Behavioral Ecology Vol. 12 No. 4: 397-401
© 2001 International Society for Behavioral Ecology
Using potential reproductive rates to predict mating competition among individuals qualified to mate
a Department of Animal Ecology, Evolutionary Biology Centre, Uppsala University, Norbyvägen 18D, S-752 36 Uppsala, Sweden b Department of Zoology, Stockholm University, S-106 91 Stockholm, Sweden c Department of Biological and Environmental Sciences, University of Jyväskylä, PO Box 35, FIN-40351 Jyväskylä, Finland d University of California, Department of Ecology, Evolution and Marine Biology, Santa Barbara, CA 93106-9610, USA
Address correspondence to I. Ahnesjö, Department of Animal Ecology, Evolutionary Biology Centre, Uppsala University, Norbyvägen 18D, S-752 36 Uppsala, Sweden. E-mail: ingrid.ahnesjo{at}ebc.uu.se .
Received 1 June 2000; revised 21 August 2000; accepted 1 September 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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The potential reproductive rate (PRR), which is the offspring production per unit time each sex would achieve if unconstrained by mate availability, often differs between the sexes. An increasing sexual difference in PRR predicts an intensified mating competition among the sex with the higher PRR. The use of PRR can provide detailed predictions of when, where, and how the intensity in mating competition and hence sexual selection will vary. Previous models have focused on the "time out" from mate searching as a major component of PRR. Here, we suggest some improvements and clarifications: in a population where individuals have to compete for specific resources that are prerequisites for mating (e.g., nest sites), individuals unable to obtain such a resource will not qualify to mate. We suggest how a concept of the ratio of males and females qualified to mate, Q, can improve previous models designed to use the sexual difference in PRR to estimate the operational sex ratio (OSR). Further, when estimating the sexual difference in PRR of a population, it is important that each sex is given free access to mating partners. Jointly, this provides an empirical approach based on estimates of Q and the sexual difference in PRR.
Key words: mating competition, operational sex ratio, OSR, adult sex ratio, potential reproductive rate, PRR, qualified to mate, resource competition.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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A prominent explanatory model for predicting the direction and intensity of competition for access to mates is based on the sexual difference in potential reproductive rates (PRR; Andersson, 1994
; Clutton-Brock and Parker,
1992; Kvarnemo and
Ahnesjö, 1996;
Parker and Simmons, 1996,
Reynolds, 1996), where PRR is
the potential offspring production per unit time. There is a close association
between PRR (Clutton-Brock and Parker,
1992; Kvarnemo and
Ahnesjö, 1996;
Parker and Simmons, 1996) and
the operational sex ratio (OSR; the ratio of sexually active males and females
at a given time and place; Emlen,
1976; Emlen and Oring,
1977). A sexual difference in PRR will shift the OSR toward the
potentially faster reproducing sex. Together with PRR, the sex ratio in the
mating pool will obviously also influence the OSR.
The traditional explanation for why males, more often than females, compete
for access to mating partners, is that females invest more than males in
reproduction (Trivers, 1972).
However, this has proven difficult to test because any measurement of parental
investment should include all fitness costs of all expenditures of
reproduction in both sexes (Clutton-Brock,
1991; Evans, 1990;
Knapton, 1984). Therefore, we
argue like several authors before us
(Clutton-Brock and Parker,
1992; Clutton-Brock and
Vincent, 1991; Parker and
Simmons, 1996) that a more accessible empirical approach is to
measure the sexual difference in PRR of a population and then estimate the
OSR. Not only does this approach provide an estimate of OSR and mating
competition, but also an avenue for understanding the mechanisms governing
spatial and temporal variations in OSR. The advantages of using PRR are
becoming increasingly recognized (e.g.,
Ahnesjö,
1995; Balshine-Earn,
1996; Berglund et al.,
1989; Debuse et al.,
1999; Kvarnemo,
1994; Masonjones and Lewis
2000; Okuda, 1999;
Pröhl and
Hödl, 1999;
Simmons, 1995;
Wiklund et al., 1998;
Wootton et al., 1995). In this
paper we aim to promote further use of PRR by clarifying and developing some
of its important aspects.
In a population, sexual selection may occur for many reasons, such as
mating competition, resource competition, and sperm competition. Out of these,
it is only mating competition that can be estimated by a sexual difference in
PRR and any consequent bias in OSR. In contrast, when resources (other than
mates) that are prerequisites for mating are limited, competition for these
resources will occur. Although such resource competition may result in sexual
selection, it will not be predicted by any sexual difference in PRR. Nor will
sperm competition, which occurs after mating, be predicted by models using
PRR, and possible indirect effects of sperm competition on PRR have been found
to be of minor importance (Simmons and
Parker, 1996). In addition, prominent variation in mate quality
may result in competition for high-quality mates. Yet, its influence on mating
competition has been predicted to be minor in comparison to that of sex
differences in PRR (Johnstone et al.,
1996) and will not be considered further in this paper.
There are several important factors that need to be considered to predict and understand mating competition. First, there is a need to understand the consequences of resource competition on mating competition without confounding these two, and we suggest how this can be incorporated by identifying the ratio of males and females qualified to mate (i.e., those able to enter the mating pool) when using PRR to estimate the OSR in a population. Second, PRR has been approached in several ways, resulting in slightly different definitions and estimates, based on different assumptions, which we will try to clarify. Third, we outline a general empirical approach estimating the OSR by the use of the sexual difference in PRR among the individuals qualified to mate.
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The sex ratio of males and females qualified to mate |
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TOPABSTRACTINTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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Previous calculations and models of PRR and OSR have generally been based on the adult sex ratio (e.g., Clutton-Brock and Parker, 1992
; Parker and
Simmons, 1996). However, as mentioned by Clutton-Brock and Parker
(1992), this may sometimes
cause problems. To illustrate our point, imagine a species where the adult sex
ratio is even and individuals of one sex construct a nest and then provide
care for the offspring. For simplicity, we also assume that the "time
out" periods (time between matings spent not ready to mate; see the
time-out model below) of males and females are equal and that there is one
mating per clutch. In that case one would predict similar intensities in
mating competition among both sexes. However, if there is a severe shortage of
nest sites, which represents a resource necessary for reproduction, there will
be strong competition among individuals of the nest-holding sex for nest
sites. Then, if each nest-holding individual can only care for a limited
number of clutches (i.e., one in this example), this will result in a shortage
of nest holders with which the opposite sex can mate, creating a situation of
competition among them for nest holders, despite the even adult sex ratio
(ASR; M in Parker and Simmons,
1996) and equal PRRs.
In this scenario, the competition for nest sites is resource competition,
in contrast to the competition for nest-holding mates, which is mating
competition (Figure 1). Both
may result in sexual selection, although not necessarily for the same traits.
The intensity in resource competition within a sex cannot be estimated by the
OSR because it is the relationship between the amount of resources available
and the competitors that matters. Mating competition, in contrast, is directly
related to the OSR. A bias in the adult sex ratio may, of course, have a
strong influence on OSR, and this has been included in previous models
(Clutton-Brock and Parker,
1992; Parker and Simmons,
1996). However, in these models the possibility of profound
influences of resource competition has not been taken into account. Therefore,
we suggest that the adult sex ratio, which includes all sexually mature
individuals in the population [termed M in the models by
Clutton-Brock and Parker (1992)
and Parker and Simmons
(1996)], should be replaced by
the qualified sex ratio. We define the qualified sex ratio (Q) as the
sex ratio of individuals that are qualified to mate on the basis of being
sexually mature and also being able to be either in a "time in"
(time spent ready to mate; see the time-out model below) or a "time
out" state. To enter time in (and time out following it), an individual
must first acquire the resources that are a prerequisite for mating, such as a
nest site (Figure 1). A nest
holder can thus be considered qualified if it is potentially eligible as a
mate (whether this will be realized or not). In contrast, an individual that
has not acquired a nest site is not eligible as a mate, even though it might
be capable of mating through sneaking. In more general terms, prerequisites
for mating may include breeding and feeding territories, as well as nutritive
resources, such as nuptial gifts. There is a distinction between those
individuals being unable to acquire resources (food, for instance) to become
qualified to mate and those that have started mating and are drained of
resources after a mating. The former individuals are excluded from Q,
whereas the latter are qualified to mate, although they are in their time-out
state.
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PRR/
PRR).
One will gain a major advantage replacing the adult sex ratio with
Q because estimates of mating competition no longer will be
confounded or masked by resource competition. An example of the distinction
between resource competition and mating competition is provided, for instance,
by a study of the Pacific salmon, Oncorhynchus kisutch
(Fleming and Gross, 1994). In
this species, females were found to compete for oviposition territories, and
smaller females were less successful in acquiring and defending such
territories. As a result, males faced an intense mating competition for access
to the territorial females, favoring male body size and hooked snout length.
Further, Q can be compared to the adult sex ratio to detect resource
competition within a sex and to predict the intensity of resource competition.
Emlen and Oring (1977: 217)
dealt with the question of how resources may influence mating systems and
sexual selection. They described it as resource-defense polygyny when
"males control access to females indirectly, by monopolizing critical
resources," and vice versa for resource defense polyandry. In such
resource-defense polygamy, an individual that holds a critical resource may
enjoy a mating advantage. Still, if the number of mates the resource holder
can have is limited, the degree of polygamy may remain low. Although Emlen and
Oring (1977) focused on the
competition among the resource-holding sex, they did not pay attention to the
mating competition that may arise among the opposite sex for the
resource-holding individuals.
Some further examples from fish research illustrate the situation where the
adult sex ratio differs from Q. In the peacock blenny Salaria
pavo, males provide parental care in nest sites in rock crevices. In most
populations, males compete for and court females. However, the reverse was
found in a population in Portugal (Almada,
1995). The only substrates available in this case were old
construction bricks that lined the edges of man-made water channels. Although
excellent nest sites, these bricks were limited in numbers. Hence, in this
population, the OSR was female biased because only a small proportion of the
males were able to acquire a nest, whereas all females were producing eggs
(Almada, 1995;
Oliveira et al., 1999). As a
consequence, and despite an intense competition for nest sites among males,
the sex roles were reversed in this population, with females being more keen
competitors for mates than were males.
The influence of nest site availability on sexual selection has also been
studied in two species of gobies, Pomatoschistus minutus and P.
microps, both of which provide exclusive paternal care in nests built
under mussel shells. In P. minutus, male mating success was primarily
determined by intrasexual competition over nest sites (i.e., resource
competition) when nest sites were in shortage. In contrast, when nest sites
were available in excess, male mating success was determined to a larger
extent by female mate choice (Forsgren et
al., 1996). In P. microps, females interacted with each
other and courted more than males did when nest sites were limiting, whereas
the reverse was true in an area with excess nests (Borg
, Forsgren E, Magnhagen C, personal
communication). These differences show that since nest site availability
affects Q and therefore OSR, it will also affect the modes of sexual
selection, from intrasexual resource competition to intersexual mate
choice.
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The potential reproductive rate |
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TOPABSTRACTINTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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Potential reproductive rate is a measure of offspring production per unit time of individuals that are not constrained by availability of mating partners (Clutton-Brock and Parker, 1992
; Kvarnemo and
Ahnesjö, 1996). As a consequence of
this criterion of unconstrained access to mating partners, PRR usually differs
from the realized reproductive rates we see in natural populations. In any
sexually reproducing organism, the mean values of the realized reproductive
rates of males and females will be equal, as each offspring has one mother and
one father. Therefore, PRR cannot be measured in unmanipulated field
conditions where focal individuals cannot be guaranteed unlimited access to
mates.
There are examples where PRR has been estimated in the field, using
measurements for each sex of the time-out periods after one mating (e.g.,
Okuda, 1999;
Pröhl and
Hödl, 1999). Sometimes this is the
only feasible way to get a rough estimate of PRR. Yet, by not providing free
access to mates, one is likely to overestimate the time out of the limited sex
if it does not appear to be ready to remate due to the lack of mating
partners. In other cases, there may be a risk of underestimating the time out
if recovery and replenishment occurs during searching for a new mate. Finally,
it is not unusual that one sex is prepared to mate several times in rapid
sequence before spending the required time for recovery. In such a case, by
only measuring time out from one mating, PRR is likely to be inaccurately
estimated for this sex. In contrast, by providing unlimited access to mates,
as stressed above, one is able to accurately estimate the physiological and
ecological upper limit of the rate at which each sex, on average, potentially
can reproduce.
Clutton-Brock and Vincent
(1991) coined the term
"potential reproductive rate," but illustrated it by using the
maximum value of the realized reproductive rates recorded in the literature
for a range of species. Although having a heuristic value as an example, this
method gives an unreliable estimate because it is not known how it relates to
PRR. Moreover, subsequent empirical studies (e.g.,
Balshine-Earn, 1996) have
measured the potential reproductive rates for a range of individuals within a
population, but then only used the maximum individual value of each sex to
estimate PRR instead of the mean. As a consequence, this estimate is not
reliable for the calculation of OSR because it does not statistically
represent all the individuals in the population for which mating competition
is measured, but only one extreme male and one extreme female.
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The time-out model |
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TOPABSTRACTINTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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When individuals are ready to mate, they are said to be in a "time-in" state. In contrast, when they have mated and as a result spend time caring, replenishing gametes, or recovering somatically before being ready to mate again, they are said to be in a "time-out" state (Clutton-Brock and Parker, 1992
; Parker and Simmons,
1996). This also relates to previous divisions of reproductive
time into two categories (searching time and mating time;
Sutherland 1985;
Sutherland and De Jong 1991).
The underlying concept for the time-out model is that the OSR is equivalent to
the sexes' ratio of summed time-in periods in a population
(Clutton-Brock and Parker,
1992). However, because time-in is hard to measure, the model
compares the sexes' time-out periods instead
(Parker and Simmons, 1996).
Assuming discrete clutches, Clutton-Brock and Parker
(1992) and Parker and Simmons
(1996) divided the
reproductive cycle (T) of each sex into time out (G) from
mate searching, when not being ready to mate, and time in (S) when
being ready to mate. The three main determinants of OSR and hence mating
competition in these models are (1) the sex ratio of adult individuals
(M; males/females) (2) the inverse time out, 1/G, and (3)
the "collateral investment" (sensu
Parker and Simmons 1996). The
quotient 1/G and the collateral investment together correspond to
PRR; 1/G is a time component, whereas the collateral investment
translates into the potential number of offspring the sexes have capacities to
produce or take care of during the period of G. Collateral investment
occurs if a given reproductive event involves the time-out periods of more
than one individual of each sex, such that f females spread their
clutches between m males (Parker
and Simmons, 1996). For example, if a male has the capacity to
care for eggs from two or more females in his nest at one time, as is common
among fish with paternal care, then the collateral investments are m
2 and f = 1. Alternatively, if two or more males mate with one
female before oviposition, as is common in katydids and butterflies, each of
the two males will spend a time out, replenishing their sperm stores and
nuptial gifts, for only one female time out. Here, the collateral investments
are m = 1 and f 2. It is important to note that the
estimates of collateral investment must be based on how the time-out periods
would be distributed under free access to mates, in order to, for instance,
know the maximum number of clutches that may fit into each individual nest
(cf. Kvarnemo, 1994).
When using the model by Parker and Simmons
(1996), it is not arbitrary if
we specify the reproductive cycle T (total time in which an entire
reproductive event takes place for one sex) for the limited or limiting sex.
It is advisable to use the reproductive cycle (T) and clutch size for
the limiting sex. If choosing T for the limited sex, one will have to
do adjustments, for instance, by only using fractions of time-out periods for
the other limiting sex.
Keeping the above reservations in mind, a reproductive cycle T can
be defined as T = fGf + Sf
when females are the limiting sex, and males are then expected to compete if
T(Q - 1) > mGm - fGf [here
replacing the adult sex ratio, M
(Parker and Simmons, 1996)
with Q, see above]. However, more information can be gained beyond
which sex is the predominant competitor for access to mates, as the difference
in the inequality gives an indication of the intensity of mating competition
in the population (Emlen and Oring,
1977; Kvarnemo and
Ahnesjö, 1996;
Kvarnemo and
Ahnesjö, in press).
Parker and Simmons (1996)
approached PRR by separating it into the inverse processing time of a clutch
(i.e., 1/G) and the capacity to process multiple time-out periods of
the opposite sex within a reproductive cycle (i.e., collateral investment). In
some species, this is likely to be a useful approach to determine what governs
certain changes in OSR. In such species the reproductive cycle (T)
can easily be defined, and a mating involves an entire clutch, or a nuptial
gift, inflicting time out after a certain number of matings, as has been
demonstrated in sand gobies (Kvarnemo,
1994) and katydids (Simmons,
1995). In many other species, the reproductive cycle is harder to
determine, and the separation of PRR into time and collateral investment will
be unfeasible. A better approach is then to measure PRR as the number of
offspring produced per unit time under free access to mates, thus
incorporating both time out and collateral investment in the same estimate.
This is a more general approach, which is applicable both to species
reproducing more or less continuously for a period and to clutch-wise
reproducers. This approach could be seen as the original one, as it follows
the verbal definition of PRR in Clutton-Brock and Parker
(1992), which in turn was based
on studies that were fundamental to the development of the concept
(Berglund et al., 1989;
Gwynne, 1984).
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An empirical approach |
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TOPABSTRACTINTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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When surveying a population of animals, it may be difficult to collect estimates of the factors used in the above models (e.g., mean time-out periods or the summed time-in periods, level of potential collateral investments, and the ratio of males and females qualified to mate). In many cases it is more feasible to bring representative samples of the population into the laboratory (or field enclosures), separately provide individuals of both sexes with free access to mates, and then measure the rate of offspring production. Often, a suitable minimum time period for the measurements is the duration of one reproductive cycle of the slower sex. This will provide a mean PRR for each sex, and the sexual difference can be calculated and used to predict intensities of mating competition (Clutton-Brock and Parker, 1992
; Kvarnemo and
Ahnesjö, 1996). For the slower sex,
mean PRR is likely to equal its realized reproductive rate, whereas the faster
sex will have a higher mean reproductive rate when not being limited by the
availability of partners. Thus an outline for an empirical approach for estimating the OSR by the use of Q and PRR is as follows:
- To estimate Q, determine the ratio of males to females that
qualify to mate, either directly in the field, or by taking a representative
sample of the population into the laboratory or field enclosures. In the
laboratory it is important to maintain the adult sex ratio, spatial
distribution, size and age distribution and to provide natural levels of
resources (food, nests, etc., limited or unlimited in amount depending on what
occurs in nature).
- Determine the mean PRR for each sex separately by first determining how
many offspring each individual produces when provided with continuous free
access to mates but all the other natural constraints remain, measured under a
suitable time period (e.g., a reproductive cycle of the slower sex). Then
calculate PRR for each sex as the average number of offspring produced per
unit time in the sample.
- Multiply Q by the ratio of male PRR to female PRR to obtain OSR.
As previously suggested (Kvarnemo and
Ahnesjö, 1996), it is preferable to
transform the OSR estimates to a relative form (e.g., ranging from 0-1 or as a
percentage 0-100%) to avoid the skewed distributions characteristic of a male
to female ratio.
- An OSR departing from unity (i.e., 0.5) will then predict more intense
competition for access to mates in the faster sex or the sex with more
individuals qualified to mate.
- If the study focuses on seasonal changes in mating competition, these
estimates have to be repeated sequentially over the breeding season.
This approach has been successfully used in a sex-role reversed population
of the broad-nosed pipefish, Syngnathus typhle. In this species
Q is even, but females have to compete for males as mating partners
because, on average, females are able to produce eggs twice as fast as males
are able to brood them
(Ahnesjö,
1995; Berglund et al.,
1989), resulting in female-biased OSRs over the main part of the
breeding season (Vincent et al.,
1994).
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Discussion and conclusion |
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TOPABSTRACTINTRODUCTIONThe sex ratio of...The potential reproductive rateThe time-out modelAn empirical approachDiscussion and conclusionREFERENCES |
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When there is competition among members of one sex for resources that are prerequisites to mate, some individuals will qualify to mate, whereas others (although being sexually mature) will not. At the onset of the breeding season, the ratio of males to females qualified to mate (Q) is likely to approximate OSR. Thereafter individuals will be ready to mate or not depending on their PRR. Consequently, the OSR will vary over time. Naturally, Q may also change as new individuals become qualified to mate. We emphasize here that for each sex the PRR estimates the reproductive rate of all the mating individuals when they are not constrained by mate availability, but all other natural constraints remain. Kvarnemo and Ahnesjö (1996
) have stated that nest
site limitation among males may cause a female-biased OSR through a reduction
of PRR of the nest-holding sex. This would be the case if males without a nest
were assigned an individual PRR value of zero, thereby decreasing the
populational mean PRR for males. However, assigning zeros for nestless males
implies that they spend infinite time in a time-out state. Although
mathematically practicable, this is illogical because time-out can only result
from a mating, and a male without a nest is neither in a time-in nor a
time-out state. In addition, not including zeros for these individuals keeps
PRR an unambiguous measure of the potential rate of processing gametes and
offspring. Consequently, for both the empirical approach and the time-out
model we clearly prefer the approach of Q because it allows PRR to be
measured only for the individuals qualified to mate. Thus, an estimate of a
population's OSR is acquired by combining information on Q and the
sexual difference in PRR. Any change in Q and the sexual difference
in PRR affects the OSR, in the same or opposite directions. Hence,
male—male competition will predominantly occur when females limit male
reproduction due to more males than females being qualified to mate or due to
males having a higher PRR. Sexrole reversal with female—female
competition for access to mates will occur in opposite situations. Further,
the relationship between the bias in OSR and the intensity of mating
competition is not necessarily linear, as costs and benefits of competitive
behavior may vary with the degree of bias in the OSR. For instance, when the
OSR is strongly biased toward one sex, the costs of competition may become
very high and the intensity may then decrease, as suggested for the European
lobster (Debuse et al.,
1999).
The empirical outline presented above should be seen as complementary to
previous approaches. Although the OSR sometimes can be successfully estimated
directly by counting individuals of both sexes that are ready to mate, it is
often hard to assess when an individual is ready to mate. Furthermore, to
determine the mating competition over a mating period the OSR count will have
to be repeated frequently. The time-out model
(Parker and Simmons, 1996)
serves as another alternative, which is excellent from a theoretical
perspective. This model compares the summed time-in periods between the sexes
over a reproductive cycle, but because it is often difficult to assess if
individuals are in a time-in state, the model uses estimates of time out
instead. Yet, when incorporating the effects of sex-ratio biases, it is
crucial to use the sex ratio of qualified individuals (Q) and not of
all adult individuals (M). In addition, effects of collateral
investments (i.e., when a reproductive event involves the time out of more
than one mating partner) have to be included
(Parker and Simmons, 1996).
The empirical outline presented in this paper circumvents several of the
problems related to the time-out model by estimating Q and the sexual
difference in PRR to calculate the OSR. Furthermore, focusing on PRR enables
us to identify the factors that more prominently influence OSR. Using
information about how such key factors vary may help us produce predictions
about mating competition in different populations or for different times of
the breeding seasons. The improvements and clarifications suggested here will
facilitate accurate estimates of mating competition when conditions vary
within and between populations.
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ACKNOWLEDGEMENTS |
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We thank A. Berglund, S. Ulfstrand, E. Forsgren, L.W. Simmons, J.L. Tomkins, B.S. Tullberg, and referees for comments on the manuscript and J. Bond for inspiration.
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