Behavioral Ecology Advance Access originally published online on February 16, 2005
Behavioral Ecology 2005 16(3):566-570; doi:10.1093/beheco/ari030
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Alternative reproductive tactics and status-dependent selection
Department of Neurobiology and Behavior, Seeley G. Mudd Hall, Cornell University, Ithaca, NY 14853, USA
Address correspondence to J.S.F. Lee. E-mail: JL275{at}cornell.edu.
Received 8 July 2004; revised 5 December 2004; accepted 22 December 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
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The status-dependent selection model on alternative reproductive tactics predicts a single switch-point in status: usually all players above some status (e.g., competitive ability) should practice the tactic with the higher average payoff, while those below that point should make the "best of a bad job" by practicing the alternative, lower payoff tactic. Many empirical studies indeed show a relationship between status and tactic choice, but they do not conform to this single switch-point prediction. I modify the status-dependent selection model by considering status-dependent fitness that is mediated, at least in part, by resource acquisition (e.g., status-based competition for territories or nuptial gifts). With variation in resource quality, predicted tactic-choice distributions change: a high-status male may be territorial on a high-quality territory, a lower status male may practice an alternative tactic, and an even lower status male may be territorial on a low-quality territory. Tactic choice thus alternates as in many empirical studies and can appear to be but is not actually stochastic. As the number of theoretically predicted switch-points increases, however, mixed or mixed-conditional strategies should become more prevalent. While alternative tactics will likely usually differ in mean payoff, viewing alternative reproductive tactics as inherently "better" or "worse" (e.g., viewing cuckoldry as "worse"—the best of a bad job) is misleading if not tempered with awareness that payoff can vary greatly within tactics and overlap between tactics.
Key words: alternative reproductive tactic, best of a bad job, conditional strategy, cuckoldry, mixed strategy, status-dependent selection, switch-point, territoriality.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
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When animals choose between alternative reproductive tactics, the status-dependent selection model predicts that the decision will hinge on the relationship between the player's status and the fitness payoff associated with each tactic (Gross, 1996
). The model predicts the existence of a single switch-point in status (Repka and Gross, 1995). All players above that switch-point practice the tactic with the higher average payoff, while those below the switch-point adopt the alternative tactic to make the "best of a bad job" (sensu Dawkins, 1980; Eberhard, 1982).
Empirical data show some support for the model. Typically, individuals practicing one tactic (e.g., territoriality) have, on average, higher status than individuals practicing the other tactic (e.g., cuckoldry) (Brockmann, 2001; Gross, 1996). However, a focus on the variation within tactics yields a different interpretation: some or even considerable overlap in status often occurs between the group adopting one tactic and the group adopting the other tactic (Gerhardt et al., 1987; Kempenaers, personal communication; Kempenaers et al., 2001; Tomkins, 1999; Waltz and Wolf, 1988). But the concept of a single switch-point has been so pervasive that, with a few exceptions (e.g., Tomkins, 1999), deviations from predicted population distributions (e.g., a small male holding a territory) are often discounted by animal behaviorists as spurious data points: "mistakes" made by the focal animals or reflections of the investigator's inability to accurately measure status.
An alternative or complementary solution for the discrepancy between the existing status-dependent selection model and empirical data is that the model is incorrect in predicting that a nonoverlapping distribution (i.e., a single switch-point) should usually occur. I modify the existing model by considering status effects that are mediated by resource acquisition. This alters the predictions of the model so that in many cases status overlap between the group practicing one tactic and the group practicing the other tactic is expected.
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THE EXISTING MODEL |
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TOPABSTRACTINTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
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According to the status-dependent selection model (Figure 1; Gross, 1996
), tactic payoff varies as a function of individual status. Two lines representing the two tactics intersect once, producing a single switch-point (Appendix; Repka and Gross, 1995).
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In this model, multiple switch-points can occur if the lines curve, but with the existing model multiple switch-points caused by multiple intersection points between fitness lines should almost always result in an "orderly" or "clumped" distribution of tactics with respect to status, such that aberrant individuals should occur in groups. That pattern is rarely seen in nature; such multiple intersection points do poorly at explaining seemingly random "scatter," in which deviations from single switch-points occur in the form of aberrant individuals appearing singly, "scattered" about the status distribution. Below, I present a biologically realistic model that can lead to "scattered" multiple intersection points and tactic-choice distributions that resemble those seen in nature.
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STATUS-DEPENDENT SELECTION AND SCATTERED SWITCH-POINTS |
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TOPABSTRACTINTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
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Equations
Here I adapt the existing model so that it differentiates between direct status effects and status effects that act through resource acquisition (indirect effects). A simplified version of the model is graphically presented in Figure 2. I will consider the alternative reproductive tactics of territoriality and cuckoldry; the resource will be the territory.
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Payoff for the territorial tactic (guarding: Pg) can be described as
 | (1) |
for a discussion of multicollinearity). mu, mt, and mx are, respectively, the slopes relating status, inherent territory quality, and the interaction between status and inherent territory quality to tactic payoff. The values of mu, mt, and mx and of the intercept bg are functions of the frequency of individuals practicing each tactic [mu(f), mt(f), mx(f), bg(f)]. Pg in Equation 1 derives from multiple sources:
- mu(f)s represents the direct influence of status on Pg. For example, a female may give a male a certain number of eggs based on her evaluation of the male himself. This term does not include any effects that are mediated by territories (e.g., a female awards additional eggs based on the territory the male has obtained).
- mt(f)t represents the fitness payoff due to the obtained territory. Territories are assumed to differ from one another in inherent quality. In nature, usually only one individual can hold any given territory at a time, and individuals with higher status have precedence when choosing from the potential territories (see legend to Figure 2). This does not have to reflect a temporal precedence but could just as well result from competition among individuals that differ in status (Parker, 1974). The end result is that individuals with higher status have higher quality territories. This effect reflects the indirect influence of status on Pg; that is, when males use their status to obtain resources such as territories and when those resources then influence the total fitness payoff (see Waltz, 1982).
This term does not include the effect of the male altering the territory quality once he obtains it (see interaction term immediately below); it pertains to systems where at least some aspect of the territory's quality exists even before a male claims it (inherent quality of the territory).
- mx(f)st represents the change in Pg due to the effect of the male's status on altering the quality of his territory after he has obtained it. For example, females may award eggs based on the quality of the male's territory, which in turn may be influenced by the male's ability to tend it. This term describes the difference between the inherent quality of the territory and the quality of the territory after it has been tended. An example is algae-farming damselfish, in which bigger males cultivate better lawns by providing better defense against herbivorous intruders (e.g., Foster, 1985).
Imagine a system in which the ability of underwater substrate to support aquatic algal growth varies with water depth, such that shallower depth enables faster algal growth (depth varies as shallow, medium, and deep). Shallow water substrate is limited; higher status males outcompete lower status males for it. A higher status male also can better defend the turf against herbivorous intruders and in so doing add to the inherent growth of his turf (additional growth is a factor of male status and inherent growth). Females judge both males and their territories and "decide" on the number of eggs to lay based on both the male's status (direct status effect, e.g., a status-indicating courtship dance) and the length of the male's algal lawn (resource-mediated status effect).
For simplicity, territories affect payoff at the territorial tactic but not at the alternative tactic. (The model can be easily altered if multivariate influence is desired on both tactics.) Thus, where mc(f) is the frequency-dependent slope of the relationship between status and cuckoldry payoff and bc(f) is the frequency-dependent intercept of that line, cuckoldry payoff (Pc) is
 | (2) |
Solution for multiple switch-points
At a switch-point, the fitness payoffs of the two tactics must be equal (Parker, 1982). Setting Pg equal to Pc and solving for the status switch-point (s')
 | (3) |
Because there exist multiple values of t (i.e., territories vary in inherent quality), there exist multiple solutions for s' and therefore multiple switch-points. A crucial feature of natural systems is that higher status males obtain higher quality territories than do lower status males. As shown in the Appendix and in Figure 2A, multiple switch-points are still possible when this biological feature of status-dependent resource acquisition is taken into account. This provides a simple mechanism through which multiple intersection points and consequently multiple switch-points can occur, within the status-dependent selection framework.
Necessary conditions for multiple switch-points
Figure 2B and the Appendix show an important requirement for multiple switch-points: While the slope of the total effect (direct plus indirect effects) of status on the territoriality payoff can be greater than the slope relating status to cuckoldry success, the slope of the direct effect (mU) must be less than the slope for cuckoldry (mC). Otherwise, the minimum territory quality required for a male to choose territoriality increases with decreasing status—once a territory is declined, no subordinate will accept it.
How do these parameters relate to systems in nature—that is, when will mC be greater than mU? Strong positive relationships between status and cuckoldry success (high mC) can result when cuckolders compete with each other or with the territorial male (Kodric-Brown, 1986; Koseki and Maekawa, 2000) or when females choose the extrapair male with whom they mate (Houtman, 1992; Jennions and Petrie, 2000). Low mU could occur in systems in which the influence of the territory holder's status is largely mediated through the territory (high mT). Females may choose males based on the quality of the territories that the males acquire (Alatalo et al., 1986), or males may fight for space (territories) that contains females (Emlen and Oring, 1977; Rubenstein, 1980). In some species, such as those that defend egg oviposition sites of fixed size (e.g., rocks under which females deposit eggs, DeMartini, 1991) or harem-holders that defend feeding space for females (Shuster and Wade, 2003), the inherent size and quality of the space (territory) can directly determine the number of mates that can be acquired. A postcopulatory mechanism through which mU would be low and mT would be high is when inherent territory quality affects offspring survival, as may occur when the territory provides food or shelter for a limited number of offspring. In contrast, mU should be high, and multiple switch-points should become less likely, when female choice is based directly on male status or when males fight directly for females.
For simplicity, we use linear fitness functions. In systems with nonlinear functions, the mechanism described in this paper should be possible along regions of the status range where the relationship between status and cuckoldry success is steeper than that between status and the direct effect of status on success at territoriality.
Another requirement for multiple switch-points is variation in inherent territory quality. This condition is realistic for many systems (Rodenhouse et al., 1997; Sergio and Newton, 2003). In the example of males competing for space that contains females, the equivalent of variation in inherent territory quality is variation in the sizes of the "clumps" of females (see Shuster and Wade, 2003).
Despite differences between tactics in mean payoff, this focus on within-tactic payoff variation suggests that viewing alternative tactics as inherently "better" or "worse" (e.g., viewing cuckoldry as making the "best of a bad situation") can be misleading in systems that have multiple switch-points. Variation introduced by territory quality can lead to situations where an individual with high status will take a high-quality territory, an individual in a worse situation will cuckold, and an individual in an even worse situation will take a lower quality territory (see Figure 2A). In such scenarios there is no one tactic that is the "best of a bad job." Even though tactics may differ in mean payoff, this consideration of payoff variation within tactics may help explain empirical data that deviate from the prediction of a single switch-point.
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FROM MULTIPLE SWITCH-POINTS TO MIXED STRATEGIES |
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TOPABSTRACTINTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
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Crowley (2000)
shows how categorical, as opposed to continuous, perception of status can lead to mixed strategies in pair-wise contests (also see Hammerstein and Parker, 1982; Parker and Rubenstein, 1981). Briefly, imagine that an individual assesses its own and its opponent's status as points along a continuum. When such assessment occurs, the chances of an individual perceiving its opponent as completely equal in status are infinitesimal, so all individuals should effectively practice a pure conditional strategy. A pure conditional strategy is one in which tactic choice is deterministic. For example, a contestant that assesses itself to be higher in status escalates into combat with a probability of 1, and avoids combat with a probability of 0. In contrast, if contestants assess status categorically (e.g., three categories: small, medium, and large), then there is a greater likelihood that an individual will perceive the opponent as an equal. When an opponent is perceived as equal, tactic choice is no longer necessarily deterministic (probability is no longer necessarily 1 or 0). Instead, negative frequency dependence should lead to a mixed strategy (Maynard-Smith, 1982). In a mixed strategy, tactic choice is stochastic: a contestant that assesses its competitor to be an equal in terms of status escalates into combat with a probability of p and avoids combat with a probability of 1 – p; negative frequency dependence determines the value of p (where 0 < p < 1). Better assessment abilities reduce the ability of this mechanism to produce extensively practiced mixed strategies: as assessment abilities increase (the number of categories increases and the width of the categories decreases), mixed strategies should become increasingly rare (Crowley, 2000, 2003). As assessment abilities continue to improve, the model collapses back down to continuous assessment; pure conditional strategies become the only evolutionarily stable strategies.
This mechanism and the limitations imposed by good assessment abilities can be extended to situations where a contestant competes against a large group of individuals (games against the field), as opposed to a single competitor (Flaxman, 2000). In games against the field (such as the cuckolder-territorial game), any category that overlaps a switch-point should practice a mixed strategy. If only a single switch-point exists, as is predicted by the existing model on status-dependent selection on alternative reproductive tactics, then only one category at maximum should practice a mixed strategy. As assessment abilities improve (categories shrink in width and increase in number), the proportion of the population that practices a mixed strategy should decrease.
However, if multiple switch-points can exist, as I have shown in this paper, then an increase in the number of switch-points can lead to an increase in the number of categories that overlap switch-points and consequently lead to an increase in the number of categories that follow mixed strategies. Consequently, even in systems with good (but not perfect) assessment abilities, a large number of predicted switch-points (predicted under perfect assessment) can cause a large proportion of the population to choose between cuckoldry and territoriality stochastically (practice mixed strategies). This provides a mechanism through which extensively practiced mixed strategies can evolve. Whether a population practices a conditional strategy with multiple switch-points or a more heavily stochastic (mixed) strategy will depend on the number of switch-points and on the assessment abilities of the population.
The model described in this paper specifically concerns status-dependent selection on alternative reproductive tactics, but other approaches to decision-making are also relevant (Houston and McNamara, 1999; Orians, 1969; Parker, 1982; Shuster and Wade, 2003; Waltz, 1982). Switch-point variation may come about through a variety of mechanisms. For example, Hazel et al. (1990; Roff, 1996; Tomkins, 1999) treat decision-rule thresholds as polygenic threshold traits, with the distribution of decision-rule thresholds within a population varying with a normal distribution about a mean value. If applied to alternative mating tactics, this mechanism can lead to status overlap between tactics. Indeed, empirical studies have demonstrated heritable variation about a mean (e.g., Emlen, 1996). Logically, genetic variation must exist if the location of the switch-point is to evolve (Roff, 1996; Shuster and Wade, 2003; Tomkins and Brown, 2004). The mechanism described in this paper does not require genetic variation in thresholds to be responsible for multiple switch-points but does not preclude it either; the two mechanisms are compatible.
In this paper, I have shown how status-dependent selection on alternative reproductive tactics can be broken down into its constituent parts and how variation in one of those status-dependent parts—the inherent quality of the acquired territory—can lead to status overlap between cuckolders and territorial males. This provides a biologically realistic mechanism for status overlap in species that practice alternative reproductive tactics.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
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The single switch-point with the existing model
The payoffs for territoriality (guarding: Pg) and cuckoldry (Pc) can be simplified to the following linear equations.
 | (A1) |
 | (A2) |
At a switch-point, the fitness payoffs of the two tactics must be equal (Parker, 1982). Setting Pg equal to Pc and solving for the status switch-point (s')
 | (A3) |
Necessary conditions for multiple switch-points
A switch-point occurs when it pays an individual with a slightly higher or slightly lower status than another to adopt a different tactic. That is, switch-point "A" occurs when the following two inequalities are satisfied
 | (A4) |
 | (A5) |
Switch-point "B" occurs when inequality A6 is also satisfied, with sb > se > sh
 | (A6) |
 | (A7) |
Because by definition se > sh, the satisfaction of inequality A7 requires as a necessary condition
 | (A8) |
Performing the same operation for inequalities A4 and A5, we come to the inequality that must be satisfied for switch-point "A" to occur
 | (A9) |
Given the constraints imposed by inequality A8, the satisfaction of inequality A9 becomes more likely as tr–1 becomes smaller and se approaches sb (recall that by definition se < sb).
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ACKNOWLEDGEMENTS |
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The manuscript was improved by comments from Carlos Botero, Jack Bradbury, Jane Brockmann, Mark Elgar, Sam Flaxman, Kern Reeve, C. Dustin Rubinstein, Sheng-Feng Shen, and three anonymous reviewers. For discussion, I am grateful to Andrew Bass, Elizabeth Adkins-Regan, Paul Sherman, the Bass Lab, and the Cornell Behavior Lunch Bunch. Bart Kempenaers kindly provided a histogram of floater and resident conditions (body mass).
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REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONTHE EXISTING MODELSTATUS-DEPENDENT SELECTION AND...FROM MULTIPLE SWITCH-POINTS TO...APPENDIXREFERENCES |
|---|
Alatalo RV, Lundberg A, Glynn C, 1986. Pied flycatchers choose territory quality and not mate characteristics. Nature 323:152–153.[CrossRef]
Brockmann HJ, 2001. The evolution of alternative strategies and tactics. In: Advances in the study of behavior, Vol. 30. (Slater PJB, Rosenblatt JS, Snowdon CT, Roper TJ, eds.) New York: Academic Press 1–151.
Crowley PH, 2000. Hawks, doves, and mixed-symmetry games. J Theor Biol 204:543–563.[CrossRef][Web of Science][Medline]
Crowley PH, 2003. Origins of behavioural variability: categorical and discriminative assessment in serial contests. Anim Behav 66:427–440.[CrossRef][Web of Science]
Dawkins R, 1980. Good strategy or evolutionarily stable strategy? In: Sociobiology: beyond nature/nurture? (Silverberg J, ed). Boulder, Colarado: Westview Press; 331–367.
DeMartini EE, 1991. Spawning success of the male plainfin midshipman. 2. Substratum as a limiting spatial resource. J Exp Mar Biol Ecol 146:235–251.[CrossRef]
Eberhard WG, 1982. Beetle horn dimorphism—making the best of a bad lot. Am Nat 119:420–426.[CrossRef][Web of Science]
Emlen DJ, 1996. Artificial selection on horn length body size allometry in the horned beetle Onthophagus acuminatus (Coleoptera: Scarabaeidae). Evolution 50:1219–1230.[CrossRef][Web of Science]
Emlen ST, Oring LW, 1977. Ecology, sexual selection, and evolution of mating systems. Science 197:215–223.
Flaxman SM, 2000. The evolutionary stability of mixed strategies. Trends Ecol Evol 15:482–484.[CrossRef][Medline]
Foster SA, 1985. Size-dependent territory defense by a damselfish—a determinant of resource use by group-foraging surgeonfishes. Oecologia 67:499–505.[CrossRef][Web of Science]
Gerhardt HC, Daniel RE, Perrill SA, Schramm S, 1987. Mating-behavior and male mating success in the green treefrog. Anim Behav 35:1490–1503.[CrossRef][Web of Science]
Gross MR, 1996. Alternative reproductive strategies and tactics: diversity within sexes. Trends Ecol Evol 11:92–98.[CrossRef][Web of Science]
Hammerstein P, Parker GA, 1982. The asymmetric war of attrition. J Theor Biol 96:647–682.[CrossRef]
Hazel WN, Smock R, Johnson MD, 1990. A polygenic model for the evolution and maintenance of conditional strategies. Proc R Soc Lond B Biol Sci 242:181–187.[Medline]
Houston AI, McNamara JM, 1999. Models of adaptive behaviour. New York: Cambridge University Press.
Houtman AM, 1992. Female zebra finches choose extra-pair copulations with genetically attractive males. Proc R Soc Lond B Biol Sci 249:3–6.
Jennions MD, Petrie M, 2000. Why do females mate multiply? A review of the genetic benefits. Biol Rev 75:21–64.[Medline]
Kempenaers B, Everding S, Bishop C, Boag P, Robertson RJ, 2001. Extra-pair paternity and the reproductive role of male floaters in the tree swallow (Tachycineta bicolor). Behav Ecol Sociobiol 49:251–259.[CrossRef][Web of Science]
Kodric-Brown A, 1986. Satellites and sneakers—opportunistic male breeding tactics in pupfish (Cyprinodon-Pecosensis). Behav Ecol Sociobiol 19:425–432.[CrossRef][Web of Science]
Koseki Y, Maekawa K, 2000. Sexual selection on mature male parr of masu salmon (Oncorhynchus masou): does sneaking behavior favor small body size and less-developed sexual characters? Behav Ecol Sociobiol 48:211–217.[CrossRef][Web of Science]
Maynard-Smith J, 1982. Evolution and the theory of games. Cambridge: Cambridge University Press.
Neter J, Kutner MH, Nachtsheim CJ, Wasserman W, 1996. Applied linear statistical models. Boston: McGraw-Hill.
Orians GH, 1969. On evolution of mating systems in birds and mammals. Am Nat 103:589–603.[CrossRef][Web of Science]
Parker GA, 1974. Assessment strategy and the evolution of animal conflicts. J Theor Biol 47:223–243.[CrossRef][Web of Science][Medline]
Parker GA, 1982. Phenotype-limited evolutionarily stable strategies. In: Current problems in sociobiology (King's College Sociobiology Group, eds.). Cambridge: Cambridge University Press; 173–201.
Parker GA, Rubenstein DI, 1981. Role assessment, reserve strategy, and acquisition of information in asymmetric animal conflicts. Anim Behav 29:221–240.[CrossRef]
Repka J, Gross MR, 1995. The evolutionarily stable strategy under individual condition and tactic frequency. J Theor Biol 176:27–31.[CrossRef][Web of Science][Medline]
Rodenhouse NL, Sherry TW, Holmes RT, 1997. Site-dependent regulation of population size: a new synthesis. Ecology 78:2025–2042.[CrossRef][Web of Science]
Roff DA, 1996. The evolution of threshold traits in animals. Q Rev Biol 71:3–35.[CrossRef][Web of Science]
Rubenstein DI, 1980. On the evolution of alternative mating strategies. In: The allocation of individual behaviour (Staddon JER, ed). New York: Academic Press; 65–100.
Sergio F, Newton I, 2003. Occupancy as a measure of territory quality. J Anim Ecol 72:857–865.[CrossRef]
Shuster SM, Wade MJ, 2003. Mating systems and strategies. Princeton and Oxford: Princeton University Press.
Tomkins JL, 1999. Environmental and genetic determinants of the male forceps length dimorphism in the European earwig Forficula auricularia L. Behav Ecol Sociobiol 47:1–8.
Tomkins JL, Brown GS, 2004. Population density drives the local evolution of a threshold dimorphism. Nature 431:1099–1103.[CrossRef][Medline]
Waltz EC, 1982. Alternative mating tactics and the law of diminishing returns—the satellite threshold model. Behav Ecol Sociobiol 10:75–83.
Waltz EC, Wolf LL, 1988. Alternative mating tactics in male white-faced dragonflies (Leucorrhinia-Intacta)—plasticity of tactical options and consequences for reproductive success. Evol Ecol 2:205–231.
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