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Monthly Archives: February 2020

[18]Cancer modelling

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   Integrated Mathematical Oncology a part of Moffitt Cancer Center at Tampa focuses
   on various aspects of cancer modeling including adaptive cancer therapies that
   are currently clinically tested. These approaches that are based on a novel
   approach that considers cancer as an evolutionary disease, show usefulness of
   game theoretical models in clinical trials. IMO runs its own PhD program.

   This entry was posted in [20]Uncategorized and tagged [21]Krivan-IMO on
   [22]10/2/2020 by [23]admin.

[24]Adaptive growth of bacteria on two substrates

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   In Krivan (2006) bacterial growth on a mixture of two sugars is modeled. It is
   well know that in mixed substrates with glucose and lactose bacteria often
   utilize glucose first and then switch to lactose (or to some alternate source of
   energy). At the molecular level this switch is known as the lac operon. In this
   article I ask: Is this switch evolutionarily optimized? In other words, do
   bacteria switch between the resources at the time that  maximizes their fitness?
   To answer this question I build a model of bacterial growth on two substrates.
   The model assumes adaptive bacterial switching that maximizes bacterial per
   capita population growth rate - a proxy for bacterial fitness. Using some data
   from the literature, this model allows me to predict the time at which bacteria
   should switch. Then I compare this predicted time with observed times of
   switching for different substrates and different initial sugar concentrations.
   The observed times of switching show a very good agreement with predicted times.
   This strongly supports the idea that the molecular mechanism regulating resource
   switching is evolutionarily optimized.  This is also a  test of an optimal
   foraging theory  when populations undergo population dynamics. On contrary to the
   majority of experiments on the optimal foraging theory that do not consider
   population dynamics of foragers, this model  considers all populations dynamics.

   [26]Krivan, V. 2006. The Ideal Free Distribution and bacterial growth on two
   substrates. Theoretical Population Biology 69:181-191. 10.1016/j.tpb.2005.07.006

   This entry was posted in [27]Actual project, [28]Uncategorized and tagged
   [29]Krivan-ifd on [30]6/2/2020 by [31]admin.

[32]The Lotka-Volterra predator-prey game

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   The Lotka-Volterra predator-prey model is one of the earliest and, perhaps, the
   best known example used to explain why predators can indefinitely coexist with
   their prey. The population cycles resulting from this model are well known. In
   this article I show how adaptive behavior of prey and predators can destroy these
   cycles and stabilize population dynamics at an equilibrium. The classical
   predator-prey model assumes that interaction strength between prey and predators
   is fixed, which means that coefficients describing interactions between prey and
   predators do not change in time. However, there is increasing evidence that
   individuals adjust their activity levels in response to predation risk and
   availability of resources. For example, a high predation risk due to large
   predator numbers leads to prey behaviors that make them less vulnerable. They can
   either move to a refuge or become vigilant. However, such avoidance behaviors
   usually also decrease animal opportunities to forage which leads to
   foraging-predation risk trade-off. The present article shows that such a
   trade-off can have a strong bearing on population dynamics. In fact, while the
   classical Lotka-Volterra model has isoclines that are straight lines, the
   foraging-predation risk trade-off leads to prey (predator) isoclines with
   vertical (horizontal) segments. Rosenzweig and MacArthur in their seminal work on
   graphical stability analysis of predator-prey models showed that such isoclines
   have stabilizing effect on population dynamics because they limit maximum
   possible fluctuations in prey and predator populations. The present article shows
   that not only population fluctuations are limited, but they can even be
   completely eliminated.

   [34]Krivan, V. 2013. Behavioral refuges and predator-prey coexistence. Journal of
   Theoretical Biology 339:112-121.

   [35]Krivan, V. 2011. On the Gause predator-prey model with a refuge: A fresh look
   at the history. Journal of Theoretical Biology 274:67-73.

   [36]Krivan, V., Pryiadarshi, A. 2015. L-shaped prey isocline in the Gause
   predator-prey experiments with a prey refuge. Journal of theoretical biology
   370:21-26

   [37]Krivan, V. 2007. The Lotka-Volterra predator-prey model with
   foraging-predation risk trade-offs. American Naturalist 170: 771-782.

   This entry was posted in [38]Actual project, [39]Uncategorized and tagged
   [40]Krivan-game on [41]6/2/2020 by [42]admin.

[43]Habitat selection game

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   The habitat selection game is a game theoretical concept that describes species
   distribution in22 heterogeneous environments. For a single population, Fretwell
   and Lucas (1970) defined the Ideal Free Distribution (IFD) in patchy
   environments, under which animal payoffs in all occupied patches are the same and
   maximal. Thus, the IFD is a Nash equilibrium of a game that we call the Habitat
   Selection Game. As any strategy that uses only already occupied patches will get
   the same fitness at the Nash Equilibrium, it is not clear if the Ideal Free
   Distribution is stable with respect to mutant invasions. Cressman and Krivan
   (2006) proved that the IFD is also an Evolutionarily Stable Strategy, i.e.,
   resistant to mutant strategies. The habitat selection game was extended to two
   and multiple species. The IFD for two competing species in a two-patch
   environment was derived by Krivan and Sirot (2002). Cressman et al (2004) proved
   that this two-species IFD is also an Evolutionarily Stable Strategy for two
   populations. The effects of the IFD on population dynamics of two competing
   species was studied by Abrams et al. (2007). Evolutionarily stability under
   population dynamics were considered for multiple populations by Krivan and
   Cressman (2009) and for a single population by Cressman and Krivan (2010). Many
   results on habitat selection game for competing species or predator-prey
   interactions were reviewed in Krivan et al. (2008).

   [45]Krivan, V. 2014. The Allee-type Ideal Free Distribution. Journal of
   Mathematical Biology 69:1497-1513.

   [46]Cressman, R., Krivan, V. 2013. Two-patch population models with adaptive
   dispersal: The effects of varying dispersal speeds. Journal of Mathematical
   Biology 67:329-358.

   [47]Cressman, R., Krivan, V. 2010. The Ideal Free Distribution as an
   Evolutionarily Stable State in Density-Dependent Population Games. Oikos,
   119:1231-1242.

   [48]Krivan, V., Cressman, R., 2009. On evolutionary stability in prey-predator
   models with fast behavioral dynamics. Evolutionary Ecology Research 11:227-251.

   [49]Krivan,V., Cressman, R., Schneider, C. 2008. The Ideal Free Distribution: A
   review and synthesis of the game theoretic perspective. Theoretical Population
   Biology 73:403-425.

   [50]Abrams, P., Cressman, R., Krivan, V. 2007. The role of behavioral dynamics in
   determining the patch distributions of interacting species. American Naturalist
   169:505-518.

   [51]Cressman, R., Krivan, V. 2006. Migration dynamics for the Ideal Free
   Distribution. American Naturalist 168:384-397.

   [52]Cressman, R., Krivan, V., Garay, J. 2004. Ideal free distributions,
   evolutionary games and population dynamics in multiple species environments. The
   American Naturalist, 164(4):473-489.

   [53]Krivan, V., Sirot, E. 2002. Habitat selection by two competing species in a
   two-habitat environment. American Naturalist 160:214-234.

   This entry was posted in [54]Actual project and tagged [55]Krivan-ifd on
   [56]6/2/2020 by [57]admin.

[58]Optimal foraging game

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   Optimal foraging theory (MacArthur and Pianka, 1966; Charnov, 1976; Stephens and
   Krebs, 1986) assumes that organisms forage in such a way as to maximize their
   fitness measured as energy intake rate. These models assume a homogeneous
   environment with several resource types that a consumer encounters sequentially,
   and predict the optimal consumer diet. This line of research led to the prey
   model (also called the "diet choice"; Charnov, 1976). The basic assumption here
   is that individuals do not compete for food. The classical example of such a
   situation is the experiment with great tits where a single animal feeds on two
   food types delivered on a conveyor belt (Krebs et al., 1977; Berec et al., 2003)
   which assures that prey are not depleted by predation. Certainly, this is a very
   unrealistic assumption, and I am interested to understand how predictions of the
   optimal foraging theory are shaped when population dynamics of resources and/or
   consumers are considered (Krivan, 1996; Krivan and Sikder, 1999; Krivan and
   Eisner, 2003).  The game theoretical approach to optimal foraging is presented in
   Cressman et al. (2014).

   [60]Cressman, R., Krivan, V., Garay, J., Brown, J. 2014. Game-theoretic methods
   for functional response and optimal foraging behavior. PLoS ONE 9(2): e88773.
   doi:10.1371/journal.pone.0088773

   [61]Krivan, V. 2010. Evolutionary stability of optimal foraging: partial
   preferences in the diet and patch models. Journal of theoretical Biology
   267:486-494.

   [62]Krivan, V., Vrkoc, I. 2004. Should handled prey be considered? Some
   consequences for functional response, predator-prey dynamics and optimal foraging
   theory. Journal of theoretical Biology, 227:167-174.

   [63]Berec, M., Krivan, V., Berec, L. 2003. Are great tits (Parus major) really
   optimal foragers?. Canadian Journal of Zoology 81:780-788.

   [64]Krivan, V., Eisner, J. 2003. Optimal foraging and predator-prey dynamics III.
   Theoretical Population Biology 63:269-279.

   [65]Krivan, V. 2000. Optimal intraguild foraging and population stability.
   Theoretical Population Biology 58:79-94.

   [66]Krivan, V., Sikder, A. 1999. Optimal foraging and predator-prey dynamics II.
   Theoretical Population Biology 55:111-126.

   [67]Krivan, V. 1996. Optimal foraging and predator-prey dynamics. Theoretical
   Population Biology 49:265-290.

   This entry was posted in [68]Uncategorized and tagged [69]Krivan-oft on
   [70]6/2/2020 by [71]admin.

   Centrum matematické biologie
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   [73]Prírodovedecká fakulta
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References

   1. http://mathbio.prf.jcu.cz/en/feed/
   2. http://mathbio.prf.jcu.cz/en/comments/feed/
   3. http://mathbio.prf.jcu.cz/2020/02/
   4. http://mathbio.prf.jcu.cz/en/2020/02/
   5. http://mathbio.prf.jcu.cz/en/
   6. http://mathbio.prf.jcu.cz/en/2020/02/#content
   7. http://mathbio.prf.jcu.cz/en/
   8. http://mathbio.prf.jcu.cz/en/news/
   9. http://mathbio.prf.jcu.cz/en/people/
  10. http://mathbio.prf.jcu.cz/en/research/
  11. http://mathbio.prf.jcu.cz/en/publications/
  12. http://mathbio.prf.jcu.cz/en/teaching/
  13. http://mathbio.prf.jcu.cz/en/students/
  14. http://mathbio.prf.jcu.cz/en/links/
  15. http://mathbio.prf.jcu.cz/en/contact/
  16. http://mathbio.prf.jcu.cz/2020/02/
  17. http://mathbio.prf.jcu.cz/en/2020/02/
  18. http://mathbio.prf.jcu.cz/en/2020/02/10/cancer-modelling/
  19. http://mathbio.prf.jcu.cz/en/2020/02/10/cancer-modelling/#respond
  20. http://mathbio.prf.jcu.cz/en/category/uncategorized-en/
  21. http://mathbio.prf.jcu.cz/en/tag/krivan-imo-en/
  22. http://mathbio.prf.jcu.cz/en/2020/02/10/cancer-modelling/
  23. http://mathbio.prf.jcu.cz/en/author/admin/
  24. http://mathbio.prf.jcu.cz/en/2020/02/06/adaptivni-rust-bakterii-na-dvou-substratech/
  25. http://mathbio.prf.jcu.cz/en/2020/02/06/adaptivni-rust-bakterii-na-dvou-substratech/#respond
  26. http://baloun.entu.cas.cz/krivan/papers/Krivan2006.pdf
  27. http://mathbio.prf.jcu.cz/en/category/actual-project/
  28. http://mathbio.prf.jcu.cz/en/category/uncategorized-en/
  29. http://mathbio.prf.jcu.cz/en/tag/krivan-ifd/
  30. http://mathbio.prf.jcu.cz/en/2020/02/06/adaptivni-rust-bakterii-na-dvou-substratech/
  31. http://mathbio.prf.jcu.cz/en/author/admin/
  32. http://mathbio.prf.jcu.cz/en/2020/02/06/the-lotka-volterra-predator-prey-game/
  33. http://mathbio.prf.jcu.cz/en/2020/02/06/the-lotka-volterra-predator-prey-game/#respond
  34. http://www.sciencedirect.com/science/article/pii/S0022519312006522
  35. http://baloun.entu.cas.cz/krivan/papers/Krivan-JTB-2011.pdf
  36. http://www.sciencedirect.com/science/article/pii/S0022519315000302
  37. http://baloun.entu.cas.cz/krivan/papers/Krivan2007.pdf
  38. http://mathbio.prf.jcu.cz/en/category/actual-project/
  39. http://mathbio.prf.jcu.cz/en/category/uncategorized-en/
  40. http://mathbio.prf.jcu.cz/en/tag/krivan-game-en/
  41. http://mathbio.prf.jcu.cz/en/2020/02/06/the-lotka-volterra-predator-prey-game/
  42. http://mathbio.prf.jcu.cz/en/author/admin/
  43. http://mathbio.prf.jcu.cz/en/2020/02/06/habitat-selection-game/
  44. http://mathbio.prf.jcu.cz/en/2020/02/06/habitat-selection-game/#respond
  45. http://link.springer.com/article/10.1007/s00285-013-0742-y
  46. http://link.springer.com/article/10.1007%2Fs00285-012-0548-3
  47. http://baloun.entu.cas.cz/krivan/papers/CressmanKrivan-Oikos-2010.pdf
  48. http://baloun.entu.cas.cz/krivan/papers/KrivanCressman-EER-2009.pdf
  49. http://baloun.entu.cas.cz/krivan/papers/KrivanCressmanSchneider2008.pdf
  50. http://baloun.entu.cas.cz/krivan/papers/AbramsCressmanKrivan-AmNat-2007.pdf
  51. http://baloun.entu.cas.cz/krivan/papers/CressmanKrivan2006.pdf
  52. http://baloun.entu.cas.cz/krivan/papers/CressmanKrivanGaray2004.pdf
  53. http://baloun.entu.cas.cz/krivan/papers/KrivanSirot2002.pdf
  54. http://mathbio.prf.jcu.cz/en/category/actual-project/
  55. http://mathbio.prf.jcu.cz/en/tag/krivan-ifd/
  56. http://mathbio.prf.jcu.cz/en/2020/02/06/habitat-selection-game/
  57. http://mathbio.prf.jcu.cz/en/author/admin/
  58. http://mathbio.prf.jcu.cz/en/2020/02/06/optimal-foraging/
  59. http://mathbio.prf.jcu.cz/en/2020/02/06/optimal-foraging/#respond
  60. http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0088773
  61. http://baloun.entu.cas.cz/krivan/papers/Krivan-JTB-2010.pdf
  62. http://baloun.entu.cas.cz/krivan/papers/KrivanVrkoc2004.pdf
  63. http://baloun.entu.cas.cz/krivan/papers/BerecKrivanBerec2003.pdf
  64. http://baloun.entu.cas.cz/krivan/papers/KrivanEisner2003.pdf
  65. http://baloun.entu.cas.cz/krivan/papers/Krivan2000.pdf
  66. http://baloun.entu.cas.cz/krivan/papers/KrivanSikder1999.pdf
  67. http://baloun.entu.cas.cz/krivan/papers/Krivan1996.pdf
  68. http://mathbio.prf.jcu.cz/en/category/uncategorized-en/
  69. http://mathbio.prf.jcu.cz/en/tag/krivan-oft-en/
  70. http://mathbio.prf.jcu.cz/en/2020/02/06/optimal-foraging/
  71. http://mathbio.prf.jcu.cz/en/author/admin/
  72. http://umb.prf.jcu.cz/
  73. http://www.prf.jcu.cz/
  74. http://www.jcu.cz/