l:s'l - house sparrow research · 7 (fisher's f) of the tw9 satilples .-;hows the tjew...
TRANSCRIPT
. ,-
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l:S'l
David. G. Daw5011 •
PROJECT
Baehelor of Science with Honoura. Zoology. Vertehrate
ecology option.
Univ~rBity of Canterbury,
i966.
1
INTRODUCTION
AIM OF Tlii: STUDY
The primary aim of this study was to elucidate two aspects
of sparrow ecology - production and nest mortality.
During the study precise dt'finitiono; of tl~rms such 3S
tlfirElt-egg date", "nek:;tlinr; period", etc \\'~re derl-led
(see the a.}~pendice's), 1:. review of th-:: lite.':":lture ShC-9,:1';l
that v & gue and amb igu .:lU8 de r ini t i Otll, a.re co nimon 1y us e d ,
and that there id little indication of thE:! error in
th~ e~timated values.
Nyttr s (1955) and Cramp (1955) seem to have used the . .
techniques given here for esti~ation of first-egg dates.
though f.lye.s explains them ambiguously. They also use
categories of error, but my continuous scale of "error
index" is an innovation.
Clutch size has rarely been defined, and although
Bome authors (Lockie 1955. and Lack 1955) dt6CUBB clutch
size at length they do 80 without defining it. Snow
(1955) gives categories of precision, others (Silva. 1949
and Cramp 1955) assume that egg lbss will not result ic
any significant differend~ without adequate data to test
this assumption. The "error value" scale intrJduced
in this project is an attempt to provide a more versatile
index.
Most authors discuss neating success at great length
wi.tbout defining their terlliS. Snow (19558.) points out
Bources of serious bias. but there was insufficient time
during the preparation of this project to correct for them
all.
leg; .#IA$..._ . .4 ..
ca -iJ.
2
Much of the data come from my own seven years' (1959-
1966) study at an area in Shirley, Christchurch, where
the birds nested l$I"gely in box.es around El house. I am
ind$bted to Jim HiltoD and Philip Crosier for maintaining
visits to this area in the last two seasons while I have
been absent.
Another source of data ie the Ornithological Society ot
New Zealand nest record scheme. Th~se data are on carde
(see figure 1 for the format of these and the nature of
the data). I am indebted to Miss Neill, the nest recorda
convenor, for lending me these cards. J..n important
proportion ot them are from tb-e work of J.R. Jackson
of HOOD Hay, Christchurch. His study too iiilargely of
sparrows nesting in boxes.
The third source is a study made by Dr. CLR. -~·illia.mB
at Lincoln College in 1960 - 61, employing the O.S.N.Z.
nest record card. In th1sarea all the neets were in
"natural sitee" (ivy on a wall and niehes in buildings)
and the surroundings were rural'. I am indebted to
Dr. W~lliamB for lending me hiB data.
Th. major studyarA,a8 are shown in figure 1 wh~ch shows
their relative positions. The city ot Christchurch and
the high land ot Banks Peninsula both :probably cause
differences in mesoclimatebetween the areas.
Overseas data are given in a eeries of papers by Weaver
report~ng on work at Ithaca, New York in 19}7 and in
Summers-Smith (1963), the latter being largely the results
of a1'1 unpublisbed analysis of British nest records made
by Cramp.
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3
Sparrowe app$ar to lay on~ egg per day. In 134 records
covering the laying period only nine showed any departure
from this pattern. None of the records suggested the
laying of two eggs per day and in all nine exceptions
either the fe~ale failed to lay or an egg was apparently
lost from the clutch. In my study area the eggs were marked
and most gaps in thed.ily routine were caused by loss of
eggs rather than absence of an unmarked egg. Even with
marked eggs, 106S of a newly-laid egg cannot bedistinguisbed
from failure to lay and this could explain the six exceptions
in my data.
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4
INCUBATION }Ji:HIO:U
The usual definition of incubation period ia: "the time
from laying of the last egg of a cltitch to hatching of
that eggt'(Hp.inroth cited in Thomaon, 1964). The last
egg must be marked; .90 that it can be r~cognised until
hatching. It is commonly assumed in neat record analyses
that. in clutches that hatch completely. the 13.st egg
laid will be the l~st one to hatch. This has been 80
without except~on in some 25 marked clutches and the
assumption is used in this analysis.
Eggs are laid. between 2000 and 0700 hr~ BB no ne~ eggs
were found during afternoon visits. Su.mmers-Srdth. (1963)
gives evidence that egg5are la.id earlier than 0730 G .l·~ . ,T.
in Britain and .suggests "Eggs are normally laid early in
the morning". Be doe!'! not consider the possibility of
their bein~ laid in the late ~vening.
Whe;"l e g g3 are laid at n;i.ght and the nestd.6ited only
in dayli$ht the c;reatest error in a calculat(:d incubation
period ia !1 day. When visiting timeD average at ~idday and
the time of day has no influence on the hatching, the
mean calculated incubation period falle within .~ t day
ef the true mean incubation period (appendix I).
Figure 2 gives the frequency distribution of calculated
incubation periods. The mean is 12.1 da7s with a 95% confidence of 0.3 days. Allowing for a possible
difference from t ,he actual mean of O. ~5 days it i8 likely
the true incubation period falls within the range 11.5
to 12.5 days. Allowing for the maximum erroro! fil;ny
calculated period of t 1 day the range of incubation periods
is 10 to 1.5 daye. The diBtribution, like those of many
5
zoological Vliriatea (SLlLp&On, Roe, & L.wontin,19bO)
shows a positive skew. If it is true that "birda usually
maintain their eggs near a temperature which. promotes
the most rapid development tt (Thoffison, 1964; 396) then
the modal incubation period would be expe~ted to be nearer
the lower lim.it, producing this akeft'.
Twelve daya has been taken as the mean incubation period
in this work.
Summers-Smith (1963. citing Cramp, unpublished) gives
"the average incubation period of ninty-five clutches
8S twel~e days with a range ~f nine to ~ighteen daYB •..
it decreases with the advance of the se~150n (BI·itain)
fro·m an avel'a8:e of .., ;~ . 4 day5 in A~ril to 11 .. ) daysi!!
August. 1t heaver (19;+:~) fOlmd Cl mean of -12 duys ",: c. a
range of 10 to 16 c\ ;, JB in Ne'N York. There:'G f!G i:dicij,tioH
of any differflI1ce fl'orr! dw New i~ealLi.nd results.
p • "K ......
6
?be nestling period ~s the ~ime between the batching
of an egg And the flight of the young bird from the
nest. Where the young ~re not marked they ~V~t all
hatch on the same day if error is to he avoide1. This
was so for ~'tbout half the records (aee IIhatchir.g _~) eL"iodll)
and ortly these records were used. Svartows do not in
U1Y experience return to a nest after fledging, thOll :~h
Summers-.:lmith (1963) gives one instance where this $eelDB
to ha.e happened. The definition requires evidence
that th~ young bird flew (c.f. "number fledged").
Nest disturbance can TI!8ult inprems.ture flight. The
"nestling periods" of any nest recorda analysis are
those of disturbed nests and some will be Bmaller than
those of undisturbed nests.
','Ihen young leave tbe nest only during the day and also
the nest is visited only during the day the greatest error
in a calculated nestling period is !1t days from the
true nestlinb period. If the times of visiting the ne ~ lt
aver31oJ'e at !l.,Liday snd the time of d!iy has no jnfluerJce
ch the fli5hf_ o{ t.he youn ,,: then the l!; ~aIl calcuL,t.'!d
nestling period "till equal the actual r!can nf'stlin,"?
},eriod (app",ndix II).
F~gure 2 gives the frequency distribution of nestling
periods, half from my study and half from record cards.
Figure 3 givas comparative data from 1123 more or less
undisturbed nests" (Weaver, 1942) near Ithaca. New York.
Weaveraseigns one nestling period to each neat nnd d.oes
not state what he did if the nestlings flew over a period
of more than one day. A teat of the variance ratio
7
(Fisher's F) of the tW9 satilples .-;hows the tJew Ze~\land
earople to be significu,ntly r: i or~ V'Qriable (p (" 0.005) than
tbat from ~~W York. The difference could be dU6 to qne
or Dlore of the following three factors:
1 Weaver uses ne::>tling periods of nests rather than of
individuals.
2 His study ~as done in a restricted locality (c.f.
the whole of New Zealand) .
.2 His study was in one breeding season (c.f. several).
With this in view it cannot be concluded I'leaver l ,s mean
of 13.6 days (not 1·'L4 see Weaver; 187) represents a
difference frDm the New Zealand value of 14.7! 1 . 1 days.1
Summers-Smith (1963) quotes Cramp1s result of a "rr.ean
nestling period .in Great Britain as 14.4 days with a
range of eleven to n:ln~t.~n daysll. This is very sinlilar
to the Ne.w Zeel.:3.nd figures (p ~o. a in a IIt-testll ).
'l' h\ iS in this dtudy 15 days ha;) been assumed for th<e mean
nestling period.
·1 Such ranges for a mean in this paper are 95'}6 confi.dence
intervals and not standard errors which are biased
for small samples.
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NL:;T.ber " c"! I n BREEDING , (first- egg- d~tes)
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20 1
HOON HAY
LINCOLN
,---fL--J I
1'--1
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[ -=:l
J o . . r:::===;' ! OCT NOV
~ Stockton-on-Tees. Britain -0--0-- Ithaca, N,y'
. -' - . - Shirley 1 NZ
/'\ .. .. .... Hoci') hay l' . '
\ '\
DEC
"1)\'" / \.,'" /. -._--l' \"'. tT·"<:.~,')/ \ . / " y.. \:;w.'< .
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JAN
Eist::wher;:, NZ, 1J -20
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. ~,-"'-d~"'" ~-o-o
I MAY JUN I JUL1-Brltain
OCT NOV DEC JAN - N-=w Zealand
COMPARISON OF BREEDING SEASONS (First- egg- dates)
Fjgur~ 3
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8
AJiy readily definable dat,e within the sequence of breeding;.
may be used to describe the bre~ding season. The first
egg date is chos~n as it is easily defined and is cotnnlon
both tc nests that succeed and those that fail to produce
fledged young.
Appendix 11'1 covers the methods of estimation of first
egg date and its lIerror ind,ex t' .
Figure 3 shows that the dietribution of first-egg dntes
fro~ any restricted locality io trimodal (or quadrimadal
in one case) with &he modes spaced about five weekt 8)art.
'i'he~e mod~s are '-;lor,~ ,m~rked in cverscas data (Weaver
1939 and SIlUlmtH's-S'ilith, 1963). This is probatly because
the oversetlS data are in each case from one breeding
ijeaaon while Loth New Zealand samples are fronl several
seasons. Another possibility ia that the New Zea16I'.d
siulples contain less accurate data than the overseas
sa.mples (the Ne\\' Zealand data h2Wan erTor index of ';::ive daIS
or less, no indicattion was given of the accuracy of the
overseas data).
The time bet~e~n the laying of the first egg and the
flying of the young averages JO days (clutch 8iz.e+
inCUbation period • nestlin~ period). The interval
between the bre8jing 5ea~on modes i~ ~tOLt 35 day~; thiA
~uggest5 that the mod.s could repre~ent sUG~e ' ~i~~
clutches if about fi\Te da..i"s elapse between the flt,dt:ing
of one braD .} a,nd the laying of rh':') :irst ee;g ef t::'e next
clutch.
--", . .. _._.,.-. ____ II'I!filrit=5P.., ....... '.i .... ~:,'JL~ . • ~ .. " .... ~ ,' ., '-' - " c" " " '" , "'" . .. , .. ..
I f
9
Weaver (19)9) explains the modes: nsfter these first
broods le~t other adults were able to start laying in
the same sites ..•.. Adults that nested during the first
period did not nest during the second period unless
~he first broods were interrupted ..••• these adults
were free to neBt again during the third period ..• tt
SWNt.ere-Snlith (1963) explains the modes in .a different
way: IIThe56 however do not merely correspond to fir ,:, t,
second and third clutches; the second peak .•• conaisted
of first and second clutches and the third peak consisted
Cif first ., second and third clutches". He hypothe;:;i.s cd
that the breeding is coordinated within a sparrow colony
by "colJUllunal diB plays 11 : 11 i t c an be se 'en t ha t as gOOT!
as the first cycle of breed~ng b~gins th~re is a ctriking
falling off in the numbe-r of displays. It appears that
if the first-year pairs miss the t i rst cycle of'oreeaing
they have to await the Atimulus of the second peak of
d-is plays, tha.t comes onte the first lot of brood 3 hu.E;.
fledged, bf~ fore they can begin br~eding'i.He preI'.H!.ot~
some data suggesting lat~ first and second clutches
tend to fall in the second .ana thir. modal regiona
respectively.
Figure 3 contrasts the breeding seasons in the three
major study areas (figure 1). The breeding modes fall
later at Hoan Hay and Lincoln than at Shirley . 'l'he
small size of the early Lincoln !!lodes would seem
tQ b~ an artifact of uneven searching effort - tber~ is
evidence in the data suggesting a more iritense effOrt
in the late pnrt of the seasOn. HOwever the diff~rence
in the pattern of Shirley and Hoon Hay ia significant
. .. --"" ........ ~
i ' ·
f ~ ." ~' ~ ,
10
i (p < 0.001 ina chi-squo!ire test). This difference amounts ii ~ to about two weeks over a dista.nce of only five mil~B. ~ .
~ ) ,"
6 Cold air drainage from the hills (Iigure 1) may cause
a later spring in Roan Hay than in Shirley and also
Shirley c.ould be more subject to the warming effect
known torc~ties.
The differences between Stoekton-on-Teea and Ithaca
(figure 3) were Bupposec;i by Sunt.'ll8rs-Smith (1963) to
epresent a lat~tudin.l trend; however tbe differ~nceB
shown here over a distance of only five miles would
cast doubt on all but the largest latitudinal differences.
'" " -- "'l ".
~ •• _ _ ._ --:1'.'
'ri!- . : -~l~ · ~>< .. -~.: '
CLUTCH SlLaE
In a neat records analys:i.s clutch size is used to index
the prod.uction of the female and different definitions
are need~d for determinate and indeterminate layers.
Tor lndeterminst.e layers the de:Uni tion of clutch size
i8 the maximum number of eggs in the nest at any time.
For determinate layers it is the actual nurr:ber of eggs
laid b~; th~ female. Only for determinate layers is an
allowance made £or egg loss during the laying period.
"
There is strong evid.ence that the house sparrow is tl.l\
indeterminate layer (ThoXl\Bon, 1964; 422) and no such
allowance need be made. Appendix IV gives the theory of
clutch size estimation, and the \terrer value" for
the t'indeterminate layer" column of table IV.1 are tho~e
employed in this analysis.
TABLE
Nean clutch sizes
error value
Sept-Oct Nov Dec Jan-Feb whole number of seaSon clutche~
t--- ~l· o ---.. r----- - -. ,
-; . 85 ! 111 I ~ ey I
I ., ~<6 '3.7'7 3.89 J 3.83 -,. 06 I ).82 --1 192 ---t- . ----. -- .. - -- -- t· -.. -- - .. -.-. .... -\ .. _ . . • • •• : ' w
.- . "._ "'--- ....:.--... -<6 I 3.89
k6 ; i nay j .. coIn U :ords
3·31 4.00
4.00 ~ 4. -10 3·77 39
4;00 3.96 28 - -1-(6
I 3.71 3·79 3.89 4.00 3.81 277
--_. . i--------"'---.
Table 1 summarises the clutchs1zes from the three major
.tudie.s and all50 thoee from the entire Ne. Z.ealand sample • .. X t;;85ta failed to show any significant differences betw •• n
clutch t'liz •• from the three major are", .0 the apparent
l ~,
12
differencea could be due to chance. The :first two rows
of table 1 examine the effect of error value. All errors
in an estimated clutch size are minimizine ones (appendix
IV) so it would be expected that the larger the error
value of a. sample the smaller would be its mean. This
is .seen to be generaJ.ly true (especially as the sample
from Jan~Feb is 8mall and more subject to chance ertors).
Howeve.r the ~ffect is small in t .his sample - the consideration
of a ~arge number of clutches with error values less than
6 reeultingin a mean difference of only 0.03 eggs.
SUffi1TIers-Smith gives less quantitative comparative information .
.sucmer8-S~ith (1963): "It! Great Britain clutches of four
are commonest, accounting for almost half of the ones
reported, five is next with slightly over a quarter and
three making up approximately a sixth; clutches of six
and Beven were recorded - only thre~ caseS of the latter
o,ut of 702 nests .•.. Tbe average clutch size in Britain
is 4.1 <!!nd relIlains very nearly constant throughout the
breeding seascn. rising from 4.0 in April to a maximum
of 4.3 in the second half of June and then decreasing
f to slightly le5s than four towards the end of summer."
t ~eaver (1943) gives the mean size of 38 clutches aa
4.73. t-teste show both these Americlln figures and the
British ones to be significantly different froni the
New Zealand mean (p< 0.001), The co::nparison ie difficult
to interpret a~ both the New Zealand and the American
samples are from limited areas and may not t.ypify the
clutch size for those areaS.
Summers-Smith gives no i .ndication that the seasonal
variations· be presents 'are significant, but these British data
fit the more usual pattern of a p~ak in mid-season
(Lack,1947).
.... __ ..... _c_ ...... :r:~,~ '~~, ... ""' .... ~~ ... _~.-.. _ .~' .. - ......... _ ....... .. . __ ..... ,-...- .. ,: - ~.:. .. -".- -- ~~ - .. , - ",
HATCHING P.J:::f;IOD
The hatching period may b~ defined a8 the time between
th.e hatching of the first egg and that of the last egg.
Of 83 records. 47 clutches hatched within a day, 34 within two days and 2 within three days. Cramp (cited
13
in Summers-Sniith, 1963) "found that hatching extended
beyond twenty-four hours in twenty-seven out of ninty-fivft
clutches "
The hatching period would seem to average;! about a jay
with an upper limit a.t about two d9.Y3 . ThioS is to bp.
expected :IF; incuhution normally be f .ins ,)n the penul tin'!l ·~e
ct':g and 80 the last egg would be hatchinE . on the .:;tl/erC.l/.;e,
o day lat~r than the others.
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Nl!,;STINCi ~UCC~;;)
The traditional approach to nesting success is to
calculate three ratios. These are:
"h8tehing success" =
i!breeding success" =
"nestling success" =
brood size clutch size
number fledged clutch size
number fledged brood size
14
Snow (195;.) has discussed the sources of bias in the
estifilati.on of these ratios and has shown that earlier
work failed to cor~ect for ~hem all. One of ~hese
biases 16 that it is eaaier tc record failure than
success and though Snowclaiu:[, to have corrected for it
he does not give details of his method. There WaR
insufficient time .... to develop a method of correct.ion
When pr~paring this project and so all the ratios
t will be biased in such a way as to minimize the nesting l \' success. The data will be comparable to that given in
all analyses except that of Snow (195~.
Appendix V giveS the theory of itbrood size" estimation
and the error values given in ta'ple V.1 were used in
,: this 5tudy.
f ~: f The number of young in th~ nest 10 daya after hatching
w.s used as an estimate of the "number fledged!!. This
Dumber waB given the error value of ubrood size" and
.a8 corrected for aDy corpses found subsequent to the
tenth day. The "nuJllber .fledged ll 'A'ill have a positive
bias - young dying during the fledging p~riod, but not
fo\!nd, being considered successfully fledged.
~: . ';,;.' " " .
. ~ :~ .',
15
Tables 2 and 3 give the breeding 6ucr:ess for data froll!
Snirley (clutch sizes and numbers fledged with error
values less than two). No other9ample provided enough
data for comparison. Table 2 Bhows u significant seasonal
difference in the proportion of t.he eggl5 p:,'oducine;·
fledged young. eggs l~id in the middl. of ~rie season
being more 8ucces::Iful than thl)se laid at either eflii.
The same t.r~nd is present in the number fledged per
clutch. Table 3 6hows that the lar~~r clutches had a gre.ter
proportion of eggs producing fl~dged young (though this
freren~e w~s not significant). Larger ~lutches also
produced more fledged young per clutch; the maximum
number being for a clutch of five or larger.
Lack (1954)ccnsiders that lithe clutch-size of. each
speci.s of bird haa been adapted by natural selection
to correspond with the large~tnumber of young for
which the parents can. on the average, provide enough
food. It The usual clutch size in the sparrow i8 four
(B.b"Ure 4) put a clutch of five produces more flying
young. Thi .. s need not be jnconiSistent with Lack's
hypothe3is of Ir.aximal contribution to the next generation
Juvenile di6p~r6al would r~8ult in the effective
:ien:e eiztt forsparr9wB being consid2rably ID.l" ,~er than
the Shirley study area and other parts of the area
lccupied could be more favourable to nestling survival.
) Some sparrOwB may be better able to rear five young
~han othersa.!'ld these could lay larger clutches.
2 'l'he young from clutches of five could be les8 well
f ed than th056 f.romc lutchN~ of four and may not
survive 80 well after leaving the nest.
.~ -.
Time
Sept-Oct
Nov -Dec 10
Dec 11 -Jan
Clutch size
5 4
3 2
1
all
Time
Sept-Oct
~l,rov-Dec 10
Dec 11-J&n
Clutch eize
5 4
3
2
1
all
BHl:;J!:.oING .')UCC.L~~.
TABLE 2
No. of eggs Proportion .fledged
221 0.231
100 0.4b3
1:;·1 0.428
p «0.005
TABLE 3
No. of eggs Proportion fledged
80 0·,'75 280 0.361
~7 0.276 12 0.167
1 0.0
460 0·341
0.25 >p >0.1
liAtCHING ~UCCESS
TA:Dl£ 4
No. of eggs PI-oportiorl hatched
236 0.508 112 0.750
140 0.600
p< 0.005
TABLE 5
No. of eggs Proportion hatched
80 0.662
296 0.632
99 0.445 12 0.250
1 1.0
48.8 0.590
p« 0.005
No. fledged per clutch
0.85
1.79
1.65
ITo. fledged per clutch
1.03
'1. 44
0.828 0.334 0.0 1.29
No. hatched per clutch
No. per
1.87
2.90
2.27
hatched c.lutch
3·31 2.53
1.33
0·50
1.0
2.22
• .," .ertM*e~ ... ,...,. ...... -.. ~. ' ., ... , -- -.. ~ . 1 , I
1 i
i.
I t l I t
I 1 J i f T
t \;
i I ~.
':6
4 Parents feeding broods of five may be at a dis·t,ulvantage
in avoiding predators or in competing with their tellow~
(C~dy. 1966) ~ More of their genes might survive to th~
next seasDn if they were able tD srend more time at these
-8ctivi ties t and thuB improve their own chance of survival.
Nest Ulort~lity may be subdivided into egg and youhg
mortality. The egg mortality ie measured by "hatch-:ng
Ruccess ll . T~ble 4 shows that the proportion of eggs
tru~t hat.ch shows the B&me seasonal pattern aa th~
br~ed1ng success, and table 5 shows that a greater
proportion and ntimber hatcbes the larger the clutch
sizl\.
l·~ortality ()f the young is measured by "nestling success".
Table 6 shows that the proportion of young that survive
to ten days increases with decreasing brood size. 'This
trend counterbalancee that in hatChing success and
ref;ults in the lack of eignifi.cance in the trend s hcwn
for breedingaucces-s, Table 7 shows that the nestling
success has the Same seasonal trend as the other two ratios.
These trends ar~ illuetrated in figures 5 and 6. The
eggs in larger clutches have a better chance of hatching
than those in smaller ones, pos6iblybecause these larger
cIu tch~B are laid by mO.re e.xperienced (older) birds.
Thi!! re6ult~ in the larger clutches producing m·')re fletlged
young p~r egg despite the fact that smaller broods
have less mortality than larger ones. Both egg and
young mortality are higher at the ends of the breeding
season ·than in tbe middle . This could well be the
selection pressure that caused the Besaonal trend in
clutcb sizes (figure 4).
----~ .... ~~ .:. ~-:;. --:--- .. ~ ... ----.. . - . ," ...
t
~ ~ ? :.:
Time
Sept-Oct
Nov-Dee 10
Dee 11-Jan
Brood
5
4
3 2
1
all
size
NESTLING SUCCESS
TAbLE 6
No: o.t · young. Proportion No. fledged fledged brood per
97 O.5~7 1.71
96 0.677 2.~1
61 0.639 1.86 \ p =. 0.75
TABLE 7
No of Proportion No. fledged young fledged !'er brood
-,----- .-.--------.-----35
1=12
84
254
0.571
0.563
0.643 1.000
0.667 0.618
O.OS< p< 0.025
2.06
2.2'5
1.93
2.00
Q.66'7
1.99
I 60~
I
o L ..
20 .
0
I
20 J I r
I Di
! 20~ ,
I OJ
1
~
n I !
I
S~PT-OCT I
~ \
I
NOV
! -~ ~
OEC 11 j L~
I ; I
J mean JAN-FEB n ~
I L=:J 2 3 4 5
SEASONAL INCREASE IN CWTCH SIZE
Figure 4
I---·~'""-~·'- " ·
l f ; / ' .. . '
1?
This •••• on.l tr.nciis giv.n in the last row of table 1 .
A l.a.st-square. regre.sion line fitted to these data ga.ve
the increlllent o-! clutch SiB. increase per month a.s 0.0954
eggs. Th. 95% confidence interval of this increment is
0.0846 eggs. Aa zero does nQt lie within the confid.nce
rang~ of the increment the tr~nd shown i.!S l3ignificant at
th& 95% level.
Cramp (1955) gives mortality fie;Ul't?S for British bircls,
these are compared in table 8 with thoee from this study
and from Summers-Smith (1963).
TAHLE 8
% Hatching success Nestling success Breeding.
Greenfinch 74 77
Robin 71 77
Song Thrush 71 78 Willow Warbler 83 71
Spotted Flycatcher 78 81
Sp.rro .... (Britain) 71 74
Sparrow (N. Z. ) 59 62
This shows that the nesting success of sparrows in the
Shirley study area "as unusually low. This need Dot b.
typical of Ne. Zealand as a whole and may bea local
variation. More inf'orraation would be needed before it
would be profitable to speculate ori. causes.
53
55
55
58
63
53 34
~ ., .. " .~-~..,r ..
18
ACKNO-VLEOOFJ>1.ENTS
T.G.Dix and G.C.B.Poore were of significant help while
writing arid Dr. B.StonehoU84t criticised most of the
first dJ'aft.
The 8tatietica~ eatimation of breeding parameters from
nest records d~ta fa inve8tigat~d in d~tail.
Nest records for th~ house sparrow (P.:::.s.ser dowest::ic\J.s L.)
from New Zealnnd &,re an<llysed )"sing 'Gherllethoda de.-elopl'!d.
}\O!it of the datu came from thre~ areaS near Ghristchurch.
Th. i'ollow.illg conclusion!'!! are reached:
Sparrows lay one egg a day.
IncubaUonperiods range from 10 to 15 days with a mean ot 12.
Nestling periods range from 11 to 19 days with a mean of 15.
The breeding season (first-egg dates) begins in m.id Septembe~'
and ends in mid Fabruary and significant differences in
Lroing "' ;~re shown between two areaS five [tiles apart.
'fite distribution of clutches in each area was trimodal.
'l'he mean clutch eizeie 3. tS1 eggs and there is an
increase in clutch size a$ the ee~son progresses.
All eggs of a clutch hatch within two days.
t-!ean hatching succeSB i5 59%, nestling 8uccelS862% and
breeding Buccess 34% for an area near Christchurch.
Clutches laid in the middle of the season are more
succe86ful than those Iaill at the beginning'.
A clutch of five produces the la~8e8t number of flying
.~~.+ .... ,
_ ..... _. ______ O-... r._* ___ • __ n_ . ..,..., __ .",.. . ~ .. ......... ~, -.. . , .. ~ . ~. "" .... _. ···· . ...l l
~ J
:·1 1 i
t ! f f \
~. ,
young.
Theee r.8ult~ are compared with other work on the
sparrow and other birds.
Cody,M.L. (1966) A general theory of clutch size.
~volution 20: 174 - 184. ~ Cramp,S. (1955) The brceding of the Willow Va~bler.
~ S t ud'y 2:1 21 - 135.
Lack,D. (1947) The significance of clutch-f.iiz " .
.!.!?!! 89: 302 - 352.
19
Lack,D. (195lf) The Natural Regula.tion of Animal Numbera.
Oxford.
Lack,D. (1955) British tits (Parue ap}>.) in nesting
noxee.Ardea: 43: 50 - 84. Lockie.J.D. (1955) The breeding and feeding of jackdaws
and rooks with notes o.n carrion crowa and other
Corvidae. ~ 97: 341 - 369.
Myers,M.T. (1955) The breeding of blackbird~ Bong thrush
and mi.stle thrl1sh in Great Britain. Part I.
Breeding seasona. Bird Study 2: 2 - 24.
Silva,E.T. (1949) Nest records of the song-thrush.
British Birds 42: 97 - 111.
Simpeon,G.G., Roe,A. ,& Lewontin,R.C. ('1960) Quantitative
Zoology. Harcourt, Brace.
Snow.n.W. (1955) The breeding of blackbird, song thrush,
and mistl. thrush in Great Britain. Part II.
Clutch-size. Bird StudI 2: 72 - 84.
Snow,D.W. (1955a) The ,breeding of blackbird, song th~ush
and l!iistle thrush in Great Britain. Part Ill.
Neating success. Bi.rd Scudy 2: 169 - 178.
. '. ~.
-------...... ---.. .-.. -.--~ .. '~.-.. ,-~ .~...-. . .. , ~ .. ..... ..
$
f ,
20
SUnlmers-.:Jmith,J.D. (1963) The House Sparrow. Collins.
Thom.eon,A.L. (1964) A New Dictionary of Birds. Nelson.
Weaver,R.L. (1939) Win~er observations and a study of
the nesting of English SparrowB. Bird Banding
10: 73 - 79. Weaver,R.L. (1942) Growth and developaent of English
.sparrows. Wilson~. 54: 183 - 191.
Weaver,R.L. (1943) Reproduction in English Sparrows.
Auk 60: 62 - 74.
," " ", ~~ ", ~ .. < . '. :.; .;-..
r . ': : - ' ." _.L .,
~~""~"'_."""""_f ...... __ ----.-,;--...... --.~ _______ .......a ........ ~.:......... ........ .. ,. .. • • •.....
~ : ....
FIG. !·1
egg dt$~Qv."d
ro::d:::J I
I l'\ su<.h I •.•. I days
V, calculated pet"ioQ
.ssu~cl .l .... d
..' I I
CL ... '-I
Yol.I.ng discovered
1 ot:=?
-~ eS9
2+ Y\ daY$ ha1ched ~,
·4l:;:;""me::do
h .. khd
GREATEST MINIMIZING ERROR 2"',..-3-n
I n such : •.. days
I " ...
I
~ Actual ?~riod 1 + 1"\ day~ ~
la~sum~d ~ni\.t..:hed
FIG. 1'2
ew-.... ol"
t~ys
3 .. n days
GREATES T MAXIMIZING ERROR ~ + 1'\ -.:2. - n = 1 Day
d isc.o\le~ed
/9 assumed
. L1l1il'\~ tir"l\e
FIG. 1-4
mean ... i s.i1i'(\~timQ
assuW'M}4
kat'kil'\~ ti~Q
I NCUaATION PER10D ESTIMATION
I
P
KEY
-.::--_....--------~ .. ------.-·~ .... tb . b ... · .... ·~ ..... ~. iiiIo ". "rn:,, "'nrW '""' .... .e:ef:pj ri' "=f. ""~'-":I.I€ W 'f · ... ab
APP£NDIX I
THE 'l'llEORY OF INCUBATION Fl:i:iHODESTUlATIOH
In figure 1.1 and the subs~quent figures a simple model
i8 set up to represent the times involved in deducing
incubat10Q periods (th. ti~. being along the horizontal
axis). When calculating incubation periods by the subtraction
of dates the events conce.rned D.re a.ssumed to haveoccurr~d
at aidcb.y on the days they were discovered.
~"igures 1. 1 and 1.2 illustrate th~ gras test error
minimizing the actual incubation period and maximizing
that period respectively_ The assumptions required are:
Ca) That eggs are laid only at night.
(b) Th~ nests ar~ visited onlw during the day.
(c) Hatching can occur at any time of the day or night.
The resulting upper and lower limits to the error of
the calculated incubatLm period are "! 1 day.
It should be noted that if there il3 a more circumscribed
tilt& during the night (e.g. just before dawn) when eggl3
are laid, then one or both of th~ limits would be reduced
ill magnitude. SirLilarly if the egga tend to hatch in
only part of the diurnal cycle then again one or both
of the limits would be ~.duced.
l:dWli Pili)oSIBU IH TH.~ CALCULA'I'.t;D ~AN Pi!,;lUOD
! irror in mean layins date (figure 1. 3). Given the
above three aS5umptions the mean assumed laying time
will lie between t and i days more than, the actual mean
laying time:
I = L + (t to i)
B Error in mean hatching da teCfigure I. 4-) • In this
caltulation two addition~l assu~ptions are required:
., ... -- . - .
(a) The time of day or night has no influence on hatching.
i. e. rLean hatching time is hell -way through the period
considered.
(b) The visits of the observer similarly average at midday.
Then the mean assumed hatching time will be T day more
than the nlean actual hatching time:
h=H-+t
C The period.
The actual ineubatioll period is: P. 1i - L The assumed period is! p = h - I
= H - L ... t - (i to i) x P +i to P - i
i. e. the calculated mean period will be _i thin i- day of
the actual m&an period.
. . . .. - .' ..
. .- . . r ~ :. -...
. ~~:'I . .. ~
._~_--~--__ ~-.--. .. ~~ __ ... ~~~~.~." •• ti&, j.".:.! rT !.i ··'_~~~'_~ ' .. A •• •• ..:,- . _. ___ .-~ ' . '" . - .
; "
. ::, ,'f -,fi "f
t
APPENDIX 11
THE THEORY OF N.:i:STLING PERIOD ESTINATION - . .
Using similar modela to those in appen~ix 1 the errors
inhe~ent in estimation of n~stling periods can be deduced.
~ POSSIBLE .B! INDIVIDUAL CALCULATED P~lODS I
. t-T Figures 11.1 and II. 2 illustrate the greatest Itrr()r
~ . ,
. ~
j
maximizi~g the actual nestling period and minimizing that
period respectively_ The assumptions required are:
(a) Hatching can occur at any time of the day or night.
(b) The neatsare visited only during the day.
(c) The young lea.,e the nest olll,. during the day.
Then the upper and lower limits to the error of the
calculated nestling period are! 1t days.
If eggs ba~ch in ~nly part of the diurnal cycle or the
young fly in only part of the day, then one or both at
·l the limits w·ou·ld be reduced.
~ PO.:)SIBLE l1! TH~ }.E~N CALCULATED FEHIOl)
r A Error in the mean flying date (figure 11.3).
Given the &Bdumptions above a.nd also:
(a) 'rhe time of day has no influence on leaving the nest.
Le. the mean leaving time will be half-way througb any
daylight period considered.
(b) The observers' visits average at midday.
Then the mean assumed flying time 'Nill be i day more than
the mean actual flying time:
" : " ·r·.,. ·'·····
_---...... ----... --........ --e5...,' • ...,- ,...-irirth __ ··_'n:ti' ... · .... * ....... ·_n .... t t ___ .... _ ..... -..:-_· ....... ~ ..... · ___ -..;·_· __ _
I . .
r f i. r
c 1:::l I
~ FIG. n'1
f')ul'ld visit
l • t I l 0* ' .... ",day""" !-...-=o i
' t ,
~ ~c.tl.l;al ?~ ... iod 1t ;. n cl~Y'-1 Ciilcl.ll'lted pe1"iod 3 • n days
GREATEST MAXIMIZING ERROR
• I
t .... n days . .... ,1 I I
f~~~ to b~,9°1'l·
..---1-., .~ : I r:::::::1 ""--r- r I
J 3;. n -1t - n = 1i day!>
hund to be qcne : :9
F~---- Actual p~riod 3,t + n day' -------II!~
~ Cal('LlLated paricd 1 • \'\ d~y.s ----iII~
FIG. Il'2 GREATEST MINIMIZING ERROR
For conventions
sce appendix I r: : j I
FIG. n'3
I~ = I
NESTLING PERIOD ESTIMATION
~ I I I
• 1.).. d 2 + n - 3! - r\ :; - a. ay'
: . . -: ~ .< .
.,.-.~-- .. ... ~ ,'. --_ ......... _-- _. -_ .. _ .. , _ .. " _ .. ~-. ....--:- ~ " .
B It has been shown (appendix I) that:
i • ~ + i but n~t~ the additional
aS8uIDption (.) required to obtain this result.
C 'l'b.period.
The actual nestling period ~8:
The assumed period is:
N • F H n = t - b
~ F - H + t - t
. i i. e. the calculated mean period will be equal to the .;
. r--
, , , ..
1 " I
> I
t
·f . I
actual mean period •
..... , .... - ..... - ~.
t (
. ' : .. I}··
AFP~l~.uIA III
When the date of appearance of the first egg is not
recorded in the data it is still possible to deduce
that date from other evidence. With a knowl.edge of
incubation period, nestling period and laying interval
a beet ~stimate (D) of the first-.gg date c~n be made.
In table Ill.1 th& various kindl1 of evidence a.nd
corresponding methods of deducing the moat likely
first-egg date are given. An error inclex can be
calculated for each date - these too are t.bulat~d in
table 11 1. 1.
Such an error index (E) represents the maximum err.or
in either direction of the estimated first-egg date.
i.e. the estimated first~egg dat. is the mid point at the p08sible ran~e of the true date. If then the true
dates are evenly di.stributed through their possible
r9.llge!!, the me~n estimated date will be all unbiased
estimate of th9 mean actual date.
A P~t of the laying sequence recorded. Daily laying
is assumed and the first-egg date deduced.
d • date
e c number of eggs at that date (on
which the clutcb was not complete).
Then the first egg dat., D = d • 1 - e •..•• A,
with negligible error.
B Two or more visits with the !!!lame number of egg/! in
tlle nest. An estimate of the midpoint of the incubation
period is made:
a = earliest date ~ with a full clutch~ b la la.test date ~ e = number of eggs.
Th. midpoint is estimated a8, a .b 2
The clutch will be complete at a time half the incubation
period (6 days) betore this: a + b 2 - 6
Then assuming daily laying and countins back to the
first egg:
D S ... b 6 1 • 2 - • +
a ... b -(5 .) B1 D
2 + 4 ••••••
Figure Ill.1 illustrates the model ueed to deduce the
maximum posaible error in D. It can be s~en that this
is symmetric,al and equal to half the maximum value of b - a incubation p-.!riod minus
i.e. b -a E :: 7 - -_.
2
2
'8 .
C Hatching date known. The incubation p,:,riod is assumed
and the date of clutch completion is given by: d - 12.
Then daily laying is assumed and the fir3t-egg date
calculated:
D ::: d - 12 - e .. 1
a: d -(11 .. e)
Th. error index will b. the greatest di~ference of an
individual incubation period from the mean:
E ::: 2 •.••••• III C 2
D Dates on either side of hatching known. The hatching
date ~s estimated from: d' ~ a + b 2
and substitution in equation e 1 gives:
D = a + b -(11 + e) 2
...... "" .:.. ." .. ,; .. ,~ . .:;:~ ... :., .. ~ .---",
•
"' ..
.- .-.... --.-~.--. _.', , - . -,,~ , ....... .... -... . ,. __ ..... ... . - .. _-- ,. -- . ... . " .- .. __ .... _ . .. ,
FIG.1n"
F1G. m'2
ab I I
J 1 ,
I I t
I I
.I
I I • t
CYr"QI"'T
tr"ue
.. ~t\VI\;lted m;d pt.
ab t
I 11: I b~a
-M--- ~. I .1 I I I
b'- a' 2.
·alt kl' ;.l..
e-.tiw.'11e(\ ..-(lid pt.
I I
I . I I I I ~ e(('Or -DK.i-- error ~
a+b l
e-;;titnated hatc.hi~~ 1:iri\~
:. ~ ·-.Qlc .. :.".,.f .:. ' . ''<: •
I: 1
hue hatchil'lS
-time
J
J
::l e,tiW\.t~d
hatt.h,wo.s time
.·., .;,ull =.:tWl4"" .• ~ - ~ _ c .. . -- ' "
•••. ·1Ii;_r ... · ...... _ .. ____ .. __ ------- -,,--.,.,~ . .; - ." '-"-''''''-' -~"-'-'--"'--~-.-'---'-- '-' ,~ ..... ,
'.' . ',',,! ; t
::1
~J
:; Figure 111.2 illustrates the model used to deduce the
maximumpoBsible error in D. It can be seen that this b - . .!1. is ay ••• trical and equal to --Z---. To this must be added
the possible variation of the incubation period itself
(equation C2
).
Th~n: ........
E Two or more visits with young in the nest. The mid
point of the nestling period is estimated analagously
to the mid pointo! the incubation period (se.ction B).
a + b 2
I From this must b. subtracted balt the nestling period (7) ··r
to estima.te the hatching date: dt Ill:
Substitution in equation C1 give5!
D = a • b _ 7 -(11 • e) 2
a + 2
b -(18 + e) ......... E1
Where e is the
number of young.
The error index. of the mid point estimation is (by reasoning
analagous to that in fig. 111.1) 10 _ b - a 2
To this
must be added the error of the incubation period (equation C2
).
E = 10 _ b - a + 2 2
b - a = 12 - 2 ....... E 2
F Fledging date. The ne~tling period 1s aSBumed~ to
estimah the hatching date: d' • d - 15.
vi:" .-' .'"' .
"" .- ,. ; .
_ ... ---:,:..; - .,-------,- " ~--?>- .. ... . - ",- ,.,.-. , ~ "0 ( .... . .... _ • • • __ . ..... ... _ -"~_.
. ",, - -.
Thert substitution in e=l.uation C1 giv~8:
D = d - 15 -(11 • e)
Ft where e ia the
numQer of young,
Th. error index will be the maxim\,lm error of' an individual
= d - (26 + e) · ..... ..
nestlirtg period from its a5~umed mean of '5 days plus the
error of ~quation C2
'
!!. = 5 • 2
=. 1 · ..... , . F2
f! Visits on either side of fledging. The fledgi ng date a + b ia e5timated itom: 2 artd this is substituted in
equa.tion F,.
D = a ~ b -(26 + e) · ...... . The ~rror of this astilliat~d fledging date is (analagously
. b - a ~ith the reasoning in fig. 111,2) ~. To this mtist
.:;;,
be added the error ot ~quation F2 ,
b - a. E '" 7 + 2 · ..... .
If the incubation p~riods and nestling periods were
distribut.ed normally it would be possible to jeriv~,
instead of the maXinmru possible error (E) I the distribution
givirtg the probability of an error of any given magnitud~.
Table I11.1 summarizes these methods. It should be noted
that egg or young loss.ill J:'8sult in a positive bias to
all the estimations except the first.
-.~. :
-. - ...... --- .... -...... - . , ... _'-<. ,.-- .• '-- '''--._.! i
TAB.LE III.1
Estimation of first-egg dat~.
Evidence Date Error index I
_Re_c~rd_O_f_!_ir_~t __ ~.~.~ _._ .. _._~ ._~_ .... ___ ._ .. __ ._. __ ~_o __ _
_ I _ .. ~ _ _ ' _~ . • __ _J.o .. __ _ ) ~
TW :J or more visits with I' .,. ... b (5 ) +' 7 b -Zl ! 2 - 't e . - . I
tbe same number of eggs i . 2 ! -.-_ ..... - .. _ ." _ .... _. __ .... -..... . ~. -.. . - .. ---,.-t-'--.... -.--- ,-.. .... .... - ---"-"'" . , -- ,;
I ' i I d -(11 ... e) I 2
t- -_·_·-·_,·······_····_··1 ---·---,···
Paftof laying
sequence record~d ---. -,--- - . ~ .. - - "'_ .. - '"
Hatchinl) da.te _ .. __ ._----- •. j ,
at. b_(11+e) 1 2 +b-a 2 i 2
~ 1 ... -.---.. ~+---. ----' j
Dates on either side
of hatching
a +' b -(18 + e) I 12 _ b - a . 2 I 2 with young ~
:lOdgi~~da:~-· ·· - Td -(2~-'.) r·~··- ·----1 .-.--.. -.--... -------+--- ._--._--.- +--.--.--... --1
11 I
a ~ b -(26_.:~.)l: b ; a J
Two or more visits
Visits on either side
of fledging
Where: d = the date (where only one is used as evidence) .
a = first date ~ where interval is used. an b =. second date
and • = 1:he number of eggs or young in the nest.
,;£n
~j~~~ "
. ~ .
," ..... .
.... ' . .. : :;. "0(4
__ ------- • • _ . .. . ____ _ • • _ _ . ..... .. ~~ • ......--.-;...-_ •• ~,.~ .. lo't! ... _ _ • • • _~_ ..... ____ • •
A .dl:FO~ CIJj'l'CH CONPLETION (Determinate layers)
(1) If the visits d.a not determine the date of laying
of the first egg then the error valu~ is '; 'j ual to the
number ef eggs jn the nest 01\ the first visit (~.g. in
figure IV.1 a first visit on day 4 would leav~ three
d&ys in anyone of which one egg could have be~n lost).
Error value, E - a ....• (1) where ~ is the number of
egg.s cn the first visit during laying.
(2) If the visi~s tease before the date of olutch
completion then the error value will be e4ua1 to the ~stimated
clutch size minus the number of eggs in the nest on the
last visit. (e.g. in figure IV.' a last visit on day
2 would leave t .hree days upon which one egg could have
been lost beforeclutcil completion).
E = c - b ..... (2)
where b :: the nuu:ber of eggs on
tbe last visit during laying.
and c :: the estimated clutch size.
(3) J. general formula for the error value due to egg 10s6
duri~ laying is given by the sum of these two errors
E = a '" c - b 0) Note that if a = 0 (1. e. the nest is visited the day before
the arrival of the first egg) it reduces to formula (.2 ) t
and ~bera c ~ b (i.e. t~e number of eg~B on the lS6t visit
during laying is equal to the estimated clutch size) it
red'J ('('s to formula (1).
B ~~F~ CLUTCH COMPLETION (Both determinate and indetercinate).
(1) At least one visit during laying and the first Visit
subsequent to laying. The error value is given by the
number of days between t .he last of the visits during laying
and the first subsequent visit minus the difference
between the estimated clutch size and the number of eggs
in the rtest on the last visit.
. ~ .-: .:..~-.- . " . • . : . . pt.asa . - ..... =
'.
APPENDIX IV
CLUTCH ::iIZE ESTHiATION
In every case the clutch size is estimated from the
mrucimulIl number of eggs in the nest. For determinate
layers an adjustment may be made if visits during laying
suggest egg 106S.
There are two posBible causes of error in clutch sizes.
One ilS egg lOBS during laying and the other is loas
sub8equent to laying. Egg 1088 during laying will be
important only to determinate layers. for if an
indeterldnate layer loses an egg during laying it will
lay one more egg than normally to achieve the usual
ftill clutch. Establishing complet6 determinancy is then
a difficult task a8 one must know. how many eggs a bird
would have laid if the clutch was not depleted dvring
laying. There i~ good evidence for at least a larg~
elelJlent of inda t el"'ruinancy in Bom.e birds (ThorIiscn, 1964: <+22)
but any element of determinancy will l'eSll1t in a SI/.all
contribution from error of this kind.
An !terror value" Diay be calculated for each assumed clutch
3ize. This error value may be derin~d as the number of
days upon which no visit was made and loss or one egg
could have occurred in such a .ay a6 to cause an error
in the calculated clutch size. This "error value" will
be proportional to the probability of an error but will
only show a linear relation to it if (815 seems unlikely)
there is an equal probability of an egg lose on each day •
. ........ ,1'f ...... ,."' .. _ t .... ""'i.II!I .. !t'I.III'4J'~. Pi ...... "" ...... _-,.... -'., • ."...- .••. _--..
~---- .. -------- - -' _ .. .. _ .. --- - - --"-._-_ .. _--- - - ----, .. ---------/--- ,-- -
5
5
EGGS'" 3 2 1
0 0
egg lOSii
l
, i i I i , . t ( i i ,
hold pt, of -t1 ... e
~""vb;,jt ic:.V\' pCt""iod
8f.:c:t of eG::, " ..,,/,J
lcss en
\I clutch size 'I
FIG. IV·1
--, _.,-,,< " " ase lM :C20. tDln,", "' ""~""",,---'--'- -
. ~ ,
." -; ",; ~~ .
~.: i, .~ •. '" •. :.
E = n - m -Cc - b) .•• where m = tha d.te of the
last vieit
during laying
and n- tbe date of the
first viait
after laying.
= n + b -(m .. c) .•..• B1
e .. g. in figure IV.1 if the last visit durinp; lay:Lng
Were ori day 4 and the fi·rst visit af'ter laying on day
10 then the err~r value ~6uld be:
E - 10 • 3 -(4 + 4~
= 5 and it can be seen there are
ind.ed fiVe days in .hleh an egg could have been lOBt -
daya 6 to 10.
This situation is changed when one considere completely
determinate layers. Any error fro~ the actual laying
period must be added:
E :: n + b -(m ... e) .. a + c - D ••• 0) + B1
• . • • • • • • B2
(2) Visits only with a full clutch. Tbe error value
will be the number of days between the clutch completion
and the first of the visits. If alarg. number of cases
were considered the mean incubation period would hold and
alao the extreme v1.sih with a iull clutch would average
equal distances from the midpoint of the incubation period
(see figure IV.2). Thus the mean number of days between
the completion of the clutch and the first of thea.~ visits
would be given by:
mean i.nc. per. -....:....----::-----"'">-- - p - n
2 2
where n i5 asalr.ady given and p = the date of the last
visit with unhatch,d egga. . 1 t E mean inc. per. n - n Thus th~ mean va ue 0 = 2 · -. 2 .
~t ; . 'I. ,'- ,
, t~~~~): .~:.::.
~::~~ ,;~~. ',~' . ~ . .
~. , . ;.' .
. ~ ~ ~ -~ .. -."
~' ." ' :" \
': . ;f ~'; ;-'
y " ~ . -' . .-.: ~:
: : ' . . ~, .
,-.,:. -
~- -
I
AP.PENDIX V
.bROOD SIZE ~STINATION ----~. ~ ~~~~~~
Brood Biz~ may b& taken a8 the number of eggs in a clutch
that hatch. Howeve.r & more practical definition is the
nQmber ot young in the nest at the end of the hat~hirtg
period. Thus young that die before this time ar .e not
included in the IIbrood".
An error val~e analagoUs to that tor clutch size may
be defined: the number of days upon ~hich the nest
was not visited and a young hird c ·:>uld ha.ve been lost
Jrom it in such a way as to cause an error in the
calculated brood ~ize.
Using the following symbols:
D ::: the date of th~ visit giving the estimatsd brood
8- = the date of thfOl last '.,risit before hatch.ing.
b = th~ date of hatching of the first ~gg.
c = the iis t .. of clutch cOo>pletion.
e = th~ d3.tt! of the first visit with young.
f = the date of the last visit with young.
i = the mean incubation period (12 days) •
m • the maximum j.ncu btl.t ion period ( 15 daya) .
n I: the I4san ~atching period (1 day) •
A. If the mean hatching date (d) is known the hatching
period will be over, on the averag •• at the date:
d '
and the error value will average:
E = D - ·d t
= D - (d + i) ( 1 ) •
Si·7,6.
I
_ 6 _ p - n - 2 -. • • • • •• B3 -----
'l'A.bI...E IV. 1
Err!)r values for clutch sizl!' determination.
Evidence Error value
Daily visits during clutch completion
ViGits during laying but not covering the completion and again after completion
~ . Dete:min~~._l~;.~~ ___ ~nd': orm~~a t. layer
Visits only after completion of the clutch
I n -4- a - m n 010 b -(m +c)
- ----- -------------+1- --------1
6_E..-n 2
I 6_ p - n J ___ 2~ Wh~re: a c the nu~ber of egge on the first visit during laying.
b = the number of eggs on the last visit during laying.
c = the eatimateJ clutch size.
m :0 the dat~ of the last visit duri'lg laying.
n c the date of the first vie:i,t after laying.
p = the date of the last visit with unhatched eggs.
It should be noted that all the possible errorS are such
as to minimize the true clutch size and hence an estimated
clutch si.ze will be ne«atively biased. Also the
formula using ~'pl' will work only if some eggs do hatch
subsequently.
: 'o:. :' •. ~ . -
:e If'the date of hatching of the first egg is known then:
d = b + ~
and 8ub~titution in (1) gives:
E "" D -Cb -61) (2)
C If the date of clutch completion i,s known then!
d z: c -+ i
and 8ub~titution in (1) gives:
E = D -Cc + i + i)
D If the last date before hatching and the first after
batching are known then th~ mean hatching date will be:
a T 0 d = .2. (4)
Ithaa been shown that such an estimate of the hatching
date will have an error index of e ~ a (appendix Ill).
To make this estimate of compara.ble accuracy to the
previous ones:
e - a 2 lIi" has 2 (: ....... an error
index of 2. e -. 8
, 4
or e ~ 8. 04- 4 .... , . ,. . (5 )
i.e. the first visit after hatch~ng has to be within four
days of the last visit before hatching~
Substitution of (4) in (1) gives:
E E D _(e ~ a ~ t)
.. D e + a .. 1 2
(6)
E If at least two visits with YOU1ig: are record.ed, then
the hatching date is estimated from:
d = 2 - 7 .. : ...... (7)appenciix lIlE.
"" .: >., . .t! .'.: .~·l .
j; ;,~ . ... . ~.?~;:?
.;;~:~\~~-i" {.~ . ~ , ~.
Thi~ estimate will have an error ind.ex .o!:
i - e 10 - 2
(appendix III E).
To make this estimate of compartlble accuracy to the
previou8 ones:
10 f - e
~ 2 - 2
. • f - e '" 16 y
or f 2 v e .. 16 ...... (8) .
i.e. the last visit with young must be at least eixteen
days aft·er the first 'lisit with young.
Substitution ot (7) in (1) gives:
E = D _(8 • f - 7 • t) 2
= D • 7 _(e + f + ') 2
(9 ) .•
The cO~ldition that the brocri s;ize is thenulr,ber of youn 8;
in the nest at the end of the hatching period means
that D ~U3t lie outside this petiod. This r~sults in
further limiting conditions which are tabulated in table
V.1.
"'- ; '
..
'1' J.BLE V • 1
Eati~ation of brood size.
Evidence limiting conditions Error valu&
Hatching date of first
egg (b) and one
subsequent visit (D).
Date uf cJutch completion
(c) dnd one visit
5ubsequent to hatehing (D).
L~Gt i~t~ before hatchin~
(a) and f1r~t ~fter (e)
At least t~o ViEits with
young ~here D iB ~ot the
first one.
, ---r--------------r- ---------,--,---------D - b ) 1 I D - Cb ... 1)
I , ._. j ------ _ ... ,. ----- _ . • --' - -- ~-.. - , --.. --" .. --~--~-- ----
I :
D ) 15 + C
D -e )0 1
! f ~ I D -
e + 16
e ) 1
D -Cc + 12y)
e .. ~ -+ 1 Ll ---_ . ... -------','
€' ~ .f -----2 D +- 7
. . ____ _ L ______ .. . .......... __ " ... .1. _____ _
+ 1