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The Greenland White-fronted Goose Anser albifrons flavirostris

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the hunting mortality rate K t for year t and plotted<br />

against adult annual return rate R t for that<br />

season. Under the additive mortality hypothesis,<br />

it would be predicted that annual survival rate<br />

(and hence adult return rate) decreases with increasing<br />

kill rate in a linear fashion (away from K<br />

= 1 where the linear relation is a poor approximation,<br />

see Anderson & Burnham 1976). Under<br />

the hypothesis of completely compensatory mortality,<br />

annual return rate would be independent<br />

of variation in kill rate up to a threshold point<br />

where further increases in kill rate must result in<br />

reduced annual survival (Anderson & Burnham<br />

1976). <strong>The</strong>se two states represent extremes, with<br />

the slope b in the equation:<br />

R = R 0 (1-bK) (2)<br />

In this case R represents annual adult return rate<br />

and R 0 represents this measure when no hunting<br />

occurs. <strong>The</strong> slope b would be equal to unity in<br />

complete additive hunting mortality and zero<br />

over the range of realistic hunting kill rates in<br />

complete compensatory hunting mortality. Note<br />

that this analysis only considers compensatory<br />

mortality as this relates to winter hunting kill<br />

since, by definition, the term R 0 includes the hunting<br />

kill, which occurs in Iceland and <strong>Greenland</strong>,<br />

as well as 'natural' mortality. In this analysis, R is<br />

plotted directly against K and a regression model<br />

applied of the form:<br />

R = R 0 -BK (3)<br />

<strong>The</strong> slope B was tested for significant differences<br />

from the predicted b values of 0 (perfect compensation)<br />

and 1/R 0 (completely additive hunting<br />

mortality) using t tests.<br />

<strong>The</strong> annual adult survival rate of <strong>Greenland</strong><br />

<strong>White</strong>-<strong>fronted</strong> Geese wintering at Wexford was<br />

significantly negatively correlated with kill rate<br />

during the years 1970-1999 (Figure 8.1). This regression<br />

model explained more variance than the<br />

best quadratic fit. A quadratic fit would imply<br />

initial (i.e. partial) compensation to a threshold<br />

above which hunting mortality is totally additive.<br />

<strong>The</strong> slope did not differ significantly from the<br />

expected value of 1.129 (i.e. 1/R 0 , t 26 = 0.276 P ><br />

0.05), but was significantly different from zero (t 26<br />

= 2.94, P < 0.01). Mean apparent survival during<br />

the years with hunting (0.817 ± 0.021 SE) was significantly<br />

lower than in years without (0.884 ±<br />

0.016 SE, t 26 = 2.48, P < 0.01).<br />

Crude annual adult suvival<br />

1<br />

0.9<br />

0.8<br />

0.7<br />

0.6<br />

0.5<br />

pre 1982 hunting<br />

regression<br />

post-1982 hunting<br />

protected in winter<br />

0.4<br />

0 2 4 6 8 10<br />

Hunting mortality (%)<br />

Figure 8.1. Plot of crude annual survival rate (based<br />

on adult return rates from annual census data – see<br />

text for full details) against hunting mortality rate<br />

(known bag plus 20% unretrieved losses expressed as<br />

a percentage of the peak winter count for each year).<br />

<strong>The</strong>re was a statistically significant inverse correlation<br />

between these two measures 11 .<br />

It is clear that the annual adult return rate is not a<br />

good measure of survival rate, including as it<br />

does, the balance between immigration and emigration<br />

in the Wexford wintering population<br />

which is not a 'closed' one. However, these data<br />

do strongly suggest that the return rate was directly<br />

related to the size of the kill over the period<br />

that data are available, in a way that closely<br />

resembles additive mortality.<br />

8.3 Modelling long term changes in<br />

annual adult return rates to Wexford<br />

assuming additive mortality<br />

Given the low variation in the annual probability<br />

that a bird returns to winter at Wexford and the<br />

relationship between this property and annual<br />

hunting kill, it seems sensible to construct a very<br />

simple population model assuming constant annual<br />

adult return rate. In this way, given the observed<br />

numbers of young in each winter, it is<br />

possible to generate the expected numbers of<br />

adults in year t+1 based on total numbers in year<br />

t. <strong>The</strong> assumption is made that, for the Wexford<br />

wintering group of <strong>Greenland</strong> <strong>White</strong>-<strong>fronted</strong><br />

Geese, (i) natural survival and (ii) the balance of<br />

between-year immigration and emigration are not<br />

year specific (i.e. in the absence of hunting, annual<br />

adult return rate is constant). In generating<br />

data for those years with hunting, it is further<br />

assumed that hunting mortality is completely<br />

additive, so that, in the years with hunting, annual<br />

adult return rate is the expected returning<br />

67

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