
One additional point of contrast between the dynamic and time-specific 
methods should be mentioned here. When samples available for study are 
small, the dynamic method of calculation always helpfully increases the 
number of variates (here birds alive) available for study; at the same 
time, the time-specific method decreases the number dying each year. If 
the samples are very small, the time-specific method may be useless. 
This will be illustrated by many examples in subsequent chapters. 
ee, eee 
If a mortality rate is absolutely constant from one year to 
another, it is obvious that this would require the postulation of frac- 
tional values at the lower end of a mortality series. With a mortality 
rate of 50 per cent per year, a population of 100 should die off as 50, 
25, 12.5, etc. in successive years. Because 12.5 birds cannot die off 
in real life, a constant rate of mortality can be easily distorted in 
small samples. In bird-banding analyses, this distortion appears in 
both dynamic and time-specific calculations. (Statistical workers 
will recognize that both are derived from frequency distributions of 
discontinuous variates.) In dynamic calculations, the distortion 
is greatest at the latter end of the mortality series, but Lack's 
method of calculating “birds alive at the start of each year" tends 
to carry the distortion into the early years as well. This is illus- 
trated in table lh. Mortality rates calculated by the time-specific 
Table 1h.--Distortion in Mortality Rate Produced by Failure to 
' Obtain Report of the Last Death in a Hypothetical 
Mortality Series 
Mortality rate is here calculated by the dynamic life-table method. 
Tt is assumed that every dead bird is recovered but the last one 
(marked by asterisk). In nature where only a fraction of banded 
birds are recovered, and where mortality must be recorded in dis- 
continuous (nonfractional) numbers, this situation is commonly 
approached. 
Actually Alive Number Calculated  Caiculated Mor- 
Age in Population Dying Number Alive tality Rate 
at Start of during at Start per Year 
Year year of Year () 
O~-1 102) 512 1023 50.05 
1-2 512 256 511 50.10 
2=3 256 128 255 50.20 
+h 128 6h 127 50.39 
i=S 64 32 63 50. 79 
5-6 32 16 31 51.61 
6-7 16 8 15 53.33 
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