Daniel Maxin | Valparaiso University (original) (raw)
Papers by Daniel Maxin
Journal of Theoretical Biology, Aug 1, 2010
Divorce appears to be one of the least studied demographic processes, both empirically and in two... more Divorce appears to be one of the least studied demographic processes, both empirically and in two-sex demographic models. In this paper, we study mathematical as well as biological implications of the assumption that the divorce rate is positively affected by the amount of single (i.e., unmarried/unpaired) individuals in the population. We do that by modifying the classical exponential two-sex model accounting for pair formation and separation. We model the divorce rate as an increasing function of the single population size and show that the single population pressure on the established couples alters the exponential behavior of the classical model in which the divorce rate is assumed constant. In particular, the total population size becomes bounded and a unique positive equilibrium exists. In addition, a Hopf bifurcation analysis around the positive equilibrium shows that the modified model may exhibit sustained oscillations.
DOAJ (DOAJ: Directory of Open Access Journals), Oct 1, 2015
We present results from two recent mathematical biology studies that address the effect of riskta... more We present results from two recent mathematical biology studies that address the effect of risktaking behavior on epidemic models. We show that when risk-taking prevails over risk-avoidance, it is possible to show a detrimental and counterintuitive effect from increasing vaccination and treatment rates over certain critical time intervals. In addition, when risk-taking has a cumulative effect within the population, a lower transmission rate from diagnosed infected individuals may prevent the intended effect of vaccination.
We describe several population models exposed to a mild lifelong sexually transmitted disease, i.... more We describe several population models exposed to a mild lifelong sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify these models to include non-reproductive groups consisting of those isolated from sexual contact and those who are sexually active but infertile due to choice, medical or other reasons. We analyze the potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels. We also analyze the difference between being sexually active and abstained within the non-reproductive class and its impact on the epidemic reproductive number and the nature of the bifurcation around the disease-free equilibrium. We provide a comparison with our models introduced in a previous paper which include only the isolated from sexual contact class.
Nonlinearity, Nov 9, 2017
We establish boundedness results for a model of mutualism with an arbitrary number of species whi... more We establish boundedness results for a model of mutualism with an arbitrary number of species which encompasses several classic two-species models, even when extended to their respective multidimensional versions. These conditions are obtained under fairly general assumptions on the mathematical form of the functions modelling the mutualistic interactions and are expressed in terms of reproductive ratios at high population densities introduced ad hoc. We then discuss particular cases in which there is a single threshold parameter separating boundedness from unboundedness. The situation in which the unboundedness is caused by a particular subset of species is also of concern.
International Journal of Biomathematics, Feb 20, 2017
We analyze the global stability of the coexisting equilibria for several models of commensalism, ... more We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.
Journal of Theoretical Biology, Feb 1, 2014
Host manipulation by sexually transmitted parasites which increases host mating rate and thus par... more Host manipulation by sexually transmitted parasites which increases host mating rate and thus parasite transmission rate has long been viewed as a plausible parasite adaptation. However, empirical evidence for it is rare. Here, using an adaptive dynamics approach to evolution, we explore conditions under which such diseaseinduced mating enhancement is (or is not) likely to occur. We find that increased mating success is less likely to evolve if the host reproduction rate, or the baseline disease transmission rate, are reduced, and the parasite affects just one sex, compared to when it affects both. We also find that it is less likely to evolve if the virulence-transmission trade-off curve is stronger, since we assume that enhanced disease transmission can only be achieved at the cost of increased virulence and as this trade-off is concave. In addition, we demonstrate that if disease-induced mating enhancement is equally acting in both sexes the mating system has no effect
Journal of Mathematical Biology, Jun 28, 2011
Sterilizing pathogens are commonly assumed not to affect longevity of infected individuals, and i... more Sterilizing pathogens are commonly assumed not to affect longevity of infected individuals, and if they do then negatively. Examples abound, however, of species in which the absence of reproduction actually increases life expectancy. This happens because by decreasing the energy outlay on reproduction individuals with lowered reproduction can live longer. Alternatively, fertile individuals are more susceptible to predators or parasitoids if the latter can capitalize on mating signals of the former. Here we develop and analyze an SI epidemiological model to explore whether and to what extent does such a life expectancy prolongation due to sterilizing pathogens affect host dynamics. In particular, we are interested in an added value of increased life expectancy on the possibility of successful pest control, that is, the effect of increased lifespan and hence increased potential of the infected individuals to spread the disease on pest control effectiveness. We show that although the parameter range in which we observe an effect of increased lifespan of the sterilized individuals is not large, the effect itself can be significant. In particular, the increase in pest control effectiveness can be very dramatic when disease transmission efficiency is close to birth rate, mortality rate of susceptibles is relatively high (i.e., the species is relatively shortlived), and sterilization efficiency is relatively high. Our results thus characterize pathogens that are promising candidates for an effective pest control and that might possibly be engineered if not occurring naturally.
Journal of Applied Ecology, Mar 29, 2016
1. Continual effort is needed to reduce the impact of exotic species in the context of increased ... more 1. Continual effort is needed to reduce the impact of exotic species in the context of increased globalization. Any innovation in this respect would be an asset. 2. We assess the potential of combining two pest control techniques: the well-established sterile insect technique (SIT) and a novel male-killing technique (MKT), which comprises inoculation of a pest population with bacteria that kill the infected male embryos. 3. Population models are developed to assess the efficiency of using the MKT for insect pest control, either alone or together with the SIT. We seek for conditions under which the MKT weakens requirements on the SIT. 4. Regarding the SIT, we consider both non-heritable and inherited sterility. In both cases, the MKT and SIT benefit one another. The MKT may prevent the SIT from failing when not enough sterilized males are released due to high production costs and/or uncertainty on their mating ability following a high irradiation dose. Conversely, with already established SIT, pest eradication can be achieved after introduction of male-killing bacteria with lower vertical transmission efficiency than if the MKT was applied alone. 5. For tephritid fruit flies with non-heritable sterility, maximal impact of the SIT is achieved when the released males are fully sterile. Conversely, for lepidopterans with inherited sterility, maximal impact of the SIT is achieved for intermediate irradiation doses. In both cases, increasing vertical transmission efficiency of male-killing bacteria benefits the SIT; high enough vertical transmission efficiency allows for pest eradication where the SIT is absent or induces only pest suppression when used alone. 6. Synthesis and applications. While both techniques can suppress or eliminate the pest on their own, combined application of the male-killing technique and the sterile insect technique substantially increases pest control efficiency. If male-killing bacteria are already established in the pest, any assessment of the sterile insect technique needs to account for their presence; otherwise, management recommendations could be exaggerated and unnecessarily costly.
Journal of Mathematical Biology, Jun 15, 2014
We analyze the effect of sterilization in the infected hosts in several epidemiological models in... more We analyze the effect of sterilization in the infected hosts in several epidemiological models involving infectious diseases that can be transmitted both vertically and horizontally. Sterilizing pathogens can be used as pest control agents by intentionally inoculating the target population, with the goal of reducing or eliminating it completely. Contrary to previous models that did not include vertical transmission we found that the population size at the endemic equilibrium may actually increase with higher levels of sterility. This effect is proved to exist for low to high efficiencies of vertical transmission. On the other hand, if the disease is sexually transmitted and the host reproduction and disease transmission are both consistently mediated by mating,
We study the demographic and epidemiological effects of isolation from reproduction in heterogene... more We study the demographic and epidemiological effects of isolation from reproduction in heterogeneous populations. We aim at establishing under what conditions the isolation from reproduction and/or sexual activity can cause the population to go extinct or to reach a disease free ...
Journal of Theoretical Biology, 2012
Individuals often stop reproducing some time before they die. In this paper we compose and analyz... more Individuals often stop reproducing some time before they die. In this paper we compose and analyze a logistic, two-sex population model in which individuals form pairs just to mate (i.e. pair bonds are ephemeral) and later move on to sexually abstaining groups. Using this model, we study the impact of sexually abstaining groups on persistence of a benign sexually transmitted infection (STI) in populations with such ephemeral pair bonds. We observe that the presence of sexually abstaining groups cannot prevent an STI from invasion or eliminate it when already present if the transition rates to the sexually abstaining groups are independent of the infection status of individuals (susceptible or infected). On the other hand, if they depend on that status, the presence of sexually abstaining groups can prevent an STI from invasion or eliminate it when present. Specifically, in the simple case of sex-independent vital parameters, this happens if the transition rate of the
Proceedings of The Royal Society B: Biological Sciences, Nov 7, 2015
Early male-killing (MK) bacteria are vertically transmitted reproductive parasites which kill mal... more Early male-killing (MK) bacteria are vertically transmitted reproductive parasites which kill male offspring that inherit them. Whereas their incidence is well documented, characteristics allowing originally non-MK bacteria to gradually evolve MK ability remain unclear. We show that horizontal transmission is a mechanism enabling vertically transmitted bacteria to evolve fully efficient MK under a wide range of host and parasite characteristics, especially when the efficacy of vertical transmission is high. We also show that an almost 100% vertically transmitted and 100% effective male-killer may evolve from a purely horizontally transmitted non-MK ancestor, and that a 100% efficient male-killer can form a stable coexistence only with a non-MK bacterial strain. Our findings are in line with the empirical evidence on current MK bacteria, explain their high efficacy in killing infected male embryos and their variability within and across insect taxa, and suggest that they may have evolved independently in phylogenetically distinct species.
Journal of Mind and Medical Sciences
We propose a computer modeling approach for SARS-CoV-2 transmission that can be preferable to a p... more We propose a computer modeling approach for SARS-CoV-2 transmission that can be preferable to a purely mathematical framework. It is illustrated its functionality in a specific case of indoor transmission. Based on literature, we assume that infection is due to aerosols with viral particles that persist and accumulate for hours in the air even after the persons who produced them left the space. We incorporate also restricted opening hours as a mitigation measure and one possible behavioral change in response to this measure. It is shown via several examples how this algorithmic modeling approach can be used to run various scenarios in order to predict the efficacy of the intervention.
Le Centre pour la Communication Scientifique Directe - HAL - Inria, 2022
International Journal of Biomathematics, 2017
We analyze the global stability of the coexisting equilibria for several models of commensalism, ... more We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher-order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.
Mathematical Biosciences and Engineering, 2015
We analyze the dynamics of three models of mutualism, establishing the global stability of coexis... more We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.
We establish boundedness results for a model of mutualism with an arbitrary number of species whi... more We establish boundedness results for a model of mutualism with an arbitrary number of species which encompasses several classic two-species models, even when extended to their respective multidimensional versions. These conditions are obtained under fairly general assumptions on the mathematical form of the functions modelling the mutualistic interactions and are expressed in terms of reproductive ratios at high population densities introduced ad hoc. We then discuss particular cases in which there is a single threshold parameter separating boundedness from unboundedness. The situation in which the unboundedness is caused by a particular subset of species is also of concern
Journal of Biological Dynamics, 2017
Many models of mutualism have been proposed and studied individually. In this paper, we develop a... more Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation. Our generalization also allows each of the mutualists to be subject to a weak Allee effect. Moreover, we find that if one of the interacting species is subject to a strong Allee effect, then the mutualism can overcome it and cause a unique coexistence equilibrium to be globally stable.
Journal of Theoretical Biology, Aug 1, 2010
Divorce appears to be one of the least studied demographic processes, both empirically and in two... more Divorce appears to be one of the least studied demographic processes, both empirically and in two-sex demographic models. In this paper, we study mathematical as well as biological implications of the assumption that the divorce rate is positively affected by the amount of single (i.e., unmarried/unpaired) individuals in the population. We do that by modifying the classical exponential two-sex model accounting for pair formation and separation. We model the divorce rate as an increasing function of the single population size and show that the single population pressure on the established couples alters the exponential behavior of the classical model in which the divorce rate is assumed constant. In particular, the total population size becomes bounded and a unique positive equilibrium exists. In addition, a Hopf bifurcation analysis around the positive equilibrium shows that the modified model may exhibit sustained oscillations.
DOAJ (DOAJ: Directory of Open Access Journals), Oct 1, 2015
We present results from two recent mathematical biology studies that address the effect of riskta... more We present results from two recent mathematical biology studies that address the effect of risktaking behavior on epidemic models. We show that when risk-taking prevails over risk-avoidance, it is possible to show a detrimental and counterintuitive effect from increasing vaccination and treatment rates over certain critical time intervals. In addition, when risk-taking has a cumulative effect within the population, a lower transmission rate from diagnosed infected individuals may prevent the intended effect of vaccination.
We describe several population models exposed to a mild lifelong sexually transmitted disease, i.... more We describe several population models exposed to a mild lifelong sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify these models to include non-reproductive groups consisting of those isolated from sexual contact and those who are sexually active but infertile due to choice, medical or other reasons. We analyze the potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels. We also analyze the difference between being sexually active and abstained within the non-reproductive class and its impact on the epidemic reproductive number and the nature of the bifurcation around the disease-free equilibrium. We provide a comparison with our models introduced in a previous paper which include only the isolated from sexual contact class.
Nonlinearity, Nov 9, 2017
We establish boundedness results for a model of mutualism with an arbitrary number of species whi... more We establish boundedness results for a model of mutualism with an arbitrary number of species which encompasses several classic two-species models, even when extended to their respective multidimensional versions. These conditions are obtained under fairly general assumptions on the mathematical form of the functions modelling the mutualistic interactions and are expressed in terms of reproductive ratios at high population densities introduced ad hoc. We then discuss particular cases in which there is a single threshold parameter separating boundedness from unboundedness. The situation in which the unboundedness is caused by a particular subset of species is also of concern.
International Journal of Biomathematics, Feb 20, 2017
We analyze the global stability of the coexisting equilibria for several models of commensalism, ... more We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.
Journal of Theoretical Biology, Feb 1, 2014
Host manipulation by sexually transmitted parasites which increases host mating rate and thus par... more Host manipulation by sexually transmitted parasites which increases host mating rate and thus parasite transmission rate has long been viewed as a plausible parasite adaptation. However, empirical evidence for it is rare. Here, using an adaptive dynamics approach to evolution, we explore conditions under which such diseaseinduced mating enhancement is (or is not) likely to occur. We find that increased mating success is less likely to evolve if the host reproduction rate, or the baseline disease transmission rate, are reduced, and the parasite affects just one sex, compared to when it affects both. We also find that it is less likely to evolve if the virulence-transmission trade-off curve is stronger, since we assume that enhanced disease transmission can only be achieved at the cost of increased virulence and as this trade-off is concave. In addition, we demonstrate that if disease-induced mating enhancement is equally acting in both sexes the mating system has no effect
Journal of Mathematical Biology, Jun 28, 2011
Sterilizing pathogens are commonly assumed not to affect longevity of infected individuals, and i... more Sterilizing pathogens are commonly assumed not to affect longevity of infected individuals, and if they do then negatively. Examples abound, however, of species in which the absence of reproduction actually increases life expectancy. This happens because by decreasing the energy outlay on reproduction individuals with lowered reproduction can live longer. Alternatively, fertile individuals are more susceptible to predators or parasitoids if the latter can capitalize on mating signals of the former. Here we develop and analyze an SI epidemiological model to explore whether and to what extent does such a life expectancy prolongation due to sterilizing pathogens affect host dynamics. In particular, we are interested in an added value of increased life expectancy on the possibility of successful pest control, that is, the effect of increased lifespan and hence increased potential of the infected individuals to spread the disease on pest control effectiveness. We show that although the parameter range in which we observe an effect of increased lifespan of the sterilized individuals is not large, the effect itself can be significant. In particular, the increase in pest control effectiveness can be very dramatic when disease transmission efficiency is close to birth rate, mortality rate of susceptibles is relatively high (i.e., the species is relatively shortlived), and sterilization efficiency is relatively high. Our results thus characterize pathogens that are promising candidates for an effective pest control and that might possibly be engineered if not occurring naturally.
Journal of Applied Ecology, Mar 29, 2016
1. Continual effort is needed to reduce the impact of exotic species in the context of increased ... more 1. Continual effort is needed to reduce the impact of exotic species in the context of increased globalization. Any innovation in this respect would be an asset. 2. We assess the potential of combining two pest control techniques: the well-established sterile insect technique (SIT) and a novel male-killing technique (MKT), which comprises inoculation of a pest population with bacteria that kill the infected male embryos. 3. Population models are developed to assess the efficiency of using the MKT for insect pest control, either alone or together with the SIT. We seek for conditions under which the MKT weakens requirements on the SIT. 4. Regarding the SIT, we consider both non-heritable and inherited sterility. In both cases, the MKT and SIT benefit one another. The MKT may prevent the SIT from failing when not enough sterilized males are released due to high production costs and/or uncertainty on their mating ability following a high irradiation dose. Conversely, with already established SIT, pest eradication can be achieved after introduction of male-killing bacteria with lower vertical transmission efficiency than if the MKT was applied alone. 5. For tephritid fruit flies with non-heritable sterility, maximal impact of the SIT is achieved when the released males are fully sterile. Conversely, for lepidopterans with inherited sterility, maximal impact of the SIT is achieved for intermediate irradiation doses. In both cases, increasing vertical transmission efficiency of male-killing bacteria benefits the SIT; high enough vertical transmission efficiency allows for pest eradication where the SIT is absent or induces only pest suppression when used alone. 6. Synthesis and applications. While both techniques can suppress or eliminate the pest on their own, combined application of the male-killing technique and the sterile insect technique substantially increases pest control efficiency. If male-killing bacteria are already established in the pest, any assessment of the sterile insect technique needs to account for their presence; otherwise, management recommendations could be exaggerated and unnecessarily costly.
Journal of Mathematical Biology, Jun 15, 2014
We analyze the effect of sterilization in the infected hosts in several epidemiological models in... more We analyze the effect of sterilization in the infected hosts in several epidemiological models involving infectious diseases that can be transmitted both vertically and horizontally. Sterilizing pathogens can be used as pest control agents by intentionally inoculating the target population, with the goal of reducing or eliminating it completely. Contrary to previous models that did not include vertical transmission we found that the population size at the endemic equilibrium may actually increase with higher levels of sterility. This effect is proved to exist for low to high efficiencies of vertical transmission. On the other hand, if the disease is sexually transmitted and the host reproduction and disease transmission are both consistently mediated by mating,
We study the demographic and epidemiological effects of isolation from reproduction in heterogene... more We study the demographic and epidemiological effects of isolation from reproduction in heterogeneous populations. We aim at establishing under what conditions the isolation from reproduction and/or sexual activity can cause the population to go extinct or to reach a disease free ...
Journal of Theoretical Biology, 2012
Individuals often stop reproducing some time before they die. In this paper we compose and analyz... more Individuals often stop reproducing some time before they die. In this paper we compose and analyze a logistic, two-sex population model in which individuals form pairs just to mate (i.e. pair bonds are ephemeral) and later move on to sexually abstaining groups. Using this model, we study the impact of sexually abstaining groups on persistence of a benign sexually transmitted infection (STI) in populations with such ephemeral pair bonds. We observe that the presence of sexually abstaining groups cannot prevent an STI from invasion or eliminate it when already present if the transition rates to the sexually abstaining groups are independent of the infection status of individuals (susceptible or infected). On the other hand, if they depend on that status, the presence of sexually abstaining groups can prevent an STI from invasion or eliminate it when present. Specifically, in the simple case of sex-independent vital parameters, this happens if the transition rate of the
Proceedings of The Royal Society B: Biological Sciences, Nov 7, 2015
Early male-killing (MK) bacteria are vertically transmitted reproductive parasites which kill mal... more Early male-killing (MK) bacteria are vertically transmitted reproductive parasites which kill male offspring that inherit them. Whereas their incidence is well documented, characteristics allowing originally non-MK bacteria to gradually evolve MK ability remain unclear. We show that horizontal transmission is a mechanism enabling vertically transmitted bacteria to evolve fully efficient MK under a wide range of host and parasite characteristics, especially when the efficacy of vertical transmission is high. We also show that an almost 100% vertically transmitted and 100% effective male-killer may evolve from a purely horizontally transmitted non-MK ancestor, and that a 100% efficient male-killer can form a stable coexistence only with a non-MK bacterial strain. Our findings are in line with the empirical evidence on current MK bacteria, explain their high efficacy in killing infected male embryos and their variability within and across insect taxa, and suggest that they may have evolved independently in phylogenetically distinct species.
Journal of Mind and Medical Sciences
We propose a computer modeling approach for SARS-CoV-2 transmission that can be preferable to a p... more We propose a computer modeling approach for SARS-CoV-2 transmission that can be preferable to a purely mathematical framework. It is illustrated its functionality in a specific case of indoor transmission. Based on literature, we assume that infection is due to aerosols with viral particles that persist and accumulate for hours in the air even after the persons who produced them left the space. We incorporate also restricted opening hours as a mitigation measure and one possible behavioral change in response to this measure. It is shown via several examples how this algorithmic modeling approach can be used to run various scenarios in order to predict the efficacy of the intervention.
Le Centre pour la Communication Scientifique Directe - HAL - Inria, 2022
International Journal of Biomathematics, 2017
We analyze the global stability of the coexisting equilibria for several models of commensalism, ... more We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher-order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.
Mathematical Biosciences and Engineering, 2015
We analyze the dynamics of three models of mutualism, establishing the global stability of coexis... more We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.
We establish boundedness results for a model of mutualism with an arbitrary number of species whi... more We establish boundedness results for a model of mutualism with an arbitrary number of species which encompasses several classic two-species models, even when extended to their respective multidimensional versions. These conditions are obtained under fairly general assumptions on the mathematical form of the functions modelling the mutualistic interactions and are expressed in terms of reproductive ratios at high population densities introduced ad hoc. We then discuss particular cases in which there is a single threshold parameter separating boundedness from unboundedness. The situation in which the unboundedness is caused by a particular subset of species is also of concern
Journal of Biological Dynamics, 2017
Many models of mutualism have been proposed and studied individually. In this paper, we develop a... more Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation. Our generalization also allows each of the mutualists to be subject to a weak Allee effect. Moreover, we find that if one of the interacting species is subject to a strong Allee effect, then the mutualism can overcome it and cause a unique coexistence equilibrium to be globally stable.