vol. 172, no. 3the american naturalistseptember 2008
A Theoretical Investigation of the Effect of Latitude
on Avian Life Histories
John M. McNamara,1,*Zolta ´n Barta,1,2,3,†Martin Wikelski,4,‡and Alasdair I. Houston3,§
1. Department of Mathematics, University of Bristol, University
Walk, Bristol BS8 1TW, United Kingdom;
2. Department of Evolutionary Zoology, University of Debrecen,
Debrecen Egyetem te ´r 1., 4032, Hungary;
3. School of Biological Sciences, University of Bristol, Woodland
Road, Bristol BS8 1UG, United Kingdom;
4. Department of Ecology and Evolutionary Biology, Princeton
University, Princeton, New Jersey 08544; and Max Planck Institute
for Ornithology, Schlossallee 2, 78315 Radolfzell, Germany
Submitted April 2, 2007; Accepted February 19, 2008;
Electronically published July 30, 2008
Online enhancements: appendixes.
abstract: Tropical birds lay smaller clutches than birds breeding
in temperate regions and care for their young for longer. We develop
a model in which birds choose when and how often to breed and
their clutch size, depending on their foraging ability and the food
availability. The food supply is density dependent. Seasonal environ-
ments necessarily have a high food peak in summer; in winter, food
levels drop below those characteristic of constant environments. A
bird that cannot balance its energy needs during a week dies of
starvation. If adult predation is negligible, birds in low seasonal en-
vironments are constrained by low food during breeding seasons,
whereas birds in high seasonal environments die during the winter.
Low food seasonality selects for small clutch sizes, long parental care
times, greater age at first breeding, and high juvenile survival. The
inclusion of adult predation has no major effect on any life-history
variables. However, increased nest predation reduces clutch size. The
same trends with seasonality are also found in a version of the model
that includes a condition variable. Our results show that seasonal
changes in food supply are sufficient to explain the observed trends
in clutch size, care times, and age at first breeding.
Keywords: annual routine, clutch size, energy balance, parental care.
* E-mail: firstname.lastname@example.org.
Am. Nat. 2008. Vol. 172, pp. 331–345. ? 2008 by The University of Chicago.
0003-0147/2008/17203-42512$15.00. All rights reserved.
The pioneering work of Moreau (1944) and Lack (1947)
suggested that the clutch size of birds increases with lat-
itude; that is, birds that breed near the equator tend to
have smaller clutches than birds that breed away from the
equator. Subsequent work has provided a rigorous justi-
fication of this trend by using two ways to demonstrate
the effects of latitude. One way is to investigate the life-
history parameters for a species that breeds at a range of
latitudes. This method has been applied to the tree swallow
Tachycineta bicolor (Dunn et al. 2000), the great tit Parus
major (Sanz 1998), the flicker Colaptes auratus (Koenig
1984), the house wren Troglodytes aedon (Young 1994),
and the stonechat Saxicola torquata (Ko ¨nig and Gwinner
1995). As an example, Dunn et al. (2000) found a signif-
icant increase in the clutch size of tree swallowswithbreed-
ing latitude in North America. The second method is to
carry out a comparative analysis (e.g., Bo ¨hning-Gaese et
al. 2000; Martin et al. 2000; Cardillo 2002; Martin 2002).
Bo ¨hning-Gaese et al. (2000) analyzed the clutch size of
373 species of North American birds and 252 species of
European birds and found a significant increase in clutch
size with latitude. The number of clutches per year de-
creased with latitude.
There is evidence that the clutch size pattern is linked
to environmental parameters, such as the seasonal food
flush, or seasonality of migrants (Ricklefs 1980; Lepage
and Lloyd 2004). Further research has revealed that several
other aspects of avian life history also depend on latitude
(Ricklefs 2000a; Martin et al. 2006). Birds that breed near
the equator (“tropical birds”) care for their young for a
long time (Russell 2000; Schaefer et al. 2004; Styrsky et
al. 2005). Young tropical birds tend to have slow growth
rates (Ricklefs 1976; Bryant and Hails 1983), they do not
become mature as soon as the young of nontropicalspecies
(Skutch 1976; Russell 2000; Russell et al. 2004), and se-
nescence is delayed (Møller 2007). The view that tropical
birds tend to have high survival as adults was challenged
by Karr et al. (1990), who found no difference in the
survival of tropical and temperate forest birds, but there
332 The American Naturalist
are problems with this conclusion (Johnston et al. 1997;
Sandercock et al. 2000; Stutchbury and Morton 2001). The
comparative analysis presented by Peach et al. (2001)
shows that the survival rate of southern African songbirds
is higher than that of European songbirds. Although more
work is needed on this topic, there is evidence in support
of higher adult survival in the tropics.
traits may also have been instrumental in shaping wide-
and tropical birds (Ricklefs 1976; Weathers 1979, 1997;
Klaassen and Drent 1991; Klaassen 1994; Tieleman et al.
2005). In general, tropical birds have lower metabolic rates,
that is, a slower “pace of life” (Wikelski et al. 2003; Wiersma
et al. 2007). Metabolic rate is often seen as the major hub
in the network of physiological mechanismsunderlyinglife-
history traits and is potentially a heritable trait (Wikelski et
al. 2003). Differences in metabolic rate are expected to me-
diate some or all of the major life-history trade-offs men-
tioned above (Ricklefs and Wikelski 2002).
Understanding the relative influence of the proposed
ultimate reasons underlying latitudinal life-history gradi-
ents is a major challenge (Cody 1966; Martin 1996; Car-
dillo 2002). Various explanations have been suggested, the
most popular being based on differences in food and pre-
dation, both of which could be mediated by differences
in day length and temperature. One of the more widely
accepted explanations to date for latitudinal clutch size
variation has been Ashmole’s hypothesis, which states that
clutch size is higher at higher latitudes because of the
seasonal flush of resources resulting from fewer competing
consumers in more-seasonal environments (Ashmole
1963). As one travels toward the poles, annual variations
in day length, incident solar radiation, and primary pro-
ductivity grow more extreme. On this view, what is im-
portant is not the maximum level of resources over the
year but the maximum level relative to the minimum level.
Ashmole’s (1963) ideas were elaborated and strengthened
by Ricklefs (1980), who estimated the relative availability
of food by the ratio between primary plant production in
summer and that in winter. Using such a measure, re-
searchers found significant positive correlations between
the relative summer productivity and clutch size in wood-
peckers (Koenig 1984, 1986) and various passerines (Rick-
lefs 1980), including tree swallows (Dunn et al. 2000).
An alternative explanation (not exclusive to the one
above) is that high nest predation rates in the tropics are
ultimately responsible for small clutch sizes. It has been
suggested that high nest predation could select for multiple
renesting attempts, short development time, and small
eggs and clutches (Martin 1996). However, high nest pre-
dation could also result in slower development rates be-
cause adults might reduce their nest attentiveness and
parental feeding visits, resulting in food limitation (Gha-
lambor and Martin 2001). The empirical evidence for the
influence of nest predation on avian life-history traits is
mixed. Robinson et al. (2000) found high interannual var-
iation in nest predation rate in tropical Panama, as well
as extensive overlap of the absolute levels of nest predation
between tropical and temperate-zone habitats (see also
Martin et al. 2006). Another study comparing ecologically
and phylogenetically similar species in North America and
subtropical South America suggested that nest predation
may explain clutch size differences within, but not be-
tween, latitudes (Martin et al. 2000). Other possible ex-
planations are based on ambient temperature (e.g., Reid
et al. 2000; Cooper et al. 2005) and the consequences of
microbial infection for embryo mortality before the onset
of full incubation (Cook et al. 2003, 2005; Beissinger et
In summary, it appears that there exist too many po-
tential selective influences on clutch size and other life-
history traits to explore them with verbal arguments alone.
We suggest that the time is ripe for developingananalytical
model that includes most of the factors mentioned above
and using it to establish how these factors could influence
the life histories of tropical and temperate-zone birds. We
believe that previous accounts of the effect of latitude on
life-history evolution in birds are limited for two related
reasons. If population size is stable, then there are con-
straints on life-history parameters (e.g., Ricklefs 1977a,
1977b; Charnov 1986, 1993; Sutherland et al. 1986). Al-
though Lack (1947) and Ashmole (1963) discussed such
constraints, they were not included in a formal model of
latitude, and hence their full implications were not per-
ceived. When the previous accounts were being developed,
it was not possible to construct appropriate models be-
cause there was no adequate theoretical basis. An adequate
model must consider how the seasonality of the environ-
ment influences optimal behavior over the entire year.This
requires a model of optimal annual routines. Houston and
McNamara (1999; see also McNamara and Houston 2008)
describe a powerful general framework for finding such
In this article, we provide the first explicit and self-
consistent account of a latitudinal trend in a suite of life-
history parameters. It is not feasible to explore all possible
explanations; instead, we concentrate on whether trends
can be explained by Ashmole’s (1963) hypothesis. Our aim
in this article is to show that the interaction between sea-
sonality of food and density dependence is sufficient to
explain many of the differences that have been observed
between tropical and temperate bird species. We are not
claiming that no other factors operate, nor are we claiming
that latitudinal trends will always exist. What we are saying
Effect of Latitude on Avian Life Histories333
Figure 1: Mean and standard deviation in foraging efficiency as a function of age. The three cases shown are, from top to bottom, fast maturation,
baseline, and slow maturation. Details of functions are given in appendix A in the online edition of the American Naturalist.
is that if all else is equal, then the seasonality of food is a
We predict breeding phenology by analyzing the optimal
scheduling of reproductive activities over the annual cycle,
using a model of a schematic bird. In this model, the food
supply varies over the year but is the same at a given time
and latitude in successive years. Thus, there is no year-to-
year variation. The food supply is density dependent, and
to check the robustness of our results, we consider more
than one form of density dependence. We are primarily
concerned with the effects of the constraint imposed by
the food supply when there is no predationandhowresults
are modified when there is a trade-off between obtaining
food and avoiding predation.
There are 52 decision epochs per year (weekly decisions).
A bird at the start of week t (time t) has the following
options. If the bird has no brood, it can (a) delay—that
is, not start a brood—or (b) start—that is, lay a clutch of
eggs. If it decides to start a brood, it must choose its clutch
size, n (a positive integer). Production of the brood takes
one time unit, so the eggs appear at time
has a brood, it can (a) keep or (b) abandon the brood.
This takes place instantaneously at time t. The decision
taken and the food supply determine the amount of time
. If the birdt ? 1
during the week that is spent foraging (see below). This
time, u, is thus an outcome of the reproductive decisions.
Time of year
andt p 52
year. Food availability at time t is
is midwinter,is midsummer,
of the following
t p 0
is midwinter and time
t p 26
t p 0
t ? 13
g(t) p A1 ? ? sin
p . (1)
Here the parameter ?Fcharacterizes the degree of season-
ality in the food supply. The parameter A is a measure of
the overall food availability in the environment. In the
basic model, we assume that density dependence acts
through the constant A; specifically, A decreases as average
annual population size increases. To investigate the ro-
bustness of results to the form of density dependence as-
sumed, we also consider an alternative form in appendix
D in the online edition of the American Naturalist.
Efficiency and Energy Intake
The ability of a bird to obtain food tends to increase as
it gets older, that is, as it matures (e.g., Weathers and
Sullivan 1989). Specifically, a bird’s foraging efficiency v
increases fromat birth to its maximum value
v p 0
334The American Naturalist
. The details of this increase are given in appendix
A in the online edition of the American Naturalist. We
present results for three scenarios, which we refer to as
“slow maturation,” “baseline,” and “fast maturation” (fig.
1). We explicitly assume that the parent does not know
the exact efficiency of its offspring during care or at aban-
donment, although the longer the care period, the greater
the mean efficiency. A bird with efficiency v that forages
for a time u in week t finds food with energetic content
v p 1
Energy Expenditure and Balance
We assume that the energy expenditure over a week equals
the energy intake. This seems a reasonable assumption for
a small bird, although balance over a single week would
be a poor approximation for a large bird.
The resting metabolic expenditure in week t is c(t). In
our baseline case, we assume thermoneutrality and that
one unit of energy is used while resting at all times of year
( for all t). The rate of expenditure increases byc(t) p 1
m while a bird is searching for food. Thus, a bird that
delays breeding expends energy
A bird with maximum efficiency that starts a clutch
expends energy Dneston building the nest and expends
energy Doffon each egg produced. Its total expenditure if
it produces n eggs is thusc(t) ? mu ? D
ing care, it supplies each offspring with food of energy
content Foffeach week. Its rate of findingfoodwhilesearch-
ing is the same regardless of whether it is finding food for
itself or its offspring. We assume, however, that the bird
is a central-place forager (Orians and Pearson 1979) while
feeding young, transporting food found at the foraging
area to the nest at rate D. Thus, it takes total time
to transport the required amount of food tou p nF /D
a clutch of size n. During transport, metabolic rate is in-
creased above the resting rate by mfly. Overall weekly ex-
penditure is thusc(t) ? mu ? m u
uYcan be found are given in appendix B in the online
edition of the American Naturalist.
during a week.c(t) ? mu
. Details of how u and
Efficiency and Reproduction
We have no state variable representing physiological ma-
turity in our model, so that even a newly independent
offspring is physiologically capable of reproduction. How-
ever, the low foraging efficiency of a young bird(seeabove)
makes it harder for it to obtain food for itself and any
young. Since immature birds are liable to be poorer at
other aspects of reproduction, we additionally assume that
an immature bird with efficiency v expends energy
on building the nest and that during transport of
food to the young, it increases its metabolic rate above
the resting rate by
disadvantage parameter. In the baseline case,
ever, as we demonstrate in “Robustness of the Results,”
most results are highly robust to the choice of this
. We refer to J as the juvenile
. How-J p 2
Sources of Mortality
(i) If a bird cannot balance its energy expenditure and
energy gain during a week, it dies of starvation. We en-
visage that, because of uncertainties in the weather and
other disturbances, the totaltime availabletoforageduring
a week is a random variable. We take our time unit so
that this random variable has mean 1. Motivated by this,
we consider a bird that requires time utotto obtain suf-
ficient food (in the case of a single bird,
for young,). Then the bird manages to bal-u
p u ? u
ance its energy needs with probability
the parameter K is large, so that the probability of energy
balance is almost a step function that drops from 1 to 0
at . Note that a bird with young always has theu
chance to reduce the probability that it will starve by aban-
doning the young. (ii) Death from predationoccursduring
a week with probability mu2. (iii) Mortality from all other
sources occurs with constant probability J during a week.
; if caringu
1/(1 ? u )
If the young are abandoned by the parent at time t, they
become independent immediately (i.e., at t). If the parent
does not abandon at t but dies between times t and t ?
, all young become independent at time1
parent does not abandon at t and survives until time
, then the nest is predated between t andt ? 1
all young die, with probability moff.
. If thet ? 1
andt ? 1
A strategy is a rule specifying how a bird’s choice of action
depends on the bird’s efficiency, reproductive status (i.e.,
whether there are dependent young and the age and the
number of any dependent young), and time of year. Con-
sider an environment with given food availability over the
year, as specified by the function g. Within this environ-
ment, a strategy has an associated annual projection ma-
trix. The fitness of the strategy is the maximum eigenvalue
of this projection matrix (Caswell 2001). This is the as-
ymptotic annual proportional growth rate in numbers fol-
lowing the strategy within the fixed environment. The
strategy maximizing fitness within this environment can
be found by dynamic programming (McNamara 1991;
Houston and McNamara 1999; Clark and Mangel 2000).
Following Metz et al. (1992), we seek an evolutionarily
Effect of Latitude on Avian Life Histories335
Table 1: Definition of parameters
Seasonality in the food supply
Weekly resting metabolic expenditure
Proportion of available time (daylight) in the week spent foraging
Additional metabolic expenditure per unit time foraging
Additional metabolic expenditure per unit time transporting food to the young
Expenditure per egg produced
Expenditure on nest construction
Rate of transport of energy in food from the foraging area to the nest
Weekly energy requirement of each offspring
Parental predation risk parameter
.01 (predation risk)
.0025 (energy constraint),
.0005 (predation risk)
Weekly background mortality risk to parent
Weekly predation risk to young
200 (energy constraint),
40 (predation risk)
JJuvenile disadvantage factor for reproduction by inexperienced birds2.0
Figure 2: Food availability g(t) (eq. ) at evolutionary stability as a
function of time of year t for various values of the seasonality in the
food supply ?F. Energy-constraint baseline case.
stable strategy (ESS). That is, we seek a strategy such that
if almost all population members adopt this strategy, then
no rare mutant within this population has higher fitness.
To find this strategy when density dependence acts
through the parameter A (eq. ), we adjust A during
computation so that the maximum fitness equals 1. Then,
as is shown in appendix D, the strategy that maximizes
fitness for this A is the unique ESS. When density depen-
dence has more complex forms, a more computationally
intensive procedure is required (app. D).
Results in the Energy-Constraint Case
We first consider what we refer to as the “energy-con-
straint” version of our model. In this version, we assume
that there is no nest predation. Birds are thermoneutral,
so that seasonality is solely the result of seasonal changes
in the available food (c(t) p 1
almost negligible (); it is not 0 so as to avoid
m p 10
degenerate cases in which breeding and not breeding are
both optimal. The survival function
p 1 K p 200
not an exact step function because in that case, fitness
would be a discontinuous function of the environmental
food parameter A and there may be no ESS.
In this version, there is essentially no penalty for high
foraging intensity, provided that the bird’s food require-
ment does not compel it to forage for close to the whole
week. Consequently, a bird will always breed if doing so
is energetically possible and provides any small advantage.
This version therefore allows us to investigate the effects
of the constraint imposed by the food supply.
for all t). Predation risk is
1/(1 ? u )
). The survival function is
Results are first presented for five cases of the energy-
constraint version. The first case has baseline maturation
(fig. 1) and baseline parameters (table 1). Two cases differ
from this baseline in terms of the food requirements of
dependent young. These cases are labeled “low need”
( ) and “high need” (F
beled “fast maturation” and “slow maturation” differ from
the baseline case in the rate at which young gain foraging
efficiency (fig. 1).
). The cases la-F
Effects of the Constraint on EnergyIntakeImposedbyDensity
Dependence. The mean food in the environment (as mea-
sured by the parameter A) adjusts with ?Fso that the
336The American Naturalist
population has stable density at the ESS. An adjustment
that improved (reduced) food at all times of year would
necessarily increase (decrease) population growth rate, so
that the population density would not be stable. It follows
that as ?Fincreases, midwinter food must decrease and
midsummer food must increase. Figure 2 illustrates the
change in food availability as seasonality changes. As fig-
ures 2 and 3A show, as ?Fincreases from 0 to 0.6, mid-
winter food availability typically decreases by around 10%.
Given function (1), this implies that the increase in mid-
summer food availability is typically more than 300%. In
other words, the winters get a little worse, but thesummers
get a lot better.
For low ?F, the annual bottleneck is during breeding
(which may be in winter; fig. 3). For higher ?F, breeding
occurs in spring or summer, and the bottleneck is for
nonbreeding birds in winter.
For low ?F, the breeding bottleneck is greatest in the
high-need case, which has the greatest cost of care of one
offspring, so this case has the highest midwinterfoodavail-
ability and hence the smallest equilibrium winter popu-
lation density. For high ?F, a parent can easily care for at
least one offspring, so the high-need case no longer has
the greatest midwinter food availability (fig. 3A). At high
?F, the major limiting factor is survival of young over
winter, so the slow-maturation case has the highest mid-
winter food availability (fig. 3A).
Mean Care Times and the Number of Clutches per Year.
Consider first the case
? p 0
from one breeding attempt become independent, there is
no possible advantage to delay, and it is optimal to breed
again after the minimum possible delay (1 week). Thus,
in this case, care times plus 1 week and mean numbers
of clutches per year are inversely proportional (see fig. 3B,
3C). Care times are mainly determined by the time needed
for newly independent young to have sufficient foraging
efficiency to survive (fig. 3B). Thus, care times are long
when efficiency increases slowly (slow-maturation case)
and short when gain is rapid (fast-maturation case). Be-
cause food is better when breeding is hard (high-need
case), care times are also shorter in that case. Note that
this shorter care time arises without an assumption that
high need means faster development.
As ?Fincreases, the care period becomes constrained
because there is not enough food to supply even one off-
spring in winter. All care must now fit into a seasonal
breeding window. Thus, the first clutch is always laid at
the start of the breeding window, and reproduction be-
comes locked into the annual cycle. We refer to the phe-
nomena of locking into the annual cycle as entrainment
(McNamara et al. 2004). For each case, there is a critical
value of ?Fbelow which there is no entrainment and above
. In this case, after young
which reproduction is entrained. The transition to en-
trainment occurs when the number of clutches first
switches to 1 as ?Fincreases (fig. 3C). Typically, entrain-
ment sets in before
? p 0.1
constrained case is exceptional because the young gain
foraging efficiency slowly and the optimal care time is still
longer than a year when
? p 0.1
As ?Fincreases, there is more food available in summer.
Thus, young are able to care for themselves at a younger
age. Care times tend to decrease, and it becomes possible
to fit more than one clutch into the breeding window (fig.
3B, 3C). The number of clutches per year increases mono-
tonically with increasing ?Fin all cases (fig. 3C).
There is more food overall as ?Fincreases and the sum-
mer becomes much better. Thus, thedurationofthebreed-
ing window increases as ?Fincreases. This leads to longer
care periods for ranges of ?Fover which clutch number
per year is constant in the constrained cases. The increase
in the length of the breeding window and the increase in
the number of clutches produced result in alternating slow
increases and abrupt drops in the mean care period as ?F
increases (fig. 3B).
. The slow-maturation–
Lay Date. The lay date of the first clutch to become in-
dependent in a year is shown in figure 3D. For the low-
?F, low-need case, it is optimal to lay in the previous year
and care over winter. This ensures that young become
independent during spring, allowing them to gain expe-
rience before winter. This strategy applies particularly
when young gain foraging efficiency slowly (slow matu-
ration) or when they gain it at a medium rate but require
less food (low need). For higher ?F, as ?Fincreases and
food in summer increases, lay dates become earlier.
Clutch Size. As seasonality increases, the food in summer
gets better, and it becomes possible to sustain a bigger
clutch. Figure 3E plots the mean number of eggs per clutch
averaged over all clutches produced in a year. When there
is more than one clutch, the first has fewer eggs than the
Year of First Breeding. Figure 3F shows the year of first
breeding. For low seasonality, there is a tendency to delay
breeding until the second year after birth unless young
gain foraging efficiency rapidly (fast-maturation case). As
seasonality increases, there is more food in summer, and
it becomes optimal to breed in the first year after birth.
Finally, for highseasonality, itis optimalforyoungtobreed
in the year of their birth.
Juvenile Survival. Figure 3G shows the survival ofjuveniles
to the end of the first winter after their time of indepen-
dence. For low seasonality, parental care lasts a year or
Effect of Latitude on Avian Life Histories337
more in some cases (fig. 3B). Not surprisingly, survival is
highest in these cases because juveniles are already quite
efficient foragers at independence.
As seasonality increases, all care times become shorter,
so that young are less efficient at foraging at independence.
This, combined with reduced food availability in midwin-
ter, dramatically reduces the probability that juveniles
survive their first winter. The decreased survival with in-
creasing seasonality can also be seen as an inevitable con-
sequence of the increased numbers of young produced
and the fact that populations are at a density-dependent
equilibrium. Increased seasonality increases competition
between juveniles for food (as represented by thedecreased
midwinter food), and survival is reduced.
Adult Survival. Once reproduction is entrained, adult sur-
vival is almost independent of seasonality in four of the
five cases shown in figure 3H. In these four cases, there
is little adult starvation, and survival probability is largely
determined by the background mortality. In contrast, in
the fast-maturation case, adult survival decreases strongly
with increasing seasonality. This occurs because of the low
food in midwinter. Another way to interpret this result is
to note that juveniles are typically as good at foraging as
their parents by their first winter. Thus, these individuals
are incompetition witholderbirdsoverfoodinmidwinter,
and there is high adult mortality as well as high juvenile
Robustness of the Results. In figure 3, we illustrated the
effects of changing the food requirement of dependent
young. There are four other parameters that control the
energetic consequences of breeding in our model. Two
concern initiation of breeding: Dnestis the metabolic ex-
penditure required to build the nest, and Doffis the cost
of egg production. Two concern delivery of food to the
young: mflyis the cost of transport of food, and D is the
rate of transport of food. We have investigated the ro-
bustness of our conclusions to changes in all four param-
eters. The effect of seasonality ?Fon all eight measures
presented in figure 3 is highly robust regardless of the
values of these breeding parameters (fig. C1 in the online
edition of the American Naturalist). The effects of a change
in a breeding parameter for given ?Fdepend on details
such as the number of clutches before the change (fig. C1).
There are, however, some general trends: making breeding
more difficult increases the food availability; making the
initiation of breeding more difficult increases lay date
when seasonality is low; making delivery of food to the
young more difficult tends to reduce clutch size.
Reducing the background mortality J from its baseline
value reduces overall food availability, increasing lay date
and age of first breeding (fig. C2 in the online edition of
the American Naturalist). The qualitative effect of increas-
ing ?Fis unaltered.
In the results presented in figure 3, the juvenile dis-
advantage factor . We have repeatedcalculationswithJ p 2
a range of values of the juvenile disadvantage factor J (fig.
C2). The main effect of an increase in J from
disadvantage) to is a slight increase in the age ofJ p 8
first breeding. However, the effect is surprisingly small; at
high seasonality, even an eightfold disadvantage does not
prevent juveniles from breeding in their year of birth.
Increasing J also tends to reduce the number of clutches
and eggs per clutch at high seasonality. Other measures
shown in figure 3 are highly robust to changes in ?F.
(noJ p 1
Results from the Predation-Risk Version
We now introduce a “predation-risk” version of our
model. The baseline case of this version (table 1) is iden-
tical to the baseline energy-constraint case except that (i)
background mortality is reduced, (ii) foraging incurs a
predation risk, and (iii) foraging is more stochastic
( ). We introduce more stochasticity because, inK p 40
contrast to the energy-constraint case, we want the birds
to be able to control their probability of starvation (see
McNamara and Houston 1987; Houston and McNamara
1993). By comparing predictions of the two versions, we
are able to understand what effects are primarily a con-
sequence of energy constraints and what additional effects
are the result of a trade-off between mortality (starvation
and predation) and reproduction.
The effect of changing from the energy-constraint base-
line case shown in figure 3 to the correspondingpredation-
risk baseline case is shown in figure 4. The effects of chang-
ing from each of the other four energy-constraint cases
shown in figure 3 to the corresponding predation-risk
cases are shown in figure C3 in the online edition of the
American Naturalist. In all cases, the qualitative effects of
food seasonality ?Fon each of the eight measures shown
is unaltered by the change of version. The effects of
changes in maturation speed and food need of dependent
young are also highly robust.
In the predation-risk version, predation risk increases
with foraging intensity. This tends to result in lower re-
productive effort in the predation-risk cases than in the
energy-constraint cases. This has several consequences.
Entrainment tends to set in for smaller ?Fbecause, even
if it is possible, breeding in midwinter requires high for-
aging intensity. In the predation cases, birds are usually
not up against the energy constraint when they breed, and
care times tend to be shorter; consequently, mean care
times essentially decrease monotonically with increasing
?F. The number of eggs per clutch is substantially reduced
Effect of Latitude on Avian Life Histories339
Figure 3: Effect of the seasonality in food in the energy-constraint version. Results are at evolutionary stability. Five cases are shown. The baseline
case has parameters given in table 1 and a gain in foraging efficiency shown by the middle curve in figure 1. The low-need and high-need cases
differ from this case only in the amount of food that the parent needs to supply to each dependent young (low need:
). The fast-maturation and slow-maturation cases differ from the baseline in that the efficiency gain is given by the top and bottom curvesF
in figure 1, respectively. A, Food availability in midwinter g(0). B, Mean care time of all broods. C, Mean number of clutches per year. D, Lay date
of the first clutch to become independent during a year. Note that only those cases in which breeding is entrained are shown. E, Mean number of
eggs per clutch, averaged over all clutches in one year. F, Mean year of first breeding. Here years are counted from the time of independence. The
year of first breeding is year 0 if breeding occurs before week 52 in the year of independence, year 1 if first breeding occurs in the following calendar
year, and so on. G, Probability that an individual survives from independence to the end of week 5 in the following calendar year. H, Probability
that a fully experienced bird survives a whole year.
; high need:F
at high seasonality. Age at first breeding tends to be a little
Patterns of juvenile and adult mortality are similar in
the two cases. In the predation-risk version, almost all
juvenile mortality is the result of starvation in the middle
of winter. Most adult mortality is the result of predation.
At low ?F, the main source of mortality is predation during
the first few weeks of breeding (when food is still not
abundant). For higher ?F, there is still some mortality as-
sociated with breeding, but the main sources are predation
and starvation in winter.
The Effect of Nest Predation
It is not our intention to explore the possible effects of
nest predation systematically in this article. Instead we
investigate the effect of nest predation in the simple case
where predation risk is independent of clutch size and age
of dependent young. To do so we take the predation-risk
baseline case and add a constant probability moffthat de-
pendent young will die each week. The effect of adding
this nest predation is illustrated in figure 4.
Given that mortality costs increase with increasing ef-
fort, theory predicts that the effort invested in current
reproduction should increase as the value of the current
attempt relative to future reproductive success increases.
Making nest predation higher reduces the value of the
current breeding attempt but also reduces the value of
subsequent breeding attempts. Thus, it is not immediately
clear that increased nest predation necessarily reduces the
value of the current attempt relative to that of future at-
tempts, and so it predicts a reduced effort per breeding
attempt. Note, however, that if nest predation reduced
success on each breeding attempt, then this would reduce
lifetime reproductive success if all else were held fixed.
This is, of course, not possible at a density-dependent
equilibrium. In our model, density dependence adjusts the
food supply so that food availability increases as nest pre-
dation increases (fig. 4A). This means that adults are more
likely to survive over winter and indeed have greater an-
nual survival at all levels of seasonality despite having to
make repeated breeding attempts before one is successful
(fig. 4H). This greater survival changes the balance be-
tween current and future success, making future success
relatively more important. The result is that reproductive
effort per attempt is reduced. This can be seen in both
the reduced clutch size (fig. 4E) and the increased age at
first breeding (fig. 4F) as nest predation increases.
Small birds have limited energy storage capacity relative
to their rate of energy expenditure (Stuebe and Ketterson
1982; Lehikoinen 1986). For this reason, our model as-
sumes that a bird balances its energy budget during each
week; that is, expenditure of energy equals energy intake
from food. In contrast, larger birds could potentially build
up reserves in one week and use this energy store in future
weeks. Furthermore, in addition to energy reserves, all
birds have condition measures, such as feather quality and
immune competence, that have long-term effects (Mc-
Namara and Houston 2008). We do not attempt to make
a realistic model of a specific measure of condition here.
Instead, we use a simple schematic model of condition to
investigate whether our general conclusions are robust
when effects carry over from one week to succeeding
In general, condition might be expected to deteriorate
during prolonged periods of forced hard work and to re-
cover (by moulting, in the case of feather quality) once a
bird works less hard. We extend our predation baseline
model to incorporate this effect as follows. We assume a
condition variable x that lies in the range
bird with condition x at the start of one week expends
energy at rate g during the week, its condition at the start
of the next week is
. If a0 ≤ x ≤ 1
?x p x ? a ? bg. (2)
The computations presented in figure 4 are based on the
a p 0.25
rameters, the break-even energy expenditure is
Thus, a bird that is not caring for young and forages for
a proportion of the week is just able to maintainu p 0.7
. For these pa-
g p 0.9
b p a/0.9
Effect of Latitude on Avian Life Histories341
Figure 4: Effect of seasonality in food in the predation-risk version. Results are at evolutionary stability. Five cases are shown. The predation baseline
case differs from the energy constraint baseline as indicated in table 1. Other cases differ from the predation baseline case as follows. The cases nest
0.1 and nest 0.2 include nest predation ( and 0.2, respectively). The condition 6 and condition 100 cases are for the model with a condition
variable and refer to the casesand 100, respectively (eq. ). In these cases,C p 6
see figure 3.
and(eq. ). For an explanation of panels,
a p 0.25
b p a/0.9
condition. If it works harder, its condition deteriorates; if
it works less hard, its condition improves.
We assume that a bird with condition x at the start of
the week dies during the week as a results of poor con-
dition with probability
d(x) p (1 ? x) .(3)
Figure 4 illustrates the cases
former case might be appropriate when condition is im-
mune function, as mortality increases rapidly once con-
dition deteriorates sufficiently. In the latter case, the bird
dies from poor condition only once condition is very low
(essentially 0). Thus, this case might be appropriate when
condition represents a reserve, such as energy or nutrients.
In both cases, at evolutionary stability there are significant
carryover effects from week to week; for example, con-
dition may deteriorate progressively during care of young
and take several weeks to recover afterward. Despite this,
the general effects found in the predation baseline case
persist in both of the illustrated cases of carryover (fig. 4).
and. TheC p 6C p 100
Robustness to Other Model Assumptions
Density Dependence. We have assumed that density de-
pendence acts through the parameter A. This parameter
can be regarded as decreasing with some measure of av-
erage annualpopulation density.InappendixD,weinstead
consider density dependence to be acting locally in time,
with food availability in a week being a function of pop-
ulation density that week.
Shape of the Food Availability Function. We have taken the
environmental food availability to be a sinusoidalfunction.
This dependence on time of year is probably not realistic
at high latitudes, since winters tend to be long while sum-
mers are short. Appendix E in the online edition of the
American Naturalist considers the case in which the en-
vironmental food availability behaves in this way.
Both the above modifications change the dependence
of the food supply on time of year so that it is no longer
sinusoidal (fig. D1 in the online edition of the American
Naturalist). However, as can be seen from figure D2 in
the online edition of the American Naturalist, the quali-
tative effects of seasonality on the various measures we are
concerned with are robust to the change in both the form
of density dependence and the environmental food supply.
Seasonality in Temperature
In appendix F in the online edition of the American Nat-
uralist, we investigate whether trends shown in figures 3
and 4 can also be obtained by seasonal variation in the
resting metabolic expenditure. In particular, we assume
that temperature variation is greater at high latitudes, re-
sulting in high resting metabolic expenditure in winter at
these latitudes. As can be seen from figure F1, in the ex-
amples considered, varying expenditure in this way pro-
duces rather weak effects that enhance the effect of the
variation in food supply.
Despite the importance of seasonality, relatively little work
has been done on its effects on the evolution of life his-
tories. Boyce (1979) develops a relatively simple model,
from which he concludes that a strategy with a small clutch
size and low demand for resources could be favored when
seasonality is low. Boyce’s model does not explicitly in-
corporate clutch size or predation. It also does not model
the timing of reproduction and hence cannot make pre-
dictions about phenology. Griebeler and Bo ¨hning-Gaese
(2004) model Ashmole’s hypothesis. Their model differs
from ours in several respects. They find the optimal clutch
size by evolutionary simulations. Because clutch size is the
only decision they consider, like Boyce they are unable to
make predictions about the timing of breeding, the du-
ration of care, or the age of first reproduction. In addition,
the effect of birth date on reproductive value is not in-
cluded, birds are constrained to produce exactly one clutch
per year, and the model of seasonality is schematic. In
contrast, we have developed a model that makes predic-
tions about a whole range of life-history variables, in-
cluding clutch size, number of broods, the time of year at
which breeding occurs, and the associated levels of juvenile
and adult mortality. Versions of our model incorporate
explicit predation and a condition variable. Although we
have investigated avian life histories, our approach is com-
pletely general and could be used to analyze examples of
latitudinal trends in other groups, such as mammals (Lord
342The American Naturalist
Table 2: Comparison of tropical and temperate birds
Clutches per year
Mean care time (weeks)b
Year of first breeding
Note: The comparison is based on the assumption that these regions
differ only in terms of seasonality. The first column gives the feature of
interest. The second and third columns give predictions from the model
for the predation baseline (tropical
? p 0.1
final column states whether the trend in the predictions is also seen in
aModel predictions based on case with no regional differences in
bIncludes time to build nest and lay eggs.
, temperate). The
? p 0.5
1960; Spencer and Steinhof 1968; Cockburn et al. 1983;
Temte 1993) and fish (Leggett and Carscadden 1978; Flem-
ing and Gross 1990; Johnston and Leggett 2002; Heibo et
al. 2005). Of course, the details of the models would have
to be changed to make them appropriate. For example,
environmental temperature is likely to be very important
in fish (e.g., Garvey and Marschall 2003; Charnov and
In their model of annual routines of avian moult, Barta
et al. (2006) found that the number of breeding attempts
per year increased as the environment became more sea-
sonal. They noted that this could be viewed as being in
broad agreement with data on latitudinal trends in repro-
ductive effort but pointed out that their model did not
allow birds to choose their clutch size. We have presented
and analyzed the first self-consistent model of the effect
of latitude on avian life history. In this model, the effects
of density dependence are crucial. Because of density de-
pendence, it is not the absolute level of food that is im-
portant but the maximum level over the year relative to
the minimum level, and, as we have argued, an increase
in seasonality must reduce midwinter food availability and
increase midsummer availability. This effect of seasonality
on food availability is responsible for the main effects pre-
dicted by our model.
Our model successfully predicts the observed trends in
clutch size, duration of parental care, andage atfirstbreed-
ing. The predicted trends are robust. We do not, however,
predict the trend in life span (table 2)—as we discuss
below, this could be related to the absence of a state var-
iable that represents the long-term effects of hard work.
The trend in the number of clutches per year predicted
by our model is opposite to the trend observed in the data
(Bo ¨hning-Gaese et al. 2000). There is, however, a problem
in comparing the model’s prediction to the data. The re-
sults in table 2 are for cases withnonestpredation,whereas
the data are based on nest predation, which may differ
with latitude (Stutchbury and Morton 2001).
Tropical birds generally display a slow pace of life, with
lower metabolic rates, lower growth rates, and higher lon-
gevities than many temperate-zone counterparts (e.g.,
Ricklefs 2000b; Stutchbury and Morton 2001; Ricklefs and
Wikelski 2002). If such effects are to be understood, a
more complex model is required. The evolution of met-
abolic rate will depend on the negative effects of energy
expenditure. As McNamara and Houston (2008) point
out, hard work (i.e., a high rate of energy expenditure)
has a variety of negative effects that act on different time-
scales. In this article, we have included a state variable that
represents relatively short-term effects. To find the optimal
metabolic rate for a given environment, it would be nec-
essary to include a state variable that represents the long-
term effects. To model growth, we could include a state
variable representing physiological maturity in our model.
Such a variable would typically mean that newly indepen-
dent offspring were not physiologically capable of repro-
duction. Further work could also introduce a state variable
to represent the state of repair of the body (see Kirkwood
and Rose 1991; Abrams and Ludwig 1995; Kirkwood 1997,
2002; Mangel 2001). We could then consider the evolution
of life span and senescence.
Although we compare our results to data from tropical
and temperate birds, we are not claiming or assuming that
latitudinal trends always exists. What we have shown is
that if sites differ only in the seasonality of food, then
many of the differences observed between tropical and
temperate birds can be predicted by the effect of season-
ality. In some cases, however, tropical and temperate
regions may differ in several factors, so that no simple
trend can be seen. Furthermore, it is possible to find trop-
ical areas that are seasonal. Our model predicts that if all
else is equal, a seasonal environment should produce a life
history typical of a temperate bird species. It is interesting
in this context to note that the green-rumped parrotlet
Forpus passerinus inhabits a tropical but seasonal environ-
ment close to the equator and has a large clutch size (Beis-
singer and Waltman 1991) and relatively low adult survival
rates (Sandercock et al. 2000).
A fundamental aspect of our model is the interaction
between population size and food availability. The im-
portance of this dependence can be seen in the case of
increased nest predation. As nest predation increases, den-
sity dependence adjusts the food supply so that food avail-
ability increases (fig. 4A). As a result, adults are more likely
to survive the winter and have higher annual survival at
all levels of seasonality. Because adult survival is higher,
future reproductive success becomes relatively more im-
portant, and so reproductive effort per breeding attempt
is reduced. This example reinforces the view of Barta et
Effect of Latitude on Avian Life Histories 343
al. (2006) that it is difficult to attribute an effect to food
or predation in isolation.
We have not attempted a complete analysis of nest pre-
dation. Future work could allow this source of mortality
to depend on clutch size and perhaps also on the age of
the brood: dependent young might be in the nest for the
first few weeks (subject to one level of predation) but then
be out of nest and following the parents, who are still
supplying them with food (subject to another level of
We have analyzed a relatively simple model that allows
us to isolate the effects of seasonal environments.Thebasic
version of the model does not have a state variable to
represent energy reserves; energy balance is the basic con-
straint on behavior. Models based on energy balance have
been used to investigate the ability of parent birds to raise
their young (Houston et al. 1996) and the effects of hyenas
on wild dogs (Gorman et al. 1998). In contrast to these
models, we have explored the implications of energy bal-
ance for annual routines in the presence of density-
dependent effects. Modifying the basic model to allow for-
aging to incur a predation risk did not have a strong effect,
and the qualitative trends were not changed. These trends
did not change when a state variable with carryover effects
that lasted a few weeks was added. This shows that en-
ergetic arguments of the sort proposed by Lack (1947) and
Ashmole (1963) and elaborated by Ricklefs (1980) are suf-
ficient to explain most of the latitudinal trends; see table
2 for details.
We thank S. R. Beissinger and an anonymous reviewer for
helpful comments on a previous version of this article.
J.M.M. acknowledges support from a Leverhulme Fellow-
ship. Z.B. was supported bya BiotechnologyandBiological
Sciences Research Council grant to J.M.M. and A.I.H. and
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Associate Editor: Peter D. Taylor
Editor: Michael C. Whitlock