Skip to main content
SpringerLink
Log in

Life History Evolution and Adaptive Stochastic Controls

  • Chapter
  • First Online:
Population Dynamics Based on Individual Stochasticity

Part of the book series: SpringerBriefs in Population Studies ((POPULAT))

  • 63 Accesses

Abstract

Thus far, we have examined the properties of population dynamics generated by the life history through linear and non-linear age–multi-state structured models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    \(\int _{A}d\xi \ v\left( 0,\xi \right) \nu \left( \xi \right) =1\) in Eq. (2.34).

  2. 2.

    Equation (4.46) demonstrates that Eq. (4.18) is still valid and that the adaptive mature size is independent of the adaptive control in this model.

  3. 3.

    Follow the interpretation of Eq. (2.59) in Sect. 2.5.

  4. 4.

    Note that we can treat u as a parameter in this case.

References

  • Taylor, H., Gourley, R., Lawrence, C., & Kaplan, R. (1974). Natural selection of life history attributes: an analytical approach. Theoretical Population Biology, 5(1), 104–122.

    Article  Google Scholar 

  • Leon, J. (1976). Life histories as adaptive strategies. Journal of Theoretical Biology, 60(2), 301–335.

    Article  Google Scholar 

  • Metz, J., & Diekmann, O. (1986). The dynamics of physiologically structured populations (Vol. 68). Springer.

    Google Scholar 

  • Inaba, H. (2017). Age-structured population dynamics in demography and epidemiology.

    Google Scholar 

  • Pianka, E. (1976). Natural selection of optimal reproductive tactics. American Zoologist, 16(4), 775–784.

    Article  Google Scholar 

  • Reznick, D., Bryant, M. J., & Bashey, F. (2002). r-and k-selection revisited: The role of population regulation in life-history evolution. Ecology, 83(6), 1509–1520.

    Article  Google Scholar 

  • Oizumi, R., Kuniya, T., & Enatsu, Y. (2016). Reconsideration of r/k selection theory using stochastic control theory and nonlinear structured population models. PloS One, 11(6), e0157715.

    Article  Google Scholar 

  • Øksendal, B. (2003). Stochastic differential equations: An introduction with applications. Springer.

    Google Scholar 

  • Karatzas, I., & Shreve, S. (1991). Brownian motion and stochastic calculus (Vol. 113). Springer.

    Google Scholar 

  • Iwasa, Y., & Roughgarden, J. (1984). Shoot/root balance of plants: Optimal growth of a system with many vegetative organs. Theoretical Population Biology, 25(1), 78–105.

    Article  Google Scholar 

  • Iwasa, Y., & Cohen, D. (1989). Optimal growth schedule of a perennial plant. American Naturalist, 480–505.

    Google Scholar 

  • Oizumi, R., & Inaba, H. (2021). Evolution of heterogeneity under constant and variable environments. PloS One, 16(9), e0257377.

    Article  Google Scholar 

  • Bellman, R. (2013). Dynamic programming. Courier Corporation.

    Google Scholar 

  • Yong, J., & Zhou, X. (1999). Stochastic controls: Hamiltonian systems and HJB equations (Vol. 43). Springer.

    Google Scholar 

  • Stearns, S. (1992). The evolution of life histories. Oxford: Oxford Univeristy Press.

    Google Scholar 

  • Aase, K. (1984). Optimum portfolio diversification in a general continuous-time model. Stochastic Processes and their Applications, 18(1), 81–98.

    Article  Google Scholar 

  • Shreve, S. (2004). Stochastic calculus for finance: Continuous-time models (Vol. 2). Springer.

    Google Scholar 

  • Oizumi, R. (2014). Unification theory of optimal life histories and linear demographic models in internal stochasticity. PloS One, 9(6), e98746.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Population and Social Security Research, Tokyo, Japan

    Ryo Oizumi

Authors
  1. Ryo Oizumi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ryo Oizumi .

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Oizumi, R. (2022). Life History Evolution and Adaptive Stochastic Controls. In: Population Dynamics Based on Individual Stochasticity. SpringerBriefs in Population Studies(). Springer, Singapore. https://doi.org/10.1007/978-981-19-3548-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-981-19-3548-0_4

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-3547-3

  • Online ISBN: 978-981-19-3548-0

  • eBook Packages: HistoryHistory (R0)

Publish with us

Policies and ethics

Search

Navigation