Diversity waves in collapse-driven population dynamics
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Carl R. Woese Institute for Genomic Biology, University of Illinois, Urbana-Champaign（卡尔·R·沃斯基因组生物学研究所，伊利诺伊大学厄巴纳-香槟分校）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Center for Models of Life, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔学院生命模型中心）
Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe collapses of the entire population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g. by invading bacteriophages, or for other ecosystems where infectious diseases play an important role.
The emergent dynamics of our system is cyclic "diversity waves" triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances are characterized by a bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species, while the upper peak - species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.
Humans are the ultimate ecosystem engineers who have profoundly transformed the world's landscapes in order to enhance their survival. Somewhat paradoxically, however, sometimes the unforeseen effect of this ecosystem engineering is the very collapse of the population it intended to protect. Here we use a spatial version of a standard population dynamics model of ecosystem engineers to study the colonization of unexplored virgin territories by a small settlement of engineers. We find that during the expansion phase the population density reaches values much higher than those the environment ca…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is limited by the number of resources, or by the species' similarity in resource use. Natural systems such as the extreme diversity of unicellular life in the oceans provide counter examples. It is known that mathematical models incorporating population fluctuations can lead to violations of the exclusion principle. Here we use simple eco-evolutionary models to s…
The HANDY model of Motesharrei, Rivas, and Kalnay examines interactions with the environment by human populations, both between poor and rich people, i.e., "Commoners" and "Elites". The Elites control the society's wealth and consume it at a higher rate than Commoners, whose work produces the wealth. We say a model is "Elite-dominated" when the Elites' per capita population change rate is always at least as large as the Commoners'. We can show the HANDY model always exhibits population crashes for all choices of parameter values for which it is Elite-dominated. But any such model with explicit…
A key question in the current diversity crisis is how diversity has been maintained throughout evolution and how to preserve it. Modern coexistence theories suggest that a high invasion rate of rare new types is directly related to diversity. We show that adding almost any mechanism of catastrophes to a stochastic birth, death, and mutation process with limited carrying capacity induces a novel phase transition characterized by a positive invasion rate but a low diversity. In this phase, new types emerge and grow rapidly, but the resulting growth of very large types decreases diversity. This m…
Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population before outlining the various definitions of `diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how dive…
The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T-cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T-cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T-cell pool, is known to diminish with age, but inherent experimental difficulties preclude accu…
Most infectious diseases including more than half of known human pathogens are not restricted to just one host, yet much of the mathematical modeling of infections has been limited to a single species. We investigate consequences of a single epidemic propagating in multiple species and compare and contrast it with the endemic steady state of the disease. We use the two-species Susceptible-Infected-Recovered (SIR) model to calculate the severity of post-epidemic collapses in populations of two host species as a function of their initial population sizes, the times individuals remain infectious,…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a set of evolving agents that interact competitively in a closed system, in which both the dynamics of mutations and competitive advantage emerge directly from interpreting a genome as the sides of a die. The model demonstrates sympatric speciation where new species evolve from existing ones while in contact with the entire ecosystem. Allowing free mutations b…
How self-organization leads to the emergence of structure in social populations remains a fascinating and open question in the study of complex systems. One frequently observed structure that emerges again and again across systems is that of self-similar community, i.e., homophily. We use a game theoretic perspective to explore a case in which individuals choose affiliation partnerships based on only two factors: the value they place on having social contacts, and their risk tolerance for exposure to threat derived from social contact (e.g., infectious disease, threatening ideas, etc.). We sho…
Biological functions are typically performed by groups of cells that express predominantly the same genes, yet display a continuum of phenotypes. While it is known how one genotype can generate such non-genetic diversity, it remains unclear how different phenotypes contribute to the performance of biological function at the population level. We developed a microfluidic device to simultaneously measure the phenotype and chemotactic performance of tens of thousands of individual, freely-swimming Escherichia coli as they climbed a gradient of attractant. We discovered that spatial structure spont…
Temporal Structure Mediates the Robustness and Collapse of Plant-Pollinator Networks
Helmholtz Institute for Functional Marine Biodiversity at the University of Oldenburg（奥尔登堡大学赫尔霍兹功能海洋生物多样性研究所）；Alfred Wegner institute（阿尔弗雷德·韦格纳研究所）；Institute for Chemistry and Biology of the Marine Environment（海洋环境化学与生物研究所）
Mutation and drift play opposite roles in genetics. While mutation creates diversity, drift can cause gene variants to disappear, especially when they are rare. In the absence of natural selection and migration, the balance between the drift and mutation in a well-mixed population defines its diversity. The Moran model captures the effects of these two evolutionary forces and has a counterpart in social dynamics, known as the Voter model with external opinion influencers. Two extreme outcomes of the Voter model dynamics are consensus and coexistence of opinions, which correspond to low and hig…
The "Kill the Winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the "Kill the Winner" paradigm and show that the stable coexistence state of the deterministic "Kill the Winner" model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promote…
We introduce a new dominance concept consisting of three new dominance metrics based on Lloyd's (1967) mean crowding index. The new metrics link communities and species, whereas existing ones are applicable only to communities. Our community-level metric is a function of Simpson's diversity index. For species, our metric quantifies the difference between community dominance and the dominance of a virtual community whose mean population size (per species) equals the population size of the focal species. The new metrics have at least two immediate applications: (i) acting as proxies for diversit…
Classical stochastic demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, the SAS-CFF model demonstrates that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to account for demography, I examine the simultaneous effects of environmental stochasticity on genetic diversity and population persistence. Consistent with Gillespie's analysis, if the log-fitness function is concave and allelic responses to the environment are not perfectly correlated, then per-capita growth rates o…
Recent collapses of many fisheries across the globe have challenged the mathematical approach to these systems through classic bioeconomic models. Decimated populations did not recover as fast as predicted by these models and depensatory effects were introduced to better fit the dynamics at low population abundances. Alternative to depensation, modeling captures by non-linear harvesting functions produces equivalent outcomes at small abundances, and the dynamics undergoes a bifurcation leading to population collapse and recovery once catching efforts are above or below certain thresholds, resp…
Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This body of work has primarily focused on games in which players face a simple binary choice, to "cooperate" or "defect". Real individuals, however, often exhibit behavioral diversity, varying their input to a social interaction both qualitatively and quantitatively. Here we explore how access to a greater diversity of behavioral choices impacts the evolution of so…
Facing an alarming continuing decline of wild sea cucumber resources, management strategies were developed over the past three decades to sustainably promote development, maintenance, or regeneration of wild sea cucumber fisheries. In New Caledonia (South Pacific), dedicated management efforts via restocking and sea ranching programs were implemented to cope with the overharvesting of the sandfish Holothuria scabra and the recent loss of known populations. In order to investigate genetic implications of a major H. scabra restocking program, we assessed the genetic diversity and structure of wi…
Selective sweeps affect neutral genetic diversity through hitchhiking. While this effect is limited to the local genomic region of the sweep in panmictic populations, we find that in spatially-extended populations the combined effects of many unlinked sweeps can affect patterns of ancestry (and therefore neutral genetic diversity) across the whole genome. Even low rates of sweeps can be enough to skew the spatial locations of ancestors such that neutral mutations that occur in an individual living outside a small region in the center of the range have virtually no chance of fixing in the popul…
The current rate of species extinction is rapidly approaching unprecedented highs and life on Earth presently faces a sixth mass extinction event driven by anthropogenic activity, climate change and ecological collapse. The field of conservation genetics aims at preserving species by using their levels of genetic diversity, usually measured as neutral genome-wide diversity, as a barometer for evaluating population health and extinction risk. A fundamental assumption is that higher levels of genetic diversity lead to an increase in fitness and long-term survival of a species. Here, we argue aga…
Inspired by DNA data of the human cytomegalovirus we propose a model of a two-type parasite population distributed over its hosts. The parasite is capable to persist in its host till the host dies, and to reinfect other hosts. To maintain type diversity within a host, balancing selection is assumed. For a suitable parameter regime we show that in the limit of large host and parasite populations the host state frequencies follow a dynamical system with a globally stable equilibrium, guaranteeing that both types are maintained in the parasite population for a long time on the host time scale.
Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. Here we consider a two island neutral model of speciation with continuous migration and study diversity patterns as a function of the migration probability, population size, and number of genes involved in reproductive isolation (dubbed as genome size). For small genomes, …
