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A SIMULATION ANALYSIS OF MALLARD
REPRODUCTIVE BEHAVIOR IN RELATION
TO BREEDING HABITAT

By

Glenn Raymond Dudderar

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Fisheries and Wildlife

1985

ABSTRACT

A Simulation Analysis of Mallard Reproductive
Behavior in Relation to Breeding Habitat

BY

Glenn Raymond Dudderar

A computer simulation was designed to relate
experimental measures of innate mallard breeding behavior to
breeding habitat quality and quantity as measured by numbers
of pairs, nesting chronology, and duckling production.
Weather and predation were simulated as exogeneous variables
modifying reproductive performance» The results of the
simulations were compared with 3 years each of field data
near Kindersley, Saskatchewan and in the Aspen Parkland Life
Area near Edmonton, Alberta” In all simulations, the number
of pairs calculated as needed to produce a nesting
chronology and duckling production similar to those reported
in the field studies was less than the number of indicated
pairs reported in the field studies. Weather and predation
as simulated by the model did not account for the
difference. However, in 3 of 5 simulations where weather

data from field studies was simulated, the resulting nesting

chronology'was statistically’similar to the reported nesting

chronologyu Predation rates used in the simulation that
resulted in nesting chronologies and duckling production
similar to those reported if the field studies were
identical to or slightly higher than those reported in the
field studies. In all but one simulation, the estimate of
ducklings fledged was within the range estimated in the
field studies or differed by no more than 39 percent.

The»model simulated the difference in mallard
reproductive performance between grassland and parkland
breeding habitats. However, breeding habitat quality and
quality and reported from field studies in terms of pond
numbers and change in pond numbers in the same habitat did
not correspond with the simulated measures of pair use and
duckling production per pond. Explanations of these
differences include mallard spacing mechanisms and changes
in winter and breeding habitat quality that were not

incorporated in the model.

ACKNOWLEDGEMENTS

I am gratefully indebted to Dr. Harold Prince whose
inspiration, guidance, encouragement, and patience made this
study possible. I also thank my other committee members.
Dr. Stephen Stephenson and Dr. Donald Beaver for their
willing assistance, helpful guidance, and their expedious.
yet thorough review of this dissertation. I thank Dr. Niles
Kevern as well, but especially for his unwavering support
throughout the duration of this work.

I am also grateful to Dr. Walter Conley, Dr. Stanley
Zarnoch, Dennis Harris, David Gordon, Duane Schmidt, and
John Grettenberger for their initial assistance in planning
and designing the model, and to Anthony Zagar for his
assistance in program re-coding.

A special thank you is for my wife Eleanora whose
support, comfort, and patience also made this work possible.

To Susan Hazard, my secretary, I extend my gratitude
for helping with my office duties during the final stages of
this work, and for her able and willing cooperation in the

typing of this dissertation.

TABLE OF CONTENTS

LIST OF TABLES ......................... ....... ........ .......

LIST OF FIGURES .......................... . ...................

APPENDIX .....................................................
Program Listing .........................................

iii

14

14
21

26
50
62

63

68
68

Numbers

LIST OF TABLES

Page

Response of mallard duckling production to amounts of
breeding Space varied before varying weather in order

to simulate field observations. (Data from Dzubin

and Gollop, 1969 and Sorensen, 1978) ................... 29

Response of mallard duckling production to predation
rates varied to simulate field observations. (Data
from Dzubin and Gollop, 1969 and Sorensen, 1978) ....... 30

Response of mallard duckling production to amounts

of breeding space and weather conditions varied to

simulate field observations. (Data from Dzubin and

GollOp, 1969 and Sorensen, 1978) .................. ..... 34

Response of mallard duckling production to pair numbers

and predation rates varied to simulate field obser-

vations. (Data from Dzubin and Gollop, 1969 and

Sorensen, 1978) ........................................ 39

Comparison of field data from Kindersely, Saskatchewan
to the most similar simulated response of mallard re-
productive parameters to breeding space weather, and

predation rate variables. (Data from Dzubin and
Gollop, 1969) ......... ............................ ..... 42

Comparison of field data from Edmonton, Alberta Aspen
Parkland Life Area to the most similar simulated re-

sponse of mallard reproductive parameters to breeding

space, weather and predation rate variables. (Data

from Sorensen, 1978) .. ....... .......................... 44

Comparison of actual and simulated mallard pair and
duckling production response to habitat at Kindersley,
Saskatchewan. (Data from Dzubin and Gollop, 1969) ..... 46

Comparison of actual and simulated mallard pair and

duckling production response to habitat at Edmonton,

Alberta Aspen Parkland Life Area. (Data from

Sorensen, 1978) ................... .... ................. 48

iv

Number

LIST OF FIGURES

Page
Organization of the model used to simulate the
interaction of mallard reproductive behavior with
habitat parameters ...... ..... ........................ 15
Comparison of the first nest initiation frequencies of
captive mallards housed in outdoor pens in Manitoba
to a simulated frequency. (Data from Batt and
Prince, 1979) OOOOOOOOOOOOOOOOOOOOOOO 0.0.0.0.... ...... 16

Mallard duckling mortality as a function of variation

in the number of May ponds from a known maximum and the
percent pond loss from May to June. (Data from

Stoudt, 1971) ......................................... 22

The effect of varying breeding spaces on the number and
sequence of mallard nests hatching per week.
(Data from Dzubin and Gollop, 1969) ............. ...... 27

The effect of increasing constant simulated predation
rates on numbers and sequence of mallard nests
hatched. (Data from Sorensen, 1978) ............. ..... 31

The effect of increasing varied early and late
predation rates on numbers and sequence of mallard
nests hatching per week. (Data from Sorensen, 1978) .. 32

The effect of the number of days and dates of simulated
bad weather on numbers and sequence of mallard nests
hatching per week. (Data from Sorensen, 1978) ........ 36

Comparison of actual and most similar simulated numbers
and sequences of mallard nests hatching per week.
(Data from Dzubin and Gollop, 1969 and Sorensen, 1978). 38

INTRODUCTION

Evaluations of the reproductive effort and success of a
population of mallards (51393 platyrhygchgg) breeding in a
given area have always been inexact because of the difficulties
of measuring actual breeding pairs, nests, and broods. These
population estimators are further confounded by weather,
predation, asynchronous breeding period, brood movements, and
the fact that the nest site and rearing area for broods are
not necessarily located within the defended portion of the
breeding space of a given pair. However, an experimental
study of captive mallards by Batt and Prince (1978, 1979)
produced quantitative measures of many endogenous factors
regulating mallard reproduction, making it possible to
compare experimental data to field data and thereby better
evaluate field data and mallard reproductive performance.

Because of the availability of the quantitative
measures by Batt and Prince of mallard breeding behavior in
captivity and the strong relationship of those data to
mallards breeding naturally; it was assumed that a model

could further clarify the relationships among mallard

breeding behavior, habitat quality and quantity and the
exogenous variables of weather and predation. Specifically;
it was hypothesized that innate mallard breeding behavior,
modified by climatic factors, regulates habitat use, and if
the effects of predation could be reasonably accounted for,
it could be demonstrated that the results of mallard spatial
and temporal behavior as measured by nesting chronology and
duckling production are a indication of habitat quantity and
quality. It was further hypothesized that if a general
expression of habitat quantity could be developed, changes
in habitat quality could be measured.

This study examined through computer modeling the
interactions of endogenous factors (numbers of pairs, nest
initiation rates, renesting rate, egg production, hatching
rate and brood survival) and exogenous factors (date,
weather, number of ponds, acres of wetlands and pond
quality, and predation) that may effect.breeding strategy
and reproductive success on a specific site. Comparisons
between the predictions of the model and the results of
field studies are made to evaluate both the model and the
field data and to quantitatively relate reproductive
strategy to habitat parameters in reference to current

theory.

LITERATURE REVIEW

Most mallards move to traditional wetland areas in
April or May already paired.(Hochbaum, 1944; Sowls, 1955:
Weller, 1965L A pair establishes a territory as the female

begins egg formation and nest establishment (Dzubin,

1956+I\
k/Gy///f’”
McKinney, 1965). Territories are variable in size,"?{//\2L
e

especially'between geographic regions, and probabl le '1

the relative distribution of the physical resources‘of food
and cover necessary for successful reproduction.CBellrose,

19760. Because these territories may include several ponds,

may not include the actual nesting site, and are not
defended by the drake after the onset of incubation, they
are not mutually'exclusive in either time or space and do
not fit the classic definition of territory as defined by
Lack (1966). Further, Dzubin (1969) cites evidences that
mallard drakes may defend larger breeding spaces when pair
densities are low and smaller areas when pair densities are
high.

Numerous studies have attempted to relate amounts of
wetland habitats and productivity of mallard breeding
habitat to mallard reproduction, but a complex interaction

of several factors tend to confound such attempts. .Breeding

habitats of the same type vary in productivity from area to
area (Dzubin, 1969). Stewart and Kantrud (1974) in a state-
wide study of waterfowl use of wetland habitats in North
Dakota found that seasonal and semi-permanent ponds and
lakes (Classes III and IV) were used most heavily'by
mallards and other dabbling ducks, but that use of these
types varied considerably from region to region, Similar
results were obtained by March et al. (1973) in a study of
duck populations and habitat in Wisconsin.

Waterfowl productivity also varies with time within
wetland type. Semi—permanent*wetlands increase in
productivity when flooded if the flooding is preceded by
drying due to drought or regulated drawdown. Production
gradually decreases if higher water levels exist for more
than 5 to 6 years (Weller and Fredricksonq 1974; Weller,
1976; Bishop et al. 19T9L Periodic change of water levels
produces the best amounts and distribution of drowned
vegetation, submersed and emergent vegetation, open water.
and associated invertebrate populations needed by mallards

for food and cover for reproduction. Experimental manipulations

of marsh habitat to simulate the ideal conditions of

the semi-permanent marsh by Kaminski and Prince (1961) and
Murkin et al. (1982) revealed that a 50% interspersion of
emergent vegetation and open water over drowned growth of

the previous year were most heavily utilized by mallard

pairs.

Productivity appears to vary with the density of ponds
in that the greatest productivity occurs in areas where
wetlands are the most numerous (Stoudt, 1969: Steward and
Kantrud, 1973; Krapu et al. 1983). Within any given area,
wetland density varies from year to year because many
wetlands are emphermal, temporary, or seasonal. Density of
wetlands (number of ponds) varies directly with
precipitation (Pospahala et al. 1974).

Productivity of a given area is difficult to evaluate
because mallards hens may not place the nest within the
utilized wetlands and may move their broods over a long
distance and numerous wetlands. Nests located long
distances from water (over 1,700 meters), high nest
densities in dense upland vegetation or on islands, high
nest densities in maintained wetlands during drought, and
brood movements well outside habitat used for courtship and
nesting are well documented (Keith, 1961; McKinney, 1965;
Dzubin and Gallop, 1969; Johnson et al. 1978; Trauger and
Stoudt, 1978; Giroux, 1981; Lokemoen et al. 1984).

Productivity of wetlands varies with size. Cowardin
and Johnson (1983) demonstrated that semi-permanent.
seasonal, permanent, and temporary wetlands increased in
productivity with size. Semi-permanent and seasonal are the
most productive if greater than approximately 5 ha. Semi-
permanent and permanent wetlands, however, are the most

productive at smaller sizes. The authors acknowledge.

however, that the predictive equations left considerable
variation unexplained, probably because of the interactions
of the relationships just described.

Several attempts have been made to relate wetland
numbers to productivity. Crissey (1969) found that breeding
populations in the spring correlate well (r . 0.89) with
July ponds the previous summer in the southern prairie
provinces from 1954 to 1965. However, in 1957, the number
of ponds had been declining and was average, but favorable
breeding season weather and a high breeding populations
produced the largest production during the mid 1950 period.
Cooch.(1969) attempted to relate May-July'pond ratios to
production, but encountered similar abnormalities. Hammach
and Brown (1974) tried to relate May ponds and July ponds to
production, but also found abnormalities in 1957 using July
ponds and in 1964 using May ponds. Finally'Heitmeyer and
Fredrickson (1983) found through regression analysis that
neither May or July ponds, or May and July ponds correlated
well with mallard age ratios in the fall harvest, but that
May and July ponds and departure from normal precipitation
the preceding winter correlated well with the age ratio (R2:
0.92) for more recent years (1969—70, 1979—80). The authors
suggest that poor winter habitat may not allow mallards to
accumulate the needed reserves of lipids and proteins to

successfully reproduce, despite favorable conditions in

breeding habitat.

Nest initiation occurs for approximately 2 months.
Pairs not ready to initiate a nest, pairs unable to
establish territories, and unpaired birds, mostly males,
move from one body of water to another, and act as a reserve
waiting for an opportunity to reproduce (Aldrich, 1973;
Humberg et al. 1976; Jackson et al. 1983).

It is difficult to count actual breeding pairs at any
one point in time or in total because of the difficulty in
determining the reproductive status of observed birds
(Dzubin, 1969). Johnson and Sargent (1977) found that lone
drakes may not represent a pair. In addition to lone pairs,
lone drakes, flocked males, and flocked pairs have been used
to estimate pairs, but Jackson et al. (1985) demonstrated
that under drought conditions up to 858 of the lone drakes
may not represent a pair.

The date of nest initiation is an individual
characteristic of the hen (Batt and Prince, 1979). Once the
female is ready to initiate a nest, a breeding territory is

established and defended by the drake. The hen lays one egg
a day until the clutch, usually'ii eggs, is completed

(Bellrose 1976). Batt and Prince (1978) established that

the decreasing clutch size of captive mallards overtime is a
function of the date of nest initiation.

If the eggs are destroyed during laying, the hen will

renest. Sowls (1955) found that with blue-

winged teal (Anas discors) and shovel ler (Spatulg 9122933)

hens, loss of a nest during laying was followed the next day
by renesting, leading him to believe there is no renesting
interval when a nest is lost during laying. In captive
mallards, Prince et a1. (1970) report a mean renesting
interval of 6.0 +3.6 days when eggs were collected on the
second day after the last egg was laid.

The effect of cold weather and precipitation on laying
is not well defined. Sowls (1955), Dane (1966), Dane and
Pearson (1971), Sorensen (1978) and Batt and Prince (1979)
report that sub-freezing temperatures and heavy precipitation
will delay the onset of nesting. Gollop (1954), Sowls
(1955), Keith (1961), Hunt et al. (1968) and Dzubin and
Gollop (1969) all report a reduction of duck nesting during
periods of inclement weather. Hunt et al. (1968) reported
that a 20-25% decrease in egg production from hand reared
mallards during "periods of heavy or prolonged rainfall, or
when below freezing temperatures prevailed for the greater
part of a 24-hour period."

Within a given locality, not all paired hens initiate
nests at the same time. In a confined experimental
population provided an ad libitum balanced diet and nesting
sites for each pair, Batt and Prince (1979) found
significant differences between hens in nest initiation
dates and that nest initiation dates are consistent with an
individual hen year to year. Batt and Prince (1979) also

noted that weather conditions delay initiation. No first

nest attempt was initiated after June 21 in the experiment
by Batt and Prince (1979), but several field studies report
a few nests, probably renests, begun after that date but no
later than June 26 (Keith, 1951; Dzubin and Gollop, 1969:
Sorensen, 1978).

During the laying period, the drake accompanies the hen
as in courtship and defends the territory (Dzubin, 1955).
If the hen is forced to abandon her nest during laying, she
usually'renests with her original mate (Humberg, 1976).
When the hen begins to incubate the clutch, the drake
gradually'loses interest and leaves the hen and the defended
area (Lebret, 1961). Drakes assemble in small groups,
usually'on larger waters and are available for hens
attempting to renest. Large groups of drakes may make it
difficult for a pair to re-mate and may relentlessly pursue
and rape hens seeking a mate, perhaps even disrupting
breeding attempts (Aldrich, 1973). During incubation the
space occupied by the pair is no longer defended and may be
occupied by a waiting pair, or by a pair attempting to
renest.

If the nest is lost during incubation, the hen goes
through a recycling period as her reproductive system
readjusts to produce more eggs. The recycling period will
be a minimum of 6-10 days (Prince et al. 1970; Batt and

Prince, 1979). If the nest is lost after 8 days of

incubation, however, the recycling time increases with each

10

succeeding day beyond the eighth day (Batt and Prince,
1979). Sowls (1955) reports a linear relationship between
the number of days into incubation and the renesting
interval.

Incubation lasts for approximately 26 days, but Prince
et al. (1969) found that the incubation time of artificially
incubated eggs varied from 23 to 30 days depending on
temperature and humidity. Prince and Batt (1979) found that
there was no significant difference in the hatchability of
eggs from first nests of adult and novice hens during their
first year in captivity; They detected a decline in
hatchability of eggs from second, third, and fourth nests,
but attributed the effect to captivity, probably because of
declining viability of the eggs. The average hatchability
of artificially incubated eggs from Manitoba birds for first
nests was approximately 75%.

After brooding the newly hatched chicks for several
hours, the hen leads the brood to wateru Considerable loss
of both individual ducklings and entire broods may occur
during this period. Distances from nest to water, weather,

dense vegetation, parasitism and predation are factors

relating to mortality of Class I broods (ducklings 1-18 days

of age as judged from size and development). Dzubin and
Gollop (1969) and Sorenson (1978) both report heavy Class I

brood loss due to exposure to cold and rain, and at the

Kindersley study site, high brood mortality was correlated

11

"1th the distance from nest to water, especially'through
dense upland vegetation. Gilmer et al. (1975) found a
similar relationship in northern Minnesota (r = -0.39).
Stoudt (1971) noted that brood mortality increases in
drought years and Pospahala et al. (1974) were able to
correlate brood size to July ponds for several areas (r =
0.90, 0.47, 0.44). They were not able to correlate brood
mortality from Class II (ducklings 19-45 days old) to Class
III (ducklings 46-55 days old) broods with the number of
July ponds (r < 0.10) using data from a study by Stoudt
(1971).

Predation on adults, nests and broods has been
difficult to measure and relate to environmental factors.
It varies among habitats, being higher (SO-60$) in prairie-
parklands and lower (20-40%) in mixed grasslands (Dzubin and
Gollop, 1969). Keith (1961) estimated summer mortality rate
of 2% for male mallards and 88 for females in southern
Alberta, while Dzubin and Gollop (1969) estimated a 496

mortality for drakes and a 5x mortality for hens in
grassland and 7% in parklands during the breeding season.

Anderson (1975) derived a 93 mortality for drakes and a 16-
18* mortality for hens from May to August. Johnson and
Sargent (1977) found similar mortality rates in a predation

study for grassland habitat.

Habitat factors associated with breeding sites, but not

necessarily a part of the wetlands utilized,also effect

12

predation rates. Nests on mammal free islands and in dense
upland vegetation experience less predation (Keith, 1961;
Duebbert, 1969; Klett et al. 1984).

Predation also varies with the species of predators
present. Common predators in parklands include crows

orgg_ brachyrhynchos), magpies (Pica pica). skunks

O

(
(

franklini), while the common predators of grasslands include

)3

ephitis mephitis), and ground squirrels (Spermophilgg

skunks, badgers (Taxidea tgxgg), mink (Mggtglg giggg),
weasels (M; rixosa, M; erminea), coyotes (Qggig latrans)
and certain raptors (Dzubin and Gollop, 1969; Johnson and
Sargent, 1977). Predator species also change over time.
Foxes (gglpgg _f_g_l__vg) and raccoons (Procyon 1939;) for
example, have become more numerous in recent years in many
areas (Sargent et a1. 1979).

Another problem exists in evaluating nest predation
losses and is dependent on sampling procedures and
calculation techniques. Miller and Johnson (1978) point out

that the fewer the search intervals, the more likely

unsuccessful nest will be missed, thus underestimating

losses. If a greater proportion of successful nests are

found than unsuccessful nests, then mortality will be
overestimated. The authors recommend the Mayfield method
(Mayfield, 1960) of calculation, which assumes a constant

success (mortality) rate and is calculated by relating the

age of nests at hatching to the age of nests when found. By

13

evaluating data collected and analyzed by Green (1977), the
authors found some daily variation but no significant
difference between the daily success rates of nests during

laying and nests during incubation.

MATERIALS AND METHODS

122M292;

The model is organized to simulate the daily events in
mallard reproductive behavior during the breeding season
(Fig. 1). The program begins by pairing drakes and hens
and assigning them a breeding status. Then, for each day in
a simulation, all nesting events are tallied - potential
nest initiation, first nests, renests, total daily nests.
nests hatched by mature hens, nests by Juvenile hens, total
nests hatched, and hens killed, .At the end of the nesting
season, all categories are summed. The eggs and young
produced by each category hen and the number of hens that
fail to nest successfully are also summed. In addition,
ducklings surviving to fledging are calculated. The program
is written in Fortran 5 and al 1 computations were done on
the Michigan State University 750 Cyber computer.

Mallard nest initiation frequencies were calculated
from original data from Batt and Prince (1979) using
information from Manitoba adult and novice birds taken from

wild populations.

14

15

 

Inputs - Daily weather - "GOOD" or BAD"

Number of Drakes, Matron Hens. Novice Hans, and Breeding Spaces
Dates of Peak Nest Initiation and Nest Termination
Cumulative Water Loss and Predation Rates

1.

__{Pair birds and assign the unpaired birds to waiting arrayF_]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

______________ 3A5! QAXQPJELSEAS'J; ..-_.-.____.._-__
Good Weather r. Bad Weather
Waiting ‘
arrays for l Increment one egg to hens in laying array ¥ Increment no eggsl
unpaired I
:i:::; [Assign hens with complete clutch to incubation] I
:::;:: 2:2: | If bad weather equals 2
l consecutive days or 3
1 Calculate hatch. remove hen. store drakegj total days remove all
4‘ 1 eggs from clutches less
than 752 complete (
Waiting . ‘
array for ___ .Initiate pairs and assign hen to laying array CI Store hen until good
pairs HIf s ace unavailab e storg pgir 1 ruggghgrgg,
Initiate pairs ready to re-nest and assign I Store hen until good
to laying array if space available weather
I
Waiting 1
array for ‘ IPair waiting birds and assign hen to laying I Store hen until good
hens ready if initiation and space available weather
to re-nest l I
2
Calculate predation and remove eggs from laying I
Recycle nests. remove incubating nests. and store hen
array in recycle or kill and remove I .
L I .
[Calculate duckling loss—l I :

 

 

 

 

Outputs - Schedules of initiation. first nests, renests, total
daily nests, matron nests completed, novice nests
completed. total nests completed.

- Matron eggs. novice eggs. mean clutch size ducklings
hatched. ducklings fledged. dead hens.

 

 

 

Figure 1. Organization of the model used to simulate the interaction of
mallard reproductive behavior with habitat parameters.

16

The frequencies were plotted and found to have a
Poisson distribution over a period of 52 days. The
following equation for a generalized Poisson distribution

was used to generate daily frequencies of nest initiation:

or = f(x.a.b:°:d) 'U‘E‘EY 26-)[1 (113511]

where DF= daily frequencies
x = days into breeding season
a = value of x where f(x) is maximal
b = value of x where f(x) = 0 for x<b
c = parameter for curve shape subsequent to a

d = parameter for curve shape prior to a

A program was written to calculate the daily
frequencies and through iteration was used to determine the
values for the variables that produced daily frequencies
approximating the experimental data (Fig. 2). Because of

the Poisson distribution, small sample size. and the
comparison of data frequencies, the Kolmogorov-Smirnov one

sample test was used to determine which combination of

values produced the frequencies which best fit the
frequencies of the data (a=13, b=60, c=13, d=3, a < 0.01)-
In the simulation model, the daily number of potential nest

initiations is calculated as follows:

17

 

 

 

 

 

 

 

 

 

 

 

 

 

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m [d
u. D
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q ‘<
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.n
A ‘<
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a H
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[-4 kl In
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CO
3
4—!
D
0‘
m
18-!
n:
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23
it N
,/:=__,... a
e_=: / .— :1:
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- - h
._=:——-*' / o
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r
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e-_=: "‘
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O O O O O O O O 0
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2:9 2
Mcnra
:nunnz
crzzc
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aoé
Figure 2. Comparison of the first nest initiation frequences of captive

mallards housed in outdoor pens in Manitoba to a simulated
frequency. (Data from Batt and Prince, 1979).

18

potential nest initiations a DP/ DF x number of pairs +
fractions of DE from the
previous day

Within the simulation program, the weather parameter
and available breeding spaces limit nest initiation. If
weather is bad or no breeding space is available» the
appropriate number of pairs are stored as ready to initiate
a nest, and are al lowed to initiate a nest only when weather
is good or when breeding space is available. Mature hens
are initiated first, thus simulating a natural sequence and
at the same time simulating lesser reproductive effort by
Juvenile hens, since hens laying later in the season produce
fewer eggs.

Breeding spaces are set by input data and are initially
estimated as the maximum number of pairs per week or nest
per week from field data. Within the model, nesting is
spatially'simulated, as recommended by Bolling (1978), by an
array for laying birds and an array for incubating birds.
The size of the laying array is equal to the number of
breeding spaces, thus simulating defended space. The
incubation array is limited to the total number of birds in
a simulation, thus accommodating any possible number of
birds.

The laying array contains the following information:
age of the hen (mature or juvenile), the number of eggs she

has laid (one per day), consecutive and total bad days. and

the number of eggs she will lay (clutch sizeL. One day of

19

bad weather terminates laying and 2 consecutive days or 3
total days of bad weather eliminates all eggs (nest abandon-
ment) unless the hen has laid 75% of her clutch, .As soon as
weather is good, laying is resumed by the addition of eggs.
one per day. If a nest is calculated to be lost to
predation during laying, eggs are set equal to zero, and
eggs are added, one per day on the next day of good weather.
When the first egg is added, the nest is counted as a
renest. The clutch size is determined by the equation from
Batt and Prince (1979), clutch size = 26.80 - 0.19x +
(0.0005)x2, where x=day of year.

When the number of eggs laid equals clutch size, the
hen, her status, number of eggs, and the day of the year
plus 26 are transferred to the incubation array. When the
day of the year equals the date assigned plus 26, the nest
is counted as hatched. Hatch rate is 758 of clutch size.
Although the hatching rate for eggs in nests in the wild
approaches 95s, the lower rate is used to account for early
duckling mortality.

If a nest is calculated to be lost to predation during

incubation then the hen is held in another array for 10

days. If she was 9 or more days into incubation, she is
held in the array for a number of days determined by the
equation x=4n44 - .644x, where xsdays into incubation when
the nest was lost Sowls (1955). When a hen or hens are

again ready to lay, if there are drakes available for

20.

pairing, the frequency of re-nesting is 1 if the day of the
year is less than 129. If not, the frequency of renesting
is calculated by the equation N = number of pairs
available for renesting x (2.55-0.012x) where N = renesting
pairs and xaday of year (Batt and Prince, 1978).

Rates of predation are derived from field data.
Predation rates reported in field data are often for early
in the nesting season and late in the nesting season, so the
model was designed to utilize two rates, with the late
predation rate being applied to all nests after the second
nest to hatch. The predation rate is divided by the number
of days the hen wil l lay and incubate and is assigned to the
predation array on the day laying begins. The daily
predation rate is then summed for al 1 hens each day to
determine the daily predation rate» The total number of
nests lost each day is the product of the total number of
nests and the daily predation rate» Nests are selected from
either the laying or incubation arrays according to their

relative abundance. For each ten nests lost, one hen is

recorded as killed and removed from the appropriate array.
The actual nests selected to be depredated is done randomly
through the use of a random number generation routine.

No mathematic expression was found in the literature to
relate duckling mortality to habitat change, so several were

developed and tested. .Although weather, predators and other

factors can be important mortality factors in any given

21

year, much duckling mortality occurs when nests are a long
distance from water or when water areas dry up in late
spring and summer. The only relationship that was
consistently reported was water loss in May and through
July. The percent deviation of the number of May ponds from
a known maximum of May ponds was combined with the percent
loss of ponds May through July and regressed against
duckling mortality; Data were used from a 14 year study by
Stoudt (1971) which was not evaluated in the simulations
(Fig. 3). As a check, a similar equation was developed
from data combined from 3 other investigations and was
similar in slope, intercept, and means of the dependent and
independent variables. Statistical significance of the
differences were not evaluated, The equation used in the
model is as follows: y = 0.167 + (0.53 x) where y = percent

duckling mortality and x = percent combined water loss.

The Simulations

Two studies, one from Kindersley, Saskatchewan and the
other from Edmonton, Alberta, Aspen Parklands Life Area

(Dzubin and Gollop, 1969; Sorensen, 1971) provided
sufficient data for model operation and hypothesis testing.
Three years of data were available in each of the
investigations. In the initial computer run for the first

year of the study, the data entered was that given in the

22

0.167 + 0.53X
r = 0.66

160

>4

120 1h0

100

60
PERCENT COMBINED WATER LOSS

 

 

 

PERCENT
DUCKLING
MORTALITY

Figure 3. Mallard duckling mortality as a function of variation in
the number of May ponds from a known maximum and the
percent pond loss from.May to June. (Data from Stoudt,
1971).

23

investigation except for the number of breeding spaces which
was estimated. If the number of nests per week and the
final nest and egg production predicted by the model were
different from the results of the field investigation, the
data entered on subsequent runs was varied to determine
which input values and combinations of values resulted in.a
nesting sequence and final production values most similar to
the results of the field investigations.

All possible variations were not used, but only those
that had meaning in a an ecological context. For example,
if all the results of the computer simulation were lower
than the field study values, predation rates were not
increased, since this could only serve to lower simulation
results, further increasing discrepancy. Bad weather data
was never added where none was reported in the field
studies. Breeding spaces were not increased beyond the
point of no effect, nor were they decreased when any further
decrease resulted in limiting nest initiations.

The procedure used for varying data inputs was as
follows. The first number of pairs used was all indicated
pairs (lone pairs + lone drakes + flocked pairs) and, if
both nesting data and production data were high, as was
always the case, predation rates were increased. If this
failed to produce results similar to the field results,

predation rates were reset to the initial values and the

number of breeding spaces was increased or decreased until

24

the pattern of the nest hatching sequence resembled the
pattern of the results in the field studyu Predation rates
were then increased or decreased in a direction that would
produce production values similar to the values reported in
the field study. If this failed, the number of pairs was
reduced to lone pairs and lone drakes, and then breeding
spaces and predation were varied accordingly: This process
was reiterated until the final results approximated the
results of the field study.

In cases where bad weather was involved,the exact dates
from the field study were used, if given. If weather was
reported in a general way (e.g. a cold snap during the week
of .H) dates were varied but only with the week reported.
Final nest hatching sequences generated by the computer that
closely resembled the results of the field study were
statistically compared with the results of the field studies
using the Walsh test as described by Seigel (1956). This
method was chosen because of the Poisson or non-normal
distribution of the nesting sequences, small sample size.
and the power of the test in detecting differences in
symmetry in distributions.

The number of breeding spaces and pairs used to
calculate the results finally'accepted.as most closely
approximating the field study results were used to
calculate, where possible, pairs per breeding space, pairs

per pond, ponds per breeding space, and acres per breeding

25

space. These results, along with the results for weather.
predation and final production were then compared
qualitatively, since statistical comparisons were not

possible.

RESULTS

Whenever the estimated number of breeding spaces was
too low to accommodate all of the pairs calculated as ready
to initiate nests within the number of days required to
complete a clutch, no nests could be calculated as
initiated. This resulted in nest initiations in excess of
the number of breeding spaces being delayed until the
estimated number of breeding spaces was high enough to
accommodate all of the pairs calculated as ready to initiate
at the time plus those previously delayed.

Consequently, the greater the discrepancy between the
number of breeding spaces estimated and the number required.
the greater was the difference between the actual nesting
sequence and the one generated by the model. For example,
in the 1957 Kindersley simulation, when the number of
breeding spaces was increased from 105 to 205 with
subsequent iterations, the pattern of the simulated
sequences began to resemble the pattern of the actual
sequence (Fig. 4), but the number of nests in the simulation
was greater than in the field data (349 vs. 229) and the

nesting sequences were significantly different (d.< 0u10).

The number of pairs used in generating Fig. 4 was the

26

27

 

 

mew .323 $8 2895:2511.

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mi .852 EC 2823:5631.

     

 

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mm“ 2: .1; mm: cm: mm~ 9+2 mmfi Nm~ mm“
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The effect of varying breeding Spaces on the number and sequence

Figure 4.

(Data from Dzubin and

O

O

of mallard nests hatchino per week.

1969).

Gollop,

28

maximum number of indicated pairs in the field study as
estimated from counts of lone pairs, lone drakes, and
flocked pairs. ‘Whenever the estimated number of breeding
spaces was too low to accommodate the number of indicated
pairs, an increase or decrease of the predation rate
resulted in little or no agreement in either the pattern of
the simulated nest sequence or in the numbers of nests in
the sequence with the patterns and numbers of nests in the
sequences from the field data.

Whenever the number of breeding spaces was adjusted so
as to be just sufficient for the number of indicated pairs
from the field investigations as in the 1957 Kindersley
simulation, the resulting production of ducklings as
calculated by the model (2991) was far greater than the
results from the field studies (2000) (Table 1). When this
discrepancy occurred, predation rates were increased in an
attempt to lower calculated production.

Increases in early and late predation rates (Fig. 5)
and in just the early rate (Fig; 6) lowered calculated
productivity, but the frequency of nest initiations as

calculated by the model differed significantly from the
results of the field studies. For example, in the 1970

Alberta Parklands simulation, 70 pairs when used with a
predation rate of 85% produced 409 ducklings versus 492 with
53% predation (Table 2). This number is larger than the

number reported in the field study (183) and the nest

29

 

 

Table 1. Response of mallard duckling production to amounts of breedine snare varied before varying weather in
order to simulate field observations. (Data from Dzubin and Collop. 1969 and Sorensen. 1978).
First Second final
ludier of Actual estimate of Resulting estimate Resulting estimate Resulting
indicated duckling breeding simulated of breeding simiated of breeding simulated
Area Date pairs production space production flare production sate production
lindersley 1956 248 1183 134 I332 100 1332 95 1332
1957 358 2000 105 2911 ISO 2954 205 2991
I958 173 860 71 1156 63 1156 57 1156
Alberta 1968 89 185 I3 676 17 681 18 685
Parkland
1969 70 238 37 676 _ 25 676
1970 101 183 42 786 9 27 768

 

 

 

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31

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memueoauaemua some .Nmm

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42
some ewe
:_ ozmmueem memmz
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a

The effect of increasing constant simulated predation rates

on numbers and sequence of mallard nests hatched (Data

Figure 5.

1978).

from Sorensen,

32

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ANmeueoauaeoua sown .Nmm

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Aumeueonomemua moan .Nmk

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ANmeucoauaeoua moan .Noo

"coaumeaua enema .muama okv zome<uszm9-.o
AquucoHumvmun mumH .NmeucoHumvmua mamas

.muaaa okv okan maz<nee<e eeemma<.ll.

 

O

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m:

4;

mH

mu

Mmu3 mmm
UZH$UF<= whwmz
ho mmmzbz

The effect of increasing varied early and late predation rates
on numbers and sequence of mallard nests hatching per week

(Data from Sorensen, 1978).

Figure 6.

33

hatching sequence differed significantly from the reported
one, 4 > 0.109.

When weather affecting nesting was described as adverse
"during the week of...", an entire week of bad weather was
entered into the simulation, This procedure resulting in
limiting laying and nest initiation far longer than actually
occurred producing a larger response in good weather than
actually'occurred (Fig. 7). Further iterations in which bad
weather was reduced by one day per iteration revealed that 3
days bad weather reduced nesting slightly too much, and 2
days or less bad weather had too little effect. Thereafter,
3 days bad weather was used, but location within the
designated week proved important (Fig. 7). The simulated
production of ducklings without bad weather was greater than
the simulated production of ducklings with the appropriate
bad weather (Table 3).

When data from the 1956 Kindersley study was used in
the simulation, the total numbers of indicated pairs was too
high a value to produce a nesting sequence similar to the
actual data, but the number of lone pairs permitted a closer
simulation (Table 5 and Fig. 8). The initial estimate of
134 breeding spaces ultimately proved too high. The
predation rates of 13% on active nests in the study when
used in the simulation resulted in the closest simulation,d

==(L012. When 178 pairs were tested with predation rates of

23%, the nesting sequence was less similar, at < 0.012.

34

Figure 7. The effect of the number of days and dates of simulated bad
weather on mallard nest hatching numbers and sequence. (Data
from Sorensen, 1978)

35

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II III ‘11 a
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$3 6583 use 2055:sz v-.. ., t. . E:
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Figure 7.

36

 

 

Table 3, Response of mallard duckling production to amounts of breeding
Space and weather conditions varied to simulate field obser-
vations. (Data from Dzubin an; Gollop, 1969 and Sorensen, 1978).
Number Actual Simulated Simulated
of initiated duckling production no production-
Area Date 4; pairs production bad weather bad weather
Kindersley 1956 248 .1183 1981 I913
Kindersley 1958 173 860 1427 1337
Alberta
Parkland 1969 70 238 342 326
Alberta
Parkland 1970 101 183 494 494

 

37

Figure 8. Comparison of the number of mallard nests hatching per
week to the results of the closest Simulation. (Data
from Dzubin and Gollop, 1969; Sorensen, 1978).

38

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Figure 8.

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39

Simulated duckling production (1443) was also higher then
the production of the closest simulation (1332) (Table 4).

The number of indicated pairs in the 1957 Kindersley
study was also too high and produced values in the nesting
sequence and duckling production (2991) (Table 1) far beyond
the field data (2000) (Table 5) and beyond what could be
reduced by simulated predation rates of 35%-50% (Table 2).
However, the number of lone pairs, 267, when used in the
simulation produced nesting sequence values and production
values below the values reported in the field study. Table
5 shows that the number of May and July ponds in 1956
exceeded the number of May and July ponds in 1957, yet the
calculated number of breeding spaces in 1956 is less than in
1957. Note, however, the bad weather in 1956 and no bad
weather in 1957.

In contrast with 1956, the estimated number of breeding
spaces for 1956 proved too low (Table 1). The first
combination of numbers for pairs, breeding spaces and
predation that produced values for the nesting sequence and
production closely resembling the field data were

respectively, 290, 167, and 15%-15% (at: 0.102) (Fig. 8).

When 300 pairs were used, predation rates of 35% also

resulted in similar duckling production to the reported

production (Table 4) but the nesting sequence was not

significantly similar to the reported sequence (at> 0.102L

40

Table 4. Response of mallard duckling production to pair numbers and predation rates varied to simulate field
Observations. (Data from Dzubin and Gallop, 1969 and Sorensen, 1979).

 

 

Resulting Resulting
Number Predation simulated Number Predation simulated Actual

Area Date ofgpairs rate Aproduction ofgpairs rate production 4production
Kinderlsey 1956 168 13 1332 I78 23 1443 1183

1957 290 15 2301 300 35 2309 2000

1958 - - - - - - -
Alberta I968 30 53 181 40 60 234 185
Parklands

1969 - - - - — - -

1970 55 53 268 65 60 318 183

 

41

 

 

 

 

Table 5. Comparison of field data from Kindersely, Saskatchewan to the most
similar simulated response of mallard reproductive parameters to breeding
Space, weather and predation rate variables. (Data from Sorensen, 1978).
1956 1957 1958
Field Simulation Field Simulation Field Simulation
data inputs data inputs Agggta inputs
Bad weather days 117-123 121-123 none none 123-130 120-122
Number of indicated
pairs* 248 168 358 290 173 148
Number of May ponds 81 - 43 - 20 -
Number of July ponds 49 - 7 - 8 -
Number of breeding spaces - 95 - 167 - 53
Combined water loss (2) - 40 0 129 - 136
Predation (2)
Early nests-all 20 - 15 - 40
-active only l3 l3 9 15 22 22
late nests -all 30 - 31 - 58
-active only 13 13 27 15 44 54
Nest Hatching Chronology Results Results Results
days Number Number Number Number Number Number
126-132 2 2 2 1 4 1
133-139 19 30 41 SS 33 30
140-146 34 44 94 91 18 23
147-153 12 0 44 56 10 9
154-160 68 76 27 34 10 47
161-167 7 6 14 16 8 3
168-174 4 2 5 9 5 19
175-181 2 O 2 5 ll 3
182-188 0 2 0 3 1 2
189-195 0 0 0 0 0 2
Total nests hatched 148 162 229 270 100 139
Total nests 210 229 301 346 193 210
Total renests 21 61 23 56 24 62
Mean eggs hatched/clutch 8.1 8.2 8.4 8.5 8.2 8.3
Total ducklings hatched 1183 1332 2000 2301 860 1156
Total ducklings fledged
Measured 356 190 223
Estimated 926 827 1448 344 256 130

 

*Field data derived from a census of lone pairs, flocked pairs, lone males and
flocked males corrected for sex ratios.

42

As with the previous studies, the number of indicated
pairs from the Kindersley 1958 field study proved too high
to produce simulation results similar to the nesting
sequence reported in the study. However, the estimated
number of breeding spaces was only slightly too high.
Nonetheless, no combination of bad weather and numbers in
the simulation produced results statistically'similar'to the
field results, x > 0.111 (Fig. 8). Note, however, the
severe drought as indicated by the number of ponds in Table
5 for 1958 and that the simulated nesting sequence for the
early part of the season closely approximates the actual
sequence. .Also note the high late predation rates used in
the simulation when compared to the field data. When lower
predation rates were used, the simulated nest sequence for
the late part of the season had values even greater than
indicated in Figure 8 and Table 5.

Simulation of the data from.Alberta Parklands 1968 was
conducted as with previous simulations, and once again, the
number of indicated pairs when used in the simulation
resulted in duckling production values that were too high
(Table 1). When the maximum number of observed pairs per
week (40) was used along with sax-60x early and late preda-
tion rates, the resulting nesting sequence values were

statistically similar (°k= 0.047), but duckling production

was high (Table 4). However, when the next lowest number of

pairs per week (30) was used in the simulation, along with

43

early and late predation rates of 538-538 which were
estimated by the author of the field study, a closer
approximation of the nesting sequence (Fig. 8) was achieved,
( O“ 0.016) and duckling production was similar to the field
data (Table 6). Note, however, that in Table 6 the values
for the numbers of nests and ducklings hatched from the
simulation are Just slightly lower than the field study
data.

It was not possible to produce a simulation that was
statistically'similar to the data from the Alberta Parklands
1969 data (4K) .111) (Fig. 8). However, the author of the
investigation reports that unusually cold weather (-60 and
-7°C) during the time (June 12—13) when most hens were
incubating resulted in "damage to some eggs" and subsequent
renesting; The model. however, eliminated these late re-
nests.

Note. however, that the model was able to simulate the
decline in nest initiations from a high starting point and a
slight increase in nest initiations at the end. These

results were achieved by setting bad weather at the
beginning of nest initiation as indicated in the field data,
and by setting the date for peak nest initiation in the
simulation at the date of the high point in the field data.

Early nest initiations in the simulation were then delayed
until good weather was indicated, thus producing a beginning

high point instead of a peak 13 days later as would normally

Table 6.

44

Comparison of field data from Edmonton, Alberta ASpen Parkland Life Area

to the most similar simulated response of mallard reproductive parameters

to breeding Space, weather and predation rate variables.

(Data from

 

 

 

Sorensen, 1978).
1968 1969 1970
Field Simulation Field Simulation Field Simulation
data inputs data inputs data inputs
Bad weather days 91-111 91-111 91 100 91-100 91-111 91-111
163-164 163-164 181-182 181-182
Numberlof indicated
pairs 89 30 70 55 101 55
Number of May ponds 43 - 158 - 150 -
Number of July ponds 20 - 50 - 70 -
Number of breeding Spaces - 18 - 25 - 27
Combined water loss (Z) - 129 - 70 - 59
Predation (2)2
Early nests 53 53 53 60 53 53
Late nests 53 53 53 50 S3 53
Nest HatchingAChronology3 Results Results Results
Days Number Number Number Number Number Number
147-153 5 4 7 11 5 3
154-160 7 7 5 10 9 12
161-167 3 5 3 6 9 9
168-174 3 4 4 5 5 6
175-181 3 1 2 2 2 2
182-188 2 2 6 1 2 1
189-195 3 0 7 4 2 1
196-202 1 0
203-209 0 0
210-216 _ __ _1_ __0_ _ _
Total nests hatched 26 23 36 39 34 34
Total nests - 40 - 67 - 60
Total renests 4 - 10 - 22 - 15
Mean eggs hatched/clutch 6.4 7.9 6.4 7.8 6.4 7.8
Tocal ducklings hatched 185 ‘ 181 238 304 183 268
Total ducklings fledged 44 27 140 140 104 139

 

1

Maximum number of indicated pairs per week including lone pairs, flocked pairs,
lone males and flocked males

2Estimated by author

3Estimated from Class I broods

4 9
Estimated from ducklings/Class I broods

45

be produced by the simulation. The increase in nest
initiations at the end of the simulated nesting sequence was
achieved by using a number of pairs greater than needed to
produce the early part of the sequence, and then raising the
reported predation rates of 538—533 to 603-60x.

The simulation of the Alberta Parklands 1970 field
study was conducted as all previous simulations, and the
field observation of a maximum of 55 lone pairs and lone
drakes per week and the field study estimate of early and
late predation rates of 533-538 produced the simulation
results most closely approximating the field data, d= 0.047
(Table 6 and Fig. 8). A higher number of pairs and a higher
predation rate resulted in a greater number of ducklings
produced (Table 4).

When the numbers of pairs in both the Xindersley field
data and simulations are compared with habitat over the 3
year period, the number of ponds decreases with each
succeeding year (drought), while the number of pairs/pond
and pairs/acre increases in both field and simulations
(Table 7). The number of breeding spaces does not vary with
the number of ponds, but note in Table 5 that 1957 and 1959
had bad weather during the breeding season. The number of
PondS/breeding Space and acres/breeding space both decrease

with drought. Duckling production, reported or simulated.

does not vary with pond numbers.

46

Table 7. Comparison of actual and simulated mallard pair and duckling
production response to habitat at Kindersley, Saskatchewan.
(Data from Dzubin and Gollop, 1969).

 

 

 

 

 

1956 1957 1958
Field Model Field Model Field Model

Censused pairs 248 - 358 - 173
Calculated breeding

pairs (nests-renests) - 101 - 214 - 77
May ponds 81 - 43 - 20 -
Total wetland acres 642 - 573 - 176 -
Pairs/pond 3.1 1.2 8.3 5.0 8.6 3.8
Number of breeding

spaces - 95 - 167 - 53
Pairs/breeding Space - 1.1 - 1.4 - 1.4
Ponds/breeding Space - 0.9 - 0.3 - 0.4
Acres/breeding space - 6.4 - 3.4 - 3.3
Duckling production 1183 1332 2000 2301 860 1156

- per pond 14.6 16.4 46.5 53.5 43.0 57.8

- per breeding space - 14.0 - 37.7 21.8

 

47

When the number of pairs in both the Alberta Parklands
field data and simulations are compared with habitat over
the 3 year period, the number of ponds increases abruptly in
1969 and 1970, while the number of pairs per pond in both
field and simulations generally'decreased (Table 8). The
number of breeding spaces does not vary with the number of
ponds, but note in Table 6 the bad weather during the 1969
breeding season. The number of pairs/breeding space remains
constant while the number of ponds/breeding spaces
increases. Duckling production does not vary with pond
numbers.

In Table 5, the number of simulated nests hatched
exceeds the measured hatch in a1 1 cases, and the authors of
the field study report that not all nests were found in nest
searches. Correspondingly, the simulated number of
ducklings hatched proportionally exceeds the measured hatch.
This is not the case for 1969 and 1970 in Table 6. .Although
the number of nests hatched differ between the field data
and the simulation by 3 and 0, in both cases the simulated
number of ducklings fledged is much larger than the number

from the field data. During both of the years. the author

reports severe weather in June that he believes destroyed
many late nests and Class I broods.

Note that the simulated numbers of ducklings fledged in
Tables 5 and 6 are very close to or falls within range of

the numbers of ducklings estimated and/or measured in the

48

Table 8. Comparison of actual and simulated mallard pair and duckling
production response to habitat at Edmonton, Alberta Aspen
Parkland Life Area. (Data from Sorensen, 1978).

 

1968 1969 1970
Field Model Field Model Field Model

 

Maximum number of

indicated pairs/week 62 - 89 - 101 -
Calculated pairs

(nests-renests) - 13 - 17 - 19
May ponds 43 - 158 - 150 -
Pairs/pond 1.4 0.3 0.6 0.1 0.8 0.1
Number of breeding spaces - 18 - 25 - 27
Pairs/breeding space - 0.7 - 0.7 - 0.7
Ponds/breeding space - 2.4 - 6.3 - 5.6
Duckling production 185 181 238 304 183 268
- per pond 4.3 4.2 1.5 1.9 1.2 1.7

- per breeding space - 10.0 - 12.2 - 9.9

 

49

field studies in 4 of the 6 years simulated. However, in
Kindersley 1959 and Alberta Parklands 1968, the duckling
mortality between hatching and fledging is overestimated.
Although the mortality in Alberta Parklands 1970 appears to
be underestimated, the simulated number of ducklings hatched
is higher than the number reported for probable reasons

previously discussed.

I)!

a,
.64.

of

DISCUSSION

If the model is in fact a reasonably accurate
simulation of mallard breeding biology; it demonstrates how
a phenotypic expression of a genetic trait can be used to
better evaluate the performance of a species within its
habitat, and the relative suitability of the habitat. In
this case, the individual genetic trait is the time of nest
initiation of individual hens and the resulting distribution
of nesting frequencies of the local population. Exogenous
variables, however, can greatly alter the response and must
be considered.

The importance of knowing the actual number of breeding
pairs is one of the most obvious results of this study. In
the Kindersley study, the number of indicated pairs in 1956
and 1958 were approximately twice the number of pairs
estimated by the model, and in the Alberta Parklands study,

the number of indicated pairs was approximately 5 times the

number of predicted pairs. The model indicates that had all
indicated pairs actually nested, the resulting nesting

sequence would have been similar in pattern, but with double

or up to five-fold the number of nests.

50

5.1

It has been established that the number of indicated
mallard pairs includes birds not actually'paired, especially
during drought (Johnson and Sargent, 1977; Jackson et al.,
1985L. Although this relationship offers a partial
explanation for why the simulations estimated fewer nesting
paris than the number of indicated pairs, it does not
explain the range of differences from year to year. The
percent of indicated pairs simulated as nesting pairs
increased from 68 to 86% in the Kindersley area during
increasing drought, yet the percent of indicated pairs
simulated as nesting pairs varied independently with
increasing water levels in the Alberta Parkland area.

It can be argued that the indicated pairs did nest, but
that many of the nests were destroyed by predators. Were
this the case, then the field estimates of predation were
greatly underestimated. It is entirely probable that the
predation rates were underestimated as suggested by Miller
and Johnson (1978), but the predation rates required by the
model to produce statistically’comparable nesting sequences
would have been more than three times greater than the field
estimates. For example, in the 1957 Kindersley study the
number of pairs predicted by the model was 290, but the
number of indicated pairs reported in the field data was
358. When 358 pairs was used in a simulation, it required

an 858 predation rate to reduce the resulting duckling

production to a value approaching that reported in the field

52

data. That rate also produced a nest hatching sequence
statistically different than the reported sequence (d.>
0.11).

It could also be argued that in the field studies not
all nests were found and not all broods counted,thus
underestimating production. This is definitely true, but in
most of the simulations, the closest simulation estimated a
greater number of nests and ducklings than reported in the
field studies. Thus, the number of nests and ducklings
hatched predicted by the simulation may be closer to the
actual production than that reported by the field studies.

It was not possible, however, to estimate a somewhat
larger number of breeding pairs and then achieve a nesting
sequence and duckling production comparable to the reported
production by increasing predation. For example, in
simulations of the 1957 Kindersley study, 290 pairs and
predation rates of 15% produced a nesting sequence more
statistically similar to the reported sequence (x==CL102)

than when 300 pairs were used with predation rates of 20% («
>0.102).

The model does not indicate that bad weather alone

could account for why some the lack of nesting by indicated
pairs. In the 1957 Kindersley study, there were 43 May ponds
in which the model predicted 290 of 358 indicated pairs
produced 2301 ducklings, as compared to the reported

production of 2000. Therefore, the 81 ponds in May of 1956

53

should have provided habitat enough for all of the 248
indicated pairs that year. This was not the case because
the field study reported fewer nests (148 vs. 229) and less
duckling production (1183 vs. 2000) than in the 1957
investigation. The model predicted that only 168 of the 248
indicated pairs nested to produce 1332 ducklings.

When 248 pairs was used in simulation with and without
bad weather, the simulated bad weather reduced duckling
production from 1981 to 1913, but this result is much
greater than the 1183 ducklings reported in the field study.
Thus, while the model produced a similar number of ducklings
and a nest hatching sequence to those reported when bad
weather and 168 pairs was used, this does not explain why
only 168 pairs nested. These same relations can be seen in
the Alberta Parklands study where the number of ponds nearly
quadrupled between 1968 and 1969, yet indicated pairs
actually decreased in 1969 and the number of nests increased
from 24 in 1968 to only 36 in 1969 and 34 in 1970. Again,
weather was involved, but the model does not indicate that
the weather was as limiting as the number of pairs and
duckling production would indicate (Table 3).

The effect of weather, however, is not satisfactorily
simulated by this model in all cases. Although the effect
of bad weather was simulated reasonably well in the 1956

Kindersley study, it was not satisfactorily simulated in

either the 1958 Kindersley study or in the 1969 Alberta

54

Parklands study. It cannot be determined at this time if
the model simulates the effect of weather imprecisely or if
the imprecise reporting of weather is the cause of the
discrepancies, or some combination of both.

Although the model does not indicate that spring
weather in the Alberta Parklands 1969 and 1970 studies was
responsible for the lack of meetings and production, it
still may have been a determining factor. The author of the
Alberta Parklands counted broods and calculated nest
hatching from those data. If the severe weather killed
broods that went undetected, then the number of calculated
nests would be lower than actual. The model would simulate
this by correspondingly reducing the number of breeding
pairs.

Another possible explanation for why so few of the
indicated pairs nested in the Alberta Parklands study is
that the pairs arriving in the spring were not
physiologically ready to breed because of poor water
conditions in the wintering areas. The regression

equations of Heitmeyer and Fredrickson (1983) utilizing

water condition in wintering areas, May ponds and July ponds

show that water conditions on the wintering areas in 1969
and 1970 account for almost half (R2 20.496) of the
variation in the equation predicting mallard age ratios for

those years. The R2 for the entire equation was 0.922.

55

Mallard spacing behavior could have restricted nesting.
In the Kindersley studies and simulations, the calculated
number of pairs per pond increases with drought, while ponds
and acres per breeding space decrease with drought (Table
7). In the Alberta Parklands studies and simulations, the
reverse is true» With increasing wetlands numbers, pairs
per pond decrease while ponds per breeding space increases
(Table 8L .

These relationships suggest that a pair of mallards
occupy smaller areas when there is less wetland habitat and
larger areas when there is more*wetland habitat. Weather
certainly had an effect on these values, but not their
relative relationship. For example, had the weather at
Kindersley been good in 1956 and 1958 the pairs/pond, pairs/
acre, and acres/breeding space all would have been higher
for both years (Table 7). Further, since the number of
pairs/breeding space calculated from the simulation changes
little in relation to the other habitat parameters, then the
size of the breeding space must expand with increasing
wetland habitat and decrease with decreasing wetland
habitat.

Although the results of this investigation do not
suggest how large a breeding space can be, the acres/

breeding space in Table 9 for Kindersley 1956 indicate 6v4

acres. Obviously, the size could be larger.

56

Since 1958 was an extremely dry year at Kindersley, the
number of acres/breeding space that year, 3.3 acres, (Table
1) may approach the minimum size. Unfortunately that year
was poorly simulated and the number of breeding spaces is
probably over-estimated” Nevertheless, that estimate is
close to the minimum size of a wetland required to support a
mallard pair, estimated at 3.0 acres by Dzubin (1969),
approximately 4.9 acres for semi-permanent wetlands.
by Cowardin and Johnson (1983), and 1.1 acres for
experimentally manipulated marsh by Kaminski and Prince
(1981).

No evidence was discovered in this investigation of the
crowding of large numbers of indicated pairs on less habitat
resulting in lowered productions The converse was true.
because in the 1957 Kindersely study the largest number of
pairs produced the greatest number of young in a period of
declining numbers of ponds and wetland acres. However, high
densities of mallards nesting on artificial structures,
islands, and in dense upland vegetation should not
necessarily be accepted as evidence of mallard breeding in

extremely small areas. As indicated in the literature

review, mallard hens may nest a long distance from the
defended wetland area necessary to provide the food needed
to sustain reproduction (Lokemoen et al. 1984). The model,

however, did not simulate such conditions.

57

A final possible explanation as to why more of the
indicated pairs did not nest may be that the model was
simulating full utilization of available breeding habitat
and that the necessary resources for reproduction were not
available for all indicated pairs. As noted by Weller and
Fredrickson (1974), avian use of a marsh is less when there
are few pools, possibly resulting from drought, or when
there are large pools consisting mainly of open water.
possibly resulting from several years of high water levels.
Obviously, the number of pools may not indicate the
existence of the 50% interspersion of open water and aquatic
vegetation in a marsh that results in the greatest number of
pairs breeding in the marsh.

Although there were more ponds in the Kindersley area
in 1956, the seven preceeding years were years of
increasingly abundant precipitation (Pospahala et a1. 1974),
which may have produced a large number of ponds consisting
primarily of open water that had relatively lower pair use.
The ensuing drought reduced the number of ponds in 1957, but
may have created in the remaining ponds the temporary hemi-
marsh conditions most abundantly used by mallard pairs. As
the drought worsened in 1958, the ponds may have become too
few in number and contained too smal l a percent water to
maintain the high pair use. If such were the case, then the

model may'have successfully'simulated full utilization of

the available resources.

58

The same relation may have also occurred in the Alberta
Parklands study: Neither indicated pairs nor simulated
pairs increased proportionally with the increase in ponds,
but the large and sudden increase in ponds in 1969 that was
maintained in 1970 may not have permitted the development of
the hemi-marsh that would have supported increased pair use.

The model successfully'simulated.the»difference in
productivity between grassland and parkland habitat. Both
the field data and the simulations show greater pair use and
duckling productivity per pond in grassland than in parkland
habitat. Dzubin (1969) found the same relationship when
comparing data from Roseneath, Alberta and Kindersley,
Saskatchewan and attributed the difference to the difference
in average pond size of the two areas. The average pond
size in the grassland of Saskatchewan was 5.7 acres, but in
the parkland of Alberta was only 0.7 acres. This also
agrees with the prediction and qualification of Cowardin and
Johnson (1983) concerning pond size, pond conditions, and

pair‘use.
The failure of the model to successfully'simulate the

1958 Kindersley study not only points out a weakness in the
model, but perhaps best illustrates how the mallard nesting

sequence is a measure of habitat. The model closely

simulates the nesting sequence and the effects of bad

weather early in the nesting season (Fig. 8), but when the

bad weather variable is removed, the model predicts an

59

increased response in nesting and subsequent nest hatching
in the same way it did in the 1956 Kindersley simulation
(Fig. 8). ‘Yet there was not a subsequent increase in
nesting and nest hatching in 1959.

The number of May and July ponds in Table 5 show 1959
to be a year of severe drought, starting dry in May and
getting dryer through the nesting season. Note that there
were more ponds in July 1956 than in May of 1958. Thus the
reason that nesting did not increase after bad weather in
1958 as it did in 1956 appears to be because the habitat was
not available in 1958 to allow nesting. Unfortunately, the
model measures the productive capacity of wetlands as a
constant number, the number of breeding spaces. Obviously.
this factor should have been treated as a series of
functions instead of a constant.

Note that the predation rates in the Kindersley 1958
study are not equal and higher than in previous years in
both the field data and the simulations 'The rates in the
simulation are unequal and high because they somewhat
reduced the high simulated nesting sequence values, thus
making the simulation more closely resemble the actual
sequence and are probably artificially’high, especially the
late predation rate. Predation rates from the field study
may have also been too high, because a simulation using a

lower early predation rate (18%) produced a early portion of

nesting sequence more closely resembling the actual early

60

portion, but was rejected because no rationale could be
determined for using early predation rates lower than field
estimates since predation rates estimated when many hens
are laying are usually underestimated.

One obvious constant discrepancy between field data and
model simulations is with renests estimated in the field
studies and the simulated renests. Only late nests in the
field study were counted as renests, and since renesting
probably occurs throughout the season as simulated by the
model, the field estimates of renesting are probably low.

‘The equation estimating duckling survival did not
consistently predict survival for all years.(Tab1es 5(and
6). One obvious reason is that the equation did not account
for severe weather that can destroy ducklings, especially'
those in Class I broods. It also may not apply to all areas
equally well, since it was developed from the data from one
specific location. .Another explanation is that the
departure of pond numbers from the maximum number of May
ponds is a poor measure of distance of the nest from water.
the actual determining factor. A multiple regression of

mean distance of nest from water and percent pond loss May-

July may prove more reliable, but this equation was not
developed because of lack of sufficient number of years of
estimates for the distance factor.

In all successful simulations, predation rates for

early and late nesting seasons were equal (Tables 7 and 8).

61

The unequal rates in the unsuccessful simulations are, as
previously discussed, compensating for some other effect not
simulated. The constant rate of predation agrees with the
estimates of constant daily nest survival by Green (1977)
and Miller and Johnson (1978), but in all cases, the rates
were equal to or just slightly greater than the field
estimates. This is in opposition to the methods developed
by Mayfield (1960) and modified by Miller and Johnson that
show field measures of predation are usually underestimates.

No reason can be suggested for this discrepancy.

1)

2)

3)

4)

5)

CONCLUSIONS

The mallard nesting sequence, a phenotypic expression of
a distribution of mallard genotypes, can be used to
evaluate mallard reproductive performance if adjusted
for weather and predation.

Weather is an important variable controlling mallard
productivity and appears to be directly related to habi-
tat suitability.

The mallard nesting sequence can be used to evaluate
relative habitat suitability.

Mallard breeding pairs will crowd.to a density of 1 pair
per 3-5 acres of wetland habitat, but how this is
related to mallard spacing mechanism and the limits of
habitat productivity remains undetermined.

When wetlands are abundant as expressed by breeding
space, the mallard spacing behavior seems to produce

less than maximum utilization of habitat, even when

weather is taken into account.

62

LITERATURE CITED

LITERATURE CITED

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a managed glacial marsh. Iowa Agric. and H. Econ.
Exp. Stn. J. Paper No. 7403 in The Living Bird, 269-
291.

APPENDIX

68

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