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2013, 10(5&6): 1561-1586. doi: 10.3934/mbe.2013.10.1561

Mixed strategies and natural selection in resource allocation

1. 

School of Human Evolution and Social Change, Arizona State University, 900 S Cady Mall, Tempe, AZ, 85287, United States

2. 

Department of Mathematics, 2441 Sixth Street NW, Washington, DC, 20059, United States

3. 

National Institute for Biotechnology Information (NCBI), National Institutes of Health, 8600 Rockville Pike MSC 3830, Bethesda, MD 20894, United States

Received  August 2012 Revised  December 2012 Published  August 2013

An appropriate choice of strategy for resource allocation may frequently determine whether a population will be able to survive under the conditions of severe resource limitations. Here we focus on two classes of strategies allocation of resources towards rapid proliferation, or towards slower proliferation but increased physiological and environmental maintenance. We propose a generalized framework, where individuals within a population can use either strategy in different proportion for utilization of a common dynamical resource in order to maximize their fitness. We use the model to address two major questions, namely, whether either strategy is more likely to be selected for as a result of natural selection, and, if one allows for the possibility of resource over-consumption, whether either strategy is preferable for avoiding population collapse due to resource exhaustion. Analytical and numerical results suggest that the ultimate choice of strategy is determined primarily by the initial distribution of individuals in the population, and that while investment in physiological and environmental maintenance is a preferable strategy in a homogeneous population, no generalized prediction can be made about heterogeneous populations.
Citation: Irina Kareva, Faina Berezovkaya, Georgy Karev. Mixed strategies and natural selection in resource allocation. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1561-1586. doi: 10.3934/mbe.2013.10.1561
References:
[1]

A. Algar, J. Kerr and D. Currie, Quantifying the importance of regional and local filters for community trait structure in tropical and temperate zones, Ecology, 92 (2011), 903-914. doi: 10.1890/10-0606.1.

[2]

N. Bautin and E. Leontovich, "Methods and Rules for the Qualitative Study of Dynamical Systems on the Plane," Spravochnaya Matematicheskaya Biblioteka [Mathematical Reference Library], Izdat. "Nauka," Moscow, 1976.

[3]

F. S. Berezovskaya, A. S. Novozhilov and G. P. Karev., Population models with singular equilibrium, Mathematical Biosciences, 208 (2007), 270-299. doi: 10.1016/j.mbs.2006.10.006.

[4]

N. Chikatsu, Y. Nakamura, H. Sato, T. Fujita, S. Asano and T. Motokura, p53 mutations and tetraploids under r- and K-selection, Oncogene, 21 (2002), 3043-3049. doi: 10.1038/sj.onc.1205413.

[5]

J. Clark, Individuals and the variation needed for high species diversity in forest trees, Science, 327 (2010), 1129-1132. doi: 10.1126/science.1183506.

[6]

J. W. Costerton, Z. Lewandowski, D. E. Caldwell, D. R. Korber and H. M. Lappin-Scott, Microbial biofilms, Annual Reviews in Microbiology, 49 (1995), 711-745.

[7]

V. J. Denef, L. H. Kalnejais, R. S. Mueller, P. Wilmes, B. J. Baker, B. C. Thomas, N. C. VerBerkmoes, R. L. Hettich and J. F. Banfield, Proteogenomic basis for ecological divergence of closely related bacteria in natural acidophilic microbial communities, Proceedings of the National Academy of Sciences of the United States of America, 107 (2010), 2383-2390. doi: 10.1073/pnas.0907041107.

[8]

T. Dobzhansky, The evolution in the tropics, American Scientist, 38 (1950), 209-221.

[9]

J. J. Elser, M. M. Kyle, M. S. Smith and J. D. Nagy, Biological stoichiometry in human cancer, PloS ONE, 2 (2007), e1028. doi: 10.1371/journal.pone.0001028.

[10]

N. B. Grimm, S. H. Faeth, N. E. Golubiewski, C. L. Redman, J. Wu, X. Bai and J. M. Briggs, Global change and the ecology of cities, Science, 319 (2008), 756-760. doi: 10.1126/science.1150195.

[11]

G. Hardin, The tragedy of the commons, Science, 162 (1968), 1243-1248. doi: 10.1080/19390450903037302.

[12]

International Cancer Genome Consortium, International network of cancer genome projects, Nature, 464 (2010), 993-998.

[13]

J. Kapur, "Maximum-Entropy Models in Science and Engineering," John Wiley & Sons, New York, 1989.

[14]

G. P. Karev, On mathematical theory of selection: Continuous time population dynamics, Journal of Mathematical Biology, 60 (2010), 107-129. doi: 10.1007/s00285-009-0252-0.

[15]

G. P. Karev, Principle of minimum discrimination information and replica dynamics, Entropy, 12 (2010), 1673-1695. doi: 10.3390/e12071673.

[16]

I. Kareva, F. S. Berezovskaya and C. Castillo-Chavez, Transitional regimes as early warning signals in resource dependent competition models, Mathematical Biosciences, 240 (2012), 114-123. doi: 10.1016/j.mbs.2012.06.001.

[17]

D. C. Krakauer, K. M. Page and D. H. Erwin, Diversity, dilemmas, and monopolies of niche construction, American Naturalist, 173 (2009), 26-40.

[18]

Y. Kuznetsov, "Elements of Applied Bifurcation Theory," Springer, 1998.

[19]

R. H. MacArthur and R. Levins, The limiting similarity, convergence, and divergence of coexisting species, American Naturalist, 101 (1967), 377-385.

[20]

D. W. Macdonald, C. Newman, P. M. Nouvellet and C. D. Buesching, An analysis of Eurasian badger (Meles meles) population dynamics: Implications for regulatory mechanisms, Journal of Mammalogy, 90 (2009), 1392-1403.

[21]

L. M. F. Merlo, J. W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nature Reviews Cancer, 6 (2006), 924-935. doi: 10.1038/nrc2013.

[22]

E. Ostrom, "Governing the Commons: The Evolution of Institutions for Collective Action," Cambridge University Press, 1990.

[23]

E. Ostrom, A general framework for analyzing sustainability of social-ecological systems, Science, 325 (2009), 419-422. doi: 10.1126/science.1172133.

[24]

E. R. Pianka, Niche overlap and diffuse competition, Proceedings of the National Academy of Sciences of the Unites States of America, 71 (1974), 2141-2145. doi: 10.1073/pnas.71.5.2141.

[25]

B. Prakash, B. M. Veeregowda and G. Krishnappa, Biofilms: A survival strategy of bacteria, Current Science, 85 (2003), 1299-1307.

[26]

D. Reznick, M..J. Bryant and F. Bashey., r- and K-selection revisited: the role of population regulation in life history evolution, Ecology, 83.6 (Year), 1509-1520.

[27]

T. L. Russell, D. W. Lwetoijera, B. G. J. Knols, W. Takken, G. F. Killeen and H. M. Ferguson, Linking individual phenotype to density-dependent population growth: The influence of body size on the population dynamics of malaria vectors, Proceedings of the Royal Society: Biological Sciences, 278 (2011), 3142-3151. doi: 10.1098/rspb.2011.0153.

[28]

S. Stearns, The evolution of life history traits: A critique of the theory and a review of the data, Annual Review of Ecology and Systematics, 8 (1977), 145-171. doi: 10.1146/annurev.es.08.110177.001045.

[29]

S. Stearns, "The Evolution of Life Histories," Oxford University Press, USA, 1992.

[30]

S. Stearns, Life history evolution: Successes, limitations, and prospects, Naturwissenschaften, 87 (2000), 476-486. doi: 10.1007/s001140050763.

[31]

M. Stratton, P. Campbell and P. A. Futreal, The cancer genome, Nature, 458 (2009), 719-724. doi: 10.1038/nature07943.

[32]

S. B. Voytek and G. F. Joyce, Niche partitioning in the coevolution of 2 distinct RNA enzymes, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 7780-7785. doi: 10.1073/pnas.0903397106.

[33]

H. M. Wilbur, D. W. Tinkle and J. P. Collins, Environmental certainty, trophic level, and resource availability in life history evolution, American Naturalist, 108 (1974), 805-817. doi: 10.1086/282956.

show all references

References:
[1]

A. Algar, J. Kerr and D. Currie, Quantifying the importance of regional and local filters for community trait structure in tropical and temperate zones, Ecology, 92 (2011), 903-914. doi: 10.1890/10-0606.1.

[2]

N. Bautin and E. Leontovich, "Methods and Rules for the Qualitative Study of Dynamical Systems on the Plane," Spravochnaya Matematicheskaya Biblioteka [Mathematical Reference Library], Izdat. "Nauka," Moscow, 1976.

[3]

F. S. Berezovskaya, A. S. Novozhilov and G. P. Karev., Population models with singular equilibrium, Mathematical Biosciences, 208 (2007), 270-299. doi: 10.1016/j.mbs.2006.10.006.

[4]

N. Chikatsu, Y. Nakamura, H. Sato, T. Fujita, S. Asano and T. Motokura, p53 mutations and tetraploids under r- and K-selection, Oncogene, 21 (2002), 3043-3049. doi: 10.1038/sj.onc.1205413.

[5]

J. Clark, Individuals and the variation needed for high species diversity in forest trees, Science, 327 (2010), 1129-1132. doi: 10.1126/science.1183506.

[6]

J. W. Costerton, Z. Lewandowski, D. E. Caldwell, D. R. Korber and H. M. Lappin-Scott, Microbial biofilms, Annual Reviews in Microbiology, 49 (1995), 711-745.

[7]

V. J. Denef, L. H. Kalnejais, R. S. Mueller, P. Wilmes, B. J. Baker, B. C. Thomas, N. C. VerBerkmoes, R. L. Hettich and J. F. Banfield, Proteogenomic basis for ecological divergence of closely related bacteria in natural acidophilic microbial communities, Proceedings of the National Academy of Sciences of the United States of America, 107 (2010), 2383-2390. doi: 10.1073/pnas.0907041107.

[8]

T. Dobzhansky, The evolution in the tropics, American Scientist, 38 (1950), 209-221.

[9]

J. J. Elser, M. M. Kyle, M. S. Smith and J. D. Nagy, Biological stoichiometry in human cancer, PloS ONE, 2 (2007), e1028. doi: 10.1371/journal.pone.0001028.

[10]

N. B. Grimm, S. H. Faeth, N. E. Golubiewski, C. L. Redman, J. Wu, X. Bai and J. M. Briggs, Global change and the ecology of cities, Science, 319 (2008), 756-760. doi: 10.1126/science.1150195.

[11]

G. Hardin, The tragedy of the commons, Science, 162 (1968), 1243-1248. doi: 10.1080/19390450903037302.

[12]

International Cancer Genome Consortium, International network of cancer genome projects, Nature, 464 (2010), 993-998.

[13]

J. Kapur, "Maximum-Entropy Models in Science and Engineering," John Wiley & Sons, New York, 1989.

[14]

G. P. Karev, On mathematical theory of selection: Continuous time population dynamics, Journal of Mathematical Biology, 60 (2010), 107-129. doi: 10.1007/s00285-009-0252-0.

[15]

G. P. Karev, Principle of minimum discrimination information and replica dynamics, Entropy, 12 (2010), 1673-1695. doi: 10.3390/e12071673.

[16]

I. Kareva, F. S. Berezovskaya and C. Castillo-Chavez, Transitional regimes as early warning signals in resource dependent competition models, Mathematical Biosciences, 240 (2012), 114-123. doi: 10.1016/j.mbs.2012.06.001.

[17]

D. C. Krakauer, K. M. Page and D. H. Erwin, Diversity, dilemmas, and monopolies of niche construction, American Naturalist, 173 (2009), 26-40.

[18]

Y. Kuznetsov, "Elements of Applied Bifurcation Theory," Springer, 1998.

[19]

R. H. MacArthur and R. Levins, The limiting similarity, convergence, and divergence of coexisting species, American Naturalist, 101 (1967), 377-385.

[20]

D. W. Macdonald, C. Newman, P. M. Nouvellet and C. D. Buesching, An analysis of Eurasian badger (Meles meles) population dynamics: Implications for regulatory mechanisms, Journal of Mammalogy, 90 (2009), 1392-1403.

[21]

L. M. F. Merlo, J. W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nature Reviews Cancer, 6 (2006), 924-935. doi: 10.1038/nrc2013.

[22]

E. Ostrom, "Governing the Commons: The Evolution of Institutions for Collective Action," Cambridge University Press, 1990.

[23]

E. Ostrom, A general framework for analyzing sustainability of social-ecological systems, Science, 325 (2009), 419-422. doi: 10.1126/science.1172133.

[24]

E. R. Pianka, Niche overlap and diffuse competition, Proceedings of the National Academy of Sciences of the Unites States of America, 71 (1974), 2141-2145. doi: 10.1073/pnas.71.5.2141.

[25]

B. Prakash, B. M. Veeregowda and G. Krishnappa, Biofilms: A survival strategy of bacteria, Current Science, 85 (2003), 1299-1307.

[26]

D. Reznick, M..J. Bryant and F. Bashey., r- and K-selection revisited: the role of population regulation in life history evolution, Ecology, 83.6 (Year), 1509-1520.

[27]

T. L. Russell, D. W. Lwetoijera, B. G. J. Knols, W. Takken, G. F. Killeen and H. M. Ferguson, Linking individual phenotype to density-dependent population growth: The influence of body size on the population dynamics of malaria vectors, Proceedings of the Royal Society: Biological Sciences, 278 (2011), 3142-3151. doi: 10.1098/rspb.2011.0153.

[28]

S. Stearns, The evolution of life history traits: A critique of the theory and a review of the data, Annual Review of Ecology and Systematics, 8 (1977), 145-171. doi: 10.1146/annurev.es.08.110177.001045.

[29]

S. Stearns, "The Evolution of Life Histories," Oxford University Press, USA, 1992.

[30]

S. Stearns, Life history evolution: Successes, limitations, and prospects, Naturwissenschaften, 87 (2000), 476-486. doi: 10.1007/s001140050763.

[31]

M. Stratton, P. Campbell and P. A. Futreal, The cancer genome, Nature, 458 (2009), 719-724. doi: 10.1038/nature07943.

[32]

S. B. Voytek and G. F. Joyce, Niche partitioning in the coevolution of 2 distinct RNA enzymes, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 7780-7785. doi: 10.1073/pnas.0903397106.

[33]

H. M. Wilbur, D. W. Tinkle and J. P. Collins, Environmental certainty, trophic level, and resource availability in life history evolution, American Naturalist, 108 (1974), 805-817. doi: 10.1086/282956.

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