Ecology, 68(5), 1987, pp. 1351-1363
@ 1987 by the Ecological Society of America
LIFE HISTORIES OF MAMMALS: ANALYSES AMONG AND
WITHIN SPERMOPHILUS COLUMBIANUS LIFE TABLES1
RICHARD M. ZAMMUTO
KananaskisCentrefor EnvironmentalResearch,Universityof Calgary,
Seebe,Alberta TOL lXO, Canada
Abstract. Eleven theoretical predictions (or assumptions) of life history evolution are
considered for the montane Columbian ground squirrel, Spermophilus columbian us. using
age-specificsurvival and fecundity from six life tables of natural populations. The following
statements are supported among age classesamong populations, among age classeswithin
populations, and (or) within age classesamong populations: (I) mortality rates are high
after birth, drop to a minimum by age 1 yr, and then rise with age; (2) fecundity increases
with age and seldom decreasesat the last age of reproduction; (3) reproductive value and
residual reproductive value rise to a peak and then fall with age; (4) age-specificmortality
rates and. age-specific mortality covary inversely with reproductive value; (5) residual
reproductive value, survival, and survival rates covary inversely with fecundity; (6) residual
reproductive value is positively correlated with adult survival; (7) no relationships were
foun~ bet~een fecundity and successive survival probabilities in the life table; (8) no
relationshIp was found between age at maturity and life expectancy; (9) no relationship
was found b~tween litter size and generation length; (10) future fecundity is positively
~~
corr~lated
~~:~~ c
t':\"
"
~i::?~1';
I:t'~i
~
~~
I;;,~~~~
A
wIth pr~sent fecun~ity;
.and (II)
age-specific fecundity
varies inversely
with
modIfied reproductive value. LIfe hIStOrypatterns among populations, within populations,
within ageclasses,and amongspeciesarenot alwayssimilar, sothat theoreticalpredictions
should explicitly delineate the level of organization to which they pertain.
. Ke~~ords: ageat maturity; ag~-specific;
Col~mbiangrou~ squirrel;demography;
fecundity;life
histOry,life tables;mammal; mortahty;reproductivevalue;residualreproductivevalue;Sperrnophi1us
co1umbianus;
survival.
INTRODUCTION
Mammalian life history traits of natural populations
have been examined in the light of life history theory
in several interspecific studies (Millar 1977, Blueweiss
et al. 1978, Western 1979, Tuomi 1980, Millar and
Zammuto 1983, Steams 1983a). However, few studies
have examined life history traits in several populations
of one species(Smith 1978, Bronson 1979, Zammuto
and Millar 1985a, b. Dobson et al. 1986). One reason
for the lack of such studies is the difficulty of obtaining
life-table data. Accurate aging techniques and tests of
assumptions (net reproductive rate, Ro = I; intrinsic
rate of increase, r = 0; no year effects) needed to construct time-specific life tables have only recently begun
development (Zammuto and Sherman 1986), so they
are not available for many mammals. Therefore, zero
age class cohorts must be followed throughout their
lives before life tables can be constructed for most
mammals. This vastly increasesstudy logistics for longlived mammals. Even when multiple life tables are
available for a mammal, they have seldom been analyzed in light of life history theory (seeCaughley 1977:
86, Millar and Zammuto 1983).
Recent arguments suggestthat intraspecific life his-
tory patterns should consider bet-hedging theory (Murphy 1968, Chamov and Schaffer 1973, Steams 1976),
or another as yet unarticulated theory that considers
age structure (Charlesworth 1980, Steams 1983b).
Nevertheless, most predictions of bet-hedging theory
were contradicted by age-specific survival and fecundity patterns in different populations of Columbian
ground squirrels, Spermophilus columbianus (Zammuto and Millar 1985b). Perhaps other age-specific,
theoretical predictions are important for the evolution
of intraspecific life history patterns., The life history
literature contains a number of such predictions. The
purpose of this study is to evaluate the importance of
several of these predictions for the evolution ofmammalian life histories.
I consider age-specific,theoretical predictions of life
history evolution that do not directly pertain to r-K or
bet-hedging theory, using six life tables for the herbivorous, montane Columbian ground squirrel. This
species is relatively long lived (> 3 yr), allowing examination of several ageclasses,and abundant, so that
removed animals are quickly replaced. In addition,
litter size and survival within populations are relatively
stable from year to year when compared with many
rodents (Murie et al. 1980, Boag and Murie 1981), and
I Manuscriptreceived29 May 1986;revised26 November
the influence of differing environmental conditions on
1986;accepted2 December1986.
the life history and population genetics among popu-
1352
RICHARD M. ZAMMUTO
Ecology,Vol. 68, No.5
lations of this specieshas been documented (Dobson
and Kjelgaard 1985a, b, Zammuto and Millar 1985a,
b, Dobson et al. 1986).
Most oft hthe
life-table
predictions
appearing
in the
1.Iterature
at were
not di rectly
related
to r-k
or bet-
to detennine correlations among life history traits-an
approach termed the "strategic life history model"
(Tuomi and Haukioja 1979:11).
hedging theories and were testable by the data presentedhere were considered.Relationships among traits
for entire age classes were examined under the assumption, supported by Lande (1982), that life history
characteristics of age classes many times depict the
summation of life history characteristics of individuals. No doubt some of these predictions may be examined using individuals or species instead of age
classes,and conclusions from such studies may differ
from conclusions made here. Heretofore, some of these
predictions have been examined for individual Columbian ground squirrels, with results similar to those presented here (J. O. Murie and F. S. Dobson, personal
communication). The predictions considered here are:
(1) the age-specific mortality rate should be high after
birth, should drop to a minimum prior to the age at
maturation, and then should rise with age(Emlen 1970:
591, Preston 1972:168);(2) age-specificfecundity should
rise to a peak and then should fall with age (Emlen
1970:593, Preston 1972:168); (3) reproductive value
and residual reproductive value should rise to a peak
and then should fall with age (Fisher 1958:28, Pianka
and Parker 1975:457, Pianka 1976:779); (4) age-specific mortality and (or) mortality rates should be inversely related to reproductive value (Fisher 1958:29
Caughley 1966:917, Michod 1979:546); (5) residuai
reproductive value should vary inversely with age-specific fecundity (Pianka and Parker 1975:454, Snell and
King 1977:886); (6) residual reproductive value should
be positively correlated with adult survival (Williams
1966:689); (7) age-specificsurvival, survival rates, and
(or) successivesurvival probabilities in the life table
should vary inversely with age-specificfecundity (Snell
and King 1977:887, Caswell 1980:20, 1982:521); (8)
age at maturity should be positively correlated with
life expectancy (Tinkle 1969:502, Wittenberger 1979:
442); (9) litter size should be inversely related to generation length (Hirshfield and Tinkle 1975:2229); (10)
future fecundity should vary inversely with present fecundity (Caswell 1982:521); and (11) age-specific fecundity should vary inversely with modified repro-
I collected 506 Columbian ground squirrels (~l yr
old) with Conibear traps from six undisturbed populationsofsimilaradultdensity(10-15individuals/ha),
at elevations of 1300-2200 m, in the Rocky Mountains
of southwestern Alberta during 1980 and 1981. Most
of the animals present in four populations were collected so that statistics for these populations should
approach real population parameters. Two populations
were larger (> 200 individuals) than the others so individuals were sampled as randomly as possible from
thesepopulations until ~ 100 were captured. Each population was studied at the birth-pulse (see Caughley
1977:6) within 4 wk of female emergencefrom hibernation. Age (annual adhesion lines in diastema of lower
jawbone, checked against known-aged animals, following Millar and Zwickel (1972)), male maturity (males
with pigmented scrota or scrotal testeswere considered
mature), female maturity (females with embryos or
placental scarswere considered mature), and litter size
(embryos or placental scars) were detennined.
Time-specific life tables were constructed under the
assumption that stationary age-distributions were approached in these populations (seeCaughley 1977:90,
Charlesworth 1980:31, 42, 62, 78, Michod and Anderson 1980). The assumption of nearly stationary agedistributions for these populations was indirectly supported during long-tenn studies on four Columbian
ground squirrel populations in the same region and on
other populations of montane ground squirrels living
under similar undisturbed conditions (Bronson 1979,
Murie et al. 1980, Boag and Murie 1981, Dobson et
al. 1986, Zammuto and Sherman 1986). The life tables
were smoothed using the log-polynomial method described by Caughley (1977:96) to produce the greatest
similarity possible between the time-specific life tables
and the long-tenn age structures of the populations.
Age-specific survival, Ix, the proportion of animals
living to age x, and the age-specific survival rate, Px,
the proportion of animals alive at age x that survive
to agex + 1, were calculated after Caughley (1977:85)
as:
ductive ,:alue (Charlesworth 1980:242).A1th~u~ some
sample SIzes
for older
(age
4+) wIthIn
populations
are small
( < 5),age
theclasses
number
of animals
in youn-
Ix = nxlno,
where no was the number born and nx was the number
ger ageclassesallows examination of most predictions
living to age x, and as:
(see ~onley 1984:117).
Millar and Zammuto (1983) concluded that life-table characteristics of one population of a given mammal may be representative of many species.Hence, an
intra- and (or) interpopulational consideration of these
11 predictions for six populations could help elucidate
generalrelationships between age-specificsurvival and
fecundity for other populations. The approach here is
ME THODS
Px = Ix+lllx,
.
J
'"
,.
r
(1)
(2)
respectively. Age-specific mortality, dx, the probability
of dying between agesx and x + 1, and the age-specific
mortality rate, qx, the proportion of animals alive at
age x that die before age x + 1, were calculated after
Caughley (1966, 1977:85) as:
dx = Ix - Ix+l'
(3)
..
)
October 1987
TABLE I.
MAMMALIAN
LIFE TABLES
1353
Time-specific life table for population I (1300 m).
Age
Number
Smoothed
(yr)
captured
frequencYt
0
186:1:
I
2
3
4
5
43
26
19
8
5
Total
287
Ix
180§
45
27
16
9
5
mx
Ixmx
1.000
0.000
0.250
0.150
0.089
0.050
0.028
1.143
1.917
2.533
2.500
2.750
ex
0.000
Vx
1.567
vx.
1.00
0.286
2.268
4.00
0.288
2.113
4.77
0.225
1.876
4.80
0.125
1.560
4.04
0.077
1.000
2.75
Ro = I.OO~
X litter size = 3.88 :t 1.45; a = 1.14; Tc = 2.42
dx
1.00
0.750
2.86
2.85
2.27
1.54
0.00
0.100
0.061
0.039
0.022
0.028
t SeeCaughley (1977:96).
Sum of all litter sizes of collected females in population (=number born).
§ The product of the number born, no, and ~ Ixmx when Ix was calculated using the number born.
Net reproductive rate, ~ Ixmx (Pielou 1974:17).
:I:
II
and
as:
qx
=
dxllx
=
Ix-Ix+l/lx,
Age-specific
fecundity
afterCaughley(1966:9l2,
fore,
mx
males
values
912,
weighted
several
1977:82).
mx
calculated
future
where
to
Itllx
t,
was
and
m,
a female
value,
the
~
barren
103),
fe1966:
value,
1978:
vx,
was
the
was
age
of
reproductive
living
respect
to
(Williams
the
from
of
in
probability
1966)
was
,
the
age
x
females
residual
value
The
accuracy
The
age
a
at
=
maturity
[(N
(a)
to
)(a)
+
(N
next
age-interval
to
that
(6)
calculated
)(a
p
+
is
life
and
life
(Pianka
1978:
I II
y
terms
on
litter
the
size
closely
(see
should
over
describe
how
approached
tables
(9)
X'
these
depends
dynamics
Boag
and
All
reproductive
of
surviving
calculated
as:
was
~
which
species
calculated
as:
l)]/(N
+
q
the
Pielou
1974:29).
reflect
decade
been
life
a stationary
accurately
last
have
N),
(7)
q
1981,
Dobson
(Ix,
formed
before
239~.
Nonparametnc
pop-
because
relatively
J:'x,
et
dx,.
para~etnc
al.
q.x)
adult
stable
in
statIstIcal
tests
1986)..
were
were
heterogeneous
were
F).
among
used
(=a~ong
age
po~ul~tions),
ulatIons
am.ong
(=W1thm
(P
<
age
populations
classes
and
Bart-
variables
among
populatIons),
raw,
.05,
life-table
classes
1984:
the
(P < .05,
Kol(or)
variances
and
among
among
(Zar
whenever
populations
Relationships
examined
a~csme-trans-
analysIs
arcsme-tra~sfo.rmed,an.dl?-transfo~eddatawerenonnormally
dIstnbuted
wIthIn
populatIons
mogorov-Smirnov
one-sample
tests)
were
p
Mu~e
proportIons
lett-Box
Mean
with
ofa
Age-specific
life
as:
age-distribution
born
= (Ix+lllx)vx+'.
vx*
(8)
(5) the study region during this time (Murie et al. 1980,
number
t. Age-specific
calculated
one.
offurther
=
survival
, x mt,
average
Ixmx,
equalled
expectation
ex
history
ex-
106),
(I II)
probability
was
of
vx*,
with
interval
mean
Caughley
(Pianka
denominator
ex,
ulation
=
age
and
(see
the
expectancy,
as:
Vx
xlxmxl ~~
~
collected
feratio.
There-
reproductive
offspring
calculated
the
for
sex
means
values
Age-specific
of
was
as one-half
placental
scars
a 1: 1 primary
were
reduced
pectation
(mx)
1977:84)
of embryos
or
of age x, assuming
~
(4)
where
respectively.
number
males
=
Tc
(or)
w~th~n
pop-
wIthIn
each
whereNp wasthe numberoffemalesmature(pregnant age class(1-5 yr) among populations (=within ageor
lactating)
imals
6)
that
a,
the
studied
more
lation,
I
at
were
than
and
N
was
q
first
at
age
the
(whole
years,
birth-pulse,
since
Caughley
one
female
was
the
number
of
mature
in
females
an1977:
in
a poputhe
classes)
with
specific
life-table
they
pop-
correlation
were
lyzing
constant
them
at
females
age
data.
a
+
This
variation
not
1, an
estimate
within
ingful
comparisons
tional
estimates
numbers.
females
of
as:
the
mature
of
giving
mean
birth
all
have
supported
offspring
1978:
or
104),
thus
these
mean-
than
the
life
by
more
maturation-age
T c'
matured
preserved
allowed
populations
length,
(Pianka
is
and
state
to
a would
maturation-age
among
that
age
that
populations
Generation
population
at
assumption
convenas
average
the
whole
age
turnover
was
calculated
of
rate
tables
predictions
this
method,
from
populations
are
used
classes
previous
age
classes
of
and
(or)
Agewhen
because
correlations.
4,
Vo or
or
anaFor
In
in
these
figures
any
to
vo*
addition,
ex-
definition,
from
were
the
by
oldest
only
fecundity
All
completeness.
treated
data
to
their
elim-
age
classes
of
males,
analyses,
were
and
analyses.
exceptations
lost
composed
tables.
for
by
was
these
life
0.0
dropped
information
were
age
tables
usually
analyses.
not
1.0
were
3 and
in
1975).
analyzed
vo., and the lastpx, qxand vx* of all
since
ination
et al.
not
populations
weighted
approach
values
For
they
va'
(Nie
usually
among
always
these
two
were
unjustly
ulation not mature at agea. The calculationassumes ample,10, mo,
that
analyses
values
as
appear
so
and
the
the
last
in
the
1354
RICHARD M. ZAMMUTO
Ecology,Vol. 68, No.5
TABLE2. Time-specificlife table for population2 (1360 m). All Table 1 footnotesapply.
Age
(yr)
Number Smoothed
captured frequency
Ix
mx
Ixmx
ex
Vx
vx.
dx
105
58
23
12
7
95
43
24
13
7
1.000
0.453
0.253
0.137
0.074
0.000
0.339
1.667
2.167
1.500
0.000
0.154
0.422
0.297
0.111
1.960
2.119
2.004
1.854
1.581
1.00
2.21
3.34
3.10
1.72
1.00
1.87
1.68
0.93
0.22
0.547
0.200
0.116
0.063
0.042
5
1
3
0.032
0.000
0.000
1.344
0.52
0.52
0.021
6
7
2
1
1
0
0.011
0.000
1.500
2.500
0.017
0.000
1.50
2.50
0.00
0.00
0.011
0.000
0
1
2
3
4
Total
Ro=
1.000
0.000
1.00
,
X litter size= 3.75:t 1.04;a = 1.79;Tc= 2.44
209
RESULTS
AND DISCUSSION
J
.001), supporting Emlen's (1970) prediction. In pop-
Standingagestructuresdid not differ betweensexes ulations2, ~, and 5.,qx(for X
for any population (P > .05, for all Lee and Desu [1972]
Dotat),so males and females were combined for lifetable calculations (Tables 1-6). Age structures (Table
7 D = 34.2 df = 5 P < .001 Lee-Desu D ) and
li~tersizes(H = 17.9:df= 5, P .:: .01, Kruskai~Wallis
ANOV A) varied among populations.
. .
PredIctIon 1
~ 1andqx >.0)incr~ased
~P< .05) WIth age;In p~pulatl0ns 1 an.d6, It marginally
~ncreased~P = .~6) WIth a~e; but ~ld not. (P. = .1.4)
IncreasewIth ageIn populatIon 3 untIl later In hfe (FIg.
lA). qx remained relatively constant until age 5 in population 3 and then increased for two age classes(Fig.
lA). A constant qx from birth to age 5 may indicate
that animals in population 3 may possess the same
ability to respond to selective pressure from birth to
age 5 yr (Emlen 1970). Alternatively, the pattern in
The age-specific mortality rate (qx) is the life-table population 3 may be a result of the higher juvenile
parameter that is least affected by sampling biases,con- survival coupled with the lower litter size (both P <
tains the most direct information about the mortality
.05) that population 3 possessedwhen compared to the
pattern, and is the most efficient parameter for com- other populations (Tables 1-6).
paring life tables among populations (Caughley 1966,
qx usually rose with age after age 1 yr, even though
1977:87). Emlen (1970:591) predicted that qx should maturation did not occur until ages 2 or 3 yr in five
be high after birth, should drop to a minimum prior populations. Therefore, high qx usually occurred after
to the ageat maturation, and then should rise with age birth and then fell as predicted, but it usually began to
after maturation (also see Caughley 1966). That is, rise after the juvenile year, even though maturation
maximum resistanceto mortality should occur during had not occurred by then in five populations. Overall,
the pre-reproductive period and resistance should de- thesedata indicate moderate support of Em len's (1970)
creasethereafter (Williams 1957, Hamilton 1966, Em- prediction, since qx usually was high after birth, delen 1970).
creased during the pre-reproductive period, and then
Overall, qx(for x = 0, 1) was high after birth, dropped increasedwith ageashe predicted, but variation existed
to a minimum by 1 yr (r = -0.79, n = 12, P < .01; with regard to the age that qx increased with respect to
see Fig. lA), and then increased with age (for x ~ 1 maturation-age, and population 3 did not follow the
and qx > 0) among populations (r = 0.66, n = 28, P < prediction.
TABLE3. Time-specific life table for population 3 (1500 m). All Table 1 footnotes apply.
Age
(yr)
0
1
2
3
4
5
6
7
8t
Total
Number Smoothed
captured frequency
53
56
42
34
32
21
15
13
7
8
1
5
1
3
2
1
2
0
155
Ix
1.000
0.607
0.375
0.232
0.143
0.089
0.054
0.018
0.000
mx
0.000
0.000
0.529
1.083
1.833
2.000
1.500
2.000
0.000
Ixmx
ex
Vx
0.000
2.518
1.01
0.000
2.501
1.66
0.198
2.429
2.68
0.251
2.310
3.48
0.262
2.126
3.90
0.178
1.809
3.31
0.081
1.333
2.17
0.036
1.000
2.00
0.000
0.000
0.00
Ro = 1.01
X litter size = 2.94 :t 0.73; a = 2.59; Tc = 3.83
t Age class composed only of males so not used in fecundity analyses.
vx.
1.00
1.66
2.15
2.40
2.06
1.32
0.67
0.00
0.00
dx
0.393
0.232
0.143
0.089
0.054
0.035
0.036
0.018
0.000
..
}
October 1987
MAMMALIAN
LIFE TABLES
1355
TABLE4. Time-specific life table for population 4 (1675 m). All Table 1 footnotes apply.
Age
(yr)
Number Smoothed
captured frequency
0
1
2
3
4
5
114
17
23
21
5
3
Total
183
74
25
19
13
7
3
Ix
mx
1.000
0.338
0.257
0.176
0.095
0.041
0.000
0.222
1.344
1.536
2.500
2.000
X litter
Ixmx
size
These results indicate that selective intensity to decreaseqx should be highest between birth and age 1 yr
in all populations except population 3, if selective intensity to decreaseqx is highest where qx falls with age
(Williams 1957, Emlen 1970:590). Perhaps selection
operates most intensively on the juvenile age classes
in populations 1, 2, 4, 5, and 6. Poor survival in juvenile ageclassescompared with other ageclassessupports this idea (Tables 1, 2, 4-6).
Prediction
=
ex
Vx
0.000
1.907
1.01
0.075
2.683
2.99
0.345
2.214
3.64
0.270
1.773
3.35
0.238
1.432
3.36
0.082
1.000
2.00
Ro = 1.01
4.22 :t 0.89; a = 2.22; Tc = 2.94
vx*
dx
1.01
2.77
2.29
1.81
0.86
0.00
0.662
0.081
0.081
0.081
0.054
0.041
lation 4, the only population where the predicted pattern could be considered to have been followed (Table
4, Fig. 1B).
Overall, these results indicate that mx increaseswith
ageas Emlen (1970) predicted, but it seldom decreases
after peaking. Laboratory populations have displayed
the predicted decreaseafter a peak for mx (Myers and
Master 1983). Perhaps the predicted decrease of mx
with age was not observed in natural populations because most individuals died before this "aging" effect
could be observed. Alternatively,
selection for fecun-
2
Emlen (1970:593) predicted age-specific fecundity
(mx) should rise to a peak and then should fall with
age. That is, it is thought that natural selection should
push the highest possible fecundity towards earlier and
dity may not decreaseafter peaking as Emlen (1970)
predicted.
. .
Prediction 3
earlier age classesuntil opposing forces keep fecundity
from further increasing and (or) opposing forces keep
fecundity from occurring at earlier ages. After this,
selection for fecundity should decreasewith increasing
age because selective forces no longer exist for high
fecundity after high, early, successfulfecundity occurs
(Emlen 1970).
Overall, mx (for x > 0) increased with age among
populations (r = 0.60, n = 34, P < .001; Tables 1-6,
Fig. IB), and increased with age within populations 1,
3, 4, and 6 (all P < .05), whereas the positive trends
in populations 2 and 5 were not significant (both P >
.06) (Tables 1-6, Fig. IB). mx peaked at the last reproductive agein population 2 after a fall at age 5, whereas
m" remained relatively stable for ages 3-5 yr within
population 5 (Tables 2 and 5, Fig. IB). mx dropped
with age for one age class after peaking within popu-
Fisher (1958:28), Pianka and Parker (1975:457), and
Pianka (1976:779) predicted that reproductive value
(vx) and (or) residual reproductive value (vx*) should
rise to a peak and then should fall with age. The arguments for this prediction relate to those for Prediction 2, but here Vxand vx* combine survival with mx.
The following is a synthesis of arguments advanced by
Williams (1957, 1966), Emlen (1970), Pianka and Parker(1975), Pianka (1976), and Rose (1984). It is argued
that individuals risk subsequentsurvival by reproducing. The youngest ageclassthat reproduces has a greater survival risk caused by reproduction than older age
classes,because of their relative inexperience at abtaining resourcesand producing offspring. This pattern
causeseach individual in younger age classesto contribute fewer offspring to future generations than those
in older age classes.As individuals grow older, larger,
TABLE5. Time-specificlife table for population 5 (2000m). All Table 1 footnotesapply.
Age
(yr)
Number Smoothed
captured frequency
Ix
mx
Ixmx
ex
Vx
vx*
dx
0
1
134
29
115
28
1.000
0.243
0.000
0.000
0.000
0.000
1.860
3.539
1.00
4.09
1.00
4.09
4.40
3.07
0.757
0.017
3
4
5
30
16
7
22
15
8
0.191
0.130
0.070
1.765
1.800
1.750
0.337
0.234
0.123
2.047
1.538
1.000
3.63
2.74
1.75
1.87
0.94
0.00
0.061
0.060
0.070
Total
235
2
19
26
0.226
1.333
0.301
2.730
Ro = 1.00
X litter size= 3.44 :t 0.85; a = 2.13; Tc= 3.16
0.035
1356
RICHARD M. ZAMMUTO
Ecology, Vol. 68, No.5
TABLE6. Time-specific life table for population 6 (2200 m). All Table 1 footnotes apply.
Age
(yr)
Number Smoothed
captured frequency
Ix
mx
Ixmx
ex
Vx
vx*
dx
0.99
4.31
3.68
2.59
1.89
0.00
0.00
0.771
0.029
0.029
0.057
0.028
0.057
0
1
2
3
4
5
52
5
7
9
4
3
35
8
7
6
4
3
1.000
0.229
0.200
0.171
0.114
0.086
0.000
0.000
1.250
1.714
2.000
2.500
0.000
0.000
0.250
0.293
0.228
0.215
1.829
3.620
3.000
2.339
2.009
1.337
0.99
4.31
4.93
4.30
3.89
2.50
6t
1
1
0.029
0.000
0.000
1.000
0.00
Total
81
.
0.029
Ro = 0.99
Xlittersize=3.71:t0.99;a=2.25;Tc=3.37
."'
t Age classcomposedonly of malesso not usedin fecundityanalyses.
and more experienced, they obtain more resourcesand
possesslower survival risks for each offspring produced
than when they first bred. Thus, older animals contribute more offspring to future generations at a lower
cost to survival than younger animals, and therefore
Vxand vx* should increase with advancing age. After
the maximum number of offspring are contributed to
future generations (peaks of Vxand vx*), it is argued
that selective pressure to survive and reproduce is relaxed, senescenceleads to decreasedreproduction and
a peak and then fall with ageamong populations, among
species, and within most populations of mammals.
Therefore, these results are consistent with arguments
that young animals have a greater survival risk attached to reproduction than older animals and that
selective pressure to survive and reproduce is relaxed
with increasing agein mammals (Williams 1957,1966,
Rose 1984).
. .
Prediction 4
survival with increasing age, and therefore vx and vx*
decreasewith age (Williams 1957, 1966, Rose 1984).
Vx(for x ~ vrnax)rose to its maximum value with
increasing age among populations (r = 0.75, n = 21,
P < .001) and within populations 2 and 3 (both P <
.05) (Tables 1-6, Fig. lC). Similarly, vx* (for x ~ vrnax*)
marginally rose to its maximum value with increasing
age among populations (r = 0.52, n = 14, P = .06)
Fisher (1958:29), Caughley (1966:917), and Michod
(1979:546) predicted that age-specific mortality (dx)
and (or) age-specificmortality rates (qx) should covary
inversely with reproductive value (vx). That is, high
current mortality should reduce the average contribution of offspring to future generations.Michod (1979)
and Charlesworth (1980:265) questioned the biological
(Tables1-6, Fig. 1D). The predictedfall of vx (for x ~
significanceof such a relationship on mathematical
groundsof autocorrelation.For example,this predic-
vrnax)and vx* (for x ~ vrnax*)with increasing age after
each peaked was strongly supported among populations (r = - 0.69, n = 25, P < .001, and r = - 0.77,
n = 25, P < .001, respectively; Tables 1-6, Fig. lC,
D). The predicted fall ofvx (for x ~ vrnax)
with increasing
age was supported within populations 3, 5, and 6 (all
P < .05), and the fall of vx* (for x ~ vrnax*)with increasing agewas supported within populations 2-6 (all
P < .05), and marginally within population 1 (P = .06)
(Tables 1-6, Fig. lC, D). The general rise and fall pattern between Vxand ageand vx* and agehas been found
for six other mammals.
Animals of the age class where Vxpeaks contribute
the most offspring to future generations (Fisher 1958:
27). Vxpeaked for ageclasses2 or 3 yr in all populations
except population 3 where it peaked at age4 yr, where-
tion may simply indicate that if animals die they will
not produce offspring. However, this prediction may
also indicate that age classesthat are adept at resisting
mortality are also adept at successfulreproduction.
qx and vx, and dx and Vxwere correlated inversely
among populations (r = -0.72, n = 34, P < .001 and
r = -0.60, n = 39, P < .001, respectively; Tables 16, Fig. 2A, B). qxand vx were correlated inversely within
populations 1, 2, 5, and 6, and dx and vx were correlated
inversely within populations 1 and 6 (all P < .05)
(Tables 1-6). dx and Vxwere correlated inversely within
as vx* peaked at age 1 yr in all populations except
population 3 where it peaked at age 3 yr (Tables 1-6,
Population
may be noteworthy. Population 2 displayed a semibimodal peak, probably caused by a nonreproductive
5-yr-old (Table 2, Fig. lC, D). This pattern of Vxin-
2
~
5
Fig. lC, D). The pattern for vx* within population 2
dicates that, contrary to Pianka and Parker (1975:455),
. . when mx = O.
Vx* does not always maXImIZe
All data indicate that Vxand vx* usually increase to
TABLE7. Differencestbetweenstandingagestructuresofthe
six populations.
1
1
2
NS
Population
3
4
5
6
NS
NS
***
**
NS
***
*
***
**
NS
***
**
::
t Le and Desu(1972)Dstat,SIgnI
. .fi
1 1. *
eve s. P <., 05
** p <e.01,
*** P < .001,NS= P >cance
.05,overall
D = 34.2,
df= 5, P < .001.
'
:r
;;
October1987
MAMMALIAN LIFE TABLES
1.0
>-
>-
~
I-
:>
u
E
2.
.
0: 0.6
t:
~ 0.4
1.5
w
l1-
I0:
0
~ 0.2
1
o.
0
2
'3
4
AGE
5
0
6
2
(yr)
C
5
'3
4
5
AGE (yr)
D
*~..
w. 4
..
~
:>
-4
W
-J
:3
«
>
B
'3
~
. 0.8
w
I«
0
1357
~ '3
W
>
i=
0
0:
Il.
W
0:2
g2
0
0
1
0:
Il.
-J
«
:>
0
1
-
W
0:
(/)
W
0:
'3
0
0
0
12'345
0
12'34
AGE (yr)
AGE (yr)
FIG. 1. Relationships of age vs.: (A) mortality rate, qx; (B) fecundity, mx (r = 0.60, n = 34, P < .001); (C) reproductive
value, Vx;and (D) residual reproductive value, vx* for six populations of Columbian ground squirrels. Population 1 (0), 2 (~),
3 (X), 4 (0), 5 (8), and 6 (+).
age classes 1 and 2 yr (r = -0.91, n = 6, P < .05 and
r = -0.93, n = 6, P < .01, respectively), whereas qx
fecundity in an age class should diminish the contribution of offspring to future generations by future age
and Vxwere not correlated (all P > .05) within any age
class. Therefore the prediction that qx or dx should
covary inversely with Vx is supported among popula-
classes.
vx* and mx (for x > 0) were marginally correlated
inversely among populations (r = -0.36, n = 28, P =
tions, within the majority
two age classes.
.06, Tables 1-6, Fig. 2C). vx* and mx were correlated
only within population 4 (r = -0.96, n = 4, P < .05)
of populations,
and within
These results moderately support the hypothesis that
mortality-resistant
age classes are more adept at contributing offspring to future generations than age classes
and they were not correlated within any age class (all
P> .50, Tables 1-6). These results suggest that present
levels of fecundity (mx) may slightly (P = .06) reduce
not resistant to mortality, and they are also consistent
with an autocorrelative cause for these inverse relationships. Perhaps other predictions will help shed light
on this apparent theoretical and empirical underpinning (see Michod 1979 and Conclusions).
re~idual reproductive value (vx*) among populations
and within one population, whereas mx does not seem
to reduce vx* within any age class. Therefore there is
only weak support for the prediction that high fecundity in one age class diminishes the contribution
of
offspring to future generations by future age classes.
mx is a measure of reproductive effort (Williams 1966:
689, Hirshfield and Tinkle 1975:2228). Therefore, these
. .
PredIctIon 5
Pianka and Parker (1975) and Snell and King (1977)
predicted that residual reproductive value (vx*) should
vary inversely with age-specific fecundity (mx). That
is, if high fecundity has a greater cost in terms of decreased future fecundity than low fecundity, then high
results weakly (P
= .06)
support Willliams'
(1966) pre-
diction that reproductive effort should vary inversely
with vx* (contra Tuomi etal. 1983). However, Williams
(1966) suggested this relationship should be found for
interspecific comparisons, but it does not seem to exist
1358
RICHARD M. ZAMMUTO
5
..
~
00
w -4'
00
0
00
-J
<
0
0
0
.
=.
0
0
0.2
0.4
0.6
MORTALITY. dx
C
~..
.4
w
::>
3
.
0
0
w
Ct:
0
* ..
0
0.2
0
.
.
=.
_0
0.4
0.6
0.8
MORTALITY RATE, qx
1.0
4
D
0
~
«
::>
o'
0
0
.9
I
(/)
0
0
0
do.
0
0
00
0
>
0
0
0
-J
«
0
woo
0
Ct:
0.. I
.
0
::>3
0
Ct:2.
Ct:2
0..
0
W
Ct:
0
(/)
o.
0
0
0
::>
0 I
0
0
0
0
W
Ct:
-J
«
-
0
w
Ct:
0
W
0
-J
0
0
0.8
*
-J
0
0
0
0
..
~
0
0
::>
~I
d
.
0
(,)2
0
~
o.
~
I-
0
0
0
0
0
woo.
00
w
Ct:
0 00
0
-.0
0
::>
.
0
>' 3
00
(,)200
0
8
00
:J;.
0
00
W
>
i=
0
,.;40
000.
3
5
..
~
0
::>
<
>
A
000
Ecology,Vol. 68, No.5
00
0
0
0
0
0
I
1.5
2
2.5
3
0
0.05
0.1
0.15
0.2
0.25 0.3
FECUNDITY, mx
SURVIVAL, Ix
FIG.2. Relationshipsof reproductivevalue, Vxvs.: (A) mortality, dx (r = -0.60, n = 39, P < .001);and (B) mortality
rate,qx(r = -0.72, n = 34, P < .001);and relationshipsof residualreproductivevalue,vx*vs.: (C) fecundity,mx(r = -0.36,
n = 28, P = .06);and (D) survival, Ix (r = 0.69, n = 21, P < .001)for six populationsof Columbiangroundsquirrels.
0
0.5
for interspecific studies of mammals (Millar and Zammuto 1983).
. .
PredIction 6
essarily high, and vx* does not uniformly decreasewith
age (Tables 2 and 3).
v,,*and Ix (for x ~ a) were positively correlated among
populations(r = 0.69, n = 21, P < .001), but not within
Williams (1966:689) predicted that residual reproductive value (vx.) should be positively correlated with
adult survival (Ix, for x ~ a). That is, age classes(or
species) with low mortality rates should channel resourcesfor reproduction into later life instead of during
the present, since this allows low mortality to continue
by the avoidance of increased stress from breeding.
Channeling resources for reproduction into later life
also maximizes reproductive output over a lifetime and
best representsanimals in future generations. High reproductive output in the present reduces future reproductive output because it shortens lifespan and thus
reduces the average number of offspring contributed
to future generations (Williams 1966). This evolutionary reason for a correlation between vx. and Ix may be
real, but vx. and Ix may be correlated simply because
both generally decreasewith ageand (or) vx is calculated
any adult (x ~ 2) age class (all P > .25; Tables 1-6,
Fig. 2D). vx. and Ix (x ~ a) were significantly correlated
only within population 3 (r = 0.97, n = 4, P < .05).
However, all correlation coefficients between vx. and
Ix within populations exceeded 0.89, but with only 1
or 2 df, they were insignificant, suggesting that this
prediction needs further study within populations that
possess> 3-4 adult age classes.
Overall, these results support Williams' (1966) prediction among populations and are suggestiveof support within populations. However, contrary to WilIiams (1966), this positive relationship may pertain
only to intra- and interpopulational comparisons, since
it does not appear to exist for interspecific comparisons
among mammals (Millar and Zammuto 1983).
. .
PredIction 7
using Ixvalues. Nonetheless, the prediction is examined
here becausethe degree of autocorrelation is not nec-
Williams (1966), Snell and King (1977), and Caswell
(1980, 1982) predicted that age-specific survival rates
"-
t
October1987
MAMMALIAN LIFE TABLES
1359
(Px),and (or) survival (Ix), and (or) successivesurvival
mx (for x > 0) were correlated inversely among popprobabilities in the life table (lx+2/lx, Ix+3/lx,seeCaswell ulations (r = -0.38, n = 28, P < .05 and r = -0.63,
1980), should vary inversely with age-specific fecun- n = 33, P < .001, respectively;Tables 1-6, Fig. 3A,
dity (mx) (contra Gadgil and Bossert 1970: 19). That is, B) supporting the first part of Prediction 7 and falsifycosts of reproduction for a given age class should be ing Gadgil and Bossert's (1970) opposing prediction.
manifested as reduced survival for the current and sub- px and mx (for x and px > 0) were marginally correlated
sequentageclasses(Caswell 1980, 1982).Schaffer(1981) inversely only within population 4 (P = .06), whereas
and Yodzis (1981) argue Caswell's (1980) mathematics Ix and mx were correlated inversely (all P < .05) within
incorrectly assert that fecundity at age x can affect fe- populations 1, 3, and 6, and they were marginally (P =
cundity or survival at agex-I.
Schaffer (1981) argues .06) correlated inversely within population 4 (Tables
that this is only possible in the case of extended pa- 1-6). Ix and mx were correlated inversely within age
rental care. However, Caswell (1981) and Ricklefs classes2 and 3 yr (both P < .05), whereas px and mx
(1981) maintain Caswell's (1980) original assertion was were not correlated within any age class (all P > .25).
correct. Notwithstanding, the social structure of Co- Ix+2/lxand mx, and Ix+3/lx and mx were not correlated
lumbian ground squirrel populations may involve ex- among populations, within populations, or within any
tended parental care, since daughters either acquire age class (all P > .05, Tables 1-6, Fig. 3C, D).
their mother's nest site or maintain nest sites adjacent
These results indicate that current reproduction (mx)
to their mother's throughout life (Harris and Murie
may be manifested as reduced current survival (Ix), or
1984, King and Murie 1985). Therefore, there is em- reduced current survival rates px among populations,
pirical support indicating that Caswell's (1980, 1981) within some populations, and within some ageclasses,
ideas could refer to Columbian ground squirrels, so his whereas current reproduction does not appear to reprediction is examined here.
duce subsequent survival (Ix+n/lx, for n > 1) among
px (=Ix+i/lx) and mx (for x and px > 0), and Ix and populations, within populations, or within age classes.
1.0
A
..
~ 0.8
0.8
Iw.
<t
a: 06.
.
a: 0.4
~
0
0
0
00
0
0
0
U> 0.2
0
0
0..0
0
0
0:
80
0
0
0
0
0
0
1.0
1.5
2.0
FECUNDITY, mx
2.5
"'.. 0.8
3.0
C
(\J
0
0.5
1.0
1.5
2.0
FECUNDITY,mx
2.5
"'.. 0.6
3.0
D
I')
+
+
~
>-"
I- 0.6
::i
~0.5
>-"
I-
00
0
a5
~
0.4.
0
a:
a..
0
0
0
~
0.3
0
00
0
0
0
0
0.2
>
>
0
0
0
0...J
.
0
a:
a.. 0.2
<t
>0.1
>
0
a:
:;)
U>O
0
::i 0.4
0
a5
~
<t
o'
:;)
000
0
0.5
000
a:
0
0.2
.0
-> 0.4
0
0
0
000
B
.
.0
.
~
<t
>.
.
>
0
.
.
-... 06
~
<t
>
-
1.0
a:
0
0
0
0
0
0
0
0
0
.
:;)
U>O
1.0
1.5
2.0
2.5
3.0
0
0.5
1.0
1.5
2.0
2.5
3.0
FECUNDITY, mx
FECUNDITY, mx
FIG. 3. Relationships of fecundity, mx vs.: (A) survival, Ix (r = -0.63, n = 33, P < .001); (B) survival rates, px =
Ix+,/ix (r = -0.38, n = 28, P < .05); and successive survival probabilities in the life table (C) Ix+2/lx (r = -0.38, n = 19,
P= .11); and (D) IX+3/lx(r = -0.46, n = 13, P = .11) for six populations ofColurnbian ground squirrels.
0
0.5
1360
RICHARD M. ZAMMUTO
- 3.0
+
..
E'< 2.5
>-!:: 2.0
~
a
~
1.5
. ..
..
.
5
'<
~
4
~.
~
> 3
Neither life expectancy at birth (eo)or maturity (em)
were correlated with a among populations (r = 0.78,
n=6,P=.07andr=0.32,n=6,P=.54,respect
Tables1-6), eventhougha is containedwithin eo(see
.
Sutherland et al. 1986). Interspecific comparisons have
indicatedstrongcorrelationsamonga, eo,and emfor
mammals(seeMillar andZammuto 1983,Harveyand
Zammuto 1985,but seeSutherlandet al. 1986).
.
Prediction9
Hirshfield and Tinkle (1975) predicted that mean
litter size(mx)shouldbe inverselyrelatedto generation
0.5
1.0
1.5
2.0
FECUNDITY m
, x
..
..
..
a:
2.5
3.0
B
.
..
... .
~
length (Tc). That is, shortening the generation time
increases the rate at which alleles leading to high fecundity increasewithin the genepool of the population
(Hirshfield and Tinkle 1975). mx and Tc were not cor-
relatedamongthesepopulations(r = - 0.70,n = 6,
P = .13, Tables 1-6), even though mx is contained
.
Prediction10
... . .
fu 2
a:
.
A.
within Tc. Perhaps this correlation exists only among
mammalian species(Millar and Zammuto 1983).
. ..
d
Caswell(1982)predictedthatfuturefecundity(mx+l)
should vary inversely with present fecundity mx. That
is, a cost of high fecundity in any current ageclassis
~ I
g
~ 00
A
.
w 1.0
-;
...
. ... ...
.
~
~
0.5
lJ..
00
.
Ecology,Vol. 68, No.5
.
0.5
1.0
1.5
2.0
2.5
3.0
FECUNDITYm
, x
FI<;,.4. Relationshipsof fecundity, rnxvs.: (A) futur~ fecundIty, rnx+1(r = 0.59, n = 23, P < .01);and (B) modIfied
reproductivevalue, Vx+1
(r = -0.40, n = 26, P < .05) for six
populationsof Columbiangroundsquirrels.
Part of the reason that successivesurvival probabilities
(lx+n/lxfor n > 1) were not significantly correlated with
mx could have been causedby the automatic reduction
of sample size as n increased,but in general correlation
coefficients were usually small between these traits.
Further study with more age classesmay be needed to
test this portion of Prediction 7 sufficiently.
. .
PredIctIon 8
manifested as a reduction of fecundity in the next age
class because, it is argued, there is a limited amount
of energyavailable for reproduction during the lifetime
I
of an animal, and usingthis energyat young agesre-
I
duces its availability at future ages (Caswell 1982).
Conversely, mx (for mx > 0) and mX+1were positively
.
correlated among ~opulatlons (r - 0.59, n - 23, P <
.01; Tables 1-6, FIg. 4A). mx and mX+l were not correlated (all P > .10) within any population, whereas
they were correlated between adjacent age classes2 yr
(=mx) and 3 yr (=mx+l) among populations (r = 0.96,
n = 6, P < .01; Tables 1-6).
These results suggestthat high fecundity in one age
class is not costly in terms of future fecundity. One
might ask how mx can increase with age, as Prediction
2 demonstrates, if the costs of high fecundity are manifested as reduced fecundity in the next ageclass.Clearly, Emlen's (1970) and Caswell's (1982) predictions are
contradictory. The present study suggeststhat Colum-
Tinkle (1969) and Wittenberger (1979) predicted age
at maturity (a) should be positively correlated with life
expectancy (ex). That is, high survival rates should favor delayed breeding. To elaborate, it is argued that
the benefits of early breeding by young animals are
drastically reduced when survival is high because
bian ground squirrel life tables do not follow Caswell's
(1982) prediction when the costs of high fecundity are
measured in terms of reduced fecundity in the subsequent age class.
breeding habitats are more often saturated by older
animals than when survival is low, and this pattern
leads to reduced reproductive successin young breeding animals. The pattern causesyoung animals to delay
breeding, to reduce survival costs attached to breeding,
and to increase their survival, which in turn leads to
a positive correlation between age at maturity and life
Charlesworth (1980:242) predicted that age-specific
fecundity (mx) should vary inversely with modified
reproductive value (vx+.). That is, the costs of current
reproduction should reduce the contribution of offspring to future generations by the next age class. mx
and vx+I (for mx > 0) were correlated inversely among
populations (r = -0.40, n = 26, P < .05, Fig. 4B) and
within population 6 (r = -0.95, n = 4, P < .05),
expectancy (Wittenberger
1979).
"
Prediction 11
t"
October1987
MAMMALIAN LIFE TABLES
1361
TABLE8. Summary of results for each of II theoretical predictions (or assumptions) of life history evolution examined for
six life tables of the Columbian ground squirrel.
Predict.
Ion
number
I
P d. t d tt
re ICe pa ern
of variables
qxdrops,then increases
with age
D
Among populations
drop: strong,**
ul
di .
?
0 res ts supportpre ctlon.
Within populations
3 strong§
Within ageclasses
...
increase: strong, ***
2 marginal§
...
...
...
...
2
mx increases, then drops
with age
increase: strong, ***
drop: no support, NSt
I no support§
I strong
4 marginal
3
Vxincreases, then drops
increase: strong, ***
2-3 strong
drop: strong,***
2-3 marginal
I no support
...
...
increase: marginal,
5 strong
AS:!:
drop: strong, ***
strong, ***
I marginal
...
...
with age
vx* increases, then drops
with age
4
5
6
7
8
qx varies inversely with
Vx
dx varies inversely with
Vx
vx* varies inversely with
mx
vx* increaseswith adult Ix
I no support
...
.. .
Px varies inversely with
mx
Ix varies inversely with
mx
strong, *
Ix+2/lxvaries inversely
with mx
Ix+3/lxvaries inversely
with mx
no support, NS
4 strong
2 no support
2 strong
4 no support
I strong
5 no support
I strong
5? (see text)
I marginal
5 no support
3 strong
I marginal
2 no support
6 no support
no support, NS
6 no support
2 no support
a increases with eo
a increases with em
no support, NS
no support, NS
. ..
. ..
...
.. .
no support, NS
converse strongly supported, **
strong, *
...
6 no support
...
I converse strong
2 no support
3 no support
9
mx varies inversely with Tc
mx+l varies inversely
with mx
II
Vx+lvaries inversely with
mx
* P < .05, ** P < .01, *** P < .001.
10
strong, ***
marginal, AS
strong, ***
strong, ***
1 strong
5 no support
5 no support
2 strong
3 no support
5 no support
4 no support
4 no support
2 strong
3 no support
3 no support
t NS = not significant.
AS = approaches
significanceasP ~ .06.
§ Strong= significant;marginal= AS;no support= NS.
:!:
whereas no correlations existed within the other five
populations (all P > .10), and no correlations (all P >
.20) were found between any two adjacent age classes
among populations (Tables 1-6).
Theseresults indicate that current reproduction (mx)
may reduce reproductive value in the next age class
(v,"+I)amongpopulations,whereastherelationshipseldom exists within populations or between adjacent age
classes.I conclude that the costs of current reproduction may reduce the contribution of offspring to future
generations by the next age class, but that this pattern
is detected only when a large number of age classesor
populations are examined.
CONCLUSIONS
The following statements pertain to life history patterns among populations, within populations, and (or)
within age classesof the Columbian ground squirrel:
(I) maximum resistance to mortality usually occurs
during the 1st yr of life, and resistance usually decreasesthereafter (Prediction I); (2) fecundity increases
with age and seldom decreasesat the last reproductive
age (Prediction 2); (3) reproductive value and residual
reproductive value rise to a peak, then fall with age,
resulting in peak numbers of offspring being contributed to future generations by 2- or 3-yr-olds (Prediction
3); (4) high current mortality rates and current mortality may reduce the contribution of offspring to future
generations by the current age class (Prediction 4); (5)
high current fecundity may reduce current survival,
current survival rates, and current residual reproduc.
I
.
tlve va ue, whereas It probably does not reduce future
survival (Predictions 5 and 7); (6) high adult survival
may lead to high residual reproductive value through-
1362
RICHARD M. ZAMMUTO
Ecology,Vol. 68, No.5
out life (Prediction 6); (7) delayed maturity does not
clearly (P = .07) lead to increased life expectancy (prediction 8); (8) high fecundity does not seem to lead to
reduced generation time (Prediction 9); and (9) current
fecundity does not seem to reduce future fecundity,
whereas it may reduce the contribution of offspring to
future generations by the next ageclass (Predictions 10
and 11) (see Table 8 for summary).
Why have the above patterns emerged for the Columbian ground squirrel? First, maximum resistance
to
mortality
(Emlen
1970)
and high
age-specific
tality
rates(qx)
usually
occurred
during
the 1st moryr of
In sum, decreasedmortality and increased survival
seem to lead to increased fecundity, and increased fecundity seemsto lead to decreasedsurvival in the Columbian ground squirrel. Further studies on other
mammals should be carried out when data become
available to see if this intraspecific pattern is general
for other mammals. Presently, data indicate that life
cycle patterns for one mammal may be representative
of many mammals, because design constraints may
preclude significant differences in life history patterns
among
mammals
and
Zammuto
1983).withThis
studyindicated
that(Millar
patterns
among
populations,
life, preceding the age at maturity, when most (> 50%)
squirrels died (Prediction 1; Tables 1-6, Fig. 1A). After
squirrels reached maturity, the maximum number of
offspring were contributed to future generations (Predictions 2-3; Tables 1-6, Fig. lC, D). A relatively low
.
d .
.dl.ti ft
1.
morta Ity rate unng mIle,
a er resIstance to mor-
in populations, within age classes,and among species
of mammals are not always similar, so that theoretical
predictions should explicitly delineate the level of organization to which they pertain.
tality
J. J.H.~rown,H.Caswell,J.P.C?rbm,?Cox,F.S.Dobson,
S. Millar,
and anonymous
reViewers
Improved
had
developed
, was
.
associated
..
with
the
maxi-
mum number of offspnng beIng contnbuted to future
generations in most populations (Predictions 1-4).
Thus, the highest numbers of offspring were contributed to future generations by squirrels with low mort l't
t
Th.
tt
rt th h
thes's that
a 1 y ra es. IS pa ern s~ppo ~ e ypo.
1
the most adapted (mortalIty resIstant) squIrrels produce the most offspring and these offspring constitute
most of the animals in an average population of Columbian ground squirrels (also seePreston 1972: 168).
..
,.,
These consIderatIons are consIstent WIth the Idea that
the inverse relationship between mortality rates and
reproductive value may have a biological reason, as
well as a possible autocorrelative reason for being
I
preva
ent
.
m
(
nature
1
a so
Ch
see
I
ar
rth
1980.265
.
eswo
the manu-
script, J. Zammutoand J. Schieckprovided field assistance
T. Lawton and R. Harris assistedin the laboratory,T. Har~
rison and G. LeBeltypedroughdrafts,D. Boagand J. Murie
provided locationsof known-agedground squirrels,and D.
Savageassistedwith the figures.The Natural Sciencesand
Engineering
Research
Councilof Canada(grantto J. S.Millar),
the Ontario Ministry of Collegesand Universities,the UniversitiesofWesternOntarioandCalgary,
andthe Department
of Indian and Northern Affairs provided financial and (or)
facility s.upportdu~ng data,collection. Early ~rafts or the
manuscnptwere wntten whIle I held a CanadianNatIonal
Sportsmen'sFund PostdoctoralFellowshipand a subsequent
postdoctoralposition under D. Parkinsonat the University
of Calgary.The Departmentof Biology,Universityof Calgary
providedfinancialsupportthrougha teachingpositionduring
a revision.
Environmental
The
field
station
Research
of the
provided
Kananaskis
space
and
Centre
facilities
for
LITERATURE
CrrED
Blueweiss,L., H. Fox, V. Ku~ma,.D. Nakashima,R..Peters,
.
.
support for the hypothesIs that a trade-off eXIsts between fecundity and survival, since survival patterns
and S. Sams. 1978. RelatIonships between body Sizeand
some life history parameters. Oecologia (Berlin) 37:257272.
usually covaried inversely with fecundity patterns (Predictions ti5 Iand d7)'b and
high
life(P
was
h .gh
ti survival
d . 1early. inI.ti
01 owe
y I
ecun Ity ater m Ie
re. .
.
. .
dIctIon 6). Fmally, there seemed to be conflictIng answers as to whether high fecundity early in life always
leads to reduced fecundity later in life, since some fe(m
vx,* vx+1 ) were either Positivel y
cundity
,. traits0) x+I'
.
I (P di .
5 d 11)
(PredIctIon 1 or Inverse y re ctions an
correlated with current fecundity (mx). However, these
Boag,D. A., and J. O. Murie, 1981. Populationecologyof
Columbian
groundsquirrelsin southwesternAlberta, Canadian Journal of Zoology 59:2230-2240.
B
M T 1979 AltI.t d . I
. t . . th I." h .
ronson, ..
.
u ma vana ion m e lie ISt ory
of the golden-mantledground squirrel (Spermophi/us
lateralis).Ecology60:272-279.
Brooks,D. R., andE. o. Wiley, 1985. Nonequilibriumthermodynamics
and ' evolution: responsesto Booksteinand
W IC
. k en. SystematIc
Zo 0Iogy 34..89- 97.
Caswell,H. 1980. On the equivalenceof maximizing reproductivevalue and maximizing fitness.Ecology61:19-
conflicts disappear when it is realized that residual reproductive value (vx*) and modified reproductive value
-.
(
vx+l
)
con~am
'
me.asures.
0
f
.
~urvIva
1
as we
11
as ~easures
throughoutthe study.
-.
1981. Replyto commentsby Yodzis and Schaffer.
Ecology
62:1685.
1982.
Optimal
life
histories
and
the
age-specific
-..
support the fecundity/survival
ter all.
Charlesworth, B. 1980.' Evolution in age-structured populations. Cambridge University Press, Cambridge, England.
between
mx an
Vx an
mx an
Vx+l may
trade-off hypothesis af-
..
24.
of fecundIty. ThIS realIzatIon allows one to Interpret
the inverse correlations between mx and vx* and mx
and Vx+l as possibly being influenced by the survival
' / SUfVlva
. I traIts.
. Theretiore,
.
portIons
0f t hese tiecundIty
d
*
d
d
..
relatIonshIps
'!
~
ACKNOWLEDGMENTS
.
and Michod 1979). Perhaps mortality and reproductive patterns simply follow the mathematical path of
least resistance in nature (see Brooks and Wiley 1985:
89 for a similar phenomenon). Second, there is some
usually
i
costsof reproduction.Journal of TheoreticalBiology98:
519-529.
Caughley,G. 1966. Mortalitypatternsinmammals.Ecology
47.906-918
.
1977. A I ' f
b
I .
W'
New York
na YSiS 0 verte rate popu ations.
New York USA.
1I ey,
~