-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

-242-

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

-260-

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.