Hệ thống săn mồi - con mồi trong các dòng suối và sông

Theoretical Ecology - Tập 3 - Trang 175-193 - 2009
Frank M. Hilker1,2, Mark A. Lewis1,3
1Centre for Mathematical Biology, Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, Canada
2Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, UK
3Department of Biological Sciences, University of Alberta, Edmonton, Canada

Tóm tắt

Nhiều hệ thống săn mồi - con mồi được tìm thấy trong các môi trường có dòng chảy chủ yếu là một chiều như suối và sông. Những sự thay đổi trong chế độ dòng chảy tự nhiên (ví dụ: do sự quản lý của con người hoặc sự nóng lên toàn cầu) đặt các quần thể sinh học vào tình trạng rủi ro. Mục tiêu của bài báo này là phát triển một phương pháp đơn giản liên kết tốc độ dòng chảy (dòng chảy) với sự giữ lại quần thể (sự tồn tại) và rửa trôi (tuyệt chủng). Chúng tôi xem xét các hệ thống gồm con mồi và các loài săn mồi chuyên biệt, cũng như các loài săn mồi tổng quát, trong đó chúng tôi phân biệt các kịch bản tốc độ dòng chảy sau: (a) đồng sống, (b) tồn tại chỉ của con mồi hoặc (c) chỉ của các loài săn mồi (miễn là chúng là loài tổng quát), và (d) tuyệt chủng cả hai quần thể. Phương pháp được dựa trên một mô hình phản ứng - vận chuyển - khuếch tán và các phương pháp xấp xỉ tốc độ sóng truyền. Chúng tôi cho thấy rằng phương pháp này khớp tốt với tỷ lệ lan truyền quan sát được trong các mô phỏng số. Kết quả từ bài báo này có thể cung cấp một công cụ hữu ích trong việc đánh giá nhu cầu về dòng chảy trong dòng, ước tính tốc độ dòng chảy cần thiết để bảo vệ các quần thể sống ven sông.

Từ khóa

#quản lý dòng chảy #hệ sinh thái #quần thể sinh học #mô hình phản ứng - vận chuyển - khuếch tán #tuyệt chủng

Tài liệu tham khảo

Allan JD (1995) Drift. In: Allan JD (ed) Stream ecology: structure and function of running waters. Chapman & Hall, London, pp 221–237 Allan JD, Castillo MM (2007) Stream ecology. Springer, Dordrecht Anderson KE, Nisbet RM, Diehl S, Cooper SD (2005) Scaling population responses to spatial environmental variability in advection-dominated systemse. Ecol Lett 8:933–943 Anderson KE, Nisbet RM, Diehl S (2006a) Spatial scaling of consumer-resource interactions in advection-dominated systems. Am Nat 168:358–372 Anderson KE, Paul AJ, McCauley E, Jackson LJ, Post JR, Nisbet RM (2006b) Instream flow needs in streams and rivers: the importance of understanding ecological dynamics. Front Ecol Environ 4:309–318 Anderson KE, Nisbet RM, McCauley E (2008) Transient responses to spatial perturbations in advective systems. Bull Math Biol 70:1480–1502 Aronson DG, Weinberger HF (1975) Nonlinear diffusion in population genetics, combustion, and nerve propagation. In: Goldstein JA (ed) Partial differential equations and related topics. Lecture notes in mathematics, no 446. Springer, Berlin, pp 5–49 Baker EA, Coon TG (1997) Development and evaluation of alternative habitat suitability criteria for brook trout. Trans Am Fish Soc 126:65–76 Ballyk M, Smith H (1999) A model of microbial growth in a plug flow reactor with wall attachment. Math Biosci 158:95–126 Ballyk M, Dung L, Jones DA, Smith HL (1998) Effects of random motility on microbial growth and competition in a flow reactor. SIAM J Appl Math 59:573–596 Brittain JE, Eikeland TJ (1988) Invertebrate drift—a review. Hydrobiologia 166:77–93 Byers JE, Pringle JM (2006) Going against the flow: retention, range limits and invasions in advective environments. Mar Ecol Prog Ser 313:27–41 Chaudhry MH (2008) Open-channel flow, 2nd edn. Springer, New York Courchamp F, Berec L, Gascoigne J (2008) Allee effects in ecology and conservation. Oxford University Press, New York Dunbar SR (1983) Travelling wave solutions of diffusive Lotka-Volterra equations. J Math Biol 17:11–32 Dunbar SR (1984) Travelling wave solutions of diffusive Lotka-Volterra equations: a heteroclinic connection in R 4. Trans Am Math Soc 286:557–594 Everest FH, Chapman DW (1972) Habitat selection and spatial interaction by juvenile chinook salmon and steelhead trout in two Idaho streams. J Fish Res Board Can 29:91–100 Fagan WF, Lewis MA, Neubert MG, van den Driessche P (2002) Invasion theory and biological control. Ecol Lett 5:148–158 Fausch KD (1984) Profitable stream positions for salmonids: relating specific growth rate to net energy gain. Can J Zool 62:441–451 Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugenics 7:355–369 Gaylord B, Gaines SD (2000) Temperature or transport? Range limits in marine species mediated solely by flow. Am Nat 155:769–789 Hadeler KP, Rothe F (1975) Travelling fronts in nonlinear diffusion equations. J Math Biol 2:251–263 Hainzl J (1988) Stability and Hopf bifurcation in a predator-prey system with several parameters. SIAM J Appl Math 48:170–190 Hilker FM, Lewis MA, Seno H, Langlais M, Malchow H (2005) Pathogens can slow down or reverse invasion fronts of their hosts. Biological Invasions 7:817–832 Hilker FM, Langlais M, Petrovskii SV, Malchow H (2007) A diffusive SI model with Allee effect and application to FIV. Math Biosci 206:61–80 Holling CS (1961) Principles of insect predation. Annu Rev Entomol 6:163–182 Hughes NF, Dill LM (1990) Position choice by drift-feeding salmonids: model and test for Arctic grayling (Thymallus arcticus) in subarctic mountain streams, interior Alaska. Can J Fish Aquat Sci 47:2039–2048 Humphries S, Ruxton GD (2002) Is there really a drift paradox? J Anim Ecol 71:151–154 Kolmogorov AN, Petrovskii IG, Piskunov NS (1937) Étude de l’equation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bulletin Université d’Etat à Moscou, Série internationale, Section A 1:1–25 Kot M, Lewis MA, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecology 77:2027–2042 Lancaster J, Hildrew AG (1993) Characterizing in-stream flow refugia. Can J Fish Aquat Sci 50:1663–1675 Lewis MA, Kareiva P (1993) Allee dynamics and the spread of invading organisms. Theor Popul Biol 43:141–158 Lewis MA, van den Driessche P (1993) Waves of extinction from sterile insect release. Math Biosci 116:221–247 Lewis MA, Lutscher F, Hillen T (2009) Spatial dynamics in ecology. In: Lewis MA, Keener J, Maini P, Chaplain M (eds) Park City Mathematics Institute volume in Mathematical Biology, Institute for Advanced Study, Princeton Li B, Weinberger HF, Lewis MA (2005) Spreading speeds as slowest wave speeds for cooperative systems. Math Biosci 196:82–98 Ludwig D, Jones DD, Holling CS (1978) Qualitative analysis of insect outbreak systems: the spruce budworm and forest. J Anim Ecol 47:315–332 Luther R (1906) Räumliche Ausbreitung chemischer Reaktionen. Zeitschrift für Elektrochemie 12:596–600 Lutscher F, Pachepsky E, Lewis MA (2005) The effect of dispersal patterns on stream populations. SIAM J Appl Math 65:1305–1327 Lutscher F, Lewis MA, McCauley E (2006) Effects of heterogeneity on spread and persistence in rivers. Bull Math Biol 68:2129–2160 Lutscher F, McCauley E, Lewis MA (2007) Spatial patterns and coexistence mechanisms in systems with unidirectional flow. Theor Popul Biol 71:267–277 Magal C, Cosner C, Ruan S, Casas J (2008) Control of invasive hosts by generalist parasitoids. Math Med Biol 25:1–20 Malchow H, Schimansky-Geier L (1985) Noise and diffusion in bistable nonequilibrium systems. In: Teubner-Texte zur Physik, no 5. Teubner-Verlag, Leipzig Malchow H, Petrovskii S, Venturino E (2008) Spatiotemporal patterns in ecology and epidemiology: theory, models, simulations. Chapman & Hall/CRC, Boca Raton Morozov A, Petrovskii S, Li BL (2006) Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect. J Theor Biol 238:18–35 Morozov A, Ruan S, Li BL (2008) Patterns of patchy spread in multi-species reaction-diffusion models. Ecological Complexity 5(4):313–328. doi:10.1016/j.ecocom.2008.05.002 Müller K (1954) Investigations on the organic drift in north swedish streams. Tech. Rep. 34, Report of the Institute of Freshwater Research, Drottningholm Müller K (1974) Stream drift as a chronobiological phenomenon in running water ecosystems. Ann Rev Ecolog Syst 5:309–323 Müller K (1982) The colonization cycle of freshwater insects. Oecologia 52:202–207 Murray JD (2003) Mathematical biology. II: spatial models and biomedical applications, 3rd edn. Springer, Berlin Nisbet RM, Anderson KE, McCauley E, Lewis MA (2007) Response of equilibrium states to spatial environmental heterogeneity in advective systems. Math Biosci Eng 4:1–13 Nislow KH, Folt CL, Parrish DL (1999) Favorable foraging locations for young Atlantic salmon: application to habitat and population restoration. Ecol Appl 9:1085–1099 Nitzan A, Ortoleva P, Ross J (1974) Nucleation in systems with multiple stationary states. Symp Faraday Soc 9:241–253 O’Brien WJ, Showalter JJ (1993) Effects of current velocity and suspended debris on the drift feeding of Arctic grayling. Trans Am Fish Soc 122:609–615 Owen MR, Lewis MA (2001) How predation can slow, stop or reverse a prey invasion. Bull Math Biol 63:655–684 Pachepsky E, Lutscher F, Nisbet RM, Lewis MA (2005) Persistence, spread and the drift paradox. Theor Popul Biol 67:61–73 Pascual M (1993) Diffusion-induced chaos in a spatial predator–prey system. Proc R Soc Lond, B 251:1–7 Petrovskii S, Morozov A, Li BL (2005a) Regimes of biological invasion in a predator-prey system with the Allee effect. Bull Math Biol 67:637–661 Petrovskii SV, Malchow H (2001) Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. Theor Popul Biol 59:157–174 Petrovskii SV, Morozov AY, Venturino E (2002) Allee effect makes possible patchy invasion in a predator-prey system. Ecol Lett 5:345–352 Petrovskii SV, Malchow H, Li BL (2005b) An exact solution of a diffusive predator-prey system. Proc R Soc Lond A 461:1029–1053 Piccolo JJ, Hughes NF, Bryant MD (2007) Development of net energy intake models for drift-feeding juvenile coho salmon and steelhead. Environ Biol Fisches 83:259–267 Poff NL, Allan JD, Bain MB, Karr JR, Prestegaard KL, Richter BD, Sparks RE, Stromberg JC (1997) The natural flow regime. BioScience 47:769–784 Potapov AB, Lewis MA (2004) Climate and competition: the effect of moving range boundaries on habitat invasibility. Bull Math Biol 66:975–1008 Rempel LL, Richardson JS, Healey MC (1999) Flow refugia for benthic macroinvertebrates during flooding of a large river. J North Am Benthol Soc 18:34–48 Richardson WB (1992) Microcrustacea in flowing water: experimental analysis of washout times and a field test. Freshw Biol 28:217–230 Richter BD, Baumgartner JV, Wigington R, Braun DP (1997) How much water does a river need? Freshw Biol 37:231–249 Rosenzweig ML, MacArthur RH (1963) Graphical representation and stability conditions of predator-prey interactions. Am Nat 97:209–223 Rothe F (1981) Convergence to pushed fronts. Rocky Mt J Math 11:617 Sherratt JA, Smith MJ (2008) Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models. Journal of the Royal Society Interface 5:483–505 Sherratt JA, Lewis MA, Fowler AC (1995) Ecological chaos in the wake of invasion. Proc Natl Acad Sci USA 92:2524–2528 Shigesada N, Kawasaki K (1997) Biological invasions: theory and practice. Oxford University Press, Oxford Skellam JG (1951) Random dispersal in theoretical populations. Biometrika 38:196–218 Speirs DC, Gurney WSC (2001) Population persistence in rivers and estuaries. Ecology 82:1219–1237 Steele JH, Henderson EW (1981) A simple plankton model. Am Nat 117:676–691 Takahashi LT, Maidana NA, Ferreira WC, Pulino P, Yang HM (2005) Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind. Bull Math Biol 67:509–528 Turchin P (1998) Quantitative analysis of movement: measuring and modeling population redistribution in animals and plants. Sinauer, Sunderland Volterra V (1931) Leçons sur la théorie mathématique de la lutte pour la vie. Gauthier-Villars, Paris Walks DJ (2007) Persistence of plankton in flowing water. Can J Fish Aquat Sci 64:1693–1702 Wang MH, Kot M, Neubert MG (2002) Integrodifference equations, Allee effects, and invasions. J Math Biol 44:150–168 Wańkowski JWJ, Thorpe JE (1979) Spatial distribution and feeding in atlantic salmon, Salmo salar L. juveniles. J Fish Biol 14:239–247 Waters TF (1972) The drift of stream insects. Annu Rev Entomol 17:253–272 Winterbottom J, Orton S, Hildrew A (1997) Field experiments on the mobility of benthic invertebrates in a southern English stream. Freshw Biol 38:37–47