Fully accounting for nest age reduces bias when quantifying ...

Volume 123, 2021, pp. 1–23DOI: 10.1093/ornithapp/duab030

AmericanOrnithology.org

Published by Oxford University Press for the American Ornithological Society 2021. This work is written by (a) US Government employee(s) and is in the public domain in the US.

RESEARCH ARTICLE

Fully accounting for nest age reduces bias when quantifying nest survivalEmily L. Weiser*,

U.S. Geological Survey, Alaska Science Center, Anchorage, Alaska, USA

*Corresponding author: [email protected]

Submission Date: October 15, 2020; Editorial Acceptance Date: May 13, 2021; Published June 28, 2021

ABSTRACTAccurately measuring nest survival is challenging because nests must be discovered to be monitored, but nests are typ-ically not found on the first day of the nesting interval. Studies of nest survival therefore often monitor a sample that overrepresents older nests. To account for this sampling bias, a daily survival rate (DSR) is estimated and then used to calculate nest survival to the end of the interval. However, estimates of DSR (and thus nest survival) can still be biased if DSR changes with nest age and nests are not found at age 0. Including nest age as a covariate of DSR and carefully considering the method of estimating nest survival can prevent such biases, but many published studies have not fully accounted for changes in DSR with nest age. I used a simulation study to quantify biases in estimates of nest survival re-sulting from changes in DSR with nest age under a variety of scenarios. I tested four methods of estimating nest survival from the simulated datasets and evaluated the bias and variance of each estimate. Nest survival estimates were often strongly biased when DSR varied with age but DSR was assumed to be constant, as well as when the model included age as a covariate but calculated nest survival from DSR at the mean monitored nest age (the method typically used in pre-vious studies). In contrast, biases were usually avoided when nest survival was calculated as the product of age-specific estimates of DSR across the full nesting interval. However, the unbiased estimates often showed large variance, espe-cially when few nests were found at young ages. Future field studies can maximize the accuracy and precision of nest survival estimates by aiming to find nests at young ages, including age as a covariate in the DSR model, and calculating nest survival as the product of age-specific estimates of DSR when DSR changes with nest age.

Keywords: Bayesian, bias, daily survival rate, logistic-exposure model, Mayfield method, nest success

Considerar acabadamente la edad del nido reduce el sesgo al cuantificar la supervivencia del nido

RESUMENMedir con precisión la supervivencia de los nidos es un desafío porque los nidos deben ser encontrados para ser monitoreados, pero los nidos generalmente no son encontrados el primer día del intervalo de anidación. Por lo tanto, los estudios de supervivencia de nidos a menudo monitorean una muestra que sobre representa nidos más viejos. Para tener en cuenta este sesgo de muestreo, se estima una tasa de supervivencia diaria (TSD) que luego se utiliza para calcular la supervivencia del nido hasta el final del intervalo. Sin embargo, las estimaciones de la TSD (y por lo tanto de la

LAY SUMMARY

• Nest survival rates are useful tools for predicting population trends and understanding habitat quality for birds. However, nest survival rates can be difficult to measure accurately in the wild.

• Nest survival rates can be biased if nests are not discovered by researchers on the first day of the nesting interval (age 0) or if changes in daily survival probability during the nesting interval are not fully accounted for when describing cumulative nest survival from hatching to fledging.

• This study simulated nest data from known (true) survival rates to compare four methods of estimating nest survival to hatching or fledging. Each estimate was compared to the true value to measure the accuracy of each method.

• In the simulation, when all nests were found after age 0 and the daily survival rate changed with age, estimates of nest survival to hatching or fledging were often biased. Biases were prevented by (1) estimating how daily nest survival rates changed with age, rather than ignoring age; and (2) calculating the probability of a nest surviving to hatching or fledging as the product of age-specific daily survival rates.

• This study demonstrates the importance of fully accounting for nest age and provides a framework for future studies to do so.

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2 Age effects in DSR models E. L. Weiser

Ornithological Applications 123:1–23 © 2021 American Ornithological Society

supervivencia del nido) aún pueden estar sesgadas si la TSD cambia con la edad del nido y los nidos no son encontrados a la edad 0. Incluir la edad del nido como una covariable de la TSD y considerar cuidadosamente el método para estimar la supervivencia del nido pueden prevenir tales sesgos, pero muchos estudios publicados no han tenido completamente en cuenta los cambios en la TSD con la edad del nido. En este estudio usé una simulación para cuantificar los sesgos en las estimaciones de la supervivencia de los nidos que resultan de los cambios en la TSD con la edad del nido, considerando una variedad de escenarios. Evalué cuatro métodos para estimar la supervivencia de los nidos a partir de conjuntos de datos simulados y evalué el sesgo y la varianza de cada estimación. Las estimaciones de supervivencia del nido a me-nudo estuvieron fuertemente sesgadas cuando la TSD varió con la edad pero se asumió que la TSD era constante, así como cuando el modelo incluyó la edad como una covariable pero calculó la supervivencia del nido considerando la TSD a partir de la edad media monitoreada del nido (el método típicamente utilizado en los estudios previos). En contraste, los sesgos generalmente se evitaron cuando se calculó la supervivencia del nido como el producto de estimaciones de la TSD específicas por edad a lo largo de todo el intervalo de anidación. Sin embargo, las estimaciones no sesgadas a menudo mostraron una gran variación, especialmente cuando se encontraron pocos nidos a edades tempranas. Los futuros estudios de campo pueden maximizar la exactitud y precisión de las estimaciones de supervivencia de los nidos intentando encontrar nidos a edades tempranas, incluyendo la edad como una covariable en el modelo de la TSD, y calculando la supervivencia del nido como el producto de las estimaciones de la TSD específicas por edad cuando la TSD cambia con la edad del nido.

Palabras clave: Bayesiano, éxito del nido, método de Mayfield, modelo de exposición logística, sesgo, tasa de supervivencia diaria

INTRODUCTION

Nest survival is an important component of avian ecology and life history and is commonly monitored in field studies. Nest survival is typically defined as the probability of the nest surviving until at least one egg hatches (for precocial species) or at least one chick fledges (for altricial species). Estimates of nest survival are used to describe variation in breeding habitat quality (Peterson et al. 2016), predation pressure (McKinnon et al. 2014), effects of anthropogenic development and land-use change (Frantz et al. 2018), and implications of climate change (Dunn and Winkler 2008), as well as to develop population models that describe status and trends of species of concern (Robinson et al. 2020). As such, obtaining accurate and precise estimates of nest survival is an important component of studying wild populations of birds.

Accurately measuring nest survival can be challen-ging, however, because the full nesting interval is rarely observed. Monitoring nest survival is necessarily condi-tional upon observers finding a nest, and nests that fail soon after initiation are less likely to be discovered. The resulting left-truncated sample of nests can bias estimates of nest survival rates by underrepresenting nests that fail early. In a first effort to address this bias, Mayfield (1961) developed an estimator of daily survival to account for the fact that nests are typically monitored for only part of the nesting interval. With Mayfield’s method, a daily survival rate (DSR) is estimated based on the number of nests that fail and the total number of nest-days monitored, summed across all nests. DSR can then be raised to the power of the duration of the nesting interval (in days) to calculate the probability of the nest surviving to the end of the interval.

While Mayfield’s method resolves the issue of underrepresentation of nests that are predisposed

to fail, a major limitation is that it assumes constant survival over time and across nests. Subsequent work addressed this limitation by developing logistic-exposure regression models that similarly estimate DSR during only the period of observation for each nest (following discovery) but also allow the inclusion of covariates (Shaffer 2004, Johnson 2007). Including relevant covariates can help account for heterogeneity in DSR, thus representing an improvement over the Mayfield estimator. If no covariates are included in the model, estimates from the logistic-exposure model are equivalent to the Mayfield estimator (Shaffer and Thompson 2007) and equally susceptible to biases.

Careful selection of appropriate covariates is necessary to ensure that a logistic exposure model provides unbiased estimates of DSR and nest survival. Given that many nests are found sometime after the start of the nesting interval, estimates could be biased if DSR changes with nest age (i.e. from age 0 to the end of the nesting interval). Relationships between DSR and nest age have been documented in a variety of avian taxa, with negative age effects typically expected in altricial young where begging may increase conspicuousness to predators, although nest-site charac-teristics could mask that effect; and positive age effects ex-pected in ground-nesting precocial species where poorly concealed nests fail early (Skutch 1949, Martin et al. 2000, Jehle et al. 2004). In some cases, DSR may change between nest stages (laying, incubation, and nestling), and failing to account for any stage that is not monitored can bias esti-mates of cumulative nest survival (Blomberg et al. 2015). More often, however, the effect of nest age is described as a linear or quadratic relationship over the nesting interval of interest (within or across nest stages), is typically negative, and can be strong (Table 1). The widespread occurrence of a change in DSR with nest age suggests that testing for this

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E. L. Weiser Age effects in DSR models 3


TAB

LE 1

. Ch

arac

teris

tics

of d

aily

nes

t sur

viva

l stu

dies

, 201

5–20

20. S

ee M

etho

ds: L

itera

ture

Rev

iew

for d

etai

ls o

n ho

w th

ese

stud

ies

wer

e se

lect

ed fo

r inc

lusi

on. S

tudi

es a

re

sort

ed b

y th

e eff

ect o

f nes

t age

(typ

e of

test

, dire

ctio

n of

effe

ct, a

nd w

heth

er th

e eff

ect w

as su

ppor

ted)

, the

n by

taxo

nom

ic o

rder

(Cle

men

ts e

t al.

2019

). Va

lues

of D

SR a

nd c

u-m

ulat

ive

nest

surv

ival

(Ŝ) a

re re

port

ed to

the

num

ber o

f dec

imal

pla

ces p

rovi

ded

in e

ach

stud

y an

d ar

e sh

own

only

whe

n nu

mer

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val

ues w

ere

expl

icitl

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port

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the

text

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nges

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922–

0.95

80.

129

Cate

goric

al5

Stud

er e

t al.

(201

9)

10

042

0.96

4–0.

988

NR

Cate

goric

al4

Kozm

a et

al.

(201

9)

23

730

0.91

90.

157

Cate

goric

al3

Kuip

er e

t al.

(201

5)

69

7129

NR

NR

Cate

goric

al3

Mor

rison

et a

l. (2

015)

1926

0.84

21–0

.943

40.

045–

0.07

3Ca

tego

rical

5Ru

iz e

t al.

(201

7)

26

525

NR

NR

Cate

goric

al4

Kozm

a et

al.

(201

7)

43

290.

968

0.38

9Ca

tego

rical

1W

ood

et a

l. (2

016)

TAB

LE 1

. Co

ntin

ued

Dow





Nes

t age

effe

ctO

rder

Nes

ts

Nes

ting

inte

rval

(d

ays)

DSR

ŜAg

e eff

ect (

SE) a

Mod

el b

Stud

y

20

NR

0.21

4–0.

497

Cate

goric

al1

Dom

íngu

ez e

t al.

(201

5)

Gal

lifor

mes

, Col

umbi

form

es,

Pass

erifo

rmes

1925

NR

NR

-Ca

tego

rical

3Sh

ew e

t al.

(201

9)

Co

lum

bifo

rmes

, Tro

goni

form

es,

Pass

erifo

rmes

1082

26–3

70.

842–

0.97

50.

019–

0.43

0Ca

tego

rical

2Pi

erce

et a

l. (2

020)

Co

lum

bifo

rmes

, Pas

serif

orm

es42

7N

R0.

93–0

.95

0.12

–0.2

8Ca

tego

rical

3H

olou

bek

and

Jens

en (2

016)

555

NR

0.93

–0.9

6-

Cate

goric

al4

Lom

an e

t al.

(201

8)

61

320

–43

0.91

9–0.

979

0.10

1–0.

546

Cate

goric

al5

Tow

nsen

d et

al.

(201

8)N

est s

tage

: NS

Colu

mbi

form

es10

025

0.94

6–0.

972

0.25

0–0.

492

NS

3M

ote

et a

l. (2

019)

Pa

sser

iform

es25

721

0.98

20.

68N

S1

McF

arla

nd e

t al.

(201

7)

38

825

0.96

0N

RN

S1

Ald

inge

r et a

l. (2

015)

3930

0.94

9–0.

964

0.27

2N

S5

Batis

teli

et a

l. (2

019)

Not

test

edA

nser

iform

es 6

830

0.87

–0.9

70–

0.40

-2

Coss

a et

al.

(202

0)

Gal

lifor

mes

4435

0.97

630.

43-

2M

ange

linck

x et

al.

(202

0)

47

390.

877–

0.99

80.

002–

0.16

8-

NR

Gru

ber-

Had

den

et a

l. (2

016)

215

NR

NR

NR

-2

Eben

hoch

et a

l. (2

019)

147

270.

972

0.46

5-

2Pr

oett

et a

l. (2

019)

188

370.

96–0

.98

0.29

–0.4

8-

2M

illig

an e

t al.

(202

0)

10

128

0.97

0–0.

973

0.43

–0.4

6-

1G

risha

m e

t al.

(201

6)

13

728

NR

0.40

–0.4

4-

4Ty

l et a

l. (2

020)

269

30N

R-

-1

Bakn

er e

t al.

(201

9)

Podi

cipe

difo

rmes

9227

0.96

87–0

.978

20.

4421

-2

Brze

zińs

ki e

t al.

(201

8)

Colu

mbi

form

es70

726

0.96

9–0.

972

0.44

3–0.

481

-4

Schu

lz e

t al.

(201

9)

12

4050

0.98

37–0

.995

10.

440–

0.78

0-

5H

azel

and

Ven

able

s (2

017)

M

usop

hagi

form

es29

500.

990

0.60

5-

1N

dagu

rwa

et a

l. (2

016)

Ca

prim

ulgi

form

es21

200.

977

0.63

-2

Akr

esh

and

King

(201

6)

27

278

0.99

70.

775

-5

Gun

n et

al.

(202

1)

Gru

iform

es97

280.

983–

0.98

50.

505

-3

Robe

rtso

n an

d O

lsen

(201

5)

10

030

0.93

5–0.

958

0.14

3–0.

283

-4

Barz

en e

t al.

(201

8)

Char

adrii

form

es35

625

NR

0.00

0–0.

043

-2

Riec

ke e

t al.

(201

9)

70

0N

R0.

925–

0.97

4-

-1

Stoc

king

et a

l. (2

017)

112

270.

966

--

1Bo

rnem

an e

t al.

(201

6)

10

328

0.98

00.

556

-2

Kam

p et

al.

(201

5)

44

334

NR

--

4D

arra

h et

al.

(201

8)

17

0335

NR

0.27

–0.4

6-

2Sw

ift e

t al.

(202

0)

38

1N

RN

R-

-4

Stan

tial e

t al.

(201

8)

34

334

0.97

1–0.

992

0.37

1–0.

759

-3

Cohe

n et

al.

(201

6)

53

225

0.98

1–0.

998

--

2Ke

ntie

et a

l. (2

017)

714

N

RN

R-

3M

eyer

et a

l. (2

020)

205–

780

19–2

0N

RN

R-

4W

eise

r et a

l. (2

018b

)

98

220

–23

0.93

7–0.

971

0.25

–0.5

1-

2Kw

on e

t al.

(201

8)

74

1819

–28

0.97

72-

-4

Wei

ser e

t al.

(201

8a)

161–

513

28–3

10.

687–

0.99

7-

-2

Nie

mcz

ynow

icz

et a

l. (2

017)

4524

NR

NR

-1

Shar

ps e

t al.

(201

5)

TAB

LE 1

. Co

ntin

ued

Dow





Nes

t age

effe

ctO

rder

Nes

ts

Nes

ting

inte

rval

(d

ays)

DSR

ŜAg

e eff

ect (

SE) a

Mod

el b

Stud

y

3455

0.97

90.

307

-1

Kiss

ling

et a

l. (2

015)

605

21N

R-

-4

Dar

rah

(202

0)

Proc

ella

riifo

rmes

1371

172

0.98

75–0

.992

60.

114–

0.28

0-

3Jo

nes

et a

l. (2

015)

Ci

coni

iform

esN

RN

R0.

996

--

1Au

clai

r et a

l. (2

015)

330

25N

R0.

341

-2

Brus

see

et a

l. (2

016)

336

NR

NR

--

3Ch

ampa

gnon

et a

l. (2

019)

Ac

cipi

trifo

rmes

114

101

0.99

50.

634

-4

Cran

dall

et a

l. (2

015)

77N

R0.

988

0.44

-1

Segu

ra a

nd B

ó (2

018)

Pi

cifo

rmes

53–1

2439

–46

0.99

1; N

R0.

676;

NR

-2

Saab

et a

l. (2

019)

Ps

ittac

iform

es47

116

NR

0.12

2–0.

848

-2

Kem

p et

al.

(201

8)

Pass

erifo

rmes

3831

0.97

160.

3187

-1

Stud

er e

t al.

(201

8)

18

350.

96-

-2

Jaur

egui

et a

l. (2

019)

5630

0.93

3–0.

968

--

1Pr

etel

li et

al.

(201

6)

23

310.

960.

26-

2G

onza

lez

et a

l. (2

019)

4435

0.97

5–0.

992

0.41

–0.7

5-

1H

amm

ond

(201

6)

18

734

NR

0.30

-1,

5Bo

rgm

an a

nd W

olf (

2016

)

84

824

0.88

0.05

-2

Mw

angi

et a

l. (2

018)

172

230.

890–

0.95

10.

12-

3Pr

aus

and

Wei

ding

er (2

015)

79N

R0.

955–

0.95

8-

-N

RRo

ncal

li et

al.

(201

6)

12

324

0.94

4N

R-

1Sl

evin

et a

l. (2

020)

4029

0.95

640.

275

-1

Fu e

t al.

(201

6)

42

330.

951

--

3M

itche

ll et

al.

(201

7)

84

NR

NR

--

3M

eyer

et a

l. (2

015)

2985

NR

NR

--

3M

iller

et a

l. (2

017)

6726

0.94

7–0.

966

0.31

6-

5Ba

tiste

li et

al.

(202

0)

11

7N

R0.

9731

--

3D

eng

and

Zhan

g (2

016)

35N

RN

R-

-3

Bord

er e

t al.

(201

8)

30

224

0.95

90.

363

-4

Mac

ias-

Dua

rte

et a

l. (2

019)

110

NR

0.94

2–0.

947

--

1Fi

sh e

t al.

(201

9)

86

250.

936

0.19

-4

Mal

one

et a

l. (2

019)

102–

231

210.

867–

0.96

20.

059–

0.27

6-

3H

ewet

t Rag

heb

et a

l. (2

019)

228

240.

93–0

.97

--

6W

alsh

et a

l. (2

016)

155

NR

0.97

4-

-3

Forr

este

r et a

l. (2

020)

1323

21N

R0.

024–

0.71

9-

2W

eint

raub

et a

l. (2

016)

610

250.

970.

51-

3Re

idy

et a

l. (2

017)

3524

0.94

0–0.

947

0.22

7–0.

271

-3

Vass

eur a

nd L

eber

g (2

015)

53–1

3325

–33

0.95

–0.9

70.

24–0

.45

-3

Roac

h et

al.

(201

8)

23

2–26

725

–28

NR

NR

-3

Piph

er e

t al.

(201

6)

59

21–2

30.

82–0

.96

0.03

8–0.

567

-1,

5N

ovak

et a

l. (2

016)

306

270.

914

0.08

4-

2Kh

amch

a et

al.

(201

8)

44

NR

0.91

6-

-3

Foga

rty

et a

l. (2

017)

243

NR

0.90

0–0.

987

0.55

9–0.

601

-5

Mar

ini (

2017

)

21

120

–21

0.93

9–0.

961

--

2M

ahon

ey a

nd C

halfo

un (2

016)

TAB

LE 1

. Co

ntin

ued

Dow





Nes

t age

effe

ctO

rder

Nes

ts

Nes

ting

inte

rval

(d

ays)

DSR

ŜAg

e eff

ect (

SE) a

Mod

el b

Stud

y

997

NR

0.91

9–0.

981

--

3Re

idy

and

Thom

pson

(201

8)

14

NR

0.92

2–0.

971

--

5Şe

kerc

ioğl

u et

al.

(201

5)

Capr

imul

gifo

rmes

, Pas

serif

orm

es65

NR

0.96

3–1.

000

--

1O

cam

po a

nd L

ondo

ño (2

015)

A

nser

iform

es, F

alco

nifo

rmes

, St

rigifo

rmes

, Pic

iform

es,

Pass

erifo

rmes

2411

428

–64

NR

NR

-3

Baile

y an

d Bo

nter

(201

7)

Co

lum

bifo

rmes

, Psi

ttac

iform

es,

Pass

erifo

rmes

78N

R0.

629–

0.99

6-

-1

Fran

ça e

t al.

(201

6)

Co

lum

bifo

rmes

, Pas

serif

orm

es46

3N

R0.

799

--

3D

eGre

gorio

et a

l. (2

016)

162

14–2

20.

941–

1.00

0-

-1

Chm

el e

t al.

(201

8)

22

2N

RN

R-

-2

Beld

er e

t al.

(202

0)

Trog

onifo

rmes

, Pic

iform

es,

Strig

iform

es, F

alco

nifo

rmes

, Ps

ittac

iform

es, P

asse

rifor

mes

157

37–9

00.

916–

0.99

20.

19–0

.62

-3

Cock

le e

t al.

(201

5)

a Age

effe

ct is

line

ar u

nles

s ot

herw

ise

note

d (q

uadr

atic

, cub

ic, c

ateg

oric

al e

ffect

of n

est s

tage

) and

on

the

logi

t sca

le. W

hen

a qu

alita

tive

resu

lt is

sho

wn

here

(“ne

gativ

e, p

osi-

tive,

or s

uppo

rted

), th

e re

fere

nce

did

not p

rovi

de a

num

eric

al v

alue

for t

he e

ffect

. Stu

dies

did

not

exp

licitl

y st

ate

whe

ther

or n

ot n

est a

ge w

as s

tand

ardi

zed

(z-s

cale

d) u

nles

s no

ted

here

(see

foot

note

s c,

d).

b Mod

elin

g fr

amew

ork:

1 =

logi

stic

exp

osur

e in

MA

RK (

Whi

te a

nd B

urnh

am 1

999)

, 2 =

logi

stic

exp

osur

e in

MA

RK v

ia R

Mar

k (L

aake

201

3), 3

= lo

gist

ic e

xpos

ure

in o

ther

m

axim

um-li

kelih

ood

fram

ewor

k (e

.g.,

SAS

or R

), 4

= lo

gist

ic e

xpos

ure

in B

ayes

ian

fram

ewor

k, 5

= M

ayfie

ld, 6

= o

ther

.c N

est a

ge w

as st

anda

rdiz

ed (e

ffect

size

is c

hang

e pe

r SD

of m

onito

red

nest

age

s; e

xcep

t Bac

on e

t al.

(201

7) sc

aled

to 2

SD

). Ti

war

y an

d U

rfi (2

016)

did

not

repo

rt st

anda

rdiz

ing

nest

age

, but

the

mag

nitu

de o

f the

effe

ct s

ugge

sts

age

was

resc

aled

in s

ome

way

.d R

efer

ence

exp

licitl

y st

ates

that

nes

t age

was

mod

eled

on

the

natu

ral s

cale

(effe

ct s

ize

is c

hang

e pe

r 1 d

ay o

f nes

t age

).

TAB

LE 1

. Co

ntin

ued

Dow





relationship is an essential step in developing a DSR model for most species of birds.

When nests can be aged upon discovery, such as by floating, candling, or observing the egg-laying period (Westerskov 1950, Lokemoen and Koford 1996, Liebezeit et al. 2007, Rizzolo and Schmutz 2007), including age as a covariate in a logistic-exposure model is simple. However, nest survival studies do not universally consider age ef-fects. Even when age is included as a covariate of DSR, the method of calculating the estimate of cumulative nest survival to the end of the nesting interval could introduce biases, such as if DSR for the mean observed nest age is used even when the dataset does not equally represent all nest ages. Any bias in the estimate of nest survival would affect other work that relies on the estimate of DSR or nest survival, such as demographic models intended to evaluate whether a population is growing or declining (Beissinger 2002, Schaub and Abadi 2010).

While the potential age-related biases in DSR and nest survival have long been acknowledged (Johnson 1979), further work is needed to demonstrate how and when consideration of nest age is essential to produce unbiased estimates (Rotella 2007). I used a simulation study to sys-tematically explore the biases in estimates of nest survival when DSR varied with nest age and not all nests were found at the beginning of the nesting interval. Under a variety of scenarios describing biological parameters (duration of nesting interval, cumulative nest survival, relationship be-tween DSR and age) and sampling parameters (sample size and nest ages at discovery), I estimated nest survival using four methods and quantified the resulting biases relative to the true (input) value. The four methods were (1) the Mayfield method, (2) a logistic-exposure model that as-sumed DSR was constant, (3) a logistic-exposure model that included nest age as a covariate and calculated nest survival from DSR at the mean monitored nest age, and (4) the same logistic-exposure model with age as a covariate but that calculated nest survival as the product of age-specific estimates of DSR across the full nesting interval. By comparing results from these four methods, I identified which methods were more or less likely to produce biased estimates under a range of conditions when DSR changed

with age, and not all nests were found at the beginning of the nesting interval.

METHODS

Literature ReviewTo document the extent of effects of nest age on DSR and current practices in accounting for those effects in nest survival calculations, I reviewed recent ornithological literature. I searched the Web of Science (v.5.35) for the terms: ((bird OR birds) AND (daily OR “logistic exposure” OR “Program MARK” OR “Mayfield”) AND (“nest sur-vival” OR “nest success” OR “survival of nests”)) in all fields of journal articles published in English from 2015 through 2020. I retained studies that estimated daily sur-vival rates of natural (not artificial or simulated) nests of wild birds. While not intended to be an exhaustive review of the existing literature, this process produced studies on a range of taxa with a variety of methods of evaluating the effects of nest age (Table 1). From each study, I compiled (1) the taxonomic order of the study species, (2) whether the young of the species were precocial (i.e. parents do not bring food to the nest) or non-precocial (semi-precocial, semi-altricial, altricial; i.e. parents bring food to the nest), (3) duration of the nesting interval, (4) number of nests used in the DSR analysis, (5) the mean or median age at which nests were found, (6) the framework used to esti-mate DSR, (7) reported value(s) of DSR, (8) whether and how an effect of nest age was tested, (9) whether nest age was centered or standardized in the DSR model, (10) the nest age at which the reported value of DSR was calculated, and (11) how nest survival to the end of the nesting interval (Ŝ) was calculated. I used the ranges of reported values to guide development of the scenarios that I simulated as de-scribed below.

Simulated ScenariosI used a data simulation to explore the effects of model structure and scenario parameters on the accuracy of es-timates of Ŝ. I simulated a variety of scenarios (Table 2) in which parameters varied across the ranges commonly

TABLE 2. Parameters used in the simulated scenarios to evaluate biases in nest survival estimation when DSR changes with nest age and not all nests are found at the beginning of the nesting interval. All possible combinations were simulated

Variable Values tested

Number of nests monitored (n) 50, 200, 300, 500Duration of nesting interval in days (d) 20, 30, 40, 60Mean nest age at discovery (μ ad) (proportion of nesting interval) 0.25, 0.33, 0.50CV of age at discovery (CVad) 0.25, 0.50Effect of nest age on DSR (β age) –0.20, –0.10, –0.05, 0, 0.05, 0.10, 0.20Cumulative nest survival (Ŝ) 0.20, 0.30, 0.40, 0.50Estimator of nest survival (Ŝ)

CV = coefficient of variation; β age is on the logit scale, x = mean age at which nests were monitored.

Dow





observed in published studies of DSR (Table 1). For most scenarios, I used values near the medians from previous studies (Table 1), where Ŝ = 0.30, the duration of the nesting interval (d) was 30 days (from age 0 to 30), and n = 200 nests monitored. I also explored a subset of scenarios where those values were higher or lower to evaluate how those changes affected the overall patterns (Table 2). Only 4 of the 172 reviewed studies reported nest age at discovery (mean age at discovery = 35–38% of the nesting interval; Conkling et al. 2015, Ellis et al. 2015, Crimmins et al. 2016, Hewett Ragheb et al. 2019). Therefore, I tested scenarios in which the mean age at discovery (μ ad), expressed as a pro-portion of the nesting interval, was 0.25, 0.33, or 0.50. I set the coefficient of variation of the age at discovery (CVad) at either 0.25, which resulted in no nests being found at age 0 regardless of mean age at discovery, or 0.50, where some nests were always found at age 0 (Figure 1). I tested scenarios with various magnitudes of positive or negative change in DSR with age of the nest (β age = –0.20 to 0.20; Table 2) relative to a centered but unstandardized daily value of nest age, such that β age indicated the change in DSR on the logit scale with each subsequent day of nest age. For simplicity, I assumed that any relationship between DSR and age was linear on the logit scale across the nesting interval, which may be valid within a single stage (e.g., in-cubation), though field studies evaluating multiple stages (e.g., laying, incubation, and nestling periods) may want to consider nonlinear effects (Grant et al. 2005).

Data SimulationI simulated data using base functions in R 3.6.2 (R Core Team 2019) and the scenario parameters listed in Table 2. For each scenario, I randomly selected the age of dis-covery for each nest based on the mean and CV for the scenario. I assumed that nest age at discovery was known; any error in determining nest ages in field datasets would be expected to increase the variance around estimates of

DSR and Ŝ beyond what is shown here. I also assumed that nests found on the final day of the nesting interval (e.g., the hatching or fledging day) would not be included in the sample, as is standard practice in nest survival ana-lysis because those nests do not provide information on survival rates.

In each scenario, the specified β age indicated the change (on the logit scale) in DSR with each subsequent day of nest age. I evaluated age on the natural scale, centered on the midpoint of the nesting interval (e.g., centered ages –15 to 15 when raw ages spanned 0 to 30 days). For each scenario, given the value of β age, I calculated the age-specific DSR (DSRa for each age [a] of the nesting interval) that would produce the nest survival rate specified by the scenario. I used the ages at discovery and age-specific DSR to simu-late nest histories across the nesting interval, where the fate (survival or failure) of a nest on each day was drawn from a binomial distribution with a mean equal to the age-specific DSR. Nest histories prior to discovery or following failure were indicated as missing data (NA) as is standard in Bayesian DSR models. Details of the data simulation and a reproducible example are provided in a publicly available R script (Weiser 2021).

Model Fitting and Estimation of Nest SurvivalFor each simulated dataset, I calculated DSR following the Mayfield method as DSR = 1 – Nf /D, where Nf is the number of nests that failed and D is the total number of nest-days monitored (summed across nests; Mayfield 1961). I then calculated the Mayfield estimator of nest sur-vival as Ŝ m = DSRd, where d is the length of the nesting interval in days. While the Mayfield estimator is known to be biased if DSR is not constant and is rarely used with modern datasets, it served as a point of comparison for the other estimates.

I then applied two logistic-exposure models of nest sur-vival to each simulated dataset. The first model assumed

FIGURE 1. Expected distribution of nest ages at discovery given the indicated mean age at discovery (μ ad, A–C) and CV of age at dis-covery (CVad, solid versus dashed line) for simulations of daily nest encounter histories.

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DSR was constant, estimating DSR for nest i at age a from only an intercept (β 0) as logit(DSRi,a) = β 0. From this con-stant model, I calculated nest survival as Ŝc = DSRd where mean DSR was estimated as invlogit(β 0). While results from the constant logistic-exposure model are expected to match the Mayfield estimator (Shaffer and Thompson 2007), including this model served to illustrate the con-sequences of ignoring age even while using an otherwise identical modeling framework to the second logistic-exposure model. The second model included an effect of age on DSR (β age) as logit(DSRi,a) = β 0 + β age × a. I centered nest age on the mean observed value (the standard method of centering an observed covariate) so that an estimate of DSR from the intercept would represent DSR at the mean observed age (the β age term drops out when a = 0). From this model, I first calculated nest survival as ŜA0 = DSRx

d, where DSRx is the daily survival rate at the mean observed age x. This mean-age estimate is typically used to estimate Ŝ from DSR from models that include age, either when age is centered or when using Program MARK (White and Burnham 1999), which estimates mean DSR at the mean age by default (Cooch and White 2017). The mean-age es-timate would be influenced by the nest ages included in the dataset and thus potentially biased when DSR changes with age; it also does not explicitly account for the changes in DSR with nest age. To obtain a more representative es-timate of nest survival from the second logistic-exposure

model, I also calculated nest survival as ŜA1 =d∏

a=0DSRa.

This fully age-explicit estimate of nest survival thus ac-counted for both the effect of age on DSR and the full range of ages across the nesting interval, even when young ages were poorly represented in the dataset. This age-explicit estimate is described by Shaffer and Thompson (2007); a similar process can be applied over date-specific values of DSR (e.g., Geaumont et al. 2017) instead of age-specific DSR as applied here.

I applied the two logistic-exposure models (constant and with nest age as a covariate) to each simulated dataset in a Bayesian framework, which allowed integrated calculation of mean DSR, age-specific DSR, nest survival, and the 95% BCI of each estimate, and would provide full flexibility to fit relevant random and fixed effects when analyzing real datasets. Results from this simple simulation study would be very similar in other modeling frameworks. I ran the models in JAGS 3.4.0 (Plummer 2003) through the runjags package 2.0.4-6 (Denwood 2016) in R on a supercomputing platform (USGS Advanced Research Computing 2020) with wide normal priors on the intercept and β age. For each model, I ran 6 chains, discarded 200 iterations for burn-in and adaptation, thinned the iterations by 3, and retained a total of 500 iterations for inference, which was sufficient for model convergence (Gelman-Rubin statistics <1.10;

Brooks and Gelman 2012) and good mixing across chains based on visual inspection of trace plots. I saved the mean estimate of each parameter of interest (DSRa, Ŝm, Ŝc, ŜA0, and ŜA1) for each of 200 simulated datasets to represent the variance in the stochastic data simulation process. Across the 200 replicates for each scenario and model, I then cal-culated the mean and 95% CI of each parameter to esti-mate bias and variance. Code for fitting each model and calculating each estimate of nest survival is provided along with the script to simulate the data (Weiser 2021).

RESULTS

Literature ReviewThe Web of Science search returned 172 studies of daily nest survival in wild birds (Table 1). Forty-four studies in-volved species with precocial young, 129 evaluated species with non-precocial young, two tested both types (ducks and passerines, shown on separate lines in Table 1), and one involved both types tested within the same model (shown as “Mixed” in Table 1). About half did not test for any ef-fects of nest age: 59% (27/46) of those on precocial species and 43% (55/127) of those on non-precocial species (Table 1; Figure 2A). Of those that tested for an effect of nest age, 79% (15/19) of studies on precocial species and 71% (51/72) on non-precocial species tested for a continuous effect of daily nest age on DSR, such that DSR could change on a daily basis after the nest was found. The remaining studies tested for a relationship between nest age at discovery and DSR, implying that DSR was assumed to remain con-stant for each nest following discovery (4 precocial, 1 non-precocial species); or for a categorical effect of nest stage (egg-laying, incubation, nestling; 20 non-precocial species). Of those that tested for a continuous effect of daily nest age and reported the result, only 21% (3/14) of studies of precocial species and 18% (9/49) of studies of non-precocial species found no support for an age effect.

In studies that found a continuous effect of daily nest age and reported the direction of the effect, precocial spe-cies (n = 9) were split between negative (56%) and positive (44%) effects of age, while non-precocial species (n = 39) most often showed a negative relationship (44%) and less often a positive (31%) or polynomial (26%) relationship. Effects of nest age at discovery in precocial species were positive in two studies, supported but not reported in one, and unsupported in the fourth; and were negative in the one study that tested for an effect of age at discovery in non-precocial species. Categorical effects of nest stage on DSR were supported in 21% (4/19) of the studies that tested for that form of a relationship with nest age in non-precocial species. Studies that tested for effects of nest age typically did not report whether they standardized or cen-tered nest age (5 reported scaling age, 5 explicitly stated

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they did not scale age, 58 did not specify; Table 1), so I as-sumed that most were reporting effect sizes relative to age on the natural scale (i.e. the effect size indicates the change in DSR for each day of age). In studies that ap-peared to test for effects of daily nest age on the natural scale, effect sizes ranged from –0.10 to 0.10 for precocial species (n = 9) and –0.19 to 0.30 for non-precocial spe-cies (n = 39; Figure 2B).

Of the 51 studies that found support for a relationship between DSR and daily nest age (three of which did not report effect sizes and thus are not included in the above summary), only three explicitly stated the nest age for which the reported mean DSR was estimated: one aver-aged DSR across the age-specific estimates (Grendelmeier et al. 2015) and two estimated DSR at the mean (Stillman et al. 2019) or median (Crimmins et al. 2016) observed age. Two others reported that they estimated nest survival as the product of age-specific or date-specific DSR values (Domínguez et al. 2015, Shiao et al. 2015). The remaining 37 studies that found an effect of age on DSR and estimated nest survival either explicitly reported or appeared to cal-culate nest survival as Ŝ = DSRd. However, none of those 37 explicitly stated the nest age at which DSR was calculated. Twenty-four of those 37 used Program MARK (Table 1), where the default option is to estimate DSR at the mean of the explanatory covariates (including nest age), and one other reported standardizing nest age (Maziarz et al. 2019), suggesting that DSR was likely calculated at the mean nest age (standardized age = 0). For the remaining 12, it was unclear whether the reported DSR was calcu-lated at a particular nest age; if the model intercept was simply used instead, the reported value of DSR and thus nest survival would have been relevant only for the first day of the nesting interval.

SimulationsMean nest age at discovery affected the precision of the age-specific estimates of daily survival rates (DSRa; Figure 3). With a negative relationship between DSR and age (β age), values of DSRa were always precise (Figure 3A–I), even when few nests were monitored at young nest ages (μ ad = 0.50 and CVad = 0.25). Similarly, precision was high when DSR did not change with nest age because DSR was near the maximum of 1 and thus constrained to a narrow range of possible values, even when young nests were rarely monitored (Figure 3J–L). In contrast, when DSR in-creased with nest age (Figure 3M–U) and few nests were monitored at young ages (μ ad = 0.50 and CVad = 0.25), un-certainty around DSRa was large at young ages, because DSRa was able to vary more freely when it was expected to be well below 1.

As expected, simulated estimates of nest survival to the end of the nesting interval (Ŝ) from the Mayfield model and the constant logistic-exposure model were always similar to one another and often biased, especially with strong positive age effects (Figure 4, purple diamonds and blue squares). Estimates of Ŝ from these two models, which used pooled mean DSR, were affected by the distribution of monitored nest ages. Biases in these two estimates were more pronounced with a positive effect of nest age because nests typically did not fail after discovery and thus drop out of the sample, so older ages (where DSR was near 1; Figure 3) were overrepresented (Figure 5M–U). In the Mayfield and constant models when nests were found at older ages and DSR declined with age, estimates of Ŝ showed small negative biases (Figure 4C and F, purple diamonds and blue squares) because older nests, which had lower DSR, were overrepresented in the sample (Figure 5D–I). When nests were found at young to moderate ages and DSR declined

FIGURE 2. Summaries of studies evaluated for the literature review of effects of nest age on daily survival rates. (A) Proportion with each result of those studies that tested for a linear or polynomial effect of daily nest age or nest age at discovery for each type of species (precocial or non-precocial; one additional study on non-precocial birds did not report the result; one additional study pooled a mix of precocial and non-precocial species). (B) Effect of nest age on the logit scale for those studies that reported a supported linear effect of daily nest age, with a reference line at zero (points are ordered randomly within each group).

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with age, the bulk of the sample represented the middle of the nesting interval (Figure 5A, B, D, E, G, and H) and thus the pooled mean DSR from the Mayfield or constant models produced estimates of Ŝ that were unbiased (Figure 4A, B, D, and E).

The mean-age estimate of nest survival (Ŝ A0) similarly showed more pronounced biases when young ages were

poorly represented or when the age effect was strongly posi-tive (Figure 4, green circles). However, with strong nega-tive effects of nest age, this estimate was typically biased positive, unlike the estimates from the Mayfield method or the constant model. With a strong negative effect of age, the stronger curve of the relationship between DSR and age resulted in DSRa being held near 1.00 for much of the

FIGURE 3. Age-specific daily survival rate (DSR) as calculated from the true input values (thin black line) or as estimated from the model including an effect of age on DSR, depending on the direction (negative: A–I; positive: M–U) and magnitude of the age effect (β age; rows), and mean nest age at discovery as a proportion of the nesting interval (μ ad; columns) and its CV (CVad; lines). All scenarios shown here assumed 200 nests were monitored during a 30-day nesting interval with cumulative nest survival probability = 0.30.

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nesting interval before dropping sharply at the oldest ages (Figure 3A–C). In contrast to the Mayfield and constant models, the mean-age model used DSR estimated at the mean monitored age (vertical lines in Figure 5), at which point DSR was still near 1.00 (Figure 3A–C) and thus cu-mulative nest survival was overestimated.

In nearly all cases, regardless of the ages at which nests were found or the direction of the age effect on DSR, the fully age-explicit nest survival estimates (Ŝ A1), where nest survival was calculated from the product of age-specific estimates of DSR, were always unbiased (Figure 4, yellow circles). The exception occurred when the effects of nest age were strongly negative, nests were found at young ages on average, and variance around age at discovery was small (β age = –0.20, μ ad = 0.25 or 0.33, CVad = 0.25; Figure 4A and B). In those cases, the 95% CI of the estimate of Ŝ A1 (0.17–0.29 in both scenarios) fell just short of the true value (0.30), indicating a small negative bias. Although precision was high around the simulated age-specific es-timates of DSR in these scenarios (Figure 3A and B), older ages were less well represented than with μ ad = 0.50 (Figure 5A–C). The lower confidence bound on DSRa was there-fore slightly lower by the end of the nesting interval with μ ad = 0.25 (95% CI of DSR30 = 0.7060–0.8215) or μ ad = 0.33 (0.7088–0.8297) than with μ ad = 0.50 (0.7221–0.8281). Across the simulated replicates, this uncertainty around the lower bound of DSRa at the oldest nest ages was enough to bias the mean estimate of Ŝ A1 low when calculated as the product of the age-specific estimates of DSR. This bias

was only marginally significant, and in all other scenarios, Ŝ A1 was unbiased. However, the variance was often larger around Ŝ A1 than around the other estimates of nest sur-vival, especially when nests were found at older ages or β age was positive (Figure 3, error bars on yellow circles). The large variances around the age-explicit estimates resulted from wide uncertainty around extrapolated estimates of DSRa at young ages when most nests were found at older ages and β age was positive (Figure 3J–R).

The results reported above were all based on the default parameter values of n = 200, d = 30, and Ŝ = 0.30. Using a larger or smaller sample size affected variance but not bias (Figure 6A–C). Changing the nesting interval changed the total net change across the nesting interval, so a shorter nesting interval was associated with smaller biases than a longer nesting interval (Figure 6D–F). Positive biases were more pronounced with lower values of Ŝ than with higher values because the estimates had more room to vary up-ward toward the upper bound of 1.00 (Figure 6G–I). Regardless of the values of n, d, or Ŝ, the fully age-explicit estimates of nest survival (Ŝ A1) remained unbiased aside from small negative biases that were sometimes significant with strong negative effects of nest age (Figure 6).

DISCUSSION

This simulation study illustrated that when changes in DSR with nest age were not accounted for, estimates of nest survival were often biased. Biases were larger when

FIGURE 4. Predicted nest survival to the end of a 30-day nesting interval from each model (points) under various scenarios for the effect of age on DSR (β age, horizontal axis), mean age at discovery as a proportion of the nesting interval (μ ad; columns), and CV of age at discovery (rows). Estimates of nest survival were derived from the Mayfield method or logistic-exposure models with no covariates (Constant), with an age covariate but using DSR at mean monitored age (Mean-age estimate), or with an age covariate and as the product of age-specific estimates of DSR (Fully age-explicit). Values are offset on the horizontal axis so that all points are visible. All scenarios shown here assume 200 nests were monitored during a 30-day nesting interval.

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few nests were found at young ages or when the age effect was stronger, especially when the effect was positive. When the age effect was either ignored or only partially addressed by including nest age as a covariate but using the estimate of DSR for the mean monitored age, estimates of nest survival to the end of the nesting interval were some-times far greater than the true value when the age effect

was positive. Smaller but still biologically important biases were produced when the age effect was strongly negative. In contrast, nest survival estimates were usually unbiased when the model fully accounted for age effects by both estimating the effect of nest age on DSR and calculating nest survival as the product of age-specific estimates of DSR from across the full nesting interval. Only two of the

FIGURE 5. Expected number of active nest-days monitored at each nest age given the mean age at which nests are discovered (μ ad; columns) and the effect of age on DSR (β age, logit scale; rows) and for small and large CVad (lines). All scenarios assume n = 200 nests, cumulative nest survival (Ŝ) = 0.30, and nesting interval = 30 days. Vertical dotted lines indicate the mean age at which nests are active and monitored in each scenario. Asterisk indicates the mean age at which nests would be monitored if all were found at age 0.

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172 studies surveyed (Domínguez et al. 2015, Shiao et al. 2015) reported using the unbiased, age-explicit estimator of nest survival (Ŝ A1), even though effects of nest age on DSR have been commonly found.

The Mayfield estimator of nest survival has long been recognized to be biased when DSR is not constant (Rotella et al. 2004). However, my study emphasized that logistic-exposure models are no better than the Mayfield esti-mator when an effect of nest age is present but not fully accounted for. Even when the DSR model included nest age as a covariate in a logistic-exposure model, the estimate of nest survival was often strongly biased when it was cal-culated from DSR at the mean monitored nest age, which is the default option in MARK or when nest age is cen-tered or standardized in other frameworks and has been the most common method in the recent literature. The biases in nest survival demonstrated here were often large enough to have severe consequences for studies that aim to estimate nest survival or use those estimates to develop population models. Any variation among studies in bias

could also hinder meta-analyses of published values. Even for studies simply seeking to compare nest survival across sites, groups, or treatments, conclusions about differences (or lack thereof ) may be inaccurate if nest age at discovery or the relationship between DSR and nest age varies among groups. Finally, if a study seeks to estimate the effects of other covariates on nest survival, estimates of those effects could also be inaccurate if a covariate of interest interacts with nest-age (Gilbert et al. 2014). Based on the results of this simulation study, if nest age is not fully accounted for, biases and resulting consequences would be most severe when few nests are found at the beginning of the nesting interval, when DSR changes strongly with nest age, or when the effect of age on DSR is positive. In the recent lit-erature reviewed for this study, 44% of studies on precocial species and 31% of studies on non-precocial species found positive effects of nest age on DSR, suggesting that simply estimating cumulative nest survival as DSR exponentiated to the duration of the nesting interval could frequently af-fect the conclusions of nest-survival studies.

FIGURE 6. Effects of changes in the number of nests (n; A–C), length of nesting interval (D–F), and daily survival rate (DSR; G–I) on estimates of nest survival relative to the true value (dotted line). Estimates of nest survival were derived from the Mayfield method or logistic-exposure models with no covariates (Constant), with an age covariate but using DSR at mean monitored age (Mean-age es-timate), or with an age covariate and as the product of age-specific estimates of DSR (Fully age-explicit). In all scenarios shown here, unless otherwise noted, n = 200, nesting interval = 30 days, cumulative nest survival = 0.30, μ ad = 0.25, and CVad = 0.25. Values are offset on the horizontal axis so that all points are visible.

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In contrast to the biases in most estimates considered here, calculating nest survival as the product of age-specific DSR produced unbiased results in nearly every scenario, even when nests were found at older ages and DSR changed strongly with age. The exception was when effects of nest age were strongly negative and older nests were poorly represented in the sample, resulting in a small underestimate of nest survival. Under those conditions, researchers might choose to calculate nest survival using both age-specific estimates of DSR and the pooled mean DSR (e.g., from the Mayfield method or a constant model) and compare the two estimates in case the age-explicit estimate is biased low. However, in most scenarios, the potential bias in the age-explicit es-timate is much smaller than the biases resulting from the other models. Overall, the age-explicit estimate of nest survival was typically much more accurate than the other three estimators and thus represents a more ro-bust method of estimating cumulative survival than the methods most commonly used in the literature.

In some cases, calculating nest survival as the product of age-specific estimates of DSR resulted in a penalty in terms of larger variance. When DSR increased with nest age, esti-mates of age-specific DSR often showed large variance for ages at which no nests were monitored, as expected given that those estimates were necessarily extrapolated beyond the observed dataset. The uncertainty in the age-explicit estimator therefore accurately reflected the representa-tiveness of the dataset (Cooper and Miller 2007), but the large variance could limit inference for some field studies, such as those aiming to detect differences among groups or sites. Such cases would warrant a careful assessment of whether including the age effect is justified through model- or variable-selection procedures. When possible, carefully planning nest-monitoring studies to maximize the number of nests found early in the nesting interval could prevent the inflated variance and produce useful nest survival es-timates that are both accurate and precise. If finding nests early or aging nests on discovery is not possible, discussing the consequences for estimates of DSR or nest survival would help ensure that the results are interpreted in the context of nest age at discovery. When nest age is esti-mated, reporting the mean and SD of ages at which nests are found would also improve the ability to compare mean DSR values across studies.

Although the biases illustrated here depended on the as-sumptions used in this simulation, biases under other con-ditions could be different but still substantial. For example, if DSR varies nonlinearly with age (e.g., quadratic effects or nest-stage-specific patterns), the presence or direction of bias would depend on the pattern of change in DSR and the distribution of ages at which nests were monitored. Relationships between DSR and other covariates, such as day-of-season, could exacerbate or balance biases resulting

from nest-age effects, especially in systems where nesting is highly synchronized. The specific proportion of nests that would need to be found at young ages to avoid biases may therefore vary among systems. Regardless of the specific relationships present in a given system, the magnitudes of some of the biases demonstrated here emphasize the im-portance of considering age effects and finding a subset of nests at young ages.

Accounting for nest age in an analysis is straightforward, assuming nests can be accurately aged at discovery through methods such as candling or floating eggs (Westerskov 1950, Lokemoen and Koford 1996, Liebezeit et al. 2007, Rizzolo and Schmutz 2007) and if nest age is not strongly correlated with other variables of interest, such as day of the season. Testing for an effect of nest age and appropriately estimating nest survival from the product of age-specific DSR would be simple, feasible steps to ensure the integrity of nest survival analyses. The R script developed for this simulation study (Weiser 2021) can provide a template for one method of estimating age-specific DSR and unbiased, age-explicit estimates of nest survival in a Bayesian frame-work, and could be extended to include other covariates or random effects as relevant. Alternatively, if nest age is not considered in a nest survival analysis, the biases dem-onstrated here emphasize the importance of carefully interpreting the results in the context of whether conclu-sions are relevant to the broader population or study spe-cies. In some cases, such as when a study aims to compare groups and the distributions of nest ages are similar be-tween groups, testing for an effect of nest age may not be necessary. Estimates of nest survival might also remain un-biased when nest age is ignored under certain conditions, such as with small negative effects of age. In most cases, however, testing for an effect of nest age would eliminate one potential source of bias. Reporting the distribution of nest ages at discovery, explicitly defining how nest age was used to calculate DSR and cumulative nest survival, and providing numerical values for the age effect (if any) would also facilitate comparisons across studies of nest survival.

ACKNOWLEDGMENTS

I thank J. Lamb, B. Verheijen, B. Ross, V. Patil, M. Hood, and three anonymous reviewers for comments that improved earlier drafts of the manuscript.Funding statement: Support for the author was provided by the Ecosystems Mission Area of the U.S. Geological Survey.Ethics statement: No animal ethics approvals were neces-sary for this study. Any use of trade names is for descriptive purposes only and does not imply endorsement by the U.S. Government.Data depository: The values used to inform the simulations are provided in Table 2 of this paper. The R script used to sim-ulate data, apply the DSR models, and calculate each estimate

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of nest survival is publicly archived (Weiser 2021) and re-quires no additional data as input.

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