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Euonymus nanus (Celastraceae): first record for the Russian Far East

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Two small populations of Euonymus nanus were identified in the Russian Far East, near the city of Svobodny, Amur Region. The geographic coordinates are provided, and the total number of plants was estimated. Measurements of leaf blade dimensions and shoot height from these wild Russian populations (Amur Region and the Republic of Crimea) are presented and compared with published data for populations from China. Vegetative shoots were counted within randomly selected one-square-meter plots, and the total population size was extrapolated based on the overall occupied area. The average leaf size and shoot height of the Amur plants were compared with quantitative data from literature sources for wild populations in the Republic of Crimea and China.

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NEW PAEONIA ANOMALA POPULATIONS FOUND IN SURGUTSKY DISTRICT OF KHANTY-MANSIYSK AUTONOMOUS AREA - YUGRA
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The article describes two new localities of Paeonia anomala L., a rare species listedin the Red Data Book of the Khanty-Mansiysk Autonomous Area - Yugra, that were discovered in Surgutsky District. Phytocenotic, topographic and ecologic growth conditions were studied, and quantitative data on abundance, density and age composition of the populations were collected. The first population is characterized by rather high density and abundance in comparison with other populations examined earlier;the number of generative shoots is also significantly larger. Other biometric parameters (average number of shoots per plant, average number of generative and vegetative shoots, height and number of leaves on generative and vegetative shoots) are similar to those of populations that developed in the optimal ecological conditions of the forest steppe.The second population is inferior to the first one in many respects (abundance, density, height and quantity of leavesof generative and vegetative shoots); most of the plants are in the vegetative state; and the average number of shoots per plant are also small. The obtained data expand our understanding of the size and structure of the populations of this rare and endangered species in the region.

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  • 10.1002/jwmg.451
Mark‐resight and sightability modeling of a western Washington elk population
  • Aug 20, 2012
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The North Cascades (Nooksack) elk (Cervus elaphus) population declined during the 1980s, prompting a closure to state and tribal hunting in 1997 and an effort to restore the herd to former abundance. In 2005, we began a study to assess the size of the elk population, judge the effectiveness of restoration efforts, and develop a practical monitoring strategy. We concurrently evaluated 2 monitoring approaches: sightability correction modeling and mark‐resight modeling. We collected data during February–April helicopter surveys and fit logistic regression models to predict the sightability of elk groups based on group and environmental variables. We used an information‐theoretic criterion to compare 9 models of varying complexity; the best model predicted sightability of elk groups based on 1) transformed (log2) group size, 2) forest canopy cover (%), and 3) a categorical activity variable (active vs. bedded). The sightability model indicated relatively steady and modest herd growth during 2006–2011, but estimates were less than minimum‐known‐alive counts. We also used the logit‐normal mixed effects (LNME) mark‐resight model to generate estimates of total elk population size and the sizes of the adult female and branch‐antlered male subpopulations. We explored 15 LNME models to predict total population size and 12 models to predict subpopulations. Our results indicated individual heterogeneity in resighting probabilities and variation in resighting probabilities across sexes and some years. Model‐averaged estimates of total population size increased from 639 (95% CI = 570–706) in spring 2006 to 1,248 (95% CI = 1,094–1,401) in 2011. We estimated the adult female subpopulation increased from 381 (95% CI = 338–424) in spring 2006 to 573 (95% CI = 507–639) by 2011. The branch‐antlered male subpopulation estimates increased from 87 (95% CI = 54–119) to 180 (95% CI = 118–241) from spring 2006 to spring 2011. The LNME model estimates were greater than sightability model estimates and minimum‐known‐alive counts. We concluded that mark‐resight performed better and was a viable approach for monitoring this small elk population and possibly others with similar characteristics (i.e., small population and landscape scales), but this approach requires periodic marking of elk; we estimated mark‐resight costs would be about 40% greater than sightability model application costs. The utility of sightability‐correction modeling was limited by a high proportion of groups with low detectability on our densely forested landscape. © 2012 The Wildlife Society.

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Проект «Скопа в России»: основные результаты работы в 2019–2023 годах
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Demographic modeling of the endangered subtropical rainforest shrub Graptophyllum reticulatum
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The subtropical rainforest shrub Graptophyllum reticulatum (Acanthaceae) occurs in only a few populations within a 20‐kilometer range in the Sunshine Coast, south‐east Queensland, Australia. This endangered plant has been subject to habitat degradation and loss, mostly due to land clearing and urbanization. In the past decades, conservation measures such as land protection and translocation have been put in place to protect the species' wild populations. The aim of the study was to analyze the viability of the species' populations in the long term while assessing the effectiveness of land protection and translocation. Demographic data was collected every decade since 2000; for this study, we resurveyed all known populations including a translocated population and two recently discovered populations. We found that the average number of plants per population has doubled since 2000, except in one population that underwent land clearing. However, after being reduced by 70%, plant abundance in this population has been increasing, giving evidence of natural post‐clearing recovery. We developed population growth models for population viability analysis in best, average, and worst‐case scenarios to predict the species' viability over the next 100 years. All populations are expected to grow in the next 100 years, except in the worst‐case scenario in which removing land protection from the model led to an 80% decline in the total number of plants within 100 years, highlighting the importance of land protection for species' conservation. Overall, if current conservation efforts are maintained, this endangered species is likely to persist for the next 100 years.

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The human core of the shared socioeconomic pathways: Population scenarios by age, sex and level of education for all countries to 2100
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The human core of the shared socioeconomic pathways: Population scenarios by age, sex and level of education for all countries to 2100

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Colony and evolutionary dynamics of a two‐stage model with brood cannibalism and division of labor in social insects
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  • Marisabel Rodriguez‐Rodriguez + 1 more

Division of labor (DOL) is a major factor for the great success of social insects because it increases the efficiency of a social group where different individuals perform different tasks repeatedly and presumably with increased performance. Cannibalism plays an important role in regulating colony growth and development by regulating the number of individuals in a colony and increasing survival by providing access to essential nutrients and minimizing competition among colony mates. To understand the synergy effects of DOL and cannibalistic behavior on colony dynamic outcomes, we propose and study a compartmental two‐stage model using ecological and evolutionary game theory settings. Our analytical results of the ecological and evolutionary models suggest that: (1) A noncannibalistic colony can survive if the efficiency of energy investment reflecting the DOL is greater than the relative death rate of the older population. (2) A cannibalistic colony can die out if both the efficiency of energy investment and the relative cannibalism rate (where each is also reflecting the DOL) are too large; or if the relative cannibalism rate alone is too small. (3) From our numerical analysis, cannibalism can increase or reduce the colony's total population size, which greatly depends on the benefit of egg cannibalism increasing or decreasing of adult's lifespan. (4) A cannibalistic and noncannibalistic colony can experience bistability due to cooperative behavior. (5) In the evolutionary settings, DOL can prevent colony death and natural selection can preserve strong Allee effects by selecting the traits with the largest investment on brood care and the lowest cannibalism rate. (6) Evolutionary dynamics may increase the fitness of the colony, i.e., the successful production of workforce which results in the increase of total worker population size, colony survival, and reproduction. Our results suggest both cannibalism and DOLs are adaptive strategies that increase the size of the worker population, and therefore, persistence of the colony.

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  • Cite Count Icon 15
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Demographic and population responses of an apex predator to climate and its prey: a long‐term study of South Polar Skuas
  • Aug 13, 2019
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  • Nathan Pacoureau + 3 more

Ecologists widely acknowledge that a complex interplay of endogenous (density‐dependent) and exogenous (density‐independent) factors impact demographic processes. Individuals respond differently to those forces, ultimately shaping the dynamics of wild populations. Most comprehensive studies disentangling simultaneously the effects of density dependence, climate, and prey abundance while taking into account age structure were conducted in terrestrial ecosystems. However, studies on marine populations are lacking. Here we provide insight into the mechanisms affecting four vital rates of an apex Antarctic marine predator population, the South Polar SkuaCatharacta maccormicki, by combining a nearly half‐century longitudinal time series of individual life histories and abundance data, with climatic and prey abundance covariates. Using multistate capture–mark–recapture models, we estimated age classes effects on survival, breeding, successful breeding with one or two chicks and successful breeding with two chicks probabilities, and assessed the different effects of population size, climate, and prey abundance on each age‐specific demographic parameter. We found evidence for strong age effects in the four vital rates studied. Vital rates at younger ages were lower than those of older age classes for all parameters. Results clearly evidenced direct and indirect influences of local climate (summer sea ice concentration), of available prey resources (penguins), and of intrinsic factors (size of the breeding population). More covariate effects were found on reproductive rates than on survival, and younger age classes were more sensitive than the older ones. Results from a deterministic age‐structured density‐dependent matrix population model indicated greater effects of prey abundance and sea ice concentration on the total population size than on the breeding population size. Both total population size and the number of breeders were strongly affected by low values of sea ice concentration. Overall, our results highlight the greater sensitivity of reproductive traits and of younger age classes to prey abundance, climate variability, and density dependence in a marine apex predator, with important consequences on the total population size but with limited effects on the breeding population size. We discuss the mechanisms by which climate variability, prey abundance, and population size may affect differentially age‐specific vital rates, and the potential population consequences of future environmental changes.

  • Peer Review Report
  • 10.7554/elife.81692.sa0
Editor's evaluation: Dynamics of immune memory and learning in bacterial communities
  • Sep 11, 2022
  • Anne-Florence Bitbol

Article Figures and data Abstract Editor's evaluation Introduction Results Discussion Methods Appendix 1 Appendix 2 Appendix 3 Data availability References Decision letter Author response Article and author information Metrics Abstract From bacteria to humans, adaptive immune systems provide learned memories of past infections. Despite their vast biological differences, adaptive immunity shares features from microbes to vertebrates such as emergent immune diversity, long-term coexistence of hosts and pathogens, and fitness pressures from evolving pathogens and adapting hosts, yet there is no conceptual model that addresses all of these together. To this end, we propose and solve a simple phenomenological model of CRISPR-based adaptive immunity in microbes. We show that in coexisting phage and bacteria populations, immune diversity in both populations is coupled and emerges spontaneously, that bacteria track phage evolution with a context-dependent lag, and that high levels of diversity are paradoxically linked to low overall CRISPR immunity. We define average immunity, an important summary parameter predicted by our model, and use it to perform synthetic time-shift analyses on available experimental data to reveal different modalities of coevolution. Finally, immune cross-reactivity in our model leads to qualitatively different states of evolutionary dynamics, including an influenza-like traveling wave regime that resembles a similar state in models of vertebrate adaptive immunity. Our results show that CRISPR immunity provides a tractable model, both theoretically and experimentally, to understand general features of adaptive immunity. Editor's evaluation In this important work, the authors develop a theory for the coevolutionary dynamics of bacteria and phages, where the major evolutionary pressure comes from CRISPR-Cas adaptive immunity in bacteria. Through extensive stochastic numerical simulations and analytical calculations, the article presents a compelling analysis of the emergent properties of immune interactions, in the regime of a single proto-spacer and a single spacer. Some of the trends highlighted by the model are recovered from experimental data. The main results concern how diversity in both phage and bacteria population is linked and is shaped by immunity, and should be of broad interest in immunology. https://doi.org/10.7554/eLife.81692.sa0 Decision letter Reviews on Sciety eLife's review process Introduction Adaptive immunity equips organisms to survive changing pathogen attacks across their lifetime. Many diverse organisms from bacteria to humans possess adaptive immune systems, and their presence shapes the survival, diversity, and evolution of both hosts and pathogens. How adaptive immunity changes the landscape of host-pathogen coexistence, how immune diversity emerges and evolves, and how the pressures of evolving pathogens and adaptive immunity are coupled to produce unique evolutionary outcomes: all of these factors are of fundamental importance to understanding the role of adaptive immunity in populations. These questions have naturally been explored in the vertebrate adaptive immune system, which protects humans and other vertebrates from evolving pathogens. In these organisms, a diverse repertoire of T cell and B cell receptors can rapidly recognize and respond to a wide range of threats. Immune specificity is determined by the unique genetic sequence of each cell's receptor, and individuals may harbour millions to billions of unique sequences distributed across four or more orders of magnitude of abundance (Desponds et al., 2016; Mora and Walczak, 2019; de Greef et al., 2020). Quantitative frameworks to model immune diversity and clone abundance have revealed that simple low-level interactions can give rise to complex outcomes including broad distributions of clone abundance (Desponds et al., 2016; Mora and Walczak, 2019; de Greef et al., 2020; Mayer et al., 2015; Gaimann et al., 2020; Dessalles et al., 2022), long-lived biologically realistic transient states (Yan et al., 2019; Gaimann et al., 2020), and clonal restructuring following immune challenges (Childs et al., 2015; Puelma Touzel et al., 2020; Sachdeva et al., 2020; Molari et al., 2020; Gaimann et al., 2020). Phenomenological models of pathogen coevolution with the immune system have accelerated our understanding of how the fitness landscape generated by the immune system constrains pathogen evolution (Luksza and Lässig, 2014; Marchi et al., 2019; Yan et al., 2019; Schnaack and Nourmohammad, 2021; Chardès et al., 2022), how the adaptive immune system responds to rapid pathogen evolution (Wang et al., 2015; Nourmohammad et al., 2019; Schnaack and Nourmohammad, 2021; Chardès et al., 2022), and what drives pathogen extinction (Yan et al., 2019; Marchi et al., 2019 or the extinction of particular clonal cell lineages Nourmohammad et al., 2019; Sachdeva et al., 2020). These models have also explored trade-offs such as between immune receptor specificity and cross-reactivity (Mayer et al., 2015; Nourmohammad et al., 2016), between the specificity of host-pathogen discrimination and sensitivity to pathogens (Childs et al., 2015; Downie et al., 2021; Metcalf et al., 2017), between the speed of an immune response and the efficiency of that response (Schnaack and Nourmohammad, 2021), or between metabolic resource use and immune coverage (Chardès et al., 2022). All of these models have shown rich dynamics and qualitatively different states of diversity and evolution arising from simple rules. However, experiments in vertebrates are difficult: vertebrate immunity depends on a complex interplay of many cell types and experiments are time-consuming because of long generation times (Altan-Bonnet et al., 2020). Adaptive immunity in microbes is realized through the CRISPR system, conceptually related to the vertebrate adaptive immune system. The CRISPR system is functionally simple, yet it is incredibly powerful, as indicated by its widespread presence in many diverse bacteria and archaea Koonin and Makarova, 2019 and its experimentally demonstrated ability to provide strong immunity against phages (Paez-Espino et al., 2013; Paez-Espino et al., 2015; van Houte et al., 2016; Bondy-Denomy et al., 2013). Attacking phages expose their DNA to bacteria, and bacteria with a CRISPR immune system acquire small segments of phage DNA, called spacers. They store spacers in their genome and use them to recognize and destroy matching phage sequences in future infections: spacers are transcribed into RNA and guide DNA-cleaving CRISPR-associated proteins to recognize and cut re-infecting phages. Spacers provide a highly specific immune memory of infecting phages, preventing recognized phages from reproducing. In turn, phages can acquire mutations in the protospacer regions of their genome that are targeted by spacers. These features of the CRISPR immune system mean that (a) phage genetic evolution occurs by selection for escape mutants, and (b) the network of CRISPR immune interactions between bacteria and phages can be inferred by sequencing the genomes of co-living bacteria and phages. Spacer acquisition and phage mutation are rare random events, and many such events must be observed in order to understand their impact on populations. Bacteria and phages have short life cycles and can reach large population size, making it possible to build a statistical picture of the impacts of adaptive immunity. The kinetics and interactions of phages and bacteria with CRISPR systems have been the subject of numerous experiments (van Houte et al., 2016; Common et al., 2019; Common et al., 2020; Chabas et al., 2021; Dimitriu et al., 2022; Guillemet et al., 2021). Some themes have emerged from experimental studies of CRISPR immunity: (a) high spacer diversity relative to phage diversity increases the likelihood of phage extinction (van Houte et al., 2016; Common et al., 2020; Guillemet et al., 2021), (b) bacteria become more immune to phages over time (Laanto et al., 2017; Morley et al., 2017; Common et al., 2019; Pyenson and Marraffini, 2020), and (c) phages readily gain mutations (Weinberger et al., 2012a; Paez-Espino et al., 2013; Levin et al., 2013; Pyenson et al., 2017; Watson et al., 2019; Pyenson and Marraffini, 2020; Guillemet et al., 2021; Guerrero et al., 2021a) and sometimes genome rearrangements (Paez-Espino et al., 2015) to escape CRISPR targeting. Explorations of CRISPR immunity in natural environments have also documented ongoing spacer acquisition and phage escape mutations (Weinberger et al., 2012a; Guerrero et al., 2021a). Likewise, previous theoretical work has addressed the impact of parameters such as spacer acquisition rate and phage mutation rate on spacer diversity (Childs et al., 2012; Han et al., 2013; Han and Deem, 2017) and population survival and extinction (Weinberger et al., 2012b), how costs of CRISPR immunity impact bacteria-phage coexistence (Skanata and Kussell, 2021) and the maintenance of CRISPR immunity (Levin, 2010; Weinberger et al., 2012b; Westra et al., 2015; Gurney et al., 2019), how spacer diversity impacts population outcomes (He and Deem, 2010; Weinberger et al., 2012a; Childs et al., 2012; Haerter and Sneppen, 2012; Han et al., 2013; Childs et al., 2014; Bradde et al., 2017; Han and Deem, 2017), and how stochasticity and initial conditions impact population survival (Bradde et al., 2019; Chabas et al., 2018). Notably, foundational work by Childs et al., 2014; Childs et al., 2012 and Weinberger et al., 2012a; Weinberger et al., 2012b found through simulations that spacer diversity readily emerges in a population of CRISPR-competent bacteria interacting with mutating phages. However, the majority of both experiments and theory are based on observations and models of transient phenomena and short-term dynamics, while it is at long timescales that natural microbial communities experience bacteria-phage coexistence. Some notable experiments have measured long-term coexistence (Paez-Espino et al., 2015; Wei et al., 2011), and long-term sequential sequencing data from natural populations is becoming more available (Gómez and Buckling, 2011; Burstein et al., 2016), but appropriate theories to understand steady-state coexistence, sequence evolution and turnover, and immune memory in microbial populations remain rare. Because the processes of growth, death, and immune interaction are inherently random, understanding population establishment and extinction requires a fully stochastic analysis, and theoretical models that explore long-term coexistence have been partially deterministic to date (Weinberger et al., 2012a; Weinberger et al., 2012b; Childs et al., 2012; Levin et al., 2013; Childs et al., 2014; Santos et al., 2014; Weissman et al., 2018; Gurney et al., 2019). These models do not accurately capture rare stochastic events, in particular mutation, establishment, and extinction. Notable fully stochastic simulations of CRISPR immunity, on the other hand, have lacked rigorous analytic results (Han et al., 2013; Han and Deem, 2017). To understand the emergent properties of immune memory and diversity in microbial populations and how phages and bacteria coexist long-term, we developed a simple theoretical model of bacteria and phages interacting with adaptive immunity. We model a population of bacteria with CRISPR immune systems interacting with phages that can mutate to escape CRISPR targeting, building on our previous work that assumed a clonal population of phages with multiple protospacers in each phage (Bonsma-Fisher et al., 2018). We model phages with single protospacers in this work to efficiently track mutations in large populations over long timescales. We stochastically simulate thousands of bacteria-phage populations across a range of population sizes, spacer acquisition rates, spacer effectiveness rates, and phage mutation rates, and derive analytic expressions for the probability of establishment for new phage mutants, the time to extinction for phage and bacterial clones, and the dependence of bacterial spacer diversity on spacer acquisition rate, effectiveness, and phage mutation rate. Our simulations are fully stochastic and run for many thousands of generations to accurately capture the dynamics of establishment and extinction, yet the underlying model is simple enough to solve analytically. We show that even with the simplest assumptions of uniform spacer acquisition and effectiveness, complex dynamics and a wide range of outcomes of diversity and population structure are possible. We recover and reinterpret experimentally observed feaures: (a) we find that high diversity is not beneficial for bacteria when phage and bacterial diversity is strongly coupled, (b) we show that bacterial immunity can either track new phage mutations rapidly or keep a memory for a long time, but not both, and (c) we find emergent diversity resulting from selection for phage mutations that evade CRISPR targeting, linking diversity to the dynamical quantities of establishment and extinction. We compute bacterial average immunity in our simulations and in available experimental data and show that our model predicts qualitative trends that are visible in data. Finally, we show that adding immune cross-reactivity leads to qualitatively different states of evolutionary dynamics: (a) a traveling wave regime that resembles a similar state in models of vertebrate adaptive immunity (Yan et al., 2019; Marchi et al., 2019; Marchi et al., 2021) emerges when high cross-reactivity creates a fitness gradient for phage evolution, and (2) a regime of low turnover protected from new establishment by the reduced fitness of new phage mutants. Results Bacteria and phages dynamically coexist and coevolve We model bacteria and phage interacting and coevolving in a well-mixed system (Figure 1A and 'Model'). Bacteria divide by consuming nutrients and phages reproduce by creating a burst of B new phages after successfully infecting a bacterium. Bacteria can contain a single CRISPR spacer that confers immunity against phages with a matching protospacer. Phages are labelled with a single protospacer type, a binary sequence of length L=30 that can mutate to a new type during a burst with probability μ⁢L, where μ is the per-base mutation rate per generation. All simulations begin with a single clonal phage population unless otherwise specified. Figure 1 with 7 supplements see all Download asset Open asset Model description. (A) We model bacteria and phages interacting in a well-mixed vessel. We track nutrient concentration, phage population size (nV), and bacteria population size (nB). Bacteria can either have no spacer (nB0) or a spacer of type i (nBi, ∑inBi=nBs), and phages can have a single protospacer of type j (nVj). With rate α, a phage interacts with a bacterium. If the bacterium does not have a matching spacer, the phage kills with probability pV and produces a burst of B new phages, while for bacteria with a matching spacer that probability is reduced to pVs=pV⁢(1-e), 0≤e≤1. Bacteria without spacers that survive an attack have a chance to acquire a spacer with probability η, and bacteria with spacers lose them at rate r. Lower inset: average immunity is the weighted average pairwise immunity between spacer-containing bacteria and phages, given by 1-∑i,jnBi⁢nVj⁢pV⁢(i,j)pV⁢∑i,jnBi⁢nVj. The probability of a phage with protospacer j successfully infecting a bacterium with spacer i is pV⁢(i,j). (B) Three time points in a typical simulation with C0=104, e=0.95, η=10-4, and μ=10-5. Coloured circles represent unique protospacer or spacer sequences; shared sequences are shown with the same colour. The size of each circle is proportional to clone size, and new mutants are shown radially more distant from the centre. (C) Ten individual clone trajectories vs simulation time for phages (top) and bacteria (bottom). The mean clone size is shown with a horizontal dashed line. (D) Total phage, bacteria, and nutrient concentration as a function of phage success probability pV. Markers show an average over five independent simulations for different values of pV with C0=104,η=10-3,e=0.95, and μ=10-7. Solid lines show theoretical predictions for different constant values of effective e. As pV decreases, phages go extinct at a critical value given by A=1, where A=(B⁢pV-1)⁢(1-f)⁢αf⁢g. (E) Total phage and bacteria population size as a function of average bacterial immunity to phages. Colours indicate the fraction of simulations in which phage or bacteria go extinct before a set endpoint. Solid lines show the mean-field prediction. Error bars are the standard deviation across three or more independent simulations. Coexistence occurs across a wide range of parameters but is not guaranteed: below a certain success probability pV0=1B⁢(g⁢f(1-f)⁢α+1), phages are not able to reproduce often enough to overcome their base death rate due to outflow and adsorption and are driven extinct (grey area of Figure 1D; Bonsma-Fisher et al., 2018). In this expression, g is the bacterial growth rate, B is the phage burst size, α is the phage adsorption rate, f=F/(g⁢C0) is a normalized outflow rate, and C0 is the inflow nutrient concentration. This is the same extinction threshold reported by Payne et al., 2018 as the cutoff for achieving herd immunity in a well-mixed bacterial population. To a first approximation, phages must successfully infect every 1/B bacteria they encounter, but if bacteria are growing quickly, then phages must do better to overcome bacterial growth, leading to the extra terms in this expression (see 'Phage extinction threshold'). We write this extinction threshold as A=(B⁢pV-1)⁢(1-f)⁢αf⁢g. Above the phage extinction threshold (A>1), the phage population size increases with increasing pV but eventually decreases again as bacterial numbers are driven too low to support a large phage population (Bonsma-Fisher et al., 2018). A similar non-monotonicity as a function of the probability of naive bacterial resistance (1-pV) was described in theoretical work by Weinberger et al., 2012b. In our model the position of the peak in phage population size as a function of infection success probability is determined by e, the effectiveness of CRISPR spacers against phage; increasing e pushes the peak to higher pV (Figure 1D). While e is a constant parameter that determines the outcome of pairwise interactions between bacteria and phages, the bacterial population as a whole possesses an average immunity to phages that is a weighted average of all the possible pairwise interactions (Figure 1A inset). It is the overall average immunity that determines population outcomes, which we describe in detail in 'Pathogen and host diversity must be considered together'. To focus on regimes where bacteria and phages coexist, we select parameters within the deterministic coexistence regime to explore bacteria-phage coevolution. Even in this regime, stochastic extinction will eventually come for one or both populations in simulations (Figure 1E), though the timescale of extinction may be extremely long for large population sizes (Badali and Zilman, 2020). Phages are more susceptible to stochastic extinction than bacteria because of their large burst size B which increases their overall population fluctuations (Appendix 3). The length of coexistence before stochastic extinction depends on population size as well as simulation parameters and initial conditions (see 'Stochastic population extinction'): phage populations can be rescued from extinction by high mutation rate (Figure 1—figure supplement 3) or high initial protospacer diversity (Figure 1—figure supplement 6), but are more likely to go extinct if spacer effectiveness is high (Figure 1—figure supplement 1). Conversely, bacteria are more likely to go extinct if spacer effectiveness or spacer acquisition rate are low (Figure 1—figure supplement 4). Population survival and persistence in natural populations is impacted by additional factors we do not address in our model, including immigration (Volkov et al., 2003; Chabas et al., 2016, niche partitioning Simek et al., 2010; Weitz et al., 2013; Mills et al., 2013; Badali and Zilman, 2020; Voigt et al., 2021), environmental fluctuations (Abreu et al., 2020; Voigt et al., 2021), and spatial structure (Haerter et al., 2011; Haerter and Sneppen, 2012; Heilmann et al., 2010; Heilmann et al., 2012; Simmons et al., 2018; Skanata and Kussell, 2021). Across a wide range of coexistence parameters, our simulations show continual phage evolution and bacterial CRISPR adaptation in response (Figure 1B). New phage protospacer clones arise from a single founding clone by mutation, and a small fraction of new mutants grow to a large size and become established. Once phage clones become large, bacteria acquire matching spacers and an immune bacterial subpopulation becomes established. The specific protospacer and spacer types present in the population continually change as old types go extinct and new types are created by phage mutation, but the average total diversity and average overlap between bacteria and phage remains constant at steady state (Figure 8). Both bacteria and phage clones stochastically go extinct, completing the life cycle of a clonal population (Figure 1C). Phages drive stable emergent sequence diversity New phage protospacer clones continually arise and go extinct in our simulations, generating turnover in clone identity in the population. Despite constant turnover, however, the total of clones remains at steady We use the mean of bacterial clones at steady as a of system This of diversity is to the of the clone size a of the and Walczak, 2016; et al., 2020). This all clones of their such a is not appropriate when clone size distributions are broad and small clones may be but is when clone size distributions are and all clones are and Walczak, In our simulation both bacteria and phage populations clone size distributions across a range of parameters, with the of low values of spacer acquisition (Figure Figure supplement Figure supplement 4). Even at low η, however, clone size distributions are that they are not and that the mean clone size important information the clone size Figure 2 with supplements see all Download asset Open asset depends on (A) Bacteria and phage clone size distributions normalized to the measured mean clone size for and As both clone size distributions become more (B) The mean of bacterial clones depends on a parameter in the of small average immunity with high The mean of bacterial clones can be predicted by 1 for The values of are shown with Error bars are the standard deviation across three or more independent simulations. determines clonal Many factors that with transient diversity have been experimentally such as phage extinction and phage evolution at high bacterial spacer diversity (van Houte et al., 2016; Common et al., and maintenance of a diverse bacterial population when to diverse phages (Paez-Espino et al., 2015; Common et al., 2019; Guillemet et al., 2021; et al., 2019), but a conceptual to understand emergent diversity has while initial high spacer diversity phage populations pressure to the of them extinct (van Houte et al., 2016; Common et al., 2020), is the same for emergent bacterial diversity after an of observed high bacterial spacer diversity of bacterial escape from phage or an of phage In our model, phage and bacterial diversity is the of large phage clones is the same as the of bacterial clones (Figure This is also the in experimental coevolution data from Paez-Espino et al., the of phage protospacer types is on the same order of magnitude as the of bacterial spacer types across (Figure is that this of diversity may also in the a of bacteria interacting with phage in a phage and bacterial based on CRISPR spacer sequence et al., 2021a). the between bacterial diversity and phage diversity in our model, we the overall steady-state diversity by the effective phage clone mutation rate phage clone establishment probability and the time to extinction for large phage clones in 1 from the simple that the of large clones must be to their establishment rate by their average time to extinction This successfully predicts the of bacterial clones at steady state across a wide range of parameters and a wide range of diversity values (Figure Figure supplement and Figure supplement the value of the to the of clones in this regime, low acquisition that phage clones go extinct because of clonal before bacteria are able to acquire spacers (Figure Through for we find that diversity depends on a single parameter to the (Figure and this parameter is proportional to spacer effectiveness e, the probability of bacterial survival by spacer acquisition and the phage mutation rate (2) of these parameters increases diversity a higher phage mutation rate that phage diversity increases and bacterial diversity is is that their on diversity is to a than this that if the mutation rate the diversity by a of (Appendix 1). In a simple model of cell with mutations a proportional in diversity for the same in mutation rate (Appendix To understand where the dependence of diversity on these parameters come we more at each The effective phage mutation rate depends on the parameter while both the probability of establishment and the time to extinction on diversity and Appendix 3). with we find that depends on mutation rate, resulting in the dependence on mutation rate. The dependence of diversity on both e and comes from the probability of phage establishment depends on these parameters through its dependence on total population sizes and depends on not e or The phage probability of establishment is proportional to and as this Bacteria are more at high which increases the phage establishment theoretical work has predicted that diversity increases as spacer acquisition rate increases (Childs et al., we provide a for this In the following we explore phage establishment in more determines the fitness and establishment of new We find that diversity emerges in our model from the of phage clone establishment and extinction. However, phage mutants escape initial stochastic extinction and survive long enough to become established. determines the of a new phage In our model, a single phage mutation in a protospacer can overcome CRISPR targeting, which that new phage mutants can infect all bacteria well and their initial growth rate is independent of where is the rate shared death rate for phages and however, even bacteria to acquire matching the probability of establishment for new phage mutants is by theory in which CRISPR total average population sizes (Figure that the specific interaction between a phage and its matching clone can be this is because phage clones must grow to a certain size before bacteria them enough to begin to acquire and this size to be large enough to stochastic extinction (Figure The probability of phage establishment is where

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Population size in stochastic multi-patch ecological models.
  • Mar 2, 2026
  • Journal of mathematical biology
  • Alexandru Hening + 1 more

We look at the interaction of dispersal and environmental stochasticity in n-patch models. We are able to prove persistence and extinction results even in the setting when the dispersal rates are stochastic. As applications we look at Beverton-Holt and Hassell functional responses. We find explicit approximations for the total population size at stationarity when we look at slow and fast dispersal. In particular, we show that if dispersal is small then in the Beverton-Holt setting, if the carrying capacity is random, then environmental fluctuations are always detrimental and decrease the total population size. Instead, in the Hassell setting, if the inverse of the carrying capacity is made random, then environmental fluctuations always increase the population size. Fast dispersal can save populations from extinction and therefore increase the total population size. Using and modifying some approximation results due to Cuello, we find expressions for the total population size in the patch setting when the growth rates, carrying capacities, and dispersal rates are influenced by random fluctuations. We find that there is a complicated interaction between the various terms and that the covariances between the various random parameters (growth rate, carrying capacity, dispersal rate) play a key role in whether we get an increase or a decrease in the total population size. Environmental fluctuations turn to sometimes be beneficial - this shows that not only dispersal, but also environmental stochasticity can lead to an increase in population size.

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  • Cite Count Icon 47
  • 10.1016/j.ecolmodel.2016.08.012
Estimating wolf (Canis lupus) population size from number of packs and an individual based model
  • Aug 24, 2016
  • Ecological Modelling
  • Guillaume Chapron + 10 more

Estimating wolf (Canis lupus) population size from number of packs and an individual based model

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  • Cite Count Icon 79
  • 10.1016/s0378-1127(98)00320-x
Variability in seedling water status during drought within a Quercus ilex subsp. ballota population, and its relation to seedling morphology
  • Dec 1, 1998
  • Forest Ecology and Management
  • Maria Jose Leiva + 1 more

Variability in seedling water status during drought within a Quercus ilex subsp. ballota population, and its relation to seedling morphology

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  • 10.7554/elife.81692.sa1
Decision letter: Dynamics of immune memory and learning in bacterial communities
  • Sep 11, 2022
  • Barbara Bravi

Bacterial CRISPR immunity tracks phage mutations, creating immune diversity in bacterial populations that parallels phage genetic diversity and patterns of phage evolution that are determined by the type and degree of immune cross-reactivity in the CRISPR system.

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  • 10.1007/s10592-025-01730-1
Genetic marker type impacts ex situ conservation minimum sample size estimates and their variance
  • Nov 13, 2025
  • Conservation Genetics
  • Austin C Koontz + 2 more

Ex situ collections in botanic gardens safeguard plant species and their genetic diversity. While past research has typically used microsatellite markers to quantify the extent of ex situ genetic representation in botanic gardens, next-generation sequencing approaches generating thousands of single nucleotide polymorphisms (SNPs) have become more common. Several studies have examined the impact marker choice has on measures of genetic diversity and differentiation, but no evaluation on ex situ conservation metrics has been made. Additionally, minimum sample size estimates (MSSEs) for representing proportions of genetic diversity are typically reported as averages, but no study has quantified the variance surrounding MSSEs. To close these gaps, we simulated microsatellite and SNP data for species with various demographic characteristics and examined the impact different markers have on MSSEs and their variance. We found that using SNPs resulted in MSSEs twice as large as estimates based on microsatellites, and differences between SNP-based and microsatellite-based MSSEs were greater when total population sizes were larger. We also found that confidence intervals surrounding MSSEs are large, but can be decreased by using higher numbers of loci. Our results indicate that ex situ conservation metrics are sensitive to the marker type used, the number of markers, and the total size of wild populations, and that caution is needed when interpreting MSSEs based on empirical datasets that are small relative to a species’ total population size. We emphasize that the standard of conserving 95% of genetic diversity ex situ should be revisited, and that future minimum sample size recommendations to practitioners should incorporate uncertainty and account for the genetic marker being used.

  • Research Article
  • Cite Count Icon 7
  • 10.1080/09064719809362506
Effect of genotype and environment on vegetative and reproductive characteristics of lingonberry (Vaccinium vitis‐idaea L.)
  • Dec 1, 1998
  • Acta Agriculturae Scandinavica, Section B — Soil & Plant Science
  • Inger Hjalmarsson + 1 more

A field experiment was carried out using cuttings and seedlings from 11 selected clones of lingonberry (Vaccinium vitis‐idaea L.) planted at Balsgård, Sweden, in 1982. Daughter plants from two different clones and their corresponding seedling progenies were transferred to a Biothron at Alnarp, Sweden, in 1988. These two clones and their respective seedling populations were cultivated under conditions of controlled temperature and humidity, but in distinct environments with direct light and shade. Data on vegetative and reproductive growth were recorded. A small additional experiment to verify the effects of light on development was performed in frames at Alnarp. The results suggest that the genotype of wild lingonberry accessions controls their spreading ability (i.e. number of rhizomes), influences its growth, thereby affecting plant height, and determines the number of vegetative shoots, total number of shoots and berry set. Furthermore, light influences plant height, vegetative shoots and number of fertile shoots. The propagule system affects the number of both vegetative and fertile shoots. Plants derived from cuttings are superior to their corresponding seedling offspring, especially under shadow.

  • Research Article
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Medicago falcata L. Population State and Prospects for Use in North-Western Region
  • Jan 1, 2024
  • BIO Web of Conferences
  • Yaroslava M Abdushaeva

Meadows play an important role in maintaining the floristic diversity of regional floras. The phytocenotic allocation of the Medicago falcata L. population has not been sufficiently studied, as well as patterns of distribution of its units and unit groups, viability in a specific habitat under various anthropogenic influences. The growth and development of Medicago falcata L. populations under optimal conditions are becoming increasingly relevant and are promising in theoretical and applied aspects.The purpose is to study morphological characteristics and search for valuable forms of Medicago falcata L. to create varieties with high seed and feed productivity in the process of breeding work. The morphological characteristics of plants were studied depending on the age state and distribution of units in the territory they occupied. We have established that the total number of plants in the juvenile state in the population varies little from year to year, although the quantitative ratios of young plants of individual species can fluctuate significantly. This indicates that units in the juvenile state occupy a common ecological niche in the cenosis. The population of Medicago falcata L., growing in the Shelon meadow in the Soltsydistrict, differ in the methods of vegetation resumption, with numerous well-leafed shoots and high ecological plasticity. The formed meadow ecosystems depend not only on the natural conditions in their locations, but also on the influence of anthropogenic factors, which in turn affects the biogeocenosis (living organisms and their interaction with the environment) and, accordingly, the species composition of the meadow. There are rosette-free monocyclic vegetative and generative shoots, with a well-developed root system vertically and horizontally in the soil profile.

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