Convert between age-specific survivorship, survival, or mortality hazard

Convert between vectors of age-specific survivorship (lx), survival probability (px), or mortality hazard (hx). Input vectors must be arranged in order of increasing age, starting with age 0.

lx_to_px(lx)

lx_to_hx(lx)

px_to_lx(px)

px_to_hx(px)

hx_to_lx(hx)

hx_to_px(hx)

Arguments

lx

Vector of age-specific survivorship.

px

Vector of age-specific survival probabilities.

hx

Vector of age-specific mortality hazards.

Value

A vector.

Details

lx gives the proportional survivorship to the start of age class x (where survivorship at first age class is defined as 1), px gives the probability of survival between age x and x+1, and hx gives the time-averaged mortality hazard (also called force of mortality) between age x and x+1.

Note

Note that the units of time for the returned vectors (i.e., x) are the same as the (ProjectionInterval) of the MPM.

References

Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation. Sinauer Associates; 2nd edition. ISBN: 978-0878930968

Caswell, H. 2006. Applications of Markov chains in demography. pp. 319-334 in A.N. Langville and W.J. Stewart (editors) MAM2006: Markov Anniversary Meeting. Boson Books, Raleigh, North Caroline, USA

Ergon, T., Borgan, Ø., Nater, C. R., & Vindenes, Y. 2018. The utility of mortality hazard rates in population analyses. Methods in Ecology and Evolution, 9, 2046-2056. <doi:10.1111/2041-210X.13059>

Horvitz, C. & Tuljapurkar, S. 2008. Stage dynamics, period survival, and mortality plateaus. The American Naturalist 172: 203-2015. <doi:10.1086/589453>

Jones, O. R., Scheuerlein, A., Salguero-Gomez, R., Camarda, C. G., Schaible, R., Casper, B. B., Dahlgren, J. P., Ehrlén, J., García, M. B., Menges, E., Quintana-Ascencio, P. F., Caswell, H., Baudisch, A. & Vaupel, J. 2014. Diversity of ageing across the tree of life. Nature 505, 169-173. <doi:10.1038/nature12789>

Jones O. R. 2021. Life tables: Construction and interpretation In: Demographic Methods Across the Tree of Life. Edited by Salguero-Gomez R & Gamelon M. Oxford University Press. Oxford, UK. ISBN: 9780198838609

Preston, S., Heuveline, P., & Guillot, M. 2000. Demography: Measuring and Modeling Population Processes. Wiley. ISBN: 9781557864512

See also

Other life tables: age_from_stage, mpm_to_table(), qsd_converge()

Author

Patrick Barks <patrick.barks@gmail.com>

Examples

lx <- c(1, 0.8, 0.7, 0.5, 0.3, 0.1)

# convert from lx
px <- lx_to_px(lx)
hx <- lx_to_hx(lx)

# convert from px
lx <- px_to_lx(px)
hx <- px_to_hx(px)

# convert from hx
lx <- hx_to_lx(hx)
px <- hx_to_px(hx)