Effect of Resource Enrichment on a Chemostat Community of Bacteria and Bacteriophage

Total Page:16

File Type:pdf, Size:1020Kb

Effect of Resource Enrichment on a Chemostat Community of Bacteria and Bacteriophage ECOLOGY Friday Sep 18 11:35 AM ecol 78 817 Mp 2303 v File # 17sc Allen Press x DTPro 96-0380 Ecology, 78(8), 1997, pp. 2303±2315 q 1997 by the Ecological Society of America EFFECT OF RESOURCE ENRICHMENT ON A CHEMOSTAT COMMUNITY OF BACTERIA AND BACTERIOPHAGE BRENDAN J. M. BOHANNAN AND RICHARD E. LENSKI Center for Microbial Ecology, Michigan State University, East Lansing, Michigan 48824 USA Abstract. We determined the responses of a model laboratory community to resource enrichment and compared these responses to the predictions of prey-dependent and ratio- dependent food chain models. Our model community consisted of Escherichia coli B and bacteriophage T4 in chemostats supplied with different concentrations of glucose. We ob- served the following responses to enrichment: (1) a large and highly signi®cant increase in the equilibrium population density of the predator, bacteriophage T4, (2) a small but signi®cant increase in the equilibrium population density of the prey, E. coli, and (3) a large and highly signi®cant decrease in the stability of both the predator and prey popu- lations. These responses were better predicted by a prey-dependent model (altered to include a time delay between consumption and reproduction by predators) than by a ratio-dependent model. Enrichment had a large effect on evolutionary change in our system. Enrichment signi®cantly decreased the amount of time required for mutants of E. coli that were resistant to predation by bacteriophage to appear in the chemostats. Enrichment also signi®cantly increased the rate at which these bacteriophage-resistant mutants invaded the chemostats. These results were also better predicted by the prey-dependent model. Invasion by bacte- riophage-resistant mutants had a large effect on the subsequent population dynamics of both predator and prey. Both the equilibrium density and stability of the E. coli population increased following invasion, and the population shifted from being primarily limited by predators to being primarily limited by resources. After invasion by the mutants, the T4 population decreased in equilibrium density, and the population cycled with an increased period. These results were compared to the predictions of a ratio-dependent model and a prey-dependent model altered to include T4-resistant mutants. The dynamics of this com- munity were better predicted by the modi®ed prey-dependent model; however, this model was more complex mathematically than the simpler ratio-dependent model. Key words: bacteriophage T4; Escherichia coli; population dynamics; predation; prey-dependent models; ratio-dependent models; resource enrichment. INTRODUCTION plitude and period of population oscillations (Rosen- zweig 1971). The dynamics of predator±prey and other exploit- ative interactions have long been recognized as fun- These classical models are considered ``prey-depen- damentally important to the structure of ecological dent'' because they assume that the attack rate of pred- communities (Hairston et al. 1960, Paine 1966, Lub- ators depends only on the instantaneous density of prey. chenco 1978). Nonetheless, there remains considerable Some theorists have argued that the attack rate is often debate over such basic issues as the effects of resource better modeled as a function of the ratio of prey to enrichment on these interactions and how best to model predator density (Arditi and Ginzburg 1989). Such these effects (Arditi et al. 1991a, Ginzburg and Ak- ``ratio-dependent'' models make very different predic- cËakaya 1992, Diehl et al. 1993, Abrams 1994, Berry- tions concerning the effect of enrichment on prey and man et al. 1995). Classical predator±prey models (i.e., their predators. Enrichment is not predicted to be de- Lotka-Volterra models and modern variations thereof) stabilizing, and the equilibrium population sizes of both make two controversial predictions concerning the ef- predators and prey are predicted to increase in response fect of resource enrichment on prey and their predators. to enrichment. First, these models predict that enrichment will result Proponents of ratio-dependent models have sug- in an increase in the equilibrium population density of gested that this approach is superior because it captures the predator but have no effect on the equilibrium pop- the effects of heterogeneity on predator±prey dynam- ulation density of the prey (Rosenzweig 1977). Second, ics. Such heterogeneity could include differences in the classical predator±prey models predict that enrichment time scales of feeding by predators and reproduction can destabilize a predator±prey pair, increasing the am- by predators, discontinuous prey reproduction, spatial heterogeneity, and heterogeneity in prey edibility (Ar- Manuscript received 3 June 1996; revised and accepted 10 diti and Ginzburg 1989). The superiority of ratio-de- May 1997. pendent models in these situations has been hotly de- 2303 ECOLOGY Friday Sep 18 11:35 AM ecol 78 817 Mp 2304 Allen Press x DTPro File # 17sc 2304 BRENDAN J. M. BOHANNAN AND RICHARD E. LENSKI Ecology, Vol. 78, No. 8 bated (Oksanen et al. 1992, Diehl et al. 1993, Abrams bacteria increased in abundance in response to in- 1994, Gleeson 1994, AkcËakaya et al. 1995, Berryman creased nutrient input. However, they sampled the bac- et al. 1995). This debate has centered on whether ratio- teria population only twice during their 52-d experi- dependent models do indeed capture the effects of het- ment (they were primarily interested in protozoan pop- erogeneity, whether it is better to model heterogeneity ulation dynamics); if the bacteria population cycled in by using a ratio-dependent model or by explicitly in- response to predation, these estimates of population corporating heterogeneity into a prey-dependent mod- density could be inaccurate. In addition, Balciunas and el, and what the trade-offs are in using these two ap- Lawler used a heterogeneous population of bacteria in proaches. their experiments, and the increase in bacteria abun- There have been a number of attempts to answer dance could be due to an increase in the abundance of these questions using ®eld systems. Most of these at- less edible members of the mixed population. Balciunas tempts have involved comparing trophic structure and/ and Lawler found some evidence for predator mutual or trophic level biomass across natural gradients of interference and could not rule out ratio-dependent pre- productivity (e.g., Arditi et al. 1991a, Ginzburg and dation in their system. AkcËakaya 1992, Hansson 1992, Oksanen et al. 1992, Although most predator±prey theory assumes a Persson et al. 1992) or measuring the response of a ``chemostat-like'' environment (i.e., continuous input natural community to enrichment (e.g., O'Brien et al. of resources, constant mortality, etc.), both studies 1992, Wootton and Power 1993, Stow et al. 1995). The above used batch culture systems rather than chemo- results of these attempts have been inconclusive. In stats. In batch culture, an aliquot of the culture is trans- some studies prey-dependent models appeared to better ferred at regular intervals to fresh culture medium. The predict the responses (Hansson 1992, Oksanen et al. effect of such serial transfer is potentially confounding; 1992, Persson et al. 1992, Wootton and Power 1993), it was considered by Harrison (1995) to be the major while in other studies the responses appeared to be reason that he was unable to get a close ®t between better predicted by ratio-dependent models (Arditi et some of Luckinbill's data and the predictions of math- al. 1991a, Ginzburg and AkcËakaya 1992, O'Brien et ematical models. al. 1992, Schmitz 1993). The limitations inherent in We have built on these previous attempts by using using ®eld systems to test these models have been well chemostat communities of bacteria and bacteriophage discussed in the literature (e.g., Power 1992). These (viruses that feed on bacteria) to test prey-dependent limitations include dif®culty determining whether pop- and ratio-dependent models. We observed the response ulations are at or near equilibrium, problems with quan- of these communities to resource enrichment and com- tifying trophic level biomass, and dif®culty de®ning pared this response to quantitative predictions of prey- the physical boundaries of food chains. dependent and ratio-dependent models. Both predator Some of these limitations can be circumvented by and prey persisted in all replicates and we were able using laboratory model systems. Ecological experi- to estimate equilibrium densities and quantify stability ments with model laboratory systems can bridge the for all populations. In addition, bacteria and bacterio- gap between mathematical models and natural com- phage have suf®ciently short generation times that we munities, by allowing the predictions of mathematical were able to observe the effect of enrichment on the models to be rigorously examined in a biological sys- evolution of predator±prey interactions during the tem that is easily manipulated, replicated, and con- course of our experiment. trolled before such models are applied directly to nat- ural systems (Lawton 1995). Two attempts have been METHODS made to test prey-dependent and ratio-dependent mod- Experimental system els using laboratory model communities. In the ®rst attempt, Harrison (1995) reanalyzed the classic exper- Bacteria and bacteriophages have been proposed as iments of Luckinbill (1973). Luckinbill observed that ideal experimental systems for studying predator±prey decreasing the concentration
Recommended publications
  • Modeling Techniques
    Appendix A Modeling Techniques A.1 Population Growth Models Using Differential Equations Our main goal here is to introduce a few modeling techniques we use throughout this book. We do not intend however to provide here the fundamentals on modeling, a tutorial or a review. For these, we refer to other sources (DeAngelis et al. 1992; Ford 2009; Grimm et al. 2006; Kuang 1993). This Appendix is rather a refresher as well as an example of why using different modeling techniques for one and the same problem can be beneficial to understand biological processes better. We start with the simple exponential population growth to make modeling accessible even to complete beginners. Biologists generally define a population as a collection of individuals that belong to the same species and can potentially breed with each other. One of the best-known early models on population growth was outlined by Malthus (1798). He famously maintained that the human population is predicted to grow in an exponential manner, but the crucial products needed to sustain the population grow in but a linear manner. He argued that these different types of growths will trigger disasters when the population’s needs are not satisfied. The basic exponential growth model consists of a single positive feedback loop that arises from the fact that every individual (N) is predicted to have a fixed number of offspring (r), regardless of the size of the population, and thus also regardless of the remaining resources in the habitat: dN = rN dt (A.1.1) This exponential growth model had a profound effect on biology such as developing the theory of natural selection (Darwin 1859).
    [Show full text]
  • Density Dependence in Demography and Dispersal Generates Fluctuating
    Density dependence in demography and dispersal generates fluctuating invasion speeds Lauren L. Sullivana,1, Bingtuan Lib, Tom E. X. Millerc, Michael G. Neubertd, and Allison K. Shawa aDepartment of Ecology, Evolution and Behavior, University of Minnesota, Saint Paul, MN 55108; bDepartment of Mathematics, University of Louisville, Louisville, KY 40292; cDepartment of BioSciences, Program in Ecology and Evolutionary Biology, Rice University, Houston, TX 77005; and dBiology Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 Edited by Alan Hastings, University of California, Davis, CA, and approved March 30, 2017 (received for review November 23, 2016) Density dependence plays an important role in population regu- is driven by reproduction and dispersal from high-density pop- lation and is known to generate temporal fluctuations in popu- ulations behind the invasion front (13–15)]. The conventional lation density. However, the ways in which density dependence wisdom of a long-term constant invasion speed is widely applied affects spatial population processes, such as species invasions, (16, 17). are less understood. Although classical ecological theory suggests In contrast to classic approaches that emphasize a long-term that invasions should advance at a constant speed, empirical work constant speed, there is growing empirical recognition that inva- is illuminating the highly variable nature of biological invasions, sion dynamics can be highly variable and idiosyncratic (18–25). which often exhibit nonconstant spreading speeds, even in sim- There are several theoretical explanations for fluctuations in ple, controlled settings. Here, we explore endogenous density invasion speed (which we define here as any persistent tem- dependence as a mechanism for inducing variability in biologi- poral variability in spreading speed), including stochasticity in cal invasions with a set of population models that incorporate either demography or dispersal (24–28) and temporal or spatial density dependence in demographic and dispersal parameters.
    [Show full text]
  • Plant Diversity Increases with the Strength of Negative Density Dependence at the Global Scale
    RESEARCH FOREST ECOLOGY predators, pathogens, or herbivores) and/or com- petition for space and resources (2–4, 7). Numer- ous studies have documented the existence of CNDD in one or several plant species (8–12), and Plant diversity increases with the most of these studies explicitly or implicitly as- sume that stronger CNDD maintains higher spe- strength of negative density cies diversity in communities. However, only a handful of studies have explicitly examined dependence at the global scale the link between CNDD and species diversity (4, 11, 13, 14),andnostudyhasexaminedthis relationship across temperate and tropical lat- Joseph A. LaManna,1,2* Scott A. Mangan,2 Alfonso Alonso,3 Norman A. Bourg,4,5 itudes. Despite decades of study, our understand- Warren Y. Brockelman,6,7 Sarayudh Bunyavejchewin,8 Li-Wan Chang,9 ing of how processes at local scales—such as Jyh-Min Chiang,10 George B. Chuyong,11 Keith Clay,12 Richard Condit,13 density-dependent biotic interactions—influence Susan Cordell,14 Stuart J. Davies,15,16 Tucker J. Furniss,17 Christian P. Giardina,14 18 18 19,20 global patterns of biodiversity remains in flux I. A. U. Nimal Gunatilleke, C. V. Savitri Gunatilleke, Fangliang He, 1 15 21 22 23 ( , ). Robert W. Howe, Stephen P. Hubbell, Chang-Fu Hsieh, Both species-specific and more generalized 14 24 25 15,16 Faith M. Inman-Narahari, David Janík, Daniel J. Johnson, David Kenfack, mechanisms can cause CNDD, but only CNDD 3 24 26 17 Lisa Korte, Kamil Král, Andrew J. Larson, James A. Lutz, caused by species-specific mechanisms can main- 27,28 4 29 Sean M.
    [Show full text]
  • "Density Dependence and Independence"
    Density Dependence and Advanced article Independence Article Contents . Introduction: Concepts and Importance in Ecology Mark A Hixon, Oregon State University, Corvallis, Oregon, USA . Mechanisms of Density Dependence . Old Debates Resolved Darren W Johnson, Oregon State University, Corvallis, Oregon, USA . Detecting Density Dependence . Future Directions Online posting date: 15th December 2009 Density dependence occurs when the population growth parameter of interest involves population dynamics, rate, or constituent gain rates (e.g. birth and immi- including the population growth rate and the four primary gration) or loss rates (death and emigration), vary caus- demographic (or vital) rates – birth, death, immigration ally with population size or density (N). When these and emigration – although related parameters, such as growth and fecundity, are also investigated. See also: parameters do not vary with N, they are density-inde- Population Dynamics: Introduction pendent. Direct density dependence, where the popu- Use of the words ‘density dependence’ alone normally lation growth rate or gain rates vary as a negative means ‘direct density dependence’ (or compensation): the function of N, or the loss rates vary as a positive function of per capita (proportional) gain rate (population or indi- N, is necessary but not always sufficient for population vidual growth, fecundity, birth or immigration) decreases regulation. The opposite patterns, inverse density as N increases (Figure 1a) or the loss rate (death and/or dependence or the Allee effect, may push endangered emigration) increases as N increases (Figure 1b). The populations towards extinction. Direct density depend- opposite patterns are called inverse density dependence (or ence is caused by competition, and at times, predation.
    [Show full text]
  • Literature Cited in Lizards Natural History Database
    Literature Cited in Lizards Natural History database Abdala, C. S., A. S. Quinteros, and R. E. Espinoza. 2008. Two new species of Liolaemus (Iguania: Liolaemidae) from the puna of northwestern Argentina. Herpetologica 64:458-471. Abdala, C. S., D. Baldo, R. A. Juárez, and R. E. Espinoza. 2016. The first parthenogenetic pleurodont Iguanian: a new all-female Liolaemus (Squamata: Liolaemidae) from western Argentina. Copeia 104:487-497. Abdala, C. S., J. C. Acosta, M. R. Cabrera, H. J. Villaviciencio, and J. Marinero. 2009. A new Andean Liolaemus of the L. montanus series (Squamata: Iguania: Liolaemidae) from western Argentina. South American Journal of Herpetology 4:91-102. Abdala, C. S., J. L. Acosta, J. C. Acosta, B. B. Alvarez, F. Arias, L. J. Avila, . S. M. Zalba. 2012. Categorización del estado de conservación de las lagartijas y anfisbenas de la República Argentina. Cuadernos de Herpetologia 26 (Suppl. 1):215-248. Abell, A. J. 1999. Male-female spacing patterns in the lizard, Sceloporus virgatus. Amphibia-Reptilia 20:185-194. Abts, M. L. 1987. Environment and variation in life history traits of the Chuckwalla, Sauromalus obesus. Ecological Monographs 57:215-232. Achaval, F., and A. Olmos. 2003. Anfibios y reptiles del Uruguay. Montevideo, Uruguay: Facultad de Ciencias. Achaval, F., and A. Olmos. 2007. Anfibio y reptiles del Uruguay, 3rd edn. Montevideo, Uruguay: Serie Fauna 1. Ackermann, T. 2006. Schreibers Glatkopfleguan Leiocephalus schreibersii. Munich, Germany: Natur und Tier. Ackley, J. W., P. J. Muelleman, R. E. Carter, R. W. Henderson, and R. Powell. 2009. A rapid assessment of herpetofaunal diversity in variously altered habitats on Dominica.
    [Show full text]
  • STAGE STRUCTURE, DENSITY DEPENDENCE and the EFFICACY of MARINE RESERVES Colette M. St. Mary, Craig W. Osenberg, Thomas K. Frazer
    BULLETIN OF MARINE SCIENCE, 66(3): 675–690, 2000 STAGE STRUCTURE, DENSITY DEPENDENCE AND THE EFFICACY OF MARINE RESERVES Colette M. St. Mary, Craig W. Osenberg, Thomas K. Frazer and William J. Lindberg ABSTRACT The habitat requirements of fishes and other marine organisms often change with on- togeny, so many harvested species exhibit such extreme large-scale spatial segregation between life stages that all life stages cannot be protected within a single marine reserve. Nevertheless, most discussions of marine reserves have focused narrowly on single life- history events (e.g., reproduction or settlement) or a single life stage (e.g., adult or re- cruit). Instead, we hypothesize that an effective marine reserve system should often in- clude a diversity of protected habitats, each appropriate to a different life stage. In such a case, the spatial configuration of habitats within reserves, and of separate reserves across larger spatial scales, may affect how marine resources respond to reserve design. We explored these issues by developing a mathematical model of a fish population consist- ing of two benthic life stages (juvenile and adult) that use spatially distinct habitats and examined the population’s response to various management scenarios. Specifically, we varied the sizes of reserves protecting the two life stages and the degree of coupling between juvenile and adult reserves (i.e., the fraction of the protected juvenile stock that migrates into the adult reserve upon maturation). We examined the effects when density dependence operated in only the juvenile stage, only the adult stage, or both. The results demonstrated that population stage structure and the nature of density dependence should be incorporated into the design of marine reserves but did not provide robust support for the general tenet that all life stages must be protected for an effective reserve system.
    [Show full text]
  • DENSITY DEPENDENCE, the LOGISTIC EQUATION, and R- AUD
    89 DENSITY DEPENDENCE,THE LOGISTIC EQUATION, AND r- AUD K-SELECTION: A CRITIQUE AI{D AN AJ,TERNATIVEAPPROACH Jan Kozlowski Department of Animal Ecology Jagiellonlan University Karasia 6 30-060 Krak6w, POLAND Received September 18,1978; July 9, 1980 ABSTRACT: The logistic equation is a starting point of many ecological theories. Most ecologists agree that this equation is usually not conslstent Iillth observations and experlmental results but it ls argued that the slmpllclty of fhis equatlon ls the reason for this lnconsistency. In this paper I attempt to prove that the reason for inadequacy of the logistic equation l-s more fundamental: most systems qf equa- tions descrlbing the dynamlcs of population and lts resources cannot be transformed to the single equatlon for limited growth. Even if thls transformation is posslble' the K parameter depends on components of !r usually on the ratLo of mortallty rate to reproduction rate. Thls fact ls commonly overlooked because it ls assuned that denslty affects the abstract term r (popul-atlon growth rate). Because of doubts as to density-dependence and the logistlc equation, the r- and K-selectlon concept is criticLzed, both as a classiflcation system and as a predlctlve theory. It ls shown that when resources are explicltly consldered, it ls possible to prediet traits favored by natural- selectLon on a given resource level dlrectly from the descrlptlon of the system. This approach seems to be more advan- tageous than the r- and K-selection concept. I. INTRODUCTION Ttre logistic equation is a mathematical formulation of the denslty-dependent facEors concept. Though density-dependence may no longer be a burning issue lt ls dlfflcult to flnd a contemporary ecology textbook that does not contaln the loglstlc equation.
    [Show full text]
  • Drechslerella Stenobrocha Genome Illustrates the Mechanism Of
    Liu et al. BMC Genomics 2014, 15:114 http://www.biomedcentral.com/1471-2164/15/114 RESEARCH ARTICLE Open Access Drechslerella stenobrocha genome illustrates the mechanism of constricting rings and the origin of nematode predation in fungi Keke Liu1,2†, Weiwei Zhang1,2†, Yiling Lai1,2, Meichun Xiang1, Xiuna Wang1, Xinyu Zhang1 and Xingzhong Liu1* Abstract Background: Nematode-trapping fungi are a unique group of organisms that can capture nematodes using sophisticated trapping structures. The genome of Drechslerella stenobrocha, a constricting-ring-forming fungus, has been sequenced and reported, and provided new insights into the evolutionary origins of nematode predation in fungi, the trapping mechanisms, and the dual lifestyles of saprophagy and predation. Results: The genome of the fungus Drechslerella stenobrocha, which mechanically traps nematodes using a constricting ring, was sequenced. The genome was 29.02 Mb in size and was found rare instances of transposons and repeat induced point mutations, than that of Arthrobotrys oligospora. The functional proteins involved in nematode-infection, such as chitinases, subtilisins, and adhesive proteins, underwent a significant expansion in the A. oligospora genome, while there were fewer lectin genes that mediate fungus-nematode recognition in the D. stenobrocha genome. The carbohydrate-degrading enzyme catalogs in both species were similar to those of efficient cellulolytic fungi, suggesting a saprophytic origin of nematode-trapping fungi. In D. stenobrocha, the down-regulation of saprophytic enzyme genes and the up-regulation of infection-related genes during the capture of nematodes indicated a transition between dual life strategies of saprophagy and predation. The transcriptional profiles also indicated that trap formation was related to the protein kinase C (PKC) signal pathway and regulated by Zn(2)–C6 type transcription factors.
    [Show full text]
  • Counterintuitive Density-Dependent Growth in a Long-Lived Vertebrate After Removal of Nest Predators Ricky-John Spencer Iowa State University
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Digital Repository @ Iowa State University Ecology, Evolution and Organismal Biology Ecology, Evolution and Organismal Biology Publications 12-2006 Counterintuitive density-dependent growth in a long-lived vertebrate after removal of nest predators Ricky-John Spencer Iowa State University Fredric J. Janzen Iowa State University, [email protected] Michael B. Thompson University of Sydney Follow this and additional works at: http://lib.dr.iastate.edu/eeob_ag_pubs Part of the Evolution Commons, and the Population Biology Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ eeob_ag_pubs/151. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Ecology, Evolution and Organismal Biology at Iowa State University Digital Repository. It has been accepted for inclusion in Ecology, Evolution and Organismal Biology Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Counterintuitive density-dependent growth in a long-lived vertebrate after removal of nest predators Abstract Examining the phenotypic and genetic underpinnings of life-history variation in long-lived organisms is central to the study of life-history evolution. Juvenile growth and survival are often density dependent in reptiles, and theory predicts the evolution of slow growth in response to low resources (resource-limiting hypothesis), such as under densely populated conditions. However, rapid growth is predicted when exceeding some critical body size reduces the risk of mortality (mortality hypothesis).
    [Show full text]
  • 2 Wildebeest in the Serengeti: Limits to Exponential Growth
    Case Studies in Ecology and Evolution DRAFT 2 Wildebeest in the Serengeti: limits to exponential growth In the previous chapter we saw the power of exponential population growth. Even small rates of increase will eventually lead to very large populations if r stays constant. At the beginning of the 19th century Thomas Malthus wrote extensively about the power of exponential growth, pointing out that no population can continue to grow forever. Eventually the numbers of individuals will get so large that they must run out of resources. While Malthus was particularly interested in human populations, the same must be true for all kinds of species. No population can grow exponentially forever. Charles Darwin used those ideas as one of the cornerstones of his theory of natural selection. Because of the speed at which exponentially growing populations can increase in size, very few populations in nature will show exponential growth. Once a population has reached sufficient size to balance the available resource supply, there should be only minor fluctuations in numbers. Only when there is a large perturbation of the environment, such as the introduction of a species to a new area or severe reduction in population size due to hunting or disease will you find populations increasing in an exponential manner. One very well studied system for looking at population dynamics is the wildebeest Figure 2.1. top: Herd of Wildebeest. Bottom: Map (Connochaetes taurinus) on the Serengeti plains of the Serengeti-Mara ecosystem showing the of East Africa. Anthony Sinclair and Simon annual migration route. Mduma from the University of British Columbia have been studying them for 3 decades and have generated a long time series of records of population abundance.
    [Show full text]
  • 1 | Page Names: Activity 1: Population: the Goal of This Activity
    BIO 108-2017 Activity 2- population and community biology Activity 1: population: The goal of this activity is familiarize you with population biology models: In particular: growth models and how they apply to resource management Population Biology: Exponential Growth – 푑푁 = 푟푁 푑푡 This is the most basic population growth model. Growth is dependent on two terms: the existing population (N) and the intrinsic growth rate (r). r is actually a derived and instantaneous rate defined as b-d: birth – death rates. Population Biology: Logistic Growth – 푑푁 퐾 − 푁 = 푟푁( ) 푑푡 퐾 This population growth model has two parts: the left clause is the exponential part and the right clause is a dampening function that introduces density dependence to the model. K in this model is the carrying capacity of the population. Below is the logistic curve for: R=1 Starting population = 2 K=200 1 | P a g e Names: BIO 108-2017 Activity 2- population and community biology The logistic equation shown above is written in its derivative form. Recall from calculus that the second derivative of an equation can be used to determine the minimum and maximum rate of change in a population. The maximum rate of change is the point on the graph above where the population grows fastest. It is the maximum instantaneous slope. Why would we want to know this? Because it has been used as a target for management of harvested species, especially in fisheries. The idea is that harvest of populations to a size equal to the population where growth rate is highest maximizes sustainable harvest.
    [Show full text]
  • Arxiv:2009.11357V3 [Physics.Bio-Ph] 18 Apr 2021 H Rbblt Itiuino H Otrcn Common Recent Most 15]
    Virus-host interactions shape viral dispersal giving rise to distinct classes of travelling waves in spatial expansions 1 1 1, 2 3, 4 1, Michael Hunter, Nikhil Krishnan, Tongfei Liu, Wolfram M¨obius, and Diana Fusco ∗ 1Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom 2Department of Physics, University of Oxford, Oxford, OX1 3PJ, United Kingdom 3Living Systems Institute, University of Exeter, Exeter, EX4 4QD, UK 4Physics and Astronomy, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK (Dated: April 20, 2021) Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit density-dependent dispersal. Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion coefficient akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion.
    [Show full text]