. ,-

. ..~ t~ : -. ,:~ . . \ ', ...•.

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.

s milu

' c .',' TH>: O:"N'THuLOC'GL ICe d" '-.' "'IW lUL"'~D · · N'::ST R2CO~:~ CARD !'lbf> ====== - · ;.=-~=:-_:_;.;o..:,j, __ ~-=-:..: · .. ,-c::;=

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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.

' ... " : . " . ..

'IE' .. _____ ... _---....---------~~-.' .. ~.~t:.-:;.c.J" . A;. ,~~ ~~. I.. _ _..: .. ... . .6 .. -,. ..... .. ............. .': ..., ._1. .......... ,..: ......... .4 •• ~ • .. : . . . ..... -.~~~ ....... ~

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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L_ 0 ~_____________________________________ __ __ ~J ____ _

2°1 I

01 I

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20 1

HOON HAY

LINCOLN

,---fL--J I

1'--1

-, i

[ -=: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.'< .

I \ I .' .. , .... ~. \ I ....... \ I ' .' " . ,P-\\:,

JAN

Eist::wher;:, NZ, 1J -20

f.. ,,' 'w' \// , ... " '~.:-.a" . ...... . "~" Q. . 0.,·· '. , ' .' ,'"0. / ..... " ...•.. . . : .. ~ / 'c... .'

. ~,-"'-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

_" __ -~""""!'-~------'-'. --' .......... t:I'~..."Io("IIII'~.-. ~ • . -...., . ~-. -. ~ • • _ .. ... - '.' r-' .. ---

"

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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.

.: .. ' , i .~

(T,;;;:-t a,:{ ~> . ':

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I t

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