Time delays shape the eco-evolutionary dynamics of cooperation.

We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner's dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems.

Eco-evolutionary cyclic dominance among predators, prey, and parasites.

Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.

Synthesis, bio-physical and anti-leishmanial studies of some novel indolo[3,2-a]phenanthridine derivatives.

Eight indolo[3,2-a]phenanthridine derivatives have been synthesized in a regioselective manner involving intramolecular Heck-type arylation as a key step. The compounds display interesting photophysical proprties and hence evaluated for their ability to interact with ct-DNA. Preliminary biophysical studies via UV and Fluorescence spectrophotometric titration with ct-DNA, and dye displacement studies with well known intercalator ethidium bromide and the groove binder Hoechst 33,258 reveal that the binding mode is probably minor groove binding. The prepared indolophenanthridine derivatives have also been evaluated as anti-leishmanial agents for the first time. MTT-assays for cell cytotoxicity against Leishmania promastigotes and Leishmania amastigotes were studied with the compounds 10b-f, 12-14 for the determination of their IC50 values. Cytotoxicity was determined using a murine RAW 264.7 cell line and human embryonic kidney cell line HEK 293. In L. donovani amastigote assay, compounds 10e, 10f and 12 showed good activity with relatively low cytotoxicity against RAW 264.7, resulting in acceptable selectivity indices. Selectivity index determination indicated compounds to be potent anti-leishmanial agents while 10b, 10c and 14 showed moderate selectivity index. Moreover, cell-cycle analysis of four different compounds 10b, 12, 13 and 14, representative of each group, was performed by FACS as an attempt to understand the mechanism of actions of these different sub-classes of the compounds on Leishmania.

Identification of two novel thiophene analogues as inducers of autophagy mediated cell death in breast cancer cells.

Natural compounds isolated from different medicinal plants remain one of the major resources of anticancer drugs due to their enormous chemical diversity. Studies suggested therapeutic potential for various tanshinones, key bioactive lipophilic compounds from the root extracts of Salvia miltiorrhiza Bunge, against multiple cancers including breast carcinoma. We designed, synthesized and evaluated anti-cancer properties of a series of condensed and doubly condensed furophenanthraquinones of tanshinone derivatives on two breast cancer lines - MCF7 and MDA-MB-231. We identified two thiophene analogues - compounds 48 and 52 with greater anti-proliferative efficiency (~4 fold) as compared to the natural tanshinones. Mechanistically, we showed that both compounds induced autophagy mediated cell death and partial but significant restoration of cell death in the presence of autophagy inhibitor further supported this notion. Both compounds transcriptionally activated several autophagy genes responsible for autophagosome formation along with two death regulators - GADD34 and CHOP for inducing cell death. Altogether, our studies provide strong evidence to support compounds 48 and 52 as promising leads for further development as anticancer agents through modulating autophagy mechanism.

Eco-evolutionary dynamics of cooperation in the presence of policing.

Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.

Dynamics and spatio-temporal patterns in a prey-predator system with aposematic prey.

We analyze the impact of aposematic time and searching efficiency of prey on the temporal and spatio-temporal dynamics of a diffusive prey-predator system. Here, our assumption is that the prey population primarily invests its total time in two activities-(i) defense against predation and (ii) searching for food, followed by growth-induced reproduction, whereas, predators do not involve in self-defense. Moreover, we consider that the reproduction rate of prey and the rate of predation have a negative linear correlation with the amount of time invested for aposematism. Based on the presump- tions, we find that unlike searching efficiency of prey, the aposematic time can diminish the proportion in which prey and predator coexist when it crosses a certain threshold, and at the extreme aposematism, the entire population drives into the extinction. The proposed dynamics undergoes Hopf-bifurcation with respect to the searching efficiency of prey. We examine the individual effect of aposematic time and searching efficiency on the formation of regular Turing patterns-the low to medium to high val-ues of defense-time and food searching efficiency generate 'spots' to 'stripes' to 'holes' pattern, re-spectively; however, the combined impact of both presents only non-Turing 'spot' pattern with the 'predominance of predators,' which happens through the Turing-Hopf bifurcation.

Supercritical and subcritical Hopf-bifurcations in a two-delayed prey-predator system with density-dependent mortality of predator and strong Allee effect in prey.

One of the possible ways to visualize the effect of intra- and inter-species synergistic and antagonistic interactions in a natural ecosystem is the detailed analysis of the underlying prey-predator model, and the subsequent analytical findings may provide a definite justification towards the species coexistence, which often maintains biodiversity in nature. Here, our central motivation is to understand the combined effect of the Allee threshold and intra-species competition on the evolution of interacting species, which often experience delays in evolution due to its complex ecological and physiological processes. Therefore, in the present paper, we extensively analyze the stability of a two-delayed prey-predator system in the presence of strong Allee effects in prey and intra-species competition in predator. In addition, we capture the reality of time difference between the lifespan of the prey and predator through proper nondimensionalization. The two delays in the proposed retarded system correspond to the intra-specific competition-induced feedback time lag to the prey and predator gestation period. In the absence of intra-predator competition, the present dynamics unveils supercritical Hopf-bifurcation around the interior point of coexistence which is in-line with the existing literature. It is noteworthy to mention that the proposed Allee system exhibits subcritical Hopf-bifurcation in the presence of intra-species competition in predator. We confirm the occurrence of both supercritical and subcritical Hopf-bifurcations via calculating the direction and stability of Hopf-bifurcating periodic solutions using the normal form method and the center manifold theory. Moreover, the suggested delayed schema presents supercritical Hopf-bifurcation at the boundary steady-state, where the population density of prey exists at its maximum carrying capacity. We recognize the bistability between extinction and coexistence, and the proposed model also exhibits the 'chaotic concurrence between prey and predator,' which happens through the period-doubling bifurcation. The existence of chaos is validated using the estimated power spectrum and the spectrum of Lyapunov exponents. The primary finding of this paper is that Allee threshold induces the capability to the density-dependent death rate of predator towards changing the stability of 'oscillatory coexistence between prey and predator.'

Dynamics of cancer progression and suppression: A novel evolutionary game theory based approach.

In this paper, a novel mathematical approach is proposed for the dynamics of progression and suppression of cancer. We define mutant cell density, ρ(µ) (µ × ρ), as a primary factor in cancer dynamics, and use logistic growth model and replicator equation for defining the dynamics of total cell density (ρ) and mutant fraction (µ), respectively. Furthermore, in the proposed model, we introduce an analytical expression for a control parameter D (drug), to suppress the proliferation of mutants with extra fitness level σ. Lastly, we present a comparison of the proposed model with some existing models of tumour growth.