when density dependence is accelerating. Although there is a greater benefit, however, decelerating density dependence tends to destabilize populations whereas accelerating density dependence is always stable. We interpret these findings tentatively, but with promise for the understanding of the population ecology of mutualism by generating several predictions relating growth rates of mutualist populations and the strength of mutualistic interaction.

Plants attract mutualistic animals by offering a reward of nectar. Specifically, floral nectar (FN) is produced to attract pollinators, whereas extrafloral nectar (EFN) mediates indirect defenses through the attraction of mutualist predatory insects to limit herbivory. Nearly 90% of all plant species, including 75% of domesticated crops, benefit from animal-mediated pollination, which is largely facilitated by FN. Moreover, EFN represents one of the few defense mechanisms for which stable effects on plant health and fitness have been demonstrated in multiple systems, and thus plays a crucial role in the resistance phenotype of plants producing it. In spite of its central role in plant-animal interactions, the molecular events involved in the development of both floral and extrafloral nectaries (the glands that produce nectar), as well as the synthesis and secretion of the nectar itself, have been poorly understood until recently. This review will cover major recent developments in the understanding of (1) nectar chemistry and its role in plant-mutualist interactions, (2) the structure and development of nectaries, (3) nectar production, and (4) its regulation by phytohormones.

The Agricultural Revolution and plant domestication in the Near East (among its components) have fascinated generations of scholars. Here, we narrate the history of ideas underlying plant domestication research since the late 19th century. Biological and cultural perspectives are presented through two prevailing models: one views plant domestication as a protracted, unconscious evolutionary mutualistic (noncentric) process. The second advocates a punctuated, knowledge-based human initiative (centric). We scrutinize the research landscape while assessing the underlying evolutionary and cultural mechanisms. A parsimony measure indicates that the punctuated-centric view better accords with archaeological records, and the geobotany and biology of the species, and requires fewer assumptions. The protracted alternative requires many assumptions, does not account for legume biology, fails to distinguish domestication from postdomestication changes, and, therefore, is less parsimonious.

In this paper, we consider a stochastic mutualism model with Levy jumps. First of all, we show that the positive solution of the system is stochastically ultimate bounded. Then under a simple assumption, we establish sufficient and necessary conditions for the stochastic permanence and extinction of the system. The results show an important property of the Levy jumps: they are unfavorable for the permanence of the species. Moreover, when there are no Levy jumps, we show that there is a unique ergodic stationary distribution of the corresponding system under certain conditions. Some numerical simulations are introduced to validate the theoretical results.

The emergence of artificial general intelligence and the global brain provides new opportunities for realizing humanity's long quest for a more utopian existence. One possibility is a more successful implementation of the state socialist vision of a centrally managed economy, possibly controlled by an AGI “Nanny” instead of a central committee of politicians. An alternative outcome, more in keeping with the original Marxist vision of the withering away of the state, may be the mutualist vision of organizing economic and social life along voluntary lines. A number of recent developments and new ideas may facilitate this outcome. The institution of the commons, in the past available only to small geographical communities, can now be used by global communities. Open collaboration and exchange networks facilitate voluntary cooperative activity by people at dispersed physical locations. Open Production Networks can make the most complicated economic exchanges transparent to consumers, allowing them to factor ethical and sociological considerations into their purchasing decisions. Offer Networks can help people with similar interests and complementary abilities to organize joint projects and organizations. Blockchain technologies could be used to create transparent currencies in which transactions can be done openly. These and other related technologies have the potential to humanize global economic interactions, giving them more emotional resonance, as increasing affluence lessens individual and societal preoccupation with maximizing economic gain.

Metacommunity membership is influenced by habitat availability and trophic requirements. However, for multitrophic horizontally transmitted symbiont communities that are closely associated with hosts, symbiont–host interactions may affect membership criteria in novel ways. For example, failure of beneficial services from symbionts could influence the host, and in turn, the entire community. Understanding such host–symbiont feedback effects on symbiont community membership, symbiont community structure, and function is important for understanding if host–symbiont communities are fundamentally different from more traditional ecological communities. We investigate the membership criteria for a multitrophic insect symbiont community that colonizes host inflorescences at specific developmental stages termed colonization windows. The inflorescences serve as microcosm habitats. Symbionts exhibit a range of interactions from mutualism to parasitism. Hosts exhibit feedback by aborting inflorescences not pollinated by mutualistic symbionts. Habitats are consequently lost for all other symbiont species in such host-derived organs whose development is mutualist-dependent. Using empirical measurements to characterize inflorescence development, we simulate symbiont dispersal colonization across hosts. We vary host densities and lengths of symbiont colonization windows, and track the persistence of each symbiont species in the metacommunity based on its trophic requirements and resource availability within the microcosm. Since the persistence of the microcosm habitat is dictated by pollination performed by the mutualist, the mutualist fared better than all other symbionts. The length of symbiont colonization windows was positively related with colonization success and symbiont persistence. The cumulative length of the colonization windows of prey dictated predator success; diet breadth or prey colonization success did not influence predator persistence. Predators also had a greater host-plant density requirement than prey for persistence in the community. These results offer valuable insights into host densities required for maintaining symbionts, and have implications for multitrophic symbiont community stability. Special constraints can govern symbiont community membership, function and structure and symbiont persistence when host–symbiont feedback impacts host microcosm development.

Most wood-boring insects compete with wood decaying basidiomycetes for woody biomass. One clade of ambrosia beetles gained access to rotten wood – an abundant resource unsuitable to most wood-boring insects – by evolving a farming-like mutualism with a white rot polypore. Here we show the mutualist of Ambrosiodmus/Ambrosiophilus, the polypore Flavodon ambrosius, is superior in lignocellulolytic capacity compared to Ascomycota ambrosia fungi and other white rot Basidiomycota. This mutualism facilitated the evolution of large, long-lived, communal colonies with overlapping generations and egg-laying by pre-dispersal progeny females. F. ambrosius resembles other white rot Polyporales in that it causes significant weight loss in wood decay assays and strong polyphenol oxidase reactions, indicative of lignin-modifying enzymes. The symbiosis is asymmetrical: there are many species of Ambrosiodmus and Ambrosiophilus but all use a single known species of Flavodon, which determines the ecological strategy of the entire insect clade.

The mutualism theory of general intelligence (g) posits that the positive manifold arises because of mutually beneficial interactions between originally orthogonal cognitive abilities, rather than because of a genuine general construct. In a recent investigation, Gignac (2014) reported that the strength of g was largely constant from the ages of 2.5 to 90 years, which was interpreted as an indirect failure to confirm the mutualism theory of g. In this investigation, a second indirect test of the mutualism theory of g was performed. Specifically, it was hypothesized that, if the extended mutualism theory of g is plausible, then there should be some consistent, positive associations between group-level factors, controlling for the effects of a general factor. To examine this possibility, the associations between cognitive ability group-level factors were estimated across a series of seven relatively large and relatively representative samples of intelligence battery data. Next, seven single-factor models were estimated against the seven group-level inter-correlation matrices. The corresponding single-factor residual correlation matrices were observed to yield an approximately equal number of positive and negative residual correlations and an overall mean of zero. Furthermore, the only moderately consistent residual effect was a negative association between crystallised intelligence and processing speed. Although only an indirect test, the results are interpreted to be more supportive of g factor theory than mutualism.

Differences in temperature ranges and optima among poikilothermic partners in symbioses can have profound effects on their interactions and stability. In this study, we investigated how the two mutualist mycangial fungi (Ceratocystiopsis brevicomi and Entomocorticium sp. B) associated with the western pine beetle, Dendroctonus brevicomis, respond to temperature in vitro. Little variability in growth rate at the various temperatures tested occurred among isolates of C. brevicomi either within or among sites. In contrast, E. sp. B exhibited highly variable responses to mid-range temperatures among sites and within some sites, and, unlike C. brevicomi, grew not at all or only very poorly at the highest and lowest temperatures tested. This variability affected both optimal temperature and maximum growth rate. The high variability in response to some temperatures among isolates of E. sp. B in some populations indicates that the ability to capture spatial and nutritional resources can vary greatly within this species which may have considerable impact on the outcome of both inter- and intra-specific competition among the fungi within trees and the short- and long-term dynamics of the fungi with the host beetle.

We show by simulations that the main premise underlying Gignac's (2016) rejection of the mutualism model of general intelligence is incorrect. We discuss our results in the context of the debate on g-factor theory and its alternatives, especially with regard to the claim that g-factor theory is much simpler than mutualism theory.

The positive manifold associated with correlation matrices of diverse batteries of cognitive abilities has garnered a substantial amount of psychometric and theoretical consideration. General (g) factor theorists purport the positive manifold to be due to a g factor, which is believed to be representative of an important psychological construct. By contrast, the dynamic mutualism theory of the positive manifold asserts that it is an epiphenomenon, which emerges progressively during development, as a consequence of mutually beneficial interactions between originally uncorrelated cognitive processes. To test the competing dynamic mutualism versus g factor theories of the g factor, the strength of the g factor (as estimated by omega hierarchical, ωh) was plotted across the ages of 2.5 to 90 years (N = 5200). Although there was an observed increase in ωh from the ages of 2.5 to approximately 10.0, the observed slope was weak in magnitude. Furthermore, the results based on the mean of the bifactor model g loadings suggested that much, if not all, of the upward slope in ωh was due to differences in the number of subtests across age groups. Consequently, the results are interpreted to suggest that the dynamic mutualism theory of g was failed to be confirmed, however, important limitations associated with this investigation are highlighted and an alternative explanation is presented.

Evolution and maintenance of mutualism have been one of the major questions in evolutionary ecology, because it is often susceptible of invasion of non-mutualistic strategy. Some previous studies using dual-lattice model suggest that spatial structures of habitat can prevent non-mutualism from prevailing over mutualism, while the detail of the dynamics is not fully revealed. Here we explore population dynamics of the two strategies (mutualism and non-mutualism) in two species engaged in Prisoner's Dilemma game on a dual-lattice space, especially focusing on whether mutualists and non-mutualists can coexist in long-term dynamics. The habitat consists of two layers, each of which a population of species inhabits, and interspecific interaction is restricted between two corresponding sites of the layers. Each individual of the both species is either a mutualist or a non-mutualist and only the former pay cost c for benefit of the partner b. The payoff of the game affects the individuals' fecundity, while the mortality is constant. Reproduction is restricted to neighboring vacant sites of the focal individuals. Our computer simulations of the model show that even if b/c ratio remains constant, mutualists become dominant in both species over wider ranges of basic reproduction rate (reproduction rate without interspecific interaction) as b and c increase. If basic reproduction rates are asymmetric between the species or basic reproduction rates were sufficiently large, mutualists and non-mutualists can coexist in one or both species, while their population sizes often fluctuate. Transition of the final state between mutualism and non-mutualism happens rather discontinuously, then total population sizes change drastically at the transition. Moreover, we also find paradoxical cases of unilateral exploitation, i.e. one species consists of mutualists and other species non-mutualists. Additional simulations reveal that accidental extinction of the non-mutualists of one species can result in extinction of mutualist of the other species.

Current conceptual models of reciprocal interactions linking soil structure, plants and arbuscular mycorrhizal fungi emphasise positive feedbacks among the components of the system. However, dynamical systems with high dimensionality and several positive feedbacks (i.e. mutualism) are prone to instability. Further, organisms such as arbuscular mycorrhizal fungi (AMF) are obligate biotrophs of plants and are considered major biological agents in soil aggregate stabilization. With these considerations in mind, we developed dynamical models of soil ecosystems that reflect the main features of current conceptual models and empirical data, especially positive feedbacks and linear interactions among plants, AMF and the component of soil structure dependent on aggregates. We found that systems become increasingly unstable the more positive effects with Type I functional response (i.e., the growth rate of a mutualist is modified by the density of its partner through linear proportionality) are added to the model, to the point that increasing the realism of models by adding linear effects produces the most unstable systems. The present theoretical analysis thus offers a framework for modelling and suggests new directions for experimental studies on the interrelationship between soil structure, plants and AMF. Non-linearity in functional responses, spatial and temporal heterogeneity, and indirect effects can be invoked on a theoretical basis and experimentally tested in laboratory and field experiments in order to account for and buffer the local instability of the simplest of current scenarios. This first model presented here may generate interest in more explicitly representing the role of biota in soil physical structure, a phenomenon that is typically viewed in a more process- and management-focused context.

It is becoming increasingly popular to consider species interactions when managing ecological foodwebs. Such an approach is useful in determining how management can affect multiple species, with either beneficial or detrimental consequences. Identifying such actions is particularly valuable in the context of conservation decision making as funding is severely limited. This paper outlines a new approach that simplifies the resource allocation problem in a two species system for a range of species interactions: independent, mutualism, predator–prey, and competitive exclusion. We assume that both species are endangered and we do not account for decisions over time. We find that optimal funding allocation is to the conservation of the species with the highest marginal gain in expected probability of survival and that, across all except mutualist interaction types, optimal conservation funding allocation differs between species. Loss in efficiency from ignoring species interactions was most severe in predator–prey systems. The funding problem we address, where an ecosystem includes multiple threatened species, will only become more commonplace as increasing numbers of species worldwide become threatened.

This paper is concerned with a system modeling a competitor–competitor–mutualist three-species Lotka–Volterra model. By Schauder fixed point theory, the existence of positive solutions to a strongly coupled elliptic system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed and a numerical simulation is also presented. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak.

Positive interactions are widely recognized as playing a major role in the organization of community structure and diversity. As such, recent theoretical and empirical works have revealed the significant contribution of positive interactions in shaping species’ geographical distributions, particularly in harsh abiotic conditions. In this report, we explore the joint influence of local dispersal and an environmental gradient on the spatial distribution, structure and function of communities containing positive interactions. While most previous theoretical efforts were limited to modelling the dynamics of single pairs of associated species being mutualist or competitor, here we employ a spatially explicit multi-species metacommunity model covering a rich range of interspecific interactions (mutualism, competition and exploitation) along an environmental gradient. We find that mutualistic interactions dominate in communities with low diversity characterized by limited species dispersal and poor habitat quality. On the other hand, the fraction of mutualistic interactions decreases at the expense of exploitation and competition with the increase in diversity caused by higher dispersal and/or habitat quality. Our multi-species model exemplifies the ubiquitous presence of mutualistic interactions and the role of mutualistic species as facilitators for the further establishment of species during ecosystem assembly. We therefore argue that mutualism is an essential component driving the origination of complex and diverse communities.

We propose and study a mutualism model with feedback controls. By applying a new differential inequality, we show that the conditions which ensure the permanence of the system are the same as that of the model without feedback controls, which means that the feedback control variables have no influence on the persistent property of the system. Our results not only improve but also complement some existing ones.

In this article, I present a two-patch metapopulation model with locally explicit dynamics to study the effect of spatial heterogeneity and dispersal upon population interactions with variable or conditional outcomes. These are interactions that may be either detrimental or beneficial for each species depending on the balance of the density-dependent costs and benefits involved. The local dynamics respond to density-dependent α -interaction functions that may change sign, thus yielding a diversity of possible local outcomes for the association in terms of type of interaction and in the number of stable solutions. The spatiotemporal model predicts that the fragmentation of space and dispersal between patches may cause further variation in these outcomes. First, the demographic performance of a species in the association is enhanced if migrations cause a proportional increase of individuals of its own species; being so, a victim may become a mutualist or an exploiter, an excluded species may invade, and a good competitor may overcome its own carrying capacity: the ‘ enhancement effect of dispersal ’; a sort of rescue effect in source-sink dynamics. The underlying mechanisms involve an interplay between density-dependent effects of dispersal per se and the relative local and global average α -interaction functions, which involve costs and benefits at both the local and regional level that may either counteract or reinforce each other; thus, localities and/or populations may change dynamically their sink or source role in the spatial dynamics. A significant insight arises herewith: in the context of variable or conditional interactions the concept of the role of a species does not make strict sense; it becomes a spatiotemporal dynamic quality . Second, regardless of which species disperses, bifurcation of equilibria may occur in those patches that receive the migrating individuals, and annihilation of equilibria in those from where migration leaves; thus, the number of equilibria increases or decreases accordingly.

The implications of spatial and temporal structure for the maintenance of mutualism, altruism, and niche construction or ecosystem engineering have been explored by many theoretical models. Part of what these models have shown is that organisms that give up some amount of potential short-term gain in order to improve the quality of their environment can, in a variety of scenarios, persist in the face of more exploitative competitors if structure in environmental quality allows the former to preferentially benefit from their investments. The models presented here consider the additional implications of interactions between competitors in their effects on their environment (recently documented in multiple systems). Relative to when competitor types were additive, synergistic effects promoted coexistence and antagonistic effects promoted founder effects (but favored the less exploitative type when both had equal initial frequencies). Spatial and temporal patterns of patch quality and occupancy also differed markedly between scenarios, even where all three scenarios generated the same qualitative outcome. These models show that understanding both the scale over which organisms affect their environment and the degree to which organisms interact in such effects are important for interpreting patterns in environmental quality, predicting the effects of organism-environment feedback on competition, and explaining the persistence of mutualistic traits.

We present a model to describe the mutualism relationship between search engines and web sites. In the model, search engines and web sites benefit from each other while the search engines are derived products of the web sites and cannot survive independently. Our goal is to show strategies for the search engines to survive in the internet market. From mathematical analysis of the model, we show that mutualism does not always result in survival. We show various conditions under which the search engines would tend to extinction, persist or grow explosively. Then by the conditions, we deduce a series of strategies for the search engines to survive in the internet market. We present conditions under which the initial number of consumers of the search engines has little contribution to their persistence, which is in agreement with the results in previous works. Furthermore, we show novel conditions under which the initial value plays an important role in the persistence of the search engines and deduce new strategies. We also give suggestions for the web sites to cooperate with the search engines in order to form a win–win situation.

We consider interactions between a symbiont and its host in the framework of the familiar Lotka–Volterra predator–prey model, modified to allow the symbiont to benefit the host. The model includes both benefits and costs to the interaction and spans the mutualism–parasitism continuum. We use this model to explore the shift from mutualism to parasitism in plant–mycorrhizae interactions across gradients of soil fertility. We demonstrate two mechanisms by which increased soil fertility may cause interactions to change from mutualistic to parasitic: as relative benefits to the plant decrease with increasing soil fertility, the interaction between the fungus and its host turns parasitic; with two fungal species—one a mutualist and the other a cheater—increasing soil fertility can favor the cheater if mutualists have faster growth rates than cheaters.

Mutualism among species is ubiquitous in natural ecosystems but its evolution is not well understood. We provided a simple lattice model to clarify the importance of spatial structure for the evolution of mutualism. We assumed reproductive rates of two species are modified through interaction between species and examine conditions where mutualists of both species, that give some benefit to the other species with their own cost, invade non-mutualists populations. When dispersal of offspring is unlimited, we verified the evolution of mutualism is impossible under any condition. On the other hand, when the dispersal is limited to neighboring lattice sites, mutualists can invade if the ratio of cost to benefit is low and the intrinsic reproductive rate is low in case where the parameter values are symmetric between species. Under the same conditions, non-mutualists cannot invade mutualist populations, that is, the latter are evolutionarily stable. In case of asymmetric parameters, mutualists tend to invade if the average value of costs to two species is low or that of benefits is high, and if the intrinsic reproductive rate is low for one of the two species. A mechanistic explanation of why mutualists increase when the dispersal is limited is given by showing that mutualist pairs of the two species at the same lattice site rapidly increase at the initial phase of the invasion.

This paper is concerned with modeling mutualism between two populations, where one of the mutualisms indirectly occurs through environmental protection. The model consists of a system of three ordinary differential equations, incorporating threshold populations in order for mutualism to occur. A stability analysis of equilibria is carried out. In addition it is shown that in one of the cases, periodic solutions could occur.

It has been claimed that the market fosters selfishness and thereby undermines the moral basis of society. This thesis has been developed with an emphasis on market exchange. Everyday life is, however, predominantly shaped by interactions in the workplace rather than by shopping behaviour. This essay places emphasis on firm organization, rather than market interaction, in moulding cultural traits. Firms emerge in markets and thrive by kindling cooperative attitudes. In this way, the market generates nice traits in an indirect way: it encourages firm organizations that foster mutualism rather than selfishness.

Two basic models of mutualism are presented in which interactions among three species lead to mutualism between two of them. The models represent 2-species predator-prey or competition systems in which a third species acts as a mutualist with either the predator, the prey, or one of the competitors. The models include the assumptions that there is a cost of associating with the mutualist and that the mutualist population grows much more slowly than the other two populations. Special cases of these two models correspond to six qualitatively different types of mutualistic benefit, all of which are known to occur in nature: deterring predation, increasing prey availability, feeding on (or competing with) a predator, increasing competitive interactions, decreasing competitive interactions, and feeding on (or competing with) a competitor. These models and their special cases are subjected to a local stability analysis. The results show that mutualism based upon deterring predation, competing with a predator, or decreasing competitive interactions enhances local stability, while mutualism based upon increasing prey availability or increasing competitive interactions reduces local stability. These results clearly reject the idea that mutualism is an inherently unstable process, and reinforces the idea that each different kind of mutualism will have to be considered separately. Compared to 2-species models of mutualism, the 3-species models provide a more realistic representation of the structure of many mutualistic systems, the mechanisms by which one species benefits another, and the regulation of the interaction.

Mutualism arises in many qualitatively different ways, but previous 2-species models of mutualism correspond to only a few of these. Following Addicott and Freedman (1983), we present two models of mutualism in which interactions among three species lead to mutualism between two of them. One model involves interactions among a predator, a mutualist-prey, and a mutualist, while the other involves interactions among a competitor, a mutualist-competitor, and a mutualist. Given biologically reasonable constraints upon the functions in the model, we present (1) the conditions for boundedness of solutions, (2) the equilibria and their local stability, and (3) the conditions for the existence of small amplitude periodic solutions, a behavior not predicted by 2-species models of mutualism. The models include costs to the mutualist-prey or mutualist-competitor of associating with the mutualist. Analysis of special cases shows that mutualism can cause the extinction of the predator, or the reversal of competitive outcomes.

The Lotka-Volterra model of mutualism is extended to cases involving positive density-dependence. These may include such biological situations as social facilitation of breeding, predator satiation, or the joint maintenance of mutualists. Allowing both negative and positive density-dependence there are a total of 20 biologically feasible cases. In all but two of these cases, it is predicted that when a population of one mutualist is found alone, the other mutualist population will be able to increase from a small population of invaders. The exceptional cases are likely to be rare. Thus the existence of one mutualist in a habitat will generally indicate the possibility of introducing the other successfully. This prediction can be readily tested; it also may be important in practical situations involving mutualism, such as nodulation and mycorrhizal formation in agriculture and forestry. As in previous models of mutualism, the outcome is not related to the existence of stable equilibria.

An apparently mutualistic association between Metastrongylus apri and M. pudendotectus , described on the basis of field and experimental infections of swine, is analyzed using a compartment model. Exploration of the model suggests that M. apri may be facultative mutualist and M. pudendotectus , and obligate mutualist.

We present a general model for three interacting populations, where one population, called a mutualist, benefits a predator in its interaction with the prey. Biologically, there are four different ways in which the mutualist could benefit the predator: by enhancing prey growth rate, by enhancing the rate of prey capture, by providing an alternative food supply for the predator, and by enhancing the efficiency of utilization of prey, once they are ingested. We discuss examples of each type of interaction. We restrict our model to those situations in which the predator cannot survive on the prey in the absence of the mutualist. Therefore, if mutualism exists, it is obligate for the predator. Other conditions of the model include the dynamics of the prey and the mutualist alone and together in the absence of the predator. Given additional reasonable restrictions on the model, we determine the conditions for persistence, where persistence is defined as the continued existence of all three populations without any of them going extinct. There are two ways in which survival may arise in these models. Under one set of conditions, which is equivalent to the predator being able to invade a prey-mutualist system when rare, persistence will occur for any set of positive critical population sizes. Alternatively, survival will occur if there is an asymptotically stable interior equilibrium. However, the conditions for this are complex, and survival may occur only for initial populations in a limited region around the equilibrium.