Effective Population Size in Ecology and Evolution
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A Metapopulation Model with Discrete Size Structure
A METAPOPULATION MODEL WITH DISCRETE SIZE STRUCTURE MAIA MARTCHEVA¤ AND HORST R. THIEME¦ Abstract. We consider a discrete size-structured metapopulation mo- del with the proportions of patches occupied by n individuals as de- pendent variables. Adults are territorial and stay on a certain patch. The juveniles may emigrate to enter a dispersers' pool from which they can settle on another patch and become adults. Absence of coloniza- tion and absence of emigration lead to extinction of the metapopulation. We de¯ne the basic reproduction number R0 of the metapopulation as a measure for its strength of persistence. The metapopulation is uniformly weakly persistent if R0 > 1. We identify subcritical bifurcation of per- sistence equilibria from the extinction equilibrium as a source of multiple persistence equilibria: it occurs, e.g., when the immigration rate (into occupied pathes) exceeds the colonization rate (of empty patches). We determine that the persistence-optimal dispersal strategy which maxi- mizes the basic reproduction number is of bang-bang type: If the number of adults on a patch is below carrying capacity all the juveniles should stay, if it is above the carrying capacity all the juveniles should leave. 1. Introduction A metapopulation is a group of populations of the same species which occupy separate areas (patches) and are connected by dispersal. Each sep- arate population in the metapopulation is referred to as a local population. Metapopulations occur naturally or by human activity as a result of habitat loss and fragmentation. An overview of the empirical evidence for the exis- tence of metapopulation dynamics can be found in [31]. -
Effective Population Size and Genetic Conservation Criteria for Bull Trout
North American Journal of Fisheries Management 21:756±764, 2001 q Copyright by the American Fisheries Society 2001 Effective Population Size and Genetic Conservation Criteria for Bull Trout B. E. RIEMAN* U.S. Department of Agriculture Forest Service, Rocky Mountain Research Station, 316 East Myrtle, Boise, Idaho 83702, USA F. W. A LLENDORF Division of Biological Sciences, University of Montana, Missoula, Montana 59812, USA Abstract.ÐEffective population size (Ne) is an important concept in the management of threatened species like bull trout Salvelinus con¯uentus. General guidelines suggest that effective population sizes of 50 or 500 are essential to minimize inbreeding effects or maintain adaptive genetic variation, respectively. Although Ne strongly depends on census population size, it also depends on demographic and life history characteristics that complicate any estimates. This is an especially dif®cult problem for species like bull trout, which have overlapping generations; biologists may monitor annual population number but lack more detailed information on demographic population structure or life history. We used a generalized, age-structured simulation model to relate Ne to adult numbers under a range of life histories and other conditions characteristic of bull trout populations. Effective population size varied strongly with the effects of the demographic and environmental variation included in our simulations. Our most realistic estimates of Ne were between about 0.5 and 1.0 times the mean number of adults spawning annually. We conclude that cautious long-term management goals for bull trout populations should include an average of at least 1,000 adults spawning each year. Where local populations are too small, managers should seek to conserve a collection of interconnected populations that is at least large enough in total to meet this minimum. -
Routledge Handbook of Ecological and Environmental Restoration the Principles of Restoration Ecology at Population Scales
This article was downloaded by: 10.3.98.104 On: 26 Sep 2021 Access details: subscription number Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK Routledge Handbook of Ecological and Environmental Restoration Stuart K. Allison, Stephen D. Murphy The Principles of Restoration Ecology at Population Scales Publication details https://www.routledgehandbooks.com/doi/10.4324/9781315685977.ch3 Stephen D. Murphy, Michael J. McTavish, Heather A. Cray Published online on: 23 May 2017 How to cite :- Stephen D. Murphy, Michael J. McTavish, Heather A. Cray. 23 May 2017, The Principles of Restoration Ecology at Population Scales from: Routledge Handbook of Ecological and Environmental Restoration Routledge Accessed on: 26 Sep 2021 https://www.routledgehandbooks.com/doi/10.4324/9781315685977.ch3 PLEASE SCROLL DOWN FOR DOCUMENT Full terms and conditions of use: https://www.routledgehandbooks.com/legal-notices/terms This Document PDF may be used for research, teaching and private study purposes. Any substantial or systematic reproductions, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 3 THE PRINCIPLES OF RESTORATION ECOLOGY AT POPULATION SCALES Stephen D. -
Evolutionary Restoration Ecology
ch06 2/9/06 12:45 PM Page 113 189686 / Island Press / Falk Chapter 6 Evolutionary Restoration Ecology Craig A. Stockwell, Michael T. Kinnison, and Andrew P. Hendry Restoration Ecology and Evolutionary Process Restoration activities have increased dramatically in recent years, creating evolutionary chal- lenges and opportunities. Though restoration has favored a strong focus on the role of habi- tat, concerns surrounding the evolutionary ecology of populations are increasing. In this con- text, previous researchers have considered the importance of preserving extant diversity and maintaining future evolutionary potential (Montalvo et al. 1997; Lesica and Allendorf 1999), but they have usually ignored the prospect of ongoing evolution in real time. However, such contemporary evolution (changes occurring over one to a few hundred generations) appears to be relatively common in nature (Stockwell and Weeks 1999; Bone and Farres 2001; Kin- nison and Hendry 2001; Reznick and Ghalambor 2001; Ashley et al. 2003; Stockwell et al. 2003). Moreover, it is often associated with situations that may prevail in restoration projects, namely the presence of introduced populations and other anthropogenic disturbances (Stockwell and Weeks 1999; Bone and Farres 2001; Reznick and Ghalambor 2001) (Table 6.1). Any restoration program may thus entail consideration of evolution in the past, present, and future. Restoration efforts often involve dramatic and rapid shifts in habitat that may even lead to different ecological states (such as altered fire regimes) (Suding et al. 2003). Genetic variants that evolved within historically different evolutionary contexts (the past) may thus be pitted against novel and mismatched current conditions (the present). The degree of this mismatch should then determine the pattern and strength of selection acting on trait variation in such populations (Box 6.1; Figure 6.1). -
Life History Evolution in Response to Changes in Metapopulation
bioRxiv preprint doi: https://doi.org/10.1101/021683; this version posted October 9, 2015. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 1 Life history evolution in response to changes in metapopulation 2 structure in an arthropod herbivore 3 4 Authors: De Roissart A1, Wybouw N2,3, Renault D 4, Van Leeuwen T2, 3 & Bonte D1,* 5 6 Affiliations: 7 1 Ghent University, Dep. Biology, Terrestrial Ecology Unit, K.L. Ledeganckstraat 35, B-9000 8 Ghent, Belgium 9 2 Ghent University, Dep. Crop Protection, Laboratory of Agrozoology, Coupure Links 653, B- 10 9000 Ghent, Belgium 11 3 University of Amsterdam, Institute for Biodiversity and Ecosystem Dynamics, Science Park 12 904, 1098 XH Amsterdam, the Netherlands 13 4 Université de Rennes 1, UMR 6553 ECOBIO CNRS, Avenue du Gal Leclerc 263, CS 74205, 14 35042 Rennes Cedex, France 15 16 17 *Corresponding author: Dries Bonte, Ghent University, Dep. Biology, Terrestrial Ecology 18 Unit, K.L. Ledeganckstraat 35, B-9000 Ghent, Belgium. Email: [email protected]; tel: 19 0032 9 264 52 13; fax: 0032 9 264 87 94 20 21 E-mail address of the co-authors:[email protected]; [email protected]; 22 [email protected]; [email protected]; [email protected] 23 24 Manuscript type: Standard paper 25 26 Running title: Metapopulation structure and life history evolution 27 28 Key-words: metapopulation-level selection, stochasticity, Tetranychus urticae 29 30 1 bioRxiv preprint doi: https://doi.org/10.1101/021683; this version posted October 9, 2015. -
6 Metapopulations of Butterflies
Case Studies in Ecology and Evolution DRAFT 6 Metapopulations of Butterflies Butterflies inhabit an unpredictable world. Consider the checkerspot butterfly, Melitaea cinxia, also known as the Glanville Fritillary. They depend on specific host plants for larval development. The population size is buffeted by the vagaries of weather, availability of suitable host plants, and random demographic stochasticity in the small patches. The result is that local populations often go extinct when the host plants fail, or when larvae are unable to complete development before the winter. But butterflies also have wings. Even though the checkerspots are not particularly strong flyers (they move a maximum of a couple of kilometers and most individuals remain in their natal patch), butterflies occasionally move from one patch to another. Empty patches are eventually recolonized. So, over a regional scale the total number of butterflies remains nearly constant, despite the constant turnover of local populations. Professor Ilkka Hanski and his students in Finland have been studying the patterns of extinction and recolonization of habitat patches by the checkerspot butterflies for two decades on the small island of Åland in southwestern Finland. The butterflies on Åland can be described as a “metapopulation”, or “population of populations”, connected by migration. In the original formulation by Richard Levins, he imagined a case where each population was short-lived, and the persistence of the system depended on the re-colonization of empty patches by immigrants from other nearby source populations. Thus colonizations and extinctions operate in a dynamic balance that can maintain a species in the landscape of interconnected patches indefinitely. -
Population Biology & Life Tables
EXERCISE 3 Population Biology: Life Tables & Theoretical Populations The purpose of this lab is to introduce the basic principles of population biology and to allow you to manipulate and explore a few of the most common equations using some simple Mathcad© wooksheets. A good introduction of this subject can be found in a general biology text book such as Campbell (1996), while a more complete discussion of pop- ulation biology can be found in an ecology text (e.g., Begon et al. 1990) or in one of the references listed at the end of this exercise. Exercise Objectives: After you have completed this lab, you should be able to: 1. Give deÞnitions of the terms in bold type. 2. Estimate population size from capture-recapture data. 3. Compare the following sets of terms: semelparous vs. iteroparous life cycles, cohort vs. static life tables, Type I vs. II vs. III survivorship curves, density dependent vs. density independent population growth, discrete vs. continuous breeding seasons, divergent vs. dampening oscillation cycles, and time lag vs. generation time in population models. 4. Calculate lx, dx, qx, R0, Tc, and ex; and estimate r from life table data. 5. Choose the appropriate theoretical model for predicting growth of a given population. 6. Calculate population size at a particular time (Nt+1) when given its size one time unit previous (Nt) and the corre- sponding variables (e.g., r, K, T, and/or L) of the appropriate model. 7. Understand how r, K, T, and L affect population growth. Population Size A population is a localized group of individuals of the same species. -
Equilibrium Theory of Island Biogeography: a Review
Equilibrium Theory of Island Biogeography: A Review Angela D. Yu Simon A. Lei Abstract—The topography, climatic pattern, location, and origin of relationship, dispersal mechanisms and their response to islands generate unique patterns of species distribution. The equi- isolation, and species turnover. Additionally, conservation librium theory of island biogeography creates a general framework of oceanic and continental (habitat) islands is examined in in which the study of taxon distribution and broad island trends relation to minimum viable populations and areas, may be conducted. Critical components of the equilibrium theory metapopulation dynamics, and continental reserve design. include the species-area relationship, island-mainland relation- Finally, adverse anthropogenic impacts on island ecosys- ship, dispersal mechanisms, and species turnover. Because of the tems are investigated, including overexploitation of re- theoretical similarities between islands and fragmented mainland sources, habitat destruction, and introduction of exotic spe- landscapes, reserve conservation efforts have attempted to apply cies and diseases (biological invasions). Throughout this the theory of island biogeography to improve continental reserve article, theories of many researchers are re-introduced and designs, and to provide insight into metapopulation dynamics and utilized in an analytical manner. The objective of this article the SLOSS debate. However, due to extensive negative anthropo- is to review previously published data, and to reveal if any genic activities, overexploitation of resources, habitat destruction, classical and emergent theories may be brought into the as well as introduction of exotic species and associated foreign study of island biogeography and its relevance to mainland diseases (biological invasions), island conservation has recently ecosystem patterns. become a pressing issue itself. -
Metapopulations and Metacommunities: Combining Spatial and Temporal Perspectives in Plant Ecology
Journal of Ecology 2012, 100, 88–103 doi: 10.1111/j.1365-2745.2011.01917.x CENTENARY SYMPOSIUM SPECIAL FEATURE Metapopulations and metacommunities: combining spatial and temporal perspectives in plant ecology Helen M. Alexander1*, Bryan L. Foster1, Ford Ballantyne IV2, Cathy D. Collins3, Janis Antonovics4 and Robert D. Holt5 1Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045-7534, USA; 2Department of Ecology and Evolutionary Biology and Kansas Biological Survey, University of Kansas, Lawrence, KS 66045-7534, USA; 3Department of Biology, Colby College, Waterville, ME 04901-8840, USA; 4Department of Biology, University of Virginia, Charlottesville, VA 22904, USA; and 5Department of Biology, University of Florida, 223 Bartram Hall, P.O. Box 118525, Gainesville, FL 32611-8525, USA Summary 1. Metapopulation and metacommunity theories occupy a central role in ecology, but can be diffi- cult to apply to plants. Challenges include whether seed dispersal is sufficient for population connec- tivity, the role of seed banks and problems with studying colonization and extinction in long-lived and clonal plants. Further, populations often do not occupy discrete habitat patches. Despite these difficulties, we present case studies to illustrate explicit integration of spatial and temporal data in plant ecology. 2. First, on the population level, we focused on two early successional species that lack discrete hab- itat patches. Multi-year data sets taken with a grid approach and simple models permit the analysis of landscape dynamics that reflect regional as well as local processes. Using Silene latifolia,we examined colonization. We found evidence for seed dispersal and connectivity among populations across a large landscape. -
Patch Dynamics and Metapopulation Theory: the Case of Successional Species
Journal of Theoretical Biology (2001) 209 (3): 333-344. http://dx.doi.org/10.1006/jtbi.2001.2269 Patch Dynamics and Metapopulation Theory: The Case of Successional Species a a,b Priyanga Amarasekare and Hugh Possingham a National Center for Ecological Analysis and Synthesis, University of California, Santa Barbara, 735 State Street, Suite 300, Santa Barbara, CA, 93101-5504, U.S.A. b Departments of Zoology and Mathematics, The University of Queensland, St Lucia, QLD 4072, Australia Abstract We present a mathematical framework that combines extinction–colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied–suitable, empty–suitable, occupied–unsuitable and empty– unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate, extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction–colonization dynamics influences long- term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required for viable management of such species in the Florida scrub ecosystem. -
COULD R SELECTION ACCOUNT for the AFRICAN PERSONALITY and LIFE CYCLE?
Person. individ.Diff. Vol. 15, No. 6, pp. 665-675, 1993 0191-8869/93 S6.OOf0.00 Printedin Great Britain.All rightsreserved Copyright0 1993Pergamon Press Ltd COULD r SELECTION ACCOUNT FOR THE AFRICAN PERSONALITY AND LIFE CYCLE? EDWARD M. MILLER Department of Economics and Finance, University of New Orleans, New Orleans, LA 70148, U.S.A. (Received I7 November 1992; received for publication 27 April 1993) Summary-Rushton has shown that Negroids exhibit many characteristics that biologists argue result from r selection. However, the area of their origin, the African Savanna, while a highly variable environment, would not select for r characteristics. Savanna humans have not adopted the dispersal and colonization strategy to which r characteristics are suited. While r characteristics may be selected for when adult mortality is highly variable, biologists argue that where juvenile mortality is variable, K character- istics are selected for. Human variable birth rates are mathematically similar to variable juvenile birth rates. Food shortage caused by African drought induce competition, just as food shortages caused by high population. Both should select for K characteristics, which by definition contribute to success at competition. Occasional long term droughts are likely to select for long lives, late menopause, high paternal investment, high anxiety, and intelligence. These appear to be the opposite to Rushton’s r characteristics, and opposite to the traits he attributes to Negroids. Rushton (1985, 1987, 1988) has argued that Negroids (i.e. Negroes) were r selected. This idea has produced considerable scientific (Flynn, 1989; Leslie, 1990; Lynn, 1989; Roberts & Gabor, 1990; Silverman, 1990) and popular controversy (Gross, 1990; Pearson, 1991, Chapter 5), which Rushton (1989a, 1990, 1991) has responded to. -
On the Principle of Competitive Exclusion in Metapopulation Models
Appl. Math. Inf. Sci. 9, No. 4, 1739-1752 (2015) 1739 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.12785/amis/090411 On the Principle of Competitive Exclusion in Metapopulation Models Davide Belocchio, Roberto Cavoretto, Giacomo Gimmelli, Alessandro Marchino and Ezio Venturino∗ Dipartimento di Matematica “Giuseppe Peano”, Universita di Torino, via Carlo Alberto 10, 10123 Torino, Italy Received: 12 Oct. 2014, Revised: 12 Jan. 2015, Accepted: 13 Jan. 2015 Published online: 1 Jul. 2015 Abstract: In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the populations is provided. A kind of competitive exclusion principle for metapopulation systems is obtained. At the same time we show that the competitive exclusion principle at the local patch level may be prevented to hold by the migration phenomenon, i.e. two competing populations may coexist, provided that only one of them is allowed to freely move or that migrations for both occur just in one direction. Keywords: populations, competition, migrations, patches, competitive exclusion 1 Introduction metapopulation concept becomes essential to describe the natural interactions. This paper attempts the development In this paper we consider a minimal metapopulation of such an issue in this framework. Note that another model with two competing populations. It consists of two recent contribution in the context of patchy environments different environments among which migrations are considers also a transmissible disease affecting the allowed. populations, thereby introducing the concept of As migrations do occur indeed in nature, [6], the metaecoepidemic models, [30].