Behavioral Ecology Vol. 10 No. 6: 666–674
Reproductive decision-making by female
peacock wrasses: flexible versus fixed
behavioral rules in variable environments
Barney Luttbega and Robert R. Warnerb
a
Center for Population Biology and Section of Evolution and Ecology, University of California, Davis,
CA 95616, USA, and bDepartment of Ecology, Evolution, and Marine Biology, University of California,
Santa Barbara, CA 93106, USA
Because environments are temporally variable, animals may often estimate the current environmental state to inform their
behavioral choices. However, using experience may cause behavior to lag behind the current state of the environment, and
estimates may suffer from sampling errors. We used stochastic dynamic models to examine the environmental conditions that
favor flexible rather than fixed estimates and behaviors. The examination was conducted in the context of reproductive decisions
made by the female peacock wrasse (Symphodus tinca), a nearshore Mediterranean fish. Female peacock wrasses can choose to
spawn in a nest, with males that defend these nests within territories, or out of a nest, with males that defend neither territories
nor nests. A female must expend effort and time to find nesting males, and the profitability of this search, relative to spawning
with nonnesting males, changes with the density of nests and relative hatching success of eggs in and out of nests. A female
can increase her fitness by estimating the environment’s state and matching her reproductive decisions to the current environment. These estimates can be flexible and formed by experience, or fixed and formed by selection. We found that flexible
estimates based on experience do better when there is variance within and between seasons and when there is greater uncertainty. The optimal rate for forgetting experiences is set by the rate of environmental change. Comparisons of predicted female
behavior using flexible and fixed estimates with observed behavior suggest that females use estimates that are updated by
experience. Key words: Bayesian, learning, optimal forgetting, peacock wrasse, plasticity, Symphodus tinca, variable environments.
[Behav Ecol 10:666–674 (1999)]
I
n variable environments animals may improve their reproductive success by tracking their environment to guide
their behavioral choices. For behaviors that are often repeated
(such as feeding or reproducing), remembered outcomes of
past behaviors can be used to estimate the current state of the
environment (Mangel, 1990; McNamara, 1996; McNamara
and Houston, 1987; Shettleworth et al., 1988; Stephens, 1987;
Weiss, 1997). However, the net benefit of estimating the state
of the environment depends on the costs of obtaining the
information and its reliability. In this study, we used dynamic
state variable models to examine how temporal environmental
variability shapes selection for reproductive decision-making
processes in the peacock wrasse (Symphodus tinca). Our results are specific to the life history of the peacock wrasse, but
the general principles of how the advantages and disadvantages of using experience to make decisions might vary with
the environmental variability are applicable to any trade-off
of flexible versus fixed behavior.
Using a fixed seasonal pattern of behavior versus behavior
based on experience is a trade-off between stability and flexibility. The behavior of individuals using fixed seasonal behavioral patterns can anticipate environmental changes; however,
the behavior will not match irregular variation within and between seasons. Theoretical treatments have shown that phenotypic plasticity (de Jong, 1989; Via and Lande, 1985) and
learning (Mangel, 1990; Roitberg et al., 1993; Stephens, 1993)
are favored in variable environments and that flexible behav-
Address correspondence to B. Luttbeg, National Center for Ecological Analysis and Synthesis, 735 State St., Suite 300, Santa Barbara,
CA 93101, USA. E-mail: [email protected].
Received 20 November 1997; revised 22 September 1998; accepted
21 April 1999.
q 1999 International Society for Behavioral Ecology
ioral responses to the environment, whether viewed as state
dependent (Houston and McNamara, 1992) or genetically
based (Anderson, 1995; Carroll and Corneli, 1995), should
only be favored in variable environments. However, although
behavioral responses based on experience provide flexibility,
individuals can falsely identify random sampling outcomes as
larger scale environmental changes, and their estimates of the
environmental state will necessarily lag changes in the environment. If individuals cannot reliably detect the state of their
environment or if their rate of detection is slower than the
rate of environmental change, then flexible responses may
not be advantageous (Mazalov et al., 1996). There is limited
empirical support for the importance of constraints on flexible behavior. Rodd and Sokolowski (1995) found that male
guppies from only one of two populations respond flexibly to
changes in social conditions, leading the authors to suggest
time, cognitive, and error costs as possible causes of the lack
of flexibility.
To examine whether female peacock wrasses can make better reproductive decisions by flexibly estimating the state of
their environment, we created four models of different behavioral rules for choosing between reproductive options. The
behavioral rules differ in whether and how females estimate
the probability (P) of successfully searching for a nesting
male. We then compared the fitness outcomes of the rules in
environments that differ in their inter- and intraseasonal variation. Adding predictable variation within and between seasons results in individuals doing better if they estimate P based
on experience. Furthermore, the optimal rate of forgetting
experiences, which depends on the rate of environmental
change, represents a compromise between the uncertainty of
current information (due to small sample size) and the unreliability of older information (due to environmental changes). Observed behavior of female peacock wrasses most closely
Luttbeg and Warner • Flexible versus fixed behavior in variable environments
Figure 1
The proportion of females seen mating that spawned in a nest
during the 1991 breeding season (Warner et al., 1995). Daily
observations were grouped to form weekly averages. Error bars
represent 95% confidence intervals.
matches the behavior of the model using experience to estimate P.
NATURAL HISTORY
The models are based on the known reproductive behavior
of peacock wrasses, Mediterranean fish found in shallow water
near rocky substrates. Their breeding season is from mid-April
to mid-June. Large males (.22 cm length) construct nests by
inserting loose pieces of algae into a mat of attached algae.
After nest construction, there is a 2- to 3-day period during
which nesting males actively court and mate with females. Peripheral males begin to surround these nests, and there is
another 2- or 3-day period of spawnings at the nest, with peripheral males often joining the spawnings. Successful nests
contain 30,000–70,000 demersal eggs. At the end of the
spawning phase, nesting males become unreceptive to females
and protect the eggs against predation. Small males do not
construct nests and either become peripheral males that opportunistically sneak copulations on nests or pursue and court
females away from any nests. Most males are nonnesting
males, and because the brooding period is relatively long,
most nesting males are unreceptive to females (Warner et al.,
1995). Lejeune (1985), van den Berghe et al. (1989), Warner
and Lejeune (1985), Warner et al. (1995), and Wernerus
(1989) give more complete descriptions of the natural history
of the peacock wrasse.
The species is a good subject for a study of reproductive
decisions because females have two distinct options (Warner
et al., 1995). The average female lays eggs every other day,
leaving her home range to find a mate. On any given day, a
female can either have her eggs fertilized by readily available
nonnesting males, or she can search for and spawn with nesting males. Eggs placed with nesting males receive protection
from predators, while eggs outside of nests receive no care.
Individual females switch between the two modes of spawning
(Warner et al., 1995). It appears that females initially attempt
to find an acceptable nesting male and use a behavioral rule
similar to a giving-up time; out-of-nest spawnings occur after
a period of searching from nest-to-nest. Females spawn with
nesting and nonnesting males throughout the season (Figure
1). Early and late in the season, most spawnings occur out-ofnest. At mid-season, the majority of spawnings occur in nests,
but approximately 20% of spawnings are out-of-nest.
667
The relative payoffs of the two spawning options depend on
(1) the fraction of eggs that hatch when a female spawns with
a nesting or nonnesting male, (2) the probability of successfully searching for a nesting male, and (3) the costs of searching (Warner et al., 1995). Warner et al. (1995) measured the
changes in these factors during a breeding season while simultaneously monitoring female behavior. They found that
the profitability of searching for and spawning with nesting
males increased early in the breeding season and decreased
after mid-season, due to changes in the availability of nesting
males and probabilities of hatching success. Corresponding
with these environmental changes, females increased and
then decreased the proportion of their spawnings that occurred with nesting males. The alterations in female behavior
appeared to result from changes in the time a female
searched before resorting to out-of-nest spawning. Because
nests are spread over areas that are orders of magnitude larger than an individual female’s home range, she rarely has contact with more than two nesting males while foraging for food.
Females thus have limited access to information about changes in the overall reproductive environment.
There are two possible causes for the observed correspondence between female behavior and environmental changes.
First, female estimates of the environment and their resulting
behavior might change over the course of the season in a
fixed seasonal pattern that has been shaped by selection. The
behavioral pattern would tend to correspond to the average
seasonal pattern of the environment (a ‘‘rule of thumb’’; see
Warner, 1997). The second possibility is that females estimate
the current state of the environment and base their behavior
on that estimate. Such estimates could be based on experience or cues; we will only consider estimates based on experience gained through prior reproductive attempts (see Sullivan, 1994).
It is not easy to determine whether seasonal changes in female decision rules are based on fixed seasonal patterns or
sampling estimates. A field study addressing this question
would require large-scale environmental manipulations and
detailed focal observations of females over the breeding season. Here, we took the alternative approach of using models
to compare the fitness consequences of using fixed seasonal
behavioral patterns versus using estimates based on experience. We then compared the behavioral outcomes of alternative rules to the actual behavior of female peacock wrasses.
We cannot make firm conclusions about what method female
peacock wrasses are actually using, but we can make predictions about what types of environments would favor one behavioral rule over another.
METHODS
Estimation of parameters
Three parameters determine the relative payoff of searching
for nesting males and spawning with nonnesting males: (1)
egg hatching success in and out of nests, (2) the probability
of successfully searching for nesting males, and (3) the costs
of searching. We estimated the first two parameters from field
observations (Warner et al., 1995) as follows.
Egg hatching success in and out of nests is determined by
the daily risk of egg predation and the rate of egg maturation.
The survival of eggs in and out of nests, estimated from field
observations, is always higher in nests (Warner et al., 1995).
The rate at which eggs mature depends on water temperature,
which rises over the breeding season. Eggs take approximately
12 days to hatch at the beginning of the season and 6 days to
hatch at the end of the season. Combining the risk of predation and maturation times, Warner et al. (1995) estimated
Behavioral Ecology Vol. 10 No. 6
668
Universal assumptions
Figure 2
Field data on the number of eggs expected to hatch from 1500-egg
clutches left in nest (Bi: solid line) or out of nest (Bo: dashed line)
and the probability of successfully finding an acceptable nest. For
the egg-hatching data, the values for days 15, 45, 67, and 82 were
derived from data in Warner et al. (1995) and from additional
unpublished field data. Values between these points were
interpolated, with the assumption that hatching success peaked
between days 67 and 82. The solid line with squares represents the
probability of successfully finding an acceptable nesting male during
10 min of searching. The values for days 15, 45, and 75 were
derived from data in Warner et al. (1995). Values between these
points were interpolated.
The alternative models make some common assumptions
about the schedules, benefits, and costs of the two reproductive options available to female peacock wrasses. We use dynamic state variable models (Mangel and Clark, 1988; Mangel
and Ludwig, 1992) that span a 90-day breeding season with
nine 10-min periods per day. The number of days corresponds
to the length of the typical breeding season, and the number
and length of time periods is arbitrary. Females are assumed
to maximize the number of eggs they expect to hatch over
the breeding season.
A gravid female begins the day at the first of nine time
periods and can either spawn with nonnesting males (out-ofnest), who are always available, or search for and spawn with
an acceptable nesting male (in nest). If she spawns out-of-nest
or successfully searches for a nest and spawns, she is done for
the day. If the nine time periods expire and she has not
spawned, she spawns out-of-nest.
When a female searches for an acceptable male with a nest,
in the models she pays two costs. One cost is energetic, C,
with females losing 10 expected hatched eggs for each time
period of searching, s. Females generally do not feed while
searching for males; thus, the second cost of searching is a
reduced likelihood that she will be gravid on the next day.
Females start the day with a 90% chance of being gravid the
next day, and this is reduced by 10% for each period of search
so that the probability of being gravid the next day, G(s), is
G(s) 5 .9 2 .1s.
per-egg hatching success for early, mid-, and late season, for
inside and outside of nests. With these estimates and an assumed clutch size of 1500 eggs, we interpolated the number
of eggs expected to hatch from a clutch left in or out of nests
across the breeding season (Figure 2).
In any given time period, the probability that a female successfully finds an acceptable nesting male depends on the
density of nests and proportion of nests that are at the correct
stage for spawning. Warner et al. (1995) estimated the average
travel time between nests based on focal observations and estimated the proportion (Pa) of nests that are acceptable to
females based on surveys of nests during early, mid-, and late
season. Given the average travel times between nests, we calculated the expected number of nests (Ne) encountered during 10 min of search. Assuming that exactly Ne nests are encountered, the probability of not finding an acceptable nest
during 10 min of search is
Po 5 (1 2 Pa )Ne.
(1a)
The probability of finding an acceptable nest during 10 min
of search (P) is
P 5 1 2 Po,
(1b)
and these values, based on field data, are shown in Figure 2.
(2)
When a female spawns, she gains an expected number of
hatched eggs. She gains Bo(d) when she spawns out of nest,
and she gains Bi(d) when she spawns in nest (Figure 2). If
nongravid at the start of the day, a female cannot spawn that
day and is gravid the next day.
Models of behavioral rules
We present four models of female peacock wrasse reproductive decision-making rules. The models differ in the flexibility
of female behavior and in the methods females use to estimate
the state of their environment (Table 1). With each model,
females use giving-up times (GUT) to determine how long
they will search for nesting males. The GUT approach appears
to correspond with actual female behavior (Warner et al.,
1995). In the model, gravid females at the start of each day
choose a GUT, which determines how long they will search
for an acceptable nest. If that time expires without finding an
acceptable nesting male, the female discontinues searching
and spawns out of nest. Other approaches, such as choosing
whether to search at the beginning of each time period, resulted in lower fitness than GUT rules.
Constant GUT rule
In the Constant GUT model, females use a constant GUT for
all days of the season (Table 1), modeled by running a for-
Table 1
Summary of the assumptions of the four models
Model
Hatching
successes
Probability of
successful search (P)
Constant Giving-Up Time
Experience Estimates of P
No Estimates of P
Fixed Seasonal Estimates of P
Unknown
Known
Known
Known
Unknown
Estimated with experience
Unknown
Estimated with fixed pattern
Giving-up times
Do not vary
Vary with hatching success and experience
Vary with hatching success
Within seasons vary with hatching success and P ;
between seasons do not vary
Luttbeg and Warner • Flexible versus fixed behavior in variable environments
669
ward simulation (Mangel and Clark, 1988). This represents
the situation where females ignore or do not perceive changes
in their environment, and they therefore have to use inflexible behavior.
Experience Estimates of P rule
In the Experience Estimates model, females use estimates of
P based on experience and known changes in hatching success to set their GUTs (Table 1). This represents the situation
where females have flexible behavior that is shaped by their
experience.
The number of successes (hits) and failures (misses) while
searching for acceptable nests are used to estimate P. We set
h 5 number of previous search periods that ended with
finding an acceptable nest (hits)
m 5 number of previous search periods that ended
without finding an acceptable nest (misses).
(3)
Females, we assume, forget experiences at a geometric rate;
new experiences carry more weight than old experiences
(Mangel, 1990). The parameter g sets the rate of forgetting;
g 5 1 means nothing is forgotten and g 5 0 means nothing
is remembered. When a female searches during a time period
or does not search during the day (because she is not gravid
or chooses to spawn out of nest during the first time period),
the numbers of hits and misses are updated,
gh 1 1

h9 5 gh

gh
Figure 3
Beta distributions of P, the probability of a successful 10-min search,
for different counts of hits and misses. For 1,1 (hits 5 1 and misses
5 1), the beta distribution is uniform. When one of the counts is
greater (2,8 and 4,1), the distribution is shifted left or right toward
lower or higher levels of P. When the total number of counts is
increased (from 4,1 to 20,5), even when the proportion of hits and
misses is conserved, the distribution is tightened, reflecting greater
certainty in the estimate of P.
if search is successful
if search is unsuccessful
(4)
if does not search during day
gm
if search is successful

m9 5 gm 1 1 if search is unsuccessful

if does not search during day.
gm
Females use their current counts of hits and misses to estimate the value of P. This is done by estimating the probability distribution that P 5 x. Alternatively, one could estimate
the expected value of P. We chose not to take this approach
because it ignores potential nonlinear effects of asymmetries
in the probability distribution. For computation, we assumed
the probability distribution of P was a beta distribution (Abramowitz and Stegun, 1972; Hilborn and Mangel, 1997; Mangel
and Clark, 1988). We discretized the probability distribution
into 50 intervals between 0 and 1 (j 5 1 to 50), so that xj 5
j/50. We then set
(6)
1
.
x jh21(1 2 x j )m21
where Vi 5 expected number of hatched eggs spawned on
day d onward, given h, m, and GUT 5 i. If the female spawns
out-of-nest with no searching (GUT 5 0), her expected fitness
is
V0 5 Bo(d) 1 G(0)F(h9, m9, d 1 1)
1 [1 2 G(0)]F(h0, m0, d 1 2).
(9)
Bo(d) is the expected number of hatched eggs for clutches
laid out of nest on day d. G(0) is the probability the female
will be gravid the next day if she spawns without searching,
and h9 and m9 are updates of h and m (see Equations 4 and
5). The h0 and m0 represent updates of h and m when search
resumes following a day the female is nongravid.
g(gh)

h0 5 
g(gh 1 1)
if no search or unsuccessful search on day
d, followed by non-gravid on day d 1 1
if successful search on day d, followed by
non-gravid on dayd 1 1.
(10)
(7)
The beta distribution is a conjugate prior to a binomial likelihood (Lee, 1989), meaning that new information can update a previous estimate of the distribution of P by altering
the counts of hits and misses. A beta distribution of P will shift
in mean value and have a specified variance depending on
the values of h and m (Figure 3).
At the beginning of day d the female sets a GUT between
i 5 0 and 9, which is the number of time periods she will
search for an acceptable nest before stopping and spawning
out of nest (note that i is the number of periods a female is
(8)
i

Where cn is a normalization constant chosen so that
cn 5
F(h, m, d) 5 max (Vi ),
(5)
The maximum numbers of hits and misses a female can remember was arbitrarily set at 25 each and the minimum
was 1.
Pr(P 5 x j ) 5 cn x hj 21(1 2 x j )m21
willing to search and s is the number of periods the female
searched during the day). She selects a GUT to maximize her
expected fitness,
Similarly,
g(gm)

m0 5 
g(gm 1 1)

if no search or only successful search on
day d, followed by non-gravid on day
d11
if unsuccessful search on day d, followed
by non-gravid on day d 1 1.
(11)
If GUT 5 1, expected fitness is
Behavioral Ecology Vol. 10 No. 6
670
V1 5
O Pr(P 5 x )
50
j51
j
3 {x j [Bi(d) 1 G(1)F(h9, m9, d 1 1)
1 [1 2 G(1)]F(h0, m0, d 1 2)]
1 (1 2 x j )[Bo(d) 1 G(1)F(h9, m9, d 1 1)
1 [1 2 G(1)]F(h0, m0, d 1 2)]} 2 iC.
(12)
This should be interpreted as follows: if the female’s search is
successful, which occurs with a probability xj (Equation 6), she
spawns in nest, receives an expected number of hatched eggs,
Bi(d), and her counts of hits and misses are updated to h9 and
m9 if she is gravid the next day (see Equations 4 and 5) or to
h0 and m0 if she is not gravid the next day. If the female’s search
is unsuccessful, which occurs with a probability 1–xj, she spawns
out of nest, receives Bo(d), and her counts of hits and misses
are updated to h9 and m9 if she is gravid the next day (see
Equations 4 and 5) or to h0 and m0 if she is not gravid the next
day. In addition, each period of searching (in this case i 5 1)
has a cost, C, of losing 10 expected hatched eggs. The equations for the expected fitnesses for other GUTs (i 5 2 to 9) are
similar to Equation 12, but also reflect that a female may find
a mate prior to exhausting her GUT. The expected fitnesses
for GUTs 0 to 9 are evaluated using Equation 8.
No Estimates of P rule
In the No Estimates model, females use known changes in
hatching success to set their GUTs (Table 1). This represents
the situation where females ignore or do not perceive changes
in P, but they have flexible behavior that responds to changes
in hatching success. The structure of this model is a special
case of the Experience Estimates of P rule. This is modeled
by setting g 5 0, meaning that females forget all experiences
and thus have noninformative prior estimates (h 5 m 5 1)
of P.
Fixed Seasonal Estimates of P rule
In the Fixed Seasonal Estimates model, females use fixed seasonal estimates of P and known changes in hatching success
to set their GUTs (Table 1). This represents the situation
where females do not perceive changes in P, but they use
regular seasonal patterns of P and known changes in hatching
success to inform their flexible behavior. The female’s estimates of P vary within years, following the average patterns of
P, but do not vary between years. We use the empirically measured pattern of P from a single field season (Figure 2) to
represent these seasonal estimates of P. Optimal GUTs are
found in the same manner as Equations 9 and 12, but state
variables of hits and misses are replaced by the female’s estimate of P.
Environmental variation
We examined by forward-simulation how the four behavioral
rules perform in environments with different forms of variation. We created breeding seasons that differ in how P varies.
These seasons serve as ‘‘arenas,’’ in which the performance
of the behavioral rules are assessed. Each simulation starts on
the first day of the season, and females follow the GUT prescribed by the model. The type of season, which determines
the female’s probability of finding acceptable nests, is unknown to her, and her performance (number of hatched
eggs) is determined by the interaction of her behavioral rule
with the environment.
The first type of season, ‘‘standard,’’ served as a baseline
for the other seasons. The empirically derived of values of
P(d) (Figure 2) were used to characterize the season. The
behavioral rules from each model were forward-simulated in
10,000 standard season runs and the behavior and fitness outcomes recorded.
The second and third types of seasons, ‘‘bad’’ and ‘‘good,’’
were used to examine how increased predictable variation between seasons affects the performances of behavioral rules.
We produced the two seasons by adding or subtracting 0.15
from P(d).
PG(d) 5 P(d) 1 .15
PB (d) 5 P(d) 2 .15.
(13)
The behavioral rules from each model were forward-simulated in good and bad seasons, and the behavior and fitness
outcomes from 5000 runs of each were recorded.
The fourth type of season, ‘‘greater temporal variation,’’
was used to examine how increased predictable variation within seasons affects the performances of behavioral rules. We
produced four seasons by adding periodic functions to P(d).
PS1(d) 5 P(d) 1 .15 sin(d/12)
PS2(d) 5 P(d) 2 .15 sin(d/12)
P 1C (d) 5 P(d) 1 .15 cos(d/12)
P 2C (d) 5 P(d) 2 .15 cos(d/12).
(14)
The behavioral rules from each model were forward-simulated in each of the four seasons and the behavior and fitness
outcomes from 5000 runs of each simulation were recorded.
We used the average fitness outcomes from the four seasons
to represent the fitness outcomes.
The fifth type of season, ‘‘greater uncertainty,’’ was used to
examine how increased unpredictable variation affects the
performance of the behavioral rules. We produced 20 different seasons by randomly adding noise to P(d),
PV(d) 5 P(d) 1 z,
(15)
where z was randomly drawn from a normal distribution with
mean 0 and variance .0056; approximately 95% of z are between 20.15 and 0.15. The behavioral rules from each model
were forward-simulated for each of the 20 different seasons
and the behavior and fitness outcomes of 5000 runs of each
simulation were recorded.
RESULTS
Selecting representative versions of the rules
We compared the fitness outcomes of different constant GUTs
to choose a representative for the Constant GUT rule (Table
2). A constant GUT of 0 (never search) performed best, except during good seasons, from which we conclude that high
environmental variation makes constant GUTs a poor option.
We chose to use a constant GUT of 2 for comparisons with
the other rules because it was the second best representative,
and a GUT of 0 is biologically uninteresting.
We compared the fitness outcomes of different rates of forgetting, g, to choose a representative for the Experience Estimates of P rule (Table 3). The optimal rate of forgetting
varied across season types, but the geometric mean fitnesses
across seasons show a clear pattern. The geometric mean is
the proper measure of fitness when one is considering temporally fluctuating environments, because the fitness of a strategy or rule is the product of multiplication over generations
(Gillespie, 1977). Rapid forgetting (low g) and slow forgetting
(high g) yielded lower mean fitnesses than intermediate rates
of forgetting. We chose g 5 0.95 to represent the rule because
it had the highest geometric mean fitness.
Luttbeg and Warner • Flexible versus fixed behavior in variable environments
671
Table 2
Average fitness outcomes (number of hatched eggs) for the Constant Giving-Up Time (GUT) rule with
different giving-up times in the five season types
Season type
Constant
GUT
Standard
Good
0
2
4
6
8
2283
2209
2150
2097
2048
2281
3272
3599
3716
3763
Bad
2282
1047
202
2415
2888
Comparing performance of behavioral rules
In most seasons, using experience to track the environment
yielded higher fitness than ignoring the state of the environment or assuming the environment follows a typical pattern.
The Experience Estimates of P rule produced the highest geometric mean fitness, averaging across season types, and the
highest fitness in all seasons, except during standard seasons
when the Fixed Seasonal Estimates of P rule had perfect information about the environment, and during good seasons
when the No Estimates of P rule did slightly better (Table 4).
To see why females using fixed estimates outperformed females using experience during standard seasons, we look at
the model’s GUTs (Figure 4). Females using fixed estimates
had distinct transitions from spawning out of nest (GUT 0)
to always searching for nesting males (GUT 9). Females using
experience to estimate P had more gradual transitions between reproductive options. This gradual behavior is suboptimal during the standard season, but it is beneficial during
other seasons.
Adding environmental variation between seasons improved
the fitness benefits of tracking the environment with experience. The Experience Estimates of P rule was the best rule
during bad seasons and one of the best during good seasons
because variation between seasons provides a clear signal of
environmental change, and GUTs were adjusted accordingly
(Figure 5).
With the addition of environmental variation within seasons, the fitness benefits of tracking the environment with experience was improved yet further. The addition of sinusoidal
variation increased the average fitness of females using experience, but decreased fitness for the other rules. The addition
of a sinusoidal wave to a set of simulations was always matched
by the addition of an identical sinusoidal with opposite sign
Greater
variation
Greater
uncertainty
2281
2179
2005
1847
1713
2282
2209
2150
2097
2048
to a different set of simulations; therefore, changes in fitnesses
were not due to overall changes in environmental quality. The
improvement of the Experience Estimates of P rule with the
addition of intraseasonal variation shows that using experience allows individuals to react within season to environmental change and that this is beneficial when environments are
autocorrelated.
The rate of environmental change affects the optimal rate
of forgetting and how accurately environments can be tracked
(Mangel, 1990; McNamara and Houston, 1987) (Figure 6).
Increased rates of environmental fluctuations reduced the fitness of females using experience because the time lag between the environment’s state and the female detecting that
state becomes more costly. The rate of forgetting can be increased, so that estimates of the environment are more composed of recent experiences, reducing lag times. However, increasing the rate of forgetting reduces the amount of information contained in an estimate, which increases both uncertainty and the risk of sampling error.
Finally, adding non-autocorrelated variation within seasons
also improved the fitness benefits of tracking the environment
with experience. On first impression, because this added variation was unpredictable, it should not have improved the
benefits of using experience. However, females that used experience tended to use more moderate GUTs, thus avoiding
searching for too long on bad days and too short on good
days. Incorporating uncertainty, which is part of using experience, buffers individuals against using behavior that is wildly
inappropriate in uncertain environments.
DISCUSSION
Comparisons of the models demonstrate the ways using experience can benefit an individual. Advantages accrue in
Table 3
Average fitness outcomes (number of hatched eggs) for the Experience Estimates of P rule with
different rates of forgetting (g) in the five season types
Season type
g
Standard
Good
Bad
Greater
variation
Greater
uncertainty
Geometric
mean
0
0.5
0.8
0.9
0.92
0.95
0.97
0.99
2592
2601
2555
2531
2538
2569
2570
2555
3972
3918
3772
3827
3875
3953
3957
3953
376
608
1110
1790
1883
1978
2036
1951
2351
2408
2479
2659
2687
2694
2609
2337
2229
2368
2405
2448
2393
2373
2368
2301
1826
2040
2296
2573
2601
2641
2639
2541
Geometric mean assumes the five season types occur with equal probabilities.
Behavioral Ecology Vol. 10 No. 6
672
Table 4
Average fitness outcomes (number of hatched eggs) for the four rules
Season type
Model
Standard
Good
Bad
Greater
variation
Greater
uncertainty
Geometric
mean
Constant Giving-Up Time
Experience Estimates of P
No Estimates of P
Fixed Seasonal Estimates of P
2209
2569
2592
2764
3272
3953
3972
3843
1047
1978
376
617
2179
2694
2351
2480
2163
2373
2229
2162
2044
2641
1826
2038
Geometric mean assumes the five season types occur with equal probabilities.
three ways. Within a reproductive season, experience can adjust decision making to better match the current state of the
environment. Conditional responses also help to adjust overall
choice behavior to year-to-year variation in environmental
quality. These sorts of conditional responses to local environmental conditions are particularly valuable in marine species,
where sporadic recruitment and extensive dispersal can create
broad potential variation in the social and physical surroundings of an individual (Sale, 1991; Warner, 1991, 1997). Finally,
using experience incorporates uncertainty into decision making, buffering behavior against unpredictable environmental
changes.
Two potential costs of using experience to estimate the environment are behavior lagging behind environmental changes and sampling errors. We found evidence for both costs. The
costs of time lags were demonstrated when we increased the
rate of environmental fluctuations, and the fitness of individuals using experience was reduced. The costs of sampling errors were demonstrated when rapid rates of forgetting caused
reduced fitness because of the reduced information content
in estimates and greater chances of sampling errors. Thus the
two costs of using experience can be reduced by changes in
the rate of forgetting, but they push the rate in opposite directions. Avoiding time lags requires rapid forgetting, but
avoiding sampling errors requires slow forgetting. While the
Figure 4
Giving-up times for the Experience Estimates of P rule versus the
Fixed Seasonal Estimates of P rule. For females using fixed
estimates, giving-up times abruptly switch from 0 to 9 on day 33 and
back to 0 on day 85. For females using experience-based estimates,
giving-up times depend on their current counts of hits and misses.
Females that have higher estimates of P (hits 5 3, misses 5 7) start
searching earlier in the season, and females that have more certain
estimates of P (4,16 versus 2,8) make a quicker transition from not
searching to searching.
rate of forgetting depends on the rate of environmental
change (Figure 6), it will also depend on the amount and
clarity of available information. If a single experience gave an
accurate estimate of the environment, sampling errors would
be unlikely, and rapid forgetting would be favored.
Female behavior in the field is best matched by behavior
produced by females using experience to estimate the environment. In the field, female peacock wrasses gradually increase nest spawnings early in the season, but out-of-nest
spawnings occur throughout the season (Figure 1; Warner et
al., 1995). In our models, females that used fixed estimates of
P did not match this pattern; transitions between reproductive
options were abrupt, and during mid-season out-of-nest
spawnings occurred only when required at the day’s end (Figure 7). In contrast, females using experience to estimate P
showed a gradual transition between reproductive options and
chose to spawn out of nest throughout the season (Figure 7).
Female peacock wrasses appear to use behavioral rules that
incorporate experience.
We used a specific class of rules incorporating GUTs. Field
observations support this class of rules, but it is possible that
our general results could be different for a different class of
rules. One solution would be to search for an optimal class of
Figure 5
The average time elapsed before spawning out-of-nest for females
using the Experience Estimates of P rule. The average elapsed time
is calculated from females that had giving-up times , 9 as well as
females that searched during all nine time periods and then
spawned out. We scored this last class of females as spawning out
during time period 10. The higher average time elapsed before
spawning out during ‘‘good’’ seasons indicates that females in these
seasons had higher giving-up times.
Luttbeg and Warner • Flexible versus fixed behavior in variable environments
Figure 6
Success of various rates of forgetting (g) in environments with
different rates of change. Sine and cosine waves with different
frequencies were added to P(d) (Equation 14). Smaller frequencies
mean that the environment changed more rapidly. When the rate
of environmental change was slow (freq 5 20), lower rates of
forgetting (g 5 0.95) did best. When the rate of environmental
change was high (freq 5 4), rapid forgetting was favored (g 5 0.9).
The dotted line shows the level of fitness achieved by females that
used fixed seasonal estimates of P ; their success was unaffected by
the rate at which the environment changed. Rapidly changing
environments reduce the fitness advantage of individuals with
experience-based estimates of P relative to individuals with fixed
seasonal estimates of P.
rules, but this would need to be weighted by the cognitive
complexities of the rules themselves.
Based on data from a single season, it would appear that
individuals could improve their fitness by more rapidly changing between reproductive options and avoiding out-of-nest
spawnings during mid-season. However, selection acts on the
mechanisms of decision making, not the behavior of a single
day. Also, judgments of observed behavior must be made in
the context of the range and frequencies of environments that
occur. The cognitive mechanisms of decision making are the
product of selection over multiple seasons and therefore
should not be expected to be optimal for a single season. We
found that the flexible strategy of using experience to inform
reproductive decisions did the best across a range of seasons.
While there is undoubtedly variation within and between
breeding seasons, we have not specifically measured this variation. Such measurements could be used to make more specific predictions about the actual values of many of the parameters contained in the models and would go considerably beyond the general qualitative comparisons that we were able to
make here. Ultimately, the optimal mechanism for making
reproductive decisions will be determined by the variability of
the environment, but measuring this variability can be a
daunting task.
Given that the nature of environmental variability may be
critical in determining the form of the evolutionary response,
what factors should be measured? Modeling and theory can
help by suggesting a series of potentially important environmental parameters that can be treated as alternatives to be
tested. When it can be shown that a species is plastic in a
particular trait, in many cases the expectation is that the responses depend on environmental cues, such as those modeled here (Warner, 1991). Armed with a series of alternative
hypotheses about the evolution of the trait, we can have both
a list of the environmental features that should be variable
and a means of estimating their relative importance. Thus the
673
Figure 7
Proportion of females spawning in nests across the season. The
solid line with squares is the observed weekly proportion of females
that spawned in nest. Females using the Experience Estimates of P
rule (dashed line) produced proportions spawning in nest more
similar to the observed than females using the Fixed Seasonal
Estimates of P rule (solid line).
presence of phenotypic plasticity in a species can be used to
test alternative hypotheses in evolutionary and behavioral
ecology (examples in Warner, 1991). This points to the need
to sharpen our focus in studies of environmental variation
within and between seasons and selection for behavioral reactions to that variation (Elliott, 1994).
Thanks to Suzanne H. Alonzo, Susan Foster, Marc Mangel, Oswald
Schmitz, Judy Stamps, and Mary Towner for comments on the manuscript. This project was funded by National Science Foundation
grants IBN-9507178 and INT-93-22778 to R.R.W. B.L. was funded in
part by a grant to Marc Mangel from the National Sea Grant College
Program, National Oceanic and Atmospheric Administration
(NOAA), U.S. Department of Commerce, under grant number
NA36RG0537, project number 31-F-N, through the California Sea
Grant College, and in part by the California State Resources Agency.
The views expressed herein are those of the authors and do not necessarily reflect the views of NOAA or any of its subagencies. The U.S.
government is authorized to reproduce and distribute this paper for
governmental purposes.
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