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Grumbach C, Reurik FN, Segura J, Franco D, Hilker FM. The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models. J Math Biol 2023; 87:60. [PMID: 37733146 PMCID: PMC10514157 DOI: 10.1007/s00285-023-01984-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Revised: 06/04/2023] [Accepted: 08/09/2023] [Indexed: 09/22/2023]
Abstract
Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two standard density-dependent population growth functions, one in discrete and one in continuous time. A complete analysis of the discrete-time model reveals four response scenarios of the asymptotic total population size to increasing dispersal rate: (1) monotonically beneficial, (2) unimodally beneficial, (3) beneficial turning detrimental, and (4) monotonically detrimental. The same response scenarios exist for the continuous-time model, and we show that the parameter conditions are analogous between the discrete- and continuous-time setting. A detailed biological interpretation offers insight into the mechanisms underlying the response scenarios that thus improve our general understanding how potential conservation efforts affect population size.
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Affiliation(s)
- Carolin Grumbach
- Institute of Mathematics and Institute of Environmental Systems Research, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany
| | - Femke N. Reurik
- Institute of Mathematics and Institute of Environmental Systems Research, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany
| | - Juan Segura
- Department of Finance & Management Control, EADA Business School, c/ Aragó 204, 08011 Barcelona, Spain
| | - Daniel Franco
- Department of Applied Mathematics, UNED, c/ Juan del Rosal 12, 28040 Madrid, Spain
| | - Frank M. Hilker
- Institute of Mathematics and Institute of Environmental Systems Research, Osnabrück University, Barbarastraße 12, 49076 Osnabrück, Germany
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2
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Jiabu D, Li W. Impact of different invasion methods of invasive species on omnivorous food webs. Ecol Modell 2023. [DOI: 10.1016/j.ecolmodel.2022.110217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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3
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Sadykov A, Farnsworth KD. Model of two competing populations in two habitats with migration: Application to optimal marine protected area size. Theor Popul Biol 2021; 142:114-122. [PMID: 34762901 DOI: 10.1016/j.tpb.2021.10.002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Revised: 10/10/2021] [Accepted: 10/23/2021] [Indexed: 11/26/2022]
Abstract
The standard model of a single population fragmented into two patches connected by migration, was first introduced in the 1970s by Freedman and Waltman, since generating long-term research interest, though its full analysis for arbitrary values of migration rate has only been completed relatively recently. Here, we present a model of two competing species in a two-patch habitat with migrations between patches. We derive equilibrium solutions of this model for three cases of migration rate resulting in isolated, well-mixed and semi-isolated habitats. We evaluate the full range of effects of habitat, life-history and migration parameters on population sizes. Finally, we add harvesting mortality and define conditions under which introduction of a no-harvesting (protected) area may lead to increased maximum sustainable yield. The results have applications in mixed fishery management and the design of wildlife protection zones, including marine protected areas (MPAs).
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Affiliation(s)
- Alexander Sadykov
- School of Biological Sciences, Queen's University Belfast, Belfast, UK; The Centre for Ecological and Evolutionary Synthesis, University of Oslo, Oslo, Norway.
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4
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Rugiero L, Capula M, Dendi D, Petrozzi F, Fa JE, Funk SM, Burke RL, Luiselli L. Testing hypotheses of habitat use and temporal activity in relation to body plan in a Mediterranean lizard community. CAN J ZOOL 2021. [DOI: 10.1139/cjz-2021-0083] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
A body plan (bauplan) is a suite of morphological characters shared by phylogenetically related animals at some point during their development. Despite its value, the bauplan concept is still rarely employed to characterize functional groups in community ecology. Here, we examine habitat use and spatio-temporal activity correlates of an entire seven-species community of lizards with different bauplans. The study was carried out in three locations in central Italy, encompassing a complex landscape with a patchy mosaic of a wide variety of habitats and microclimates. We tested four hypotheses regarding niche breadth, habitat use, and activity patterns. The first hypothesis, niche complementarity, in which species with similar body shapes should non-randomly partition available habitats, was not supported. By contrast, the hypotheses that larger bodied species should have a wider niche breadth, that slower species should inhabit habitat types of higher cover, and species inhabiting open sunny habitats should exhibit more seasonally variable activity patterns, were all supported by the data. Sympatric lizard communities in our study area were clearly organized by autecological constraints and eco-physiological attributes.
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Affiliation(s)
- Lorenzo Rugiero
- Institute for Development, Ecology, Conservation and Cooperation, via G. Tomasi di Lampedusa 33, I-00144 Rome, Italy
| | | | - Daniele Dendi
- Institute for Development, Ecology, Conservation and Cooperation, via G. Tomasi di Lampedusa 33, I-00144 Rome, Italy
- Department of Applied and Environmental Biology, Rivers State University of Science and Technology, P.M.B. 5080, Port Harcourt, Nigeria
- Department of Zoology, University of Lomé, Lomé, Togo
| | | | - Julia E. Fa
- Department of Natural Sciences, School of Science and the Environment, Manchester Metropolitan University, Manchester, M1 5GD, UK
- Center for International Forestry Research (CIFOR), CIFOR Headquarters, Bogor, 16115, Indonesia
| | | | | | - Luca Luiselli
- Institute for Development, Ecology, Conservation and Cooperation, via G. Tomasi di Lampedusa 33, I-00144 Rome, Italy
- Department of Applied and Environmental Biology, Rivers State University of Science and Technology, P.M.B. 5080, Port Harcourt, Nigeria
- Department of Zoology, University of Lomé, Lomé, Togo
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6
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A temporal model of territorial defence with antagonistic interactions. Theor Popul Biol 2020; 134:15-35. [DOI: 10.1016/j.tpb.2020.03.005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Revised: 03/26/2020] [Accepted: 03/27/2020] [Indexed: 11/18/2022]
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7
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Maspons J, Molowny-Horas R, Sol D. Behaviour, life history and persistence in novel environments. Philos Trans R Soc Lond B Biol Sci 2019; 374:20180056. [PMID: 31352883 DOI: 10.1098/rstb.2018.0056] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Understanding what affects population growth in novel environments is fundamental to forecast organisms' responses to global change, including biological invasions and land use intensification. Novel environments are challenging because they can cause maladaptation, increasing the risk of extinction by negative population growth. Animals can avoid extinction by improving the phenotype-environment match through behavioural responses, notably matching habitat choice and learning. However, the demographic consequences of these responses remain insufficiently understood in part because they have not been analysed within a life-history context. By means of an individual-based model, we show here that matching habitat choice and learning interact with life history to influence persistence in novel environments. In maladaptive contexts, the likelihood of persisting is higher for life-history strategies that increase the value of adults over the value of offspring, even at the cost of decreasing reproduction. Such a strategy facilitates persistence in novel environments by reducing the costs of a reproductive failure while increasing the benefits of behavioural responses. Our results reinforce the view that a more predictive theory for extinction risk under rapid environmental changes requires considering behavioural responses and life history as part of a common adaptive strategy to cope with environmental changes. This article is part of the theme issue 'Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation'.
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Affiliation(s)
- Joan Maspons
- CREAF, Cerdanyola del Vallès, Catalonia 08193, Spain
| | | | - Daniel Sol
- CREAF, Cerdanyola del Vallès, Catalonia 08193, Spain.,CSIC (Centre for Ecological Research and Applied Forestries), Cerdanyola del Vallès, Catalonia 08193, Spain
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8
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Conserving large carnivores amidst human-wildlife conflict: The scope of ecological theory to guide conservation practice. FOOD WEBS 2019. [DOI: 10.1016/j.fooweb.2018.e00108] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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9
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Argasinski K, Broom M. Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics. Theory Biosci 2018; 137:33-50. [PMID: 29159683 PMCID: PMC5893772 DOI: 10.1007/s12064-017-0257-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2016] [Accepted: 10/16/2017] [Indexed: 11/13/2022]
Abstract
In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk-Dove example.
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Affiliation(s)
- K. Argasinski
- Institute of Mathematics of Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa 10, Poland
| | - M. Broom
- Department of Mathematics, City, University of London, Northampton Square, London, EC1V 0HB UK
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Kang Y, Sasmal SK, Messan K. A two-patch prey-predator model with predator dispersal driven by the predation strength. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2017; 14:843-880. [PMID: 28608701 DOI: 10.3934/mbe.2017046] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.
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Affiliation(s)
- Yun Kang
- Sciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ 85212, United States.
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11
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Ramos-Jiliberto R, Moisset de Espanés P. The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka: Comment. Ecosphere 2017. [DOI: 10.1002/ecs2.1895] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Affiliation(s)
- Rodrigo Ramos-Jiliberto
- Centro Nacional del Medio Ambiente; Universidad de Chile; Avenida Alcalde Fernando Castillo Velasco 9975 La Reina Santiago Chile
- Programas de Postgrado; Facultad de Ciencias; Pontificia Universidad Católica de Valparaíso; Avenida Brasil 2950 Valparaíso Chile
| | - Pablo Moisset de Espanés
- Instituto de Dinámica Celular y Biotecnología; Avenida Beaucheff 850 Santiago Chile
- Centro de Modelamiento Matemático; FCFM; Universidad de Chile; Avenida Beaucheff 850 Santiago Chile
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12
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Garay J, Cressman R, Xu F, Varga Z, Cabello T. Optimal Forager against Ideal Free Distributed Prey. Am Nat 2015; 186:111-22. [PMID: 26098343 DOI: 10.1086/681638] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- József Garay
- Hungarian Academy of Sciences-Eötvös University (MTA-ELTE) Theoretical Biology and Evolutionary Ecology Research Group; and Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary
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Hammill E, Fitzjohn RG, Srivastava DS. Conspecific density modulates the effect of predation on dispersal rates. Oecologia 2015; 178:1149-58. [PMID: 25820788 DOI: 10.1007/s00442-015-3303-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2014] [Accepted: 03/16/2015] [Indexed: 10/23/2022]
Abstract
Dispersal decisions underlie the spatial dynamics of metacommunities. Prey individuals may disperse to reduce the risk of either predation or starvation, and both of these risks may depend on conspecific density. Surprisingly, there is little theory examining how dispersal rates should change in response to the combined effects of predation and changes in conspecific density. We develop such a model and show that, under certain conditions, predators may induce dispersal at low prey densities but not high prey densities. We then experimentally manipulate the density of the ciliate Paramecium aurelia and the perceived presence of its predator, the flatworm Stenostomum virginiamum, in a two-patch metacommunity to parameterise the model. Paramecium dispersed in response to Stenostomum at low densities, but they reduced their dispersal in response to predation risk at high predator densities. By applying our model to the empirical data, we show that this switch in dispersal strategy, linked to increases in prey density, occurred because predators increased the difficulty or risk of dispersal. Together, the model and experiment reveal that the effects of predators on dispersal are contingent on prey density. Previous studies have sometimes reported an increase in dispersal rate when predation risk is elevated, and other times a decrease in dispersal rate. Our demonstration of a switch point, with predation risk increasing dispersal at low prey densities but reducing dispersal above a threshold of prey density, may reconcile the diversity of prey dispersal behaviours reported in these previous investigations and observed in nature.
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Affiliation(s)
- Edd Hammill
- School of the Environment, University of Technology, Sydney, Harris and Broadway, Ultimo, Sydney, NSW, 2007, Australia,
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14
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Křivan V, Jana D. Effects of animal dispersal on harvesting with protected areas. J Theor Biol 2015; 364:131-8. [DOI: 10.1016/j.jtbi.2014.09.010] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2014] [Revised: 09/02/2014] [Accepted: 09/06/2014] [Indexed: 12/01/2022]
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15
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Lin YT, Kim H, Doering CR. Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments. J Math Biol 2014; 70:647-78. [PMID: 24682331 DOI: 10.1007/s00285-014-0776-9] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2013] [Revised: 02/21/2014] [Indexed: 11/25/2022]
Abstract
The selection of dispersion is a classical problem in ecology and evolutionary biology. Deterministic dynamical models of two competing species differing only in their passive dispersal rates suggest that the lower mobility species has a competitive advantage in inhomogeneous environments, and that dispersion is a neutral characteristic in homogeneous environments. Here we consider models including local population fluctuations due to both individual movements and random birth and death events to investigate the effect of demographic stochasticity on the competition between species with different dispersal rates. In this paper, the first of two, we focus on homogeneous environments where deterministic models predict degenerate dynamics in the sense that there are many (marginally) stable equilibria with the species' coexistence ratio depending only on initial data. When demographic stochasticity is included the situation changes. A novel large carrying capacity ([Formula: see text]) asymptotic analysis, confirmed by direct numerical simulations, shows that a preference for faster dispersers emerges on a precisely defined [Formula: see text] time scale. We conclude that while there is no evolutionarily stable rate for competitors to choose in these models, the selection mechanism quantified here is the essential counterbalance in spatially inhomogeneous models including demographic fluctuations which do display an evolutionarily stable dispersal rate.
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Affiliation(s)
- Yen Ting Lin
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109-1020, USA,
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16
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Křivan V. The Allee-type ideal free distribution. J Math Biol 2013; 69:1497-513. [PMID: 24306202 DOI: 10.1007/s00285-013-0742-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Revised: 11/20/2013] [Indexed: 11/28/2022]
Abstract
The ideal free distribution (IFD) in a two-patch environment where individual fitness is positively density dependent at low population densities is studied. The IFD is defined as an evolutionarily stable strategy of the habitat selection game. It is shown that for low and high population densities only one IFD exists, but for intermediate population densities there are up to three IFDs. Population and distributional dynamics described by the replicator dynamics are studied. It is shown that distributional stability (i.e., IFD) does not imply local stability of a population equilibrium. Thus distributional stability is not sufficient for population stability. Results of this article demonstrate that the Allee effect can strongly influence not only population dynamics, but also population distribution in space.
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Affiliation(s)
- Vlastimil Křivan
- Biology Center, Academy of Sciences of the Czech Republic, and Faculty of Science, University of South Bohemia, Branišovská 31, 370 05 , Ceske Budejovice, Czech Republic,
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