Negative Frequency Dependence Research Articles

Microbial Dormancy Supports Multi-Species Coexistence Under Resource Fluctuations.

The ability for microbes to enter dormant states is adaptive under resource fluctuations and has been linked to the maintenance of diversity. Nevertheless, the mechanism by which microbial dormancy gives rise to the density-dependent feedbacks required for stable coexistence under resource fluctuations is not well understood. Via analysis of consumer-resource models, we show that the stable coexistence of dormancy and non-dormancy strategists is a consequence of the former benefiting more from resource fluctuations while simultaneously reducing overall resource variability, which sets up the requisite negative frequency dependence. Moreover, we find that dormants can coexist alongside gleaner and opportunist strategies in a competitive-exclusion-defying case of three species coexistence on a single resource. This multi-species coexistence is typically characterised by non-simple assembly rules that cannot be predicted from pairwise competition outcomes. The diversity maintained via this three-way trade-off represents a novel phenomenon that is ripe for further theoretical and empirical inquiry.

Effects of Seed Size and Frequency on Seed Dispersal and Predation by Small Mammals.

Frequency-dependent predation is common in predator-prey interactions. Size is an important characteristic of seeds and is crucial in the regeneration stage of plant seeds. However, the frequency dependence of animal predation on seed size has not been reported. In this study, we conducted a field experiment and used different sizes of Liaodong oak (Quercus wutaishanica) seeds to test the frequency dependence of intraspecific seed size selection in rodents. We used the number ratio of large to small seeds as the frequency. The results show that the rate of small seeds being eaten in situ was significantly higher than that of large seeds (p < 0.05). The rates of different-sized seeds being eaten after removal decreased with increasing frequencies, and there was no significant difference between frequencies except for 1:9 and 9:1. The rates of large seeds being scatter-hoarded were significantly higher than those of small seeds at different frequencies (p < 0.05). The eating distances after removal of large seeds were significantly longer than those of small seeds at the same frequencies (p < 0.05). Furthermore, the scatter-hoarding distances of large seeds were significantly longer than those of small seeds at three frequencies (1:9, 3:7, and 9:1) (p < 0.05). That is, rodents consumed more small seeds in situ, dispersed and scatter-hoarded more large seeds, and dispersed large seeds over longer distances. Rodents exhibited a negative frequency dependence for small seeds and a positive frequency dependence for large seeds on being eaten in situ. Moreover, rodents exhibited a negative frequency dependence for large seeds and a positive frequency dependence for small seeds on being eaten after removal and scatter-hoarding. These results reveal the frequency dependence of rodent selection on seed size and provide new insights into animal-mediated seed dispersal and the regeneration of plant populations.

When does antimicrobial resistance increase bacterial fitness? Effects of dosing, social interactions, and frequency dependence on the benefits of AmpC β-lactamases in broth, biofilms, and a gut infection model.

One of the longstanding puzzles of antimicrobial resistance is why the frequency of resistance persists at intermediate levels. Theoretical explanations for the lack of fixation of resistance include cryptic costs of resistance or negative frequency-dependence but are seldom explored experimentally. β-lactamases, which detoxify penicillin-related antibiotics, have well-characterized frequency-dependent dynamics driven by cheating and cooperation. However, bacterial physiology determines whether β-lactamases are cooperative, and we know little about the sociality or fitness of β-lactamase producers in infections. Moreover, media-based experiments constrain how we measure fitness and ignore important parameters such as infectivity and transmission among hosts. Here, we investigated the fitness effects of broad-spectrum AmpC β-lactamases in Enterobacter cloacae in broth, biofilms, and gut infections in a model insect. We quantified frequency- and dose-dependent fitness using cefotaxime, a third-generation cephalosporin. We predicted that infection dynamics would be similar to those observed in biofilms, with social protection extending over a wide dose range. We found evidence for the sociality of β-lactamases in all contexts with negative frequency-dependent selection, ensuring the persistence of wild-type bacteria, although cooperation was less prevalent in biofilms, contrary to predictions. While competitive fitness in gut infections and broth had similar dynamics, incorporating infectivity into measurements of fitness in infections significantly affected conclusions. Resistant bacteria had reduced infectivity, which limited the fitness benefits of resistance to infections challenged with low antibiotic doses and low initial frequencies of resistance. The fitness of resistant bacteria in more physiologically tolerant states (in biofilms, in infections) could be constrained by the presence of wild-type bacteria, high antibiotic doses, and limited availability of β-lactamases. One conclusion is that increased tolerance of β-lactams does not necessarily increase selection pressure for resistance. Overall, both cryptic fitness costs and frequency dependence curtailed the fitness benefits of resistance in this study.

Evolution of individual variation in a competitive trait: a theoretical analysis.

When competitive traits are costly, negative frequency dependence can maintain genetic variance. Most theoretical studies examining this problem assume binary polymorphisms, yet most trait variation in wild populations is continuous. We propose that continuous trait variation can result from continuous variation in resource quality and that, specifically, the shape of the resource distribution determines trait maintenance. We used an individual-based model to test which conditions favour the stable maintenance of variation and which cause temporal fluctuations in trait values. This approach, inspired by contrasting outcomes of previous studies regarding variance and fluctuations in trait values, clearly showed a decisive role played by the shape of resource distributions. Under extreme conditions, e.g., the absence of resource variation or with very scarce resources for weak competitors, traits evolved to a single non-competitive or highly competitive strategy, respectively. Most other distributions led to strong temporal fluctuations on trait values or the maintenance of stable, standing variation. Our results thus explain the contradicting outcomes of previous theoretical studies and, at the same time, provide hypotheses to explain the maintenance of genetic variation and individual differences. We suggest ways to empirically test the proposed effects of resource variation on trait maintenance.

Intrinsic and scattering attenuations of the Sichuan-Yunnan region in China from S coda waves

Seismic attenuation is a fundamental property of the Earth's media. Attenuation structure for the complicated geological structures with strong seismicity in the Sichuan-Yunnan region is poorly studied. In this study, we collected 108,399 waveforms of 11,517 local small earthquakes with magnitudes between 1.5 and 3.5 from January 2014 to September 2021 in the Sichuan-Yunnan region and its adjacent areas. We employed an envelope inversion technique for separating the intrinsic and scattering attenuations of the S coda wave, and obtained the intrinsic and scattering attenuation structures for frequencies between 0.25 and 8.00 Hz. The attenuation structures correlate well with the geological units, and some major faults mark the attenuation variations where historic large earthquakes have occurred. The regional average attenuation shows a negative frequency dependence. The average scattering attenuation has a faster descending rate than the average intrinsic attenuation, and is dominant at low frequencies, while at high frequencies the average intrinsic attenuation is stronger. The lateral variation in the intrinsic attenuation is consistent with the variation in heat flow, the scattering attenuation may be related to the scatter distribution and size. The total attenuation is consistent with the previous studies in this region, and the separate intrinsic and scattering attenuation may be useful in understanding regional tectonics and important in earthquake prevention and disaster reduction.

Why cultural distance can promote - or impede - group-beneficial outcomes.

Quantifying the distance between cultural groups has received substantial recent interest. A key innovation, borrowed from population genetics, is the calculation of cultural FST (CFST) statistics on datasets of human culture. Measuring the variance between groups as a fraction of total variance, FST is theoretically important in additive models of cooperation. Consistent with this, recent empirical work has confirmed that high values of pairwise CFST (measuring cultural distance) strongly predict unwillingness to cooperate with strangers in coordination vignettes. As applications for CFST increase, however, there is greater need to understand its meaning in naturalistic situations beyond additive cooperation. Focusing on games with both positive and negative frequency dependence and high-diversity, mixed equilibria, we derive a simple relationship between FST and the evolution of group-beneficial traits across a broad spectrum of social interactions. Contrary to standard assumptions, this model shows why FST can have both positive and negative marginal effects on the spread of group-beneficial traits under certain realistic conditions. These results provide broader theoretical direction for empirical applications of CFST in the evolutionary study of culture.

Evolution of realized niche breadth diversity driven by community dynamics.

Why many herbivorous insects are host plant specialists, with non-negligible exceptions, is a conundrum of evolutionary biology, especially because the host plants are not necessarily optimal larval diets. Here, I present a novel model of host plant preference evolution of two insect species. Because habitat preference evolution is contingent upon demographic dynamics, I integrate the evolutionary framework with the modern coexistence theory. The results show that the two insect species can evolve into a habitat specialist and generalist, when they experience both negative and positive frequency-dependent community dynamics. This happens because the joint action of positive and negative frequency dependence creates multiple (up to nine) eco-evolutionary equilibria. Furthermore, initial condition dependence due to positive frequency dependence allows specialization to poor habitats. Thus, evolved habitat preferences do not necessarily correlate with the performances. The model provides explanations for counterintuitive empirical patterns and mechanistic interpretations for phenomenological models of niche breadth evolution.

Negative frequency dependent selection unites ecology and evolution.

From genes to communities, understanding how diversity is maintained remains a fundamental question in biology. One challenging to identify, yet potentially ubiquitous, mechanism for the maintenance of diversity is negative frequency dependent selection (NFDS), which occurs when entities (e.g., genotypes, life history strategies, species) experience a per capita reduction in fitness with increases in relative abundance. Because NFDS allows rare entities to increase in frequency while preventing abundant entities from excluding others, we posit that negative frequency dependent selection plays a central role in the maintenance of diversity. In this review, we relate NFDS to coexistence, identify mechanisms of NFDS (e.g., mutualism, predation, parasitism), review strategies for identifying NFDS, and distinguish NFDS from other mechanisms of coexistence (e.g., storage effects, fluctuating selection). We also emphasize that NFDS is a key place where ecology and evolution intersect. Specifically, there are many examples of frequency dependent processes in ecology, but fewer cases that link this process to selection. Similarly, there are many examples of selection in evolution, but fewer cases that link changes in trait values to negative frequency dependence. Bridging these two well-developed fields of ecology and evolution will allow for mechanistic insights into the maintenance of diversity at multiple levels.

Ecology, the pace-of-life, epistatic selection and the maintenance of genetic variation in life-history genes.

Evolutionary genetics has long struggled with understanding how functional genes under selection remain polymorphic in natural populations. Taking as a starting point that natural selection is ultimately a manifestation of ecological processes, we spotlight an underemphasized and potentially ubiquitous ecological effect that may have fundamental effects on the maintenance of genetic variation. Negative frequency dependency is a well-established emergent property of density dependence in ecology, because the relative profitability of different modes of exploiting or utilizing limiting resources tends to be inversely proportional to their frequency in a population. We suggest that this may often generate negative frequency-dependent selection (NFDS) on major effect loci that affect rate-dependent physiological processes, such as metabolic rate, that are phenotypically manifested as polymorphism in pace-of-life syndromes. When such a locus under NFDS shows stable intermediate frequency polymorphism, this should generate epistatic selection potentially involving large numbers of loci with more minor effects on life-history (LH) traits. When alternative alleles at such loci show sign epistasis with a major effect locus, this associative NFDS will promote the maintenance of polygenic variation in LH genes. We provide examples of the kind of major effect loci that could be involved and suggest empirical avenues that may better inform us on the importance and reach of this process.

Patterns of frequency and density dependence are highly variable in diverse annual flowering plant communities.

Applications of ecological theory to natural communities often assume that competitive, negative density-dependent processes are the only type of interaction important for diversity maintenance. Recent advances suggest that positive interactions within trophic levels (e.g. plant-plant) may also affect plant coexistence. Though positive plant-plant interactions theoretically might result in positive or nonmonotonic frequency or density dependence (FD/DD), less is known about how commonly these patterns occur, or which ecological processes might result in such patterns in natural plant communities. In this study we test for signals of variable frequency and density dependence in annual flowering plant communities in Western Australia, and search for evidence that interactions among plants during flowering might induce positive or nonmonotonic FD/DD in flowering plants. Using four common annual wildflower species, we ask if plant fecundity exhibits positive or nonmonotonic FD/DD, and if pollinator-mediated plant-plant interactions during flowering change patterns of FD/DD relative to pollinator-independent plant interactions. Three species exhibited nonmonotonic (hump-shaped) density dependence, and only one species experienced strictly negative density dependence. Each species exhibited a different pattern of frequency dependence (positive, negative, weakly nonmonotonic, and no detectable frequency dependence). Pollinator-mediated plant-plant interactions during flowering induced both nonmonotonic density dependence and negative frequency dependence in one species. Importantly, the extent of variation in FD/DD observed in our study brings into question the dominance of negative density and frequency dependence in theory, suggesting instead that demographic responses of plants to their communities fall along a continuum of possible density- and frequency-dependent patterns.

Evolutionary coexistence in a fluctuating environment by specialization on resource level.

Microbial communities in fluctuating environments, such as oceans or the human gut, contain a wealth of diversity. This diversity contributes to the stability of communities and the functions they have in their hosts and ecosystems. To improve stability and increase production of beneficial compounds, we need to understand the underlying mechanisms causing this diversity. When nutrient levels fluctuate over time, one possibly relevant mechanism is coexistence between specialists on low and specialists on high nutrient levels. The relevance of this process is supported by the observations of coexistence in the laboratory, and by simple models, which show that negative frequency dependence of two such specialists can stabilize coexistence. However, as microbial populations are often large and fast growing, they evolve rapidly. Our aim is to determine what happens when species can evolve; whether evolutionary branching can create diversity or whether evolution will destabilize coexistence. We derive an analytical expression of the invasion fitness in fluctuating environments and use adaptive dynamics techniques to find that evolutionarily stable coexistence requires a special type of trade-off between growth at low and high nutrients. We do not find support for the necessary evolutionary trade-off in data available for the bacterium Escherichia coli and the yeast Saccharomyces cerevisiae on glucose. However, this type of data is scarce and might exist for other species or in different conditions. Moreover, we do find evidence for evolutionarily stable coexistence of the two species together. Since we find this coexistence in the scarce data that are available, we predict that specialization on resource level is a relevant mechanism for species diversity in microbial communities in fluctuating environments in natural settings.

MoS2/WSe2 vdW Heterostructures Decorated with PbS Quantum Dots for the Development of High-Performance Photovoltaic and Broadband Photodiodes.

van der Waals heterostructures (vdWHs) overcoming the lattice and processing limitations of conventional heterostructures provide an opportunity to develop high-performance 2D vdWH solar cells and photodiodes. However, it is challenging to improve the sensitivity and response speed of 2D vdWH photovoltaic devices due to the low light absorption efficiency and electron/hole traps in heterointerfaces. Here, we design a PbS/MoS2/WSe2 heterostructure photodiode in which a light-sensitive PbS quantum dot (QD) layer combined with a MoS2/WSe2 heterostructure significantly enhances the photovoltaic response. The electron current in the heterostructure is increased by the effective collection of photogenerated electrons induced by PbS QDs. The device exhibits a broadband photovoltaic response from 405 to 1064 nm with a maximum responsivity of 0.76 A/W and a specific detectivity of 5.15 × 1011 Jones. In particular, the response speed is not limited by multiple electron traps in the PbS QDs/2D material heterointerface, and a fast rising/decaying time of 43/48 μs and a -3 dB cutoff frequency of over 10 kHz are achieved. The negative differential capacitance and frequency dependence of capacitance demonstrate the presence of interface states in the MoS2/WSe2 heterointerface that hamper the improvement of the response speed. The scheme to enhance photovoltaic performance without sacrificing response speed provides opportunities for the development of high-performance 2D vdWH optoelectronic devices.

Measuring frequency-dependent selection in culture.

The frequency of a cultural trait can influence its tendency to be copied. We develop a maximum-likelihood method to measure such frequency-dependent selection from time series data, and we apply it to baby names and purebred dog preferences over the past century. The form of negative frequency dependence we infer among names explains their diversity patterns, and it replicates across the United States, France, Norway and the Netherlands. We find different growth rates for male versus female names, attributable to different rates of innovation, whereas biblical names enjoy a genuine selective advantage at all frequencies, which explains their predominance among top names. We show how frequency dependence emerges from a host of underlying selective mechanisms, including a preference for novelty that recapitulates boom-bust fads among dog owners. Our analysis of cultural evolution through frequency-dependent selection provides a quantitative account of social pressures to conform or to be different.

Stabilising role of seed banks and the maintenance of bacterial diversity

AbstractCoexisting species often exhibit negative frequency dependence due to mechanisms that promote population growth and persistence when rare. These stabilising mechanisms can maintain diversity through interspecific niche differences, but also through life‐history strategies like dormancy that buffer populations in fluctuating environments. However, there are few tests demonstrating how seed banks contribute to long‐term community dynamics and the maintenance of diversity. Using a multi‐year, high‐frequency time series of bacterial community data from a north temperate lake, we documented patterns consistent with stabilising coexistence. Bacterial taxa exhibited differential responses to seasonal environmental conditions, while seed bank dynamics helped maintain diversity over less‐favourable winter periods. Strong negative frequency dependence in rare, but metabolically active, taxa suggested a role for biotic interactions in promoting coexistence. Together, our results provide field‐based evidence that niche differences and seed banks contribute to recurring community dynamics and the long‐term maintenance of diversity in nature.

Host Specialisation, Immune Cross-Reaction and the Composition of Communities of Co-circulating Borrelia Strains

We use mathematical modelling to examine how microbial strain communities are structured by the host specialisation traits and antigenic relationships of their members. The model is quite general and broadly applicable, but we focus on Borrelia burgdorferi, the Lyme disease bacterium, transmitted by ticks to mice and birds. In this system, host specialisation driven by the evasion of innate immunity has been linked to multiple niche polymorphism, while antigenic differentiation driven by the evasion of adaptive immunity has been linked to negative frequency dependence. Our model is composed of two host species, one vector, and multiple co-circulating pathogen strains that vary in their host specificity and their antigenic distances from one another. We explore the conditions required to maintain pathogen diversity. We show that the combination of host specificity and antigenic differentiation creates an intricate niche structure. Unequivocal rules that relate the stability of a strain community directly to the trait composition of its members are elusive. However, broad patterns are evident. When antigenic differentiation is weak, stable communities are typically composed entirely of generalists that can exploit either host species equally well. As antigenic differentiation increases, more diverse stable communities emerge, typically around trait compositions of generalists, generalists and very similar specialists, and specialists roughly balanced between the two host species.

Frequency-dependent tree growth depends on climate.

Climate and competition interact to affect species' performance, such as growth and survival, and help determine species distributions and coexistence. However, it is unclear how climatic conditions modulate frequency-dependent performance, that is, how performance changes as a species becomes locally rare or common. This is critical because declines in performance as a species becomes more common (negative frequency dependence) is a signature of niche differences among species that stabilize coexistence, whereas positive frequency dependence leads to priority effects and hampers species coexistence. Here, we used dendrochronology and hierarchical models to test whether frequency-dependent growth of sugar pine (Pinus lambertiana) depends on climatic conditions. We found that growth rates were strongly dependent on annual precipitation, but no frequency dependence was evident across all years. However, there was a strong interaction between precipitation and frequency dependence, revealing stabilizing niche differences in dry years but positive frequency dependence in wet years. These differences emerged because of precipitation-driven changes in the direction and strength of both con- and heterospecific competition. Overall, these results show how stabilizing and destabilizing effects can be temporally dynamic for long-lived species and interact with climate variation.

Learning, exploitation and bias in games.

We focus on learning during development in a group of individuals that play a competitive game with each other. The game has two actions and there is negative frequency dependence. We define the distribution of actions by group members to be an equilibrium configuration if no individual can improve its payoff by unilaterally changing its action. We show that at this equilibrium, one action is preferred in the sense that those taking the preferred action have a higher payoff than those taking the other, more prosocial, action. We explore the consequences of a simple ‘unbiased’ reinforcement learning rule during development, showing that groups reach an approximate equilibrium distribution, so that some achieve a higher payoff than others. Because there is learning, an individual’s behaviour can influence the future behaviour of others. We show that, as a consequence, there is the potential for an individual to exploit others by influencing them to be the ones to take the non-preferred action. Using an evolutionary simulation, we show that population members can avoid being exploited by over-valuing rewards obtained from the preferred option during learning, an example of a bias that is ‘rational’.

Co-culture with Synechococcus facilitates growth of Prochlorococcus under ocean acidification conditions.

Anthropogenic CO2 emissions are projected to lower the pH of the ocean 0.3 units by 2100. Previous studies suggested that Prochlorococcus and Synechococcus, the numerically dominant phytoplankton in the oceans, have different responses to elevated CO2 that may result in a dramatic shift in their relative abundances in future oceans. Here we showed that the exponential growth rates of these two genera respond to future CO2 conditions in a manner similar to other cyanobacteria, but Prochlorococcus strains had significantly lower realized growth rates under elevated CO2 regimes due to poor survival after exposure to fresh culture media. Despite this, a Synechococcus strain was unable to outcompete a Prochlorococcus strain in co-culture at elevated CO2 . Under these conditions, Prochlorococcus' poor response to elevated CO2 disappeared, and Prochlorococcus' relative fitness showed negative frequency dependence, with both competitors having significant fitness advantages when initially rare. These experiments suggested that the two strains should be able to coexist indefinitely in co-culture despite sharing nearly identical nutritional requirements. We speculate that negative frequency dependence exists due to reductive Black Queen evolution that has resulted in a passively mutualistic relationship analogous to that connecting Prochlorococcus with the 'helper' heterotrophic microbes in its environment.

Soliton dynamics in an all-normal-dispersion photonic crystal fiber with frequency-dependent Kerr nonlinearity

We explore high-order soliton evolution in a composite all-normal dispersion photonic crystal fiber with frequency-dependent doping nonlinearity that can vary from positive to negative and vanish at a specific wavelength, named the zero-nonlinearity wavelength (ZNW). The change in frequency dependence of doping nonlinearity dramatically adjusts the position of the ZNW and the nonlinear strength acting on the supercontinuum spectral component. As the negative (positive) frequency dependence decreases (increases), one of two generated fundamental solitons via the combined action of negative nonlinearity and normal dispersion first has a gradually boosting soliton self-frequency shift (SSFS), and then a more suppressed SSFS, but is finally limited within an increasingly small spectral range while the other has a gradually decreasing SSFS toward the ZNW and radiates a broader and stronger phase-matched dispersive wave (DW) in the nonsolitonic region. Note that the collision between two fundamental solitons plays a significant role in regulating their temporal and spectral shift as well as energy redistribution. Furthermore, the numeric sign of the frequency dependence of doping nonlinearity provides another potential tool in controlling the spectral shift direction of fundamental solitons and DWs.

Natural enemies do not contribute to negative frequency-dependence in native and exotic grassland plants

Species’ responses to antagonists, such as fungal pathogens and insect herbivores, are part of a species’ niche and are thought to contribute to species coexistence. In theory, coexistence is supposed to be maintained by the effects of equalizing mechanisms that reduce fitness differences among species, and stabilizing mechanisms that are the result of niche differences. The presence of stabilizing niche differences is hallmarked by negative frequency-dependent per capita rates of increase. However, rigorous experimental testing of how insect herbivores and fungal pathogens contribute to negative frequency dependence among co-occurring plant species, in particular in the context of biological invasions, is scarce. We present an experimental study in a grassland in central Germany, in which we established native and exotic-dominated communities on 1 m²-plots, and reduced above- and belowground fungal pathogens and insect herbivores by applying pesticides. We manipulated the frequencies of six native and six exotic focal species, in order to assemble one dominant and five rare species per community. We quantified productivity and diversity for each community, and recorded data on per capita rates of increase and other fitness components for two native and two exotic focal species over three years. We found that native and exotic-dominated communities did not differ in their productivity and diversity. Reduction of fungi and insects increased productivity but the effect was similar for both species origins, suggesting that effects of enemy release are transitory or not existent. Negative frequency-dependence was common in our species, but could not be linked to interactions with antagonists. Although focal species responded to the reduction of antagonists, these effects were only present at low frequency, suggesting a greater importance of intraspecific competition, e.g. for resources, in explaining the observed stabilizing niche differences. Offsetting responses of the two exotic focal species to both antagonist groups highlight the significance of equalizing mechanisms among native and exotic species at the community level. Our study demonstrates the importance of both equalizing and stabilizing mechanisms in the context of biological invasions and differential contributions of antagonistic interactions to these mechanisms.