-236-
AN ESTIMATE OF HUNTING MORTALITY BASED ON THE AGE
AND SEX STRUCTURE OF THE HARVEST
D. FRASER
FISH & WILDLIFE RESEARCH BRANCH
ONTARIO MINISTRY OF NATURAL RESOURCES
Abstract: An estimate of the proportion of a herd killed
annually by hunting can be made on the basis of age-related
changes in the sex ratio of harvested animals. A description
is given of the calculations involved, and of the rationale
behind them. Harvest statistics from two heavily-hunted areas
of Ontario were analyzed in this way. In the Gogama District
the calculations indicate that the percentage harvest has in
creased steadily since the middle 1960's, in parallel with
consistent increases in hunter density. Since the total har
vest has not increased, a decline in population size is in
dicated. Aerial survey results confirm this trend. In the
Kirkland Lake District, hunter density remained uniform from
the middle 1960's to the early 1970's. The calculations show
a consistent annual harvest during this time, estimated at 11
to 14 percent of adults, with no evidence of decline In the
herd. However, more recent increases in hunter density are
reflected by an increase in the calculated percentage hunting
mortality, and indicate a decline in population numbers. The
two examples show how the new estimate of proportional kill
compares with traditional population indices.
-237-
In Ontario it is consistently observed that hunters kill
more male moose than female. This difference is evident among
yearlings and adults, but not among calves to any significant
degree. It is seen in areas where hunters are thought to fa
vour antlered animals, and in areas of very low hunting success
where conscious selection by hunters i~ felt not to occur.
From these observations it would appear that the higher har
vest of males is related to some aspect of male sexual activ
ity, not to any greater availability of males nor to hunter
preference alone. In other words, an adult male moose appears
to be statistically more vulnerable to hunting than an adult
female.
One consequence of the high vulnerabflity of m"ales is that
the bulls in the living herd come to be less numerous than cows.
Under extreme conditions males may become so scarce that, des
pite their greater vulnerability, the sex ratio of the harvest
will change to predominantly female. Suc.h a change was noted
by Cumming (1974) during a period of heavy over-hunting which
resulted in a severe depletion of a local herd.
Under less extreme conditions, however, there will still
be a gradual cha~ge in the sex ratio in relation to the age
of the animals. The purpose of this paper is to describe that
change, first in general terms and then with reference to two
heavily-hunted areas of Ontario, and to show how the change can
reveal important information about the severity of hunting.
-238-
Mortality, Male Vulnerability and Harvest Statistics
The main features of the change in sex ratio in relation
to age are illustrated in Table 1 with a simple, hypothetical
example. The table shows the fate of a year-cohort comprising
1000 males and 1000 females at the beginning of year 1. Hunt
ing claims 10 percent of the population in the first year,
with males more vulnerable than females in a ratio of 6 to 4.
In other words, 12 percent of the males and 8 percent of the
females are killed during the first year. For simplicity, it
is assumed that these percentages apply in all subsequent years
as well, and that deaths do not occur for reasons other than
hunting. In order to describe this model simply, it could be
said that the nominal hunting mortality is 10 percent each year.
aDd that the male vulnerability factor is 0.60.
The table shows, in columns 2 and 3, the expected depletion
of the males relative to the females in the living herd. Columns
4 to 6 show the resulting changes in the annual harvests. Duri~B
the first 10 years the male portion of the hunt falls from 60.00
percent to 50.13 percent, and in the 11th and subsequent years
more females are killed than males.
How the sex ratio changes in relation to age depends on tMo
factors: the proportion of the population killed each year,
and the degree to which males are more vulnerable than females.
Fig. 1 illustrates these relationships with 16 hypothetical ex
amples similar to that given in Table 1 using four levels of
hunting mortality and four levels of male vulnerability.
With uncomplicated examples such as these, we could use tne
Table l. Population and harvest statistics for a hypothetical moose herd with a nominal hunting mortality of 10 percent per year and male vulnerability of 0.60.
Year Males Females Males . Females Percent Actual at start at start Ki 11 ed Kill ed Males in % kill of year of year ki 11 of year
1 1000 1000 120 80· 60.00 10.00
2 880 920 105 73 58.93 9.96
3 774 846 92 67 57.85 9.91
4 681 778 81 62 56.76 9.87
5 599 116 71 57 55.67 9.82 , 6 527 659 63 52 54.57 9.78 '" '" 7 464 606 55 48 53.46 9.73 '" , 8 ' 408 557 49 44 52.36 9.69
9 359 513 43, 41 51. 25 9.65
10 316 472 37 37 50.13 9.61
11 278 434 33 34 49.02 9.56
12 245 399 29 31 47.91 9.52
13 215 367 25 29 46.81 9.48
14 189 338 22 27 45.70 9.44
15 167 311 20 24 44.60 9.40
16 146 286 17 22 43.50 9.36
17 129 263 15 21 42.41 9.32
18 113 242 13 19 41. 33 9.28
19 100 222 12 17 40.26 9.24
70
60
I- 50 (/) IJJ 40 > ~ 30
:::c 20 Z
(/)
IJJ ...J
10
« 70 ::E
60 I-Z 50 IJJ
U 40 0::
~ 30
20
10
~
5% 10%
15% 20%
2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18
YEAR
~. The percentage of males in the harvest after 1 to 19 years of hunting a hypothetical year-cohort. Results are shown for 5, 10, 15 and 20 percent nominal annual hunting mortality and for a male vulnerability factor of 0.55, 0.60, 0.65 and 0.70 in each case.
. '" .... o .
-241-
relationships shown in Fig. 1 to calculate the level of hunting
mortality if we knew the degree of male vulnerability and the
pattern of change in the sex ratio in relation to the age of a
cohort. For practical purposes, an obvious difficulty would be
the estimation of male vulnerability. This factor might change
with the age of the animals, or it might vary from year to year.
In any case, it would be rather difficult to estimate with con
fidence. Fig. 1, however, shows the saving grace which helps
solve this problem: within the range illustrated, the degree of
male vulnerability has little effect on the age at which the co
hort's harvest sex ratio crosses the 50 percent line. For in
stance, at a nominal annual hunting mortality of 10 percent,
the sex ratio crosses the 50 percent line between years 10 and 11
within the entire range of vulnerabilities shown in Fig. 1 (top
right-hand corner). The model, therefore, yields a statistic,
namely the age at which a cohort's harvest sex ratio thanges
from predominantly male to predominantly female. which gives
a fairly direct estimate of the average annual hunting mortality
to which the cohort has been exposed, within a wide range of
male vulnerability.
It will be noted that the mortality level in Fig. 1 and
Table 1 has been called "nominal" annual mortality. The rea
son for this is illustrated in the last column of Table 1. In
the hunt of the first year a harvest of 12 percent of the males
and 8 percent of the females does yield a total kill which re
presents 10 percent of the animals hunted. With the gradual
depletion of the males relative to the females. however. the
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same rates of 12 and 8 percent give a kill slightly less than
10 percent of the total. As the values in Table 1 illustrate,
the correction required to the "nominal" mortality is generally
small.
In order to apply these hypothetical calculations to an
actual population of moose, we need to know or assume certain
things about the animals.
First, we must know at what age sex-differential hunting
begins. In Ontario the harvest sex ratio of calves is gener
ally close to 50:50, whereas yearlings show clear signs of
higher male harvest. Accordingly, the harvest at the age of
approximately 1.5 years is taken as the first year of sex
·differential hunting.
Second. we need to know the sex ratio fo the living animals
at the beginning of the first sex-differential hunt. Ontario
experience ·suggests that this is 50:50, i.e. that yearling
males and yearling females are equally numerous at the beginning
of the hunt.
Third. we must know of any other factors which might affect
the sex ratio. Mortality from predation. disease, and other
factors does not have to be estimated unless it affects one sex
more than the other and therefore alters the sex ratio of the
population.
Fourth, it must be possible to determine the degree of male
vulnerability or else to assume that it falls within the range
of approximately 0.51 to 0.70. For Ontario moose, male vulner
ability would be difficult to calculate accurately. and it may
-243-
fluctuate a good deal. However, all the evidence suggests that
the limits of 0.51 to 0.7Q would cover the range easily.
Given all this, the age at which the harvest sex ratio of
a cohort changes from predominantly male to predominantly female
should provide an estimate of the hunting mortality to which
the cohort has been exposed. If this mortality rate has changed
substantially over the years, then the estimate should reflect
the annual hunting mortality averaged over the number of hunting
seasons which were required to produce the change in sex ratio.
Table 2 provides the basic information for these calculations.
As an example, if a cohort's harvest sex ratio became predomi
nantly female at age 11.5 years (probably as indicated by a re
gression of sex ratio on age), then the table indicates that
the cohort's nominal hunting mortality averaged over the 11 years
was 10 percent per year.
For practical purposes, information on single cohorts over
successive years would generally be difficult to obtain. More
readily available is the age and sex structure of the total har
vest from individual years with each year-class representing a
different cohort. The question arises whether these population
statistics can be used in place of cohort statistics for the
mortality calculations. If the population is subject to a con
sistent harvest level over many years, then the different cohorts
will resemble each other in their harvest sex and age structure,
and no difficulty should arise. If, however, there is a steady
increase or d~crease in percentage hunting mortality, then the
younger classes will have been subjected only to the most recent
-244-
Table 2. General Moose Harvest Analysis: Year class in which change to predominantly female harvest first occurs, in relation to the nominal percent annual kill.
Nom1nal percent kill annually
6 7 8 9
10 11
12 13 14 15 16 17 18-20 21-25
F1rst year of predom1nantly female harvest
21.5 to 22.5 17.5 to 18.5 15.5 to 16.5 13.5 to 14.5 12.5 11.5 10.5 9.5 8.5 to 9.5 8.5 7.5 7.5 6.5 to 7.5 6.5 5.5
-245-
harvest levels while the older classes will show the effects
of both the recent and the previous levels. A regression of
sex ratio on age should, therefore, give a percentage mortality
estimate which is between the average level (over a number of
years leading up to the change in sex ratio) and the most re
cent level.
In the following sections the calculations described above
are applied to two heavily-hunted areas of Ontario. Age-related
changes in harvest sex ratios are compared with changes in the
age structure of the harvest, with estimates of moose density
from aerial surveys, and with information on hunter and harvest
density.
METHODS
The methods of collecting moose harvest information in
Ontario have been described by Cumming (1974). Briefly, in
formation on hunter and harvest density is 'based on surveys
of hunters done by the district office~ from 1960 to 1967.
and by the provincial office since 1968. The information re
ported below is based on technical reports by H.G. Cumming,
J.B. Dawson, and W.A. Creighton in the Ministry Library', and
on unpublished statistics supplied by J. Barbowski of the pro
vincial office. Information on the age and sex structure of
the harvest was obtained from district jaw collections and in
spection of moose at checking stations. Determination of moose
ages was by the wear class method in early years, and by the
incisor cementum method more recently (Cumming 1974). Conver-
-246-
sion between these methods was done, when necessary, using the
matrix given by Addison and Timmermann (1974) based on a col
lection of jaws which were aged by both means. Wherever possible,
the more conservative conversion was used (i .e., grouping ages
into wear classes), and statistical analysis by nonparametric
tests was then applied. For the linear regressions involving
age, however, wear classes had to be transformed to ages by the
reverse conversion.
The aerial surveys used the method of complete counts on
selected plots as described by Timmermann (1974, p. 620). Aerial
inventories which used other methods, or which were not designed
to give a district population estimate, are omitted from the an
analysis. Details of the individual surveys, summarized below,
were obtained from unpublished reports in the district offices.
GOGAMA DISTRICT
Between the years 1953 and 1975, the Gogama Administrative
District (once known as the Gogama Division of Sudbury Adminis
trative District) had one major and several minor changes in its
boundaries. A "stiuthern nucleus area" of about 5500 km 2 , centered
around the town of Gogama has always been a part of the district;
and a "northern nucleus area" comprising about 10,400 km 2 , was a
part of the district from 1953 until 1967-6B when it was reassigned
to a different district office. Other boundary changes were com
paratively minor: additional areas totalling about 1900 km 2 were,
on different occasion~, added to or removed from the district, and
in 1973 a new area of about 1400 km 2 was added to the southern end.
-247-
Aerial Surveys
The first substantial aerial moose survey of the district
was done in 1959 using 17 randomly-selected plots of 64.8 km 2
(25 mi. 2). Since then, surveys giving reasonable coverage have
been done annually from 1965 to 1974 with the exception of 1967.
Plot size, the basis of plot selection and the actual dates of the
survey varied between years as summarized in Table 3.
In order to make an adequate comparison over years, analysis
was carried out separately for the northern and southern nucleus
areas. Fig. 2 shows the upper and lower 90 percent confidence
limits for moose density in the southern nucleus area. Confidence
limits were calculated by the distribution-free confidence in
terval described by Hollander and Wolfe (1973, p. 35) because of
obvious non-normality in the results. The statistical test of
Jonckheere and Terpstra (Hollander & Wolfe 1973, p. 120) showed
that the decline in moose density over years in the southern
nucleus area was highly'significant (!* = 6.41, f.< 0.001).
Coverage of the northern nucleus area in 1965, 1966 and 1968
consisted of 10, 13'and 17 plots respectively, permitting some
comparison of the northern and southern areas. The northern area
had a slightly lower average density in all three years (but f.> 0.05).
The decline over these years in the northern area was similar to
that in the south.
Harvest Information
Information on the sex and age of harvested animals was avail-
able for 1956 to 1975, but records from 1968 and 1969 were partly
Table 3. Number of plots, plot size, survey dates and basis.of plot selection for aerial moose surveys, Gogama District, 1959-1974.
Year No. of Plot Survey plots size dates Basis of plot selection
1959 17 64.B km 2 Jan.19-Mar.18 Random selection
1965 19 64.8 km 2 Jan.6-Feb.2 "Representative sample"
1966 22 64.8 km 2 Dec.20-Feb.4 "Systematic layout"
1968 27 41.4 km 2 Jan.6-Jan.25 Random selection
1969 12 64.8 km 2 Feb.4-Feb.20 "Systematic layout" , 64.8 km 2 N
1970 12 Jan.8-Feb.4 Same plots as previous years .... ex>
1971 12 64.8 km 2 Jan.6-Feb.l0 Same plots as previous year ,
1972 50 25.9 km 2 Jan.15-Feb.9 Random selection
1973 50 25.9 km 2 Jan . ll-Feb .15 Same plots as previous year
1974 50 25.9 km 2 Feb.l-March 1 New random selection
/
N
E ~
0.5
04
....... '0.3 IJ.J en o o :E 0.2
0.1
8
'59
p-. II 1 II 1 I~--'-I '65 '66 '68 '69 '70 '71 '12 '73 '74
YEAR·
~. Gogama Aerial Moose Surveys: The upper and lower nonparametric 90 percent confidence limits for the estimate of moose density (moose per km 2) in the Southern Nucleus Area of Gogama District for the surveys of the various years. Numbers above the bars indicate the number of plots represented.
, "" ... .., ,
-250-
destroyed .by an office fire. Since the information was based
on the boundaries of the district (or division) as they existed
at the time, there is some variation in the area represented,
expecially between 1967 and the subsequent years.
The age structure of the Gogama harvest changed substantially
between 1956 and 1975, particularly amongst the males. Figs. 3
and 4 show, for the male and female segments of the harvest, the
percentage of animals in each of six wear class categories over
successive 3-year periods. The!2 test applied to these results
showed that the change in the age structure was statistically sig
nificant for the females (t( 0.02) and highly signigicant for the
males (t~ 0.001). More detailed analysis of these changes was
done by calculating the Spearmen rank-order correlations of the
percentage of animals in each of the six categories against the
year in which the harvest occurred, and is summarized in the fig-
ure captions.
The mean age of harvested animals was calculated for each
annual hunt treating the males and females separately. Fig. 5
shows the linear regression of mean age on the year of harvest
weighted according to the number of animals aged in that year.
Sex ratios of harvested moos~ are given Table 4. The per
centage of males in the harvest increased over years for wear
class I (~ relating percentage males to the year of the har
vest ~ +0.600, t <0.01) and declined for wear class VI + VII
(Is ~ -0.641, t< 0.01). The decline in wear class VIII + IX
just missed the 5 percent level of significance (~S ~ 0.391).
The correlation between wear class number and the percentage of
I-Z w u c::: w a...
40 -
30 -
20
10
n+ill 0/0-0
0/0-0/ /0, T /' -
/ ' P //0---0 \ //
0/ \ / 0/
C
/e-e e/e ~ ~e/
1956 1959 1962 1965 1970 1973
1958 1961 1964 1967 1972 1975
• \
• IV+V .6 ....... ___ ./ '" -" . ......- . ,
'6--_6 __ -6---6 __
',~+VII A_A ___ A '
" 't. "A Viii + IX -- --A-A
1956 1959 1962 1965 1970 1973
1958 1961 1964 1967 1972 1975
~. The percentage of animals in each of six age categories (basea on wear classes) comprising the male portion of the Gogama moose harvest. Results are combined in 3-year periods spanning 1956 to 1975 with the exception of 1968 and 1969 for which records were not available. Rank-order correlations showed an increase over years in the percentage of calves (P":: 0.05) and of animals of wear class II + III (P L 0.01), and a-decrease in wear classes VI + VII (E.<. 0.01) and VIII + IV (E. <.0.001).
, '" '" -,
40 -
II+ID 30- /0, /0-0
IZ W U 0:: 20 w a.
10
0.... /,
/ .... r-0~o
0,
o ' " /. "0.... -• ,..1
'_'-../ 0
c /.\ -·"xA • IV+Y \/ ~. >( /'., / . \ ~ ,
\ ~ 'A / \,." ~-"- r.-- \iT+VII
V·~-._vn;+ IX
1956 1959 1962 1965 1970 1973 1956 1959 1962 1965 1970 1973
1958 1961 1964 1967 1972 1975 1958 1961 1964 1967 1972 1975
~. The percentage of animals in each of six age categories (based on wear classes) comprising the female portion of the Gogama moose harvest. Results are combined in 3-year periods spanning 1956 to 1975 with the exception of 1968 and 1969 for which records were not available. Rank-order correlations showed an increase over years in the percentage of calves (p..c:. 0.05) and animals of wear class II + III (P'( 0.05). and a decrease in wear class I (f. < 0.,025). -
I N
'" N
6
5 w (9
« z 4 « w :::l!
3
2
0
.~ 0
0
• • •
. ~ • • • • • -0
I ••
MALE FEMALE
1960 1965 1970 1975 1960 1965 1970 1975
YEAR
~. The linear regression of the mean age of harvested moose against the year of harvest, shown separately for male and female moose in Gogama, 1956 to 1975. The regression 1s statistically significant for the females (t=3.221, df=16, P~ 0.01) and highly significant for the males (1=~1.855, d~16, ~-~( 0.001).
, N
'" w ,
-254-
Table 4. Gogama moose harvest, 1956-1975: percentage of males in different wear-class groups.
Percent males in wear-class rou s Years N 11+111 IV+V VI+VIl VIII+IX I-IX 1956 -58 359 51.9 69.1 65.5 71.2 55.3 63.2
1959 -61 412 57.8 64.3 64.0 53.4 69.4 61.2
1962 -64 433 50.4 61.0 57.8 54.9 55.3 57.5
1965 -67 509 65.5 68.3 56.8 60.3 58.3 63.5
1970 -72 212 64.6 67.1 72.9 55.7 53.1 65.6
1973 -75 211 70.1 63.5 62.5 47.5 31. 6 62.1
1956 ** ** ** ** * -75 2136 59.2 65.5 62.0 60.2 57.6 61.8
Note: Sex ratios significantly di fferent from 50:50 at *p 0.05, **t 0.001
-255-
males in that category was low in the earlier 3-year periods,
but w.as clearly negative in 1972-75 (r:s = -0.88, t < 0.01).
The overall sex ratio (combining wear classes 1 to IX) showed
no substantial change over the years.
Table IV also shows the percentage of males in each wear
class group combined over the 18 years. The sex ratio differs
from 50:50 for wear class VIII + IX at the 5 percent level of
significance (by the binomial test, one-tailed), and well beyond
the 0.1 percent level for the other groups. Over the 18 years,
233 calves were harvested of which 51.9 percent were male. The
sex ratio of the calves does not differ significantly from unity,
and there was no indication of a change in sex ratio over years.
The wear class data were converted to ages (in years) using
the conversion matrix described above. The linear regression of
sex ratio against age, weighted as to the number of animals sexed
at each age, is shown in Fig. 6 for the six 3-year periods.
Hunter questionnaires yielded information on the total num
ber of hunters and the total moose kill in the district based
on the district (or division) boundaries as they existed at that
time. Fig. 7 shows this information expressed as the number of
hunters and the number of m09se killed per km2 .
Summary and Discussion for Gogama District
The trends in the Gogama District have no doubt been influenced
by the changes in the area. Recent increased road access coupled
with the severing, by boundary changes, of the northern area have
been accompanied by a steady increase in hunter density from 1963
to 1974.
70 -I ~ - 1956-58 1959-61
f:l 60 ~ ===:SS;::s::;==::::~-~""::::::;:::::::=.~--- 1962- 64 ~ 1965-67 <C 50 ----- ------- ----~ 1970-72
f- 40 z w u 30
~ ~: 1 ~ 1973-75 I ~ I I I I I I I
15.5 20.5
AGE (YEARS)
~. Linear regression of the percentage of males in the Gogama harvest against the age of the animals. The regression is statistically significant for years 1965-67 (P", 0.05), 1970-72 (f. <. 0.02), and 1973-75 (f.( 0.001). but not Tn the earlier years.
'" E ~ "--.J -.J ~
'" E ~
"-CJ)
a::: w I-z :::> I
0.06 0.04 0.02
0.7
0.6
0.5
0.4
0.3
0.2
0.1
~----~
KIRKLAND LAKE 0---0
GOGAMA ............ _ .. -.
~//
1960 1962 1964 1966 1968 1970 1972 1974
YEAR
~. Results of hunter questionnaires in Gogama and Kirkland Lake. Above: Estimated number of moose killed by hunting in the two districts expressed as an1mals killed per km 2. Below: Estimated numb~r of hunters in the two districts expressed as hunters per km. Information was not available for Gogama in 1968.
I N
'" " I
-258-
The moose herd has shown substantial changes during this
time. Aerial surveys show a striking decline in moose abundance
over these years. The age structure of the harvested males has
been altered substantially, declining to a mean age of 3.0 to 3.5
years, and th~ proportion of males in wear classes VI to IX has
fallen to less than 10 percent. The consistent change in the
regression of harvest sex ratio on age indicates that the percen-
tage kill has increased steadily over the period 1965 to 1975.
The actual number of animals killed per unit of area has remained
quite uniform, hovering between 0.02 and 0.04 moose per km 2. In
summary, the increase in hunter density has been accompanied by
an increase in the proportion of the herd which is killed, but
the actual number of moose harvested has not increased.
KIRKLAND LAKE DISTRICT
The first systematic aerial moose survey in the Kirkland Lake
Administrative District (formerly known as the Swastika Adminis
trative District) was done in 1959, and annual harvest statistics
are available since 1960. During this period, the district has
sustained only minor boundary changes. A nucleus area of about
13,000 km 2 has always been a part of the district, while additional
areas totalling about 1500 km 2 have been added at different times.
Aerial Surveys
The 1959 aerial moose survey consisted of 21 randonly-selected
plots, each of 64.8 km 2 (25 mi. 2). In 1968 a new random selection
-259-
was made of 34 plots, each of 41.4 km 2 (16 mi .2). A 3-year sur
vey covering about 30 percent of the district was carried out in
1970, 1971, and 1972. Totals of 70, 34, and 25 plots, each of
41.4 km 2 (16 mi .2) were flown in the three years respectively.
Different sections of the district were surveyed in each of these
years, with most plots chosen randomly from the particular section.
The following analysis is limited to the 157 plots in the nucleus
area of the district.
Fig. 8 shows the upper and lower 90 percent nonparametric
confidence limits for the estimates ot moose density from the
three surveys. The method of Jonckheere and Terpstra showed
that the decline over the three surveys just reached the 5 per
cent level of significance (~*= 1.654, t< 0.05 one-tailed).
Harvest Information
Age and sex statistics for harvested moose were available
from Kirkland Lake for years 1960 to 1974. The age structure
of the male and female harvest is shown in Figs. 9 and 10 res
pectively. The!2 test revealed that the proportion of animals
in the six age categories varied significantly over successive
3-year periods for the males (!2 = 41.71, df = 20, t< 0.01) but
not for the females. Spearman rank-order correlations showed
no clear changes over years in the percentage of animals in any
of the individual categories.
The mean age of harvested male moose showed only a marginal
decline over the years, with the weighted linear regression just
reaching the 5 percent level of significance (1 = 2.05, df = 13,
t <.0.05 , one-tailed). The mean (:!:. S.L) of the annual mean
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0.3 C\I
E ~ 17 ........
~ 26
W 0.2
en 0 0 114 ~ 0.1 ~
159 168 170-172
YEAR
~. Kirkland Lake Aerial Moose Surveys: The upper and lower nonparametric 90 percent c02fidence limits for the estimate of moose density (moose per km ) in the nucleus area of the Kirkland Lake District for the three systematic district surveys. Numbers above the bars indicate the number of plots represented.
40--1 0 ____ 0
Iz w U
30
0::: 20 w 0...
10
"'-0 _ ....... 01
/ 0.... / ............. 0 ....
........... 0 ,_
~OIi+]IT / -
/ P---d
/._ ............... C
e_e/
1960 1963 1966 1969 1972
1962 1965 1966 1971 1974
-/-----_ ............ -\ - IV+ V
1>.- -1>. __ -1>._--"--_1>. vr + ViI
---... --......... =--=-... ...-... --... Y.!!! + .IX
1960 1963 1966 1969 1972
1962 1965 1968 1971 1974
~. The percentage of animals in each of six age categories (based on wear classes) comprising the male portion of the· Kirkland Lake moose harvest. Results are combined in 3-year periods spanning 1960-1974.
I
'" '" -I
I-z w u 0::: w Q..
40 -,
/"""", / IT • TIl [] [] 30
o T 0,
.-... -, .-" __ 0'"
0_-_0_ 20
/e /e-e __
C
10 -
1960 1963 1966 1969 1972
1962 1965 1968 1971 1974
\ ./."". IVty - -• b. ___ l::I--_l::J................ _
// 'll..Y1 + Vii If .--__ • ...__.- -. y!!! t IX
1960 1963 1966 1969 1972
1962 1965 1968 1971 1974
~. The percentage of animals in each of six age categories (baseo-on wear classes) comprising the female portion of the Kirkland Lake moose harvest. Results are combined in 3-year periods spanning 1960-1974.
, N
'" N ,
-263-
ages of male moose was 3.45 ~ 0.20 years. For harvested female
moose weighted linear regression showed no tendency for the
mean age to change over the years, the mean (~S.E.) of the
annual mean ages being 3.59 ~ 0.12 years.
Table V shows the sex ratio (percentage of males) in the
harvest in relation to wear class group. In the first period
there was no indication of a change in sex ratio with age (Spear
man rank-order correlation coefficient relating sex ratio to wear
class = +0.18, n.s.). In all three subsequent periods, however,
there was a clear decline in the proportion of males with in
creasing wear class (~s = -0.67, -0.92 and -0.67 respectively,
.E < 0.05). Table V also shows the percentage of male moose in
the harvest for the 15 years combined. The binomiijl test showed
that the sex ratios were significantly different from 50:50 for
animals of wear classes I (~< 0.001), II + III (~< 0.001), and
IV + V (~< 0.05), but not for the other groups. The percentage
of males in the wear class I harvest appears to have increased
over years, but the effect does not reach the 5 percent level of
significance. Of the 517 calves harvested over the 15 years,
54.2 percent were males (~= 1.85 from the binomial test, not
significant).
Wear classes were converted to ages in the manner described
above. The weighted linear regression of the percentage of males
in the harvest against the age of the animals is shown in Fig. 11.
Based on the regression lines, the harvest remained predominantly
male at all ages in years 1960-65, but changed to predominantly
female at age 8.5, 10.5 and 6.5 years for periods 1966-68, 1969-
71, and 1972-74 respectively.
Fig. 7 shows the findings of the hunter questionnaire on the
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Table 5. Ki rk land Lake moose harvest, 1960-1974: percentage of males in different wear-class groups.
Percent males in wear class rou s Years N lI+llI IV+V VI+VlI VIlI+IX I-IX
1960 -65 390 50.0 55.1 50.6 53.3 57.1 52.8
1966 -68 690 57.4 55.4 55.7 43.4 43.7 54.5
1969 -71 769 60.4 61.6 59.4 48.2 43.5 58.6
1972 -74 985 62.5 49.9 50.3 48.9 38.7 53.8
1960 -74 2834 59.4 55.1 54.6 47.9 43.6 55.2
70
~ 60 l ""-- ______ 1960-65 -.J « 50 ::2:
~ 40~ u 30 a:: . W a... 20
10
I I I 10.5 15.5 20.5
AGE (YEARS)
F~. Linear regression lines of the percentage of males in ~kland Lake harvest against the age of the animals. The regression is statistically significant for 1966-1968 (P ~0.05). 1969-1971 (~< 0.001) and 1972-1974 (~< 0.005), but not for 1960-1965.
, N en
'" ,
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total number of hunters and the total moose harvest in the dis-
trict expressed per unit of land area.
Summary and Discussion for ~irkland Lake District
Kirkland Lake District presents quite a different picture
from Gogama. Land around Kirkland Lake is generally of higher
quality with substantial pockets of agriculture and a long
established network of road providing access for hunters. Hunter
density increased during 1964 to 1966, and remained a plateau of
0.4 to 0.5 hunters per km 2 from 1966 to 1972, before increasing
further. For many years the mean age of harvested males has
been low (around 3.5 years), and the proportion of males in wear
classes VI to IX has remained consistently about 10 percent or
less. The regression of harvest sex ratio on age maintained a
steep slope from 1966 to 1971 crossing the 50 percent line at
·age 8.5 to 10.5 years, indicating that the percentage harvest
was high but not increasing during this period. In 1972 to 1974,
the change in the regression line indicated a further increase
in the percentage harvest in the most recent years. Aerial sur
vey material was not sufficiently extensive to allow sound com
parisons, but it suggests only a moderate decline from 1959 to
1970-72.
From the various sources of evidence it appears that Kirkland
Lake sustained, through the middle 1960's and early 1970's, a level
of hunter density and percentage harvest similar to that which
has developed in Gogama only in very recent years. Similarly,
the young male structure, which Kirkland Lake has had for many
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years, has only recently developed in Gogama. Like Gogama,
Kirkland Lake also shows a clear parallel between hunter
density and the percentage of the population which is har
vested, while harvest density bears no simple relationship
to the other two variables.
DISCUSSION
Depending on the quantity and precision of harvest in
formation available, the relationship between harvest sex
ratio and age can be used in as many as three ways in moose
management.
1. Trends in the Percentage Kill
So long as the basic assumptions are met, changes in
age-related sex ratio should reflect changes over years in
the percentage of animals killed annually by hunting. This
can be a useful statistic for managers. If the percentage
kill is uniform over a number of years, and the actual num
ber of animals killed is also uniform, then the population
is apparently in equilibrium with its harvest rate. If the
percentage kill is increasing while the number of animals
killed remains the same, then the population must be in de
cline, and the harvest rate should be reduced.
The results from Kirkland Lake and Gogama illustrate both
of these patterns. During the middle 1960's and the early
1970's, Kirkland Lake had a steady percentage harvest and a
uniform number of animals killed each year in the district.
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During this period the population was apparently managing to
replace the moose which were killed by hunting, even though
hunting pressure and harvest rate were comparatively high.
In the most recent years, however, there is evidence of a
further increase in the percentage harvest with no corres
ponding increase in the number of animals killed, signifying
that the recent increase in hunter density has pushed the
harvest rate to an unacceptable level. In contrast to Kirk
land lake, Gogama has for many years shown a steady increase
in the percentage harvest with no corresponding increase in
kill density. This is possible only if the standing herd is
declining in number. Aerial survey information from the
district confirms this trend.
It is interesting to note that the Kirkland lake herd
has always sustained a higher harvest density than the Gogama
herd, and for a number of years maintained itself under levels
of harvest and hunter density which in Gogama have been ac
companied by severe depletion of the population. Here is a
clear regional difference. It would be most interesting to
know whether this is due to the superior soils of the Kirkland
Lake area.
2. Quantitative Estimate of Harvest Rate
If harvest data are sufficiently abundant and precise,
then the relationship between age and sex ratio should yield
a quantitative estimate of the percentage of adult animals
killed each year. It is important to note, however, that the
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calculations described above are rather limited for this pur
pose. For 1973-75 in Gogama the sex ratio changed to pre
dominantly female by age 8.5 years. From Table II the best
estimate of the average annu~l kill over the previous 8 years
is 13 to 14 percent. However, since the percentage kill was
apparently increasing during this time, and since the harvest
data represent the population rather than a particular cohort,
the figure of 13 to 14 percent is probably higher than the 8-
year average but lower than the harvest rate of the most re
cent years. Little more can be said.
Similarly, for Kirkland Lake the data from 1966 to 1971
suggest an annual harvest of 11 to 14 percent of adults during
the "plateau" of hunting pressure, while the results from the
most recent years suggest an average harvest of 17 to 20 per
cent during a 6-year period. Ag~in, adjustments are needed be
cause the data do not represent single cohorts, and again, the
recent increases in percentage harvest and hunter density indi
cate that the most recent harvest rates probably exceed the
levels mentioned.
Clearly these calculations require the hand of a profes
sional statistician for at least three purposes: (i) to im
prove the method of relating sex ratio to age in order to avoid
the necessity of combining data from a number of years; (ii) to
give a thorough analysis of the relationship between cohort sta
tistics and populations statistics; and (iii) to give a means
of calculating confidence limits for the estimates of hunting
mortality.
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3. Population Estimate
If the results yield a sound estimate of the percentage
of the population killed by hunting, and if the total number
of animals killed can be determined, then an estimate of the
original population size is possible. This will have to
await statistical refinement of the calculations as described
above. Suffice it to say that population estimates for Kirk
land Lake and Gogama, based on the tentative estimates of per
centage hunting mortality already given, indicate herd densi
ties much higher than the aerial survey results for the areas
would suggest. This is not surprising: the aerial survey re
sults are recognized to be an underestimate of population num
bers even though they are useful as indicators of changes over
years. Indeed, if the kill densities shown in Fig. 7 are com
pared with the population densities from aerial surveys in
Figs. 2 and 8, it will be seen that annual harvests exceeding
50 percent of the population have become commonplace~ Clearly,
aerial survey results cannot be used in estimating hunting mor
tality rates.
CONCLUDING REMARKS
When trying to assess the usefulness of various population
and harvest statistics, one is often at sea for the lack of an
objective index of known validity which will serve for comparison.
The usual alternative is to examine several different statistics,
and try to determine which ones give a consistent and plausible
picture. The usefulness of age-related sex ratio as an index of
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harvest rate must be evaluated in this way.
In general, the estimate of percentage hunting mortality
calculated from age-related sex ratio showed good agreement
with trends in hunter density and in the harvest age structure,
although the latter is not an indepen,dent index. Furthermore,
the population trends which were suggested by the harvest data
were largely confirmed by the trends in the aerial surveys.
If we accept this relatively unified picture, then certain
other statistics can be seen as highly misleading, Harvest
density showed no consistent changes to parallel the steady de
cline in the Gogama population or the more recent presumed de
cline in Kirkland Lake. Clearly, a consistent number of animals
killed in a district is no cause for comfort. Secondly, it is
sometimes said that, past a certain cut-off pOint, increases in
hunter density will cause no increase in the proportion of the
herd that is killed. Such a cut-off point may exist, but it was
not evidently reached in the present examples: rather, percen
tage hunting mortality closely paralleled hunter density even
with the herds in decline. The differences between Gogama and
Kirkland Lake suggest that any calculation of allowable harvest
will have to be made on a regional basis. For this reason, har
vest age structure alone will not indicate excessive hunting. In
both areas the male age structure responded to harvest level, with
mean age reaching about 3.5 years when the harvest rate was an es
timated 10 to 15 percent. However, this was probably an accept
able harvest rate in Kirkland Lake, while in Gogama it was not.
Other problems in the interpretation of age ratios are described
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by Caughley (1974) and by Addison and Timmerman (1974). Fi
nally, the overall sex ratio of the successive annual har
vests was conspicuously insensitive to the changes in the pop
ulations. With a very rapid and severe depletion of a herd, a
change in overall harvest sex ratio might be expected. For a
more gradual depietion, with the consequent change in the pop
ulation age structure, the statistic cannot be trusted.
ACKNOWLEDGMENTS
This paper was made possible by the efforts of the many
members of Ministry staff in the Gogama and Kirkland Lake
Districts. Mr. C. Jessop was particularly helpful in providing
the author with information.
LITERATURE CITED
ADDISON, R.B., and H.R. Timmermann. (1974) Some practical
problems in the analysis of the population dynamics
of a moose herd. Trans 10th N. Am. Moose Conf., in
press.
CAUGHLEV, G. 1974. Interpretation of age ratlos. J. Wildl.
Manage., 38: 557-562
CUMMING, H.G. 1974. Annual yield, sex and age of moose in
Ontario as indices to the effects of hunting. ~
uraliste can., 101: 539-558.
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HOLLANDER, M., and D.A. Wolfe. 1973. Nonparametric Sta
tistical Methods. New York: Wiley.
TIMMERMANN, H.R. 1974. Moose inventory methods: A review,
Naturaliste can.,!.Ql: 615-629.
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