Evolutionary Dynamics of Fearfulness and Boldness: A Stochastic Simulation Model

Abstract

A stochastic simulation model is investigated for the evolution of anti-predator behavior in birds. The main goal is to reveal the effects of population size, predation threats, and energy lost per escape on the evolutionary dynamics of fearfulness and boldness. Two pure strategies, fearfulness and boldness, are assumed to have different responses for the predator attacks and nonlethal disturbance. On the other hand, the co-existence mechanism of fearfulness and boldness is also considered. For the effects of total population size, predation threats, and energy lost per escape, our main results show that: (i) the fearful (bold) individuals will be favored in a small (large) population, i.e. in a small (large) population, the fearfulness (boldness) can be considered to be an ESS; (ii) in a population with moderate size, fearfulness would be favored under moderate predator attacks; and (iii) although the total population size is the most important factor for the evolutionary dynamics of both fearful and bold individuals, the small energy lost per escape enables the fearful individuals to have the ability to win the advantage even in a relatively large population. Finally, we show also that the co-existence of fearful and bold individuals is possible when the competitive interactions between individuals are introduced.

About the Authors:

Nan Lu

Affiliations Group of Theoretical Biology, Group of Avian Ecology, Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, P.R. China, Graduate University of Chinese Academy of Sciences, Beijing, P.R. China

Ting Ji

* E-mail: [email protected]

Affiliation: Group of Theoretical Biology, Group of Avian Ecology, Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, P.R. China

Jia-Hua Zhang

Affiliation: Group of Theoretical Biology, Group of Avian Ecology, Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, P.R. China

Yue-Hua Sun

Affiliation: Group of Theoretical Biology, Group of Avian Ecology, Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, P.R. China

Yi Tao

Affiliation: Group of Theoretical Biology, Group of Avian Ecology, Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, P.R. China

Introduction

Individuals within a single local population of the same vertebrate species differ in their propensity to take risks [1], [2], and these differences in a range of correlated behavioral traits have also been labeled as animal personality [2], [3], or behavioral syndromes [4], [5]. Furthermore, animals often show very limited behavioral plasticity and commonly differ consistently in their reaction towards the same environmental stimulus [1], [2], [4]–[6] These differences have already been indicated to have a substantial genetic basis that can be inherited from generation to generation [7]–[10]. For birds, fearfulness-boldness as an anti-predator behavior continuum varies among different species or populations [11], [12], and should partly ascribe to the dissimilar evolutionary history [13], [14].

Recently, two theoretical evolutionary game models are developed to explain how birds respond to the predation threat, i.e. the evolution of fearfulness and boldness [15], [16]. When a bird flock is threatened, birds can not immediately identify whether it is a real attack or not, the fearful bird will take flight immediately anyhow, but the bold one will on alert for some time and take flight only if the threat proves to be a real attack [15]. Therefore, there will be a trade-off between survival and reproduction [15], [16]. The fearful individuals have more chances to survive, but will have less energy left for reproduction due to more energy consumptions through taking flight than the bold one. Sirot demonstrated that the predicted levels of fearfulness are extremely variable depending on the respective frequencies of predatory attacks and simple disturbing events, and on the capacity of birds to detect and escape predators [15]. However, Ji et al. found that the simple coexistence of two pure strategies (i.e. fearfulness and boldness) is surprisingly impossible, and a small population is favorable to fearful individuals, while boldness is preferred in a large population [16]. Furthermore, Ji et al. showed also that the existence of a mixed ESS strategy is impossible [16]. They explained that such phenomenon may ascribe to the ‘dilution effects’, i.e. individuals are safer because each individual in a large population has a relatively smaller chance of being the one attacked [17]. Specifically, bold individuals will have a higher expected fitness in a large population than in a small one due to the declined predation risk and less flying energy loss [16]. Nonetheless, it is still not clear that how the dilution or risk sharing effects act on the evolutionary process, and the sensitivity of such effects also remains to be explored. Therefore, in this paper, we develop a stochastic simulation model with overlapping generations to investigate the evolution of fearfulness and boldness, and our main goal is to illustrate the effects of population size, predation risks and energy lost per escape on evolutionary dynamics of fearfulness and boldness. On the other hand, since the maintenance of variation in personality in natural populations are still largely unknown [18], a possible mechanism for the co-existence of fearfulness and boldness will be also developed through introducing the interactions between individuals.

Methods

Assumptions and model

Following Sirot and Ji et al. [15], [16], in order to explore the evolutionary dynamics of fearfulness and boldness in a bird population, a stochastic simulation model is developed. Here, for simplicity, we consider an asexual population undergoing both predatory attacks and non-lethal disturbing events [16]. Only two possible behavior traits can be exhibited when the population is disturbed, one is fearfulness (denoted by ) and the other boldness (denoted by ). According to Sirot [15], the two phenotypes and are defined as “when the population is disturbed, fearful individuals take escape immediately, but bold individuals are on the alert for some time and then take escape only if the threat proves to be a real predator attack.” This definition also implies that when the population is under predator attacks, a fearful individual should have more chances for survival since it always leaves early, but this may be unfavorable for its reproductive success because of the energy lost [15], [16], [19] . For our model, the other definitions and assumptions are given below:

1. All individuals in the population are pure strategists. The number of -individuals is denoted by , and the number of -individuals by . The total population size is denoted by , i.e. , and we further assume that is kept to be a constant at the end of each breeding season.

2. The generations are overlapping. For both phenotypes and , all individuals are assumed to have the same maximum natural life (or maximum survival age), denoted by year old. The individual's maturity age for reproduction is one year old, and the offspring will have the same phenotype with their mother [16], [20].

3. During a breeding season, the number of real predatory attacks is assumed to be a constant, denoted by , and, similarly, the number of simple disturbing events is denoted by . In order to show the change in the number of individuals during a breeding season, let and denote the numbers of - and -individuals at the starting of -th breeding season, respectively. From Sirot [15] and Ji et al. [16], let denote the relative probability that a -individual is selected by the predators, compared with a -individual. This means that if is near 0 then the -individuals are almost never attacked; conversely, if is near 1, then the risk is shared more equally by both - and - individuals. We also use to denote the probability that a -individual is captured when selected by the predator, and the probability that a -individual is captured when selected. Thus, the probabilities that the fearful individuals are selected by the predators and a single -individual is killed at the -th attack are given by

(1)where and are the numbers of - and -individuals after the -th attack, respectively. Similarly, the probabilities that the bold individuals are selected by the predators and a single -individual is killed at the -th attack are given by(2)

1. Assume that the reproduction only occurs at the end of each breeding season. During a breeding season, if a -individual survives to the time of reproduction, then the level of its energy reserves can be simply expressed as , where represents the total energy gained during a breeding season, and is the energy lost per escape. Similarly, if a -individual survives to the time of reproduction, then the level of its energy reserves is . However, the reproductive success of an individual is proportional to the level of its energy reserves in general. From Sirot [15] and Ji et al. [16], the reproductive success of an individual with energy reserves can be measured by the function where is a constant. This means that the reproductive success of a -individual is

(3)and the reproductive success of a -individual is(4)

1. Let denote the total number of the dead individuals at the time of reproduction in the -th breeding season due to the predator attacks and the limitation of individual's lifespan (i.e. the individuals with age will be eliminated from the population at the end of the -th breeding season even if these individuals are not killed by the predators). Since the total population size, , is assumed to be fixed at the end of each breeding session, the total number of offspring born in the -th breeding season should be exactly equal to . According to this definition, in the -th breeding season, the expected number of -offspring, denoted by , is

(5)where and are the numbers of - and -individuals after the -th attack, respectively (see also Eqs. 1 and 2), and similarly, the expected number of -offspring, denoted by , is(6)

1. However, in (i)-(v), the interactions between - and -individuals, i.e. the background fitnesses of - and -individuals, are ignored. Here, in order to show the effect of the background fitnesses on the evolutionary dynamics of and , the background fitnesses of - and -individuals, denoted by and , respectively, are defined by analogy to Lotka-Volterra interspecific competition as

(7)(see Refs. [16], [21]), where and are constants, and represent the effects of -individuals on themselves and -individual, respectively, and, similarly, and represent the effects of -individual on themselves and -individuals, respectively. So, under this definition, the expected numbers of - and -offspring in the -th breeding season (see Eqs. 5 and 6) can be rewritten as(8)

Stochastic simulation

According to the definitions and assumptions in section 2, the stochastic simulation is conducted:

1. At the starting of -th breeding season, the number of -individuals with age is denoted by for , i.e. , and, similarly, the number of -individuals with age is denoted by for , i.e. .

2. The probability that a -individual is killed by the predators at the -th attack is for (see Eq. 1), and the probability that a -individual is killed by the predators at the -th attack is for (see Eq. 2), where the numbers of - and -individuals with age after -th attack are denoted by and , respectively, for (i.e. and ) (see the assumption (iii) in section 2).

3. At the end of the -th breeding season, the total number of dead individuals at the time of reproduction is , where the term represents the number of dead individuals because of the predator attacks and the term is the total number of individuals with age after the -th attack (see the assumption (v) in section 2).

4. The numbers of new born - and -individuals at the end of the -th breeding season are given by Eqs. 5 and 6, respectively (see also the assumption (v) in section 2).

For given the initial condition (i.e. the initial proportions of - and -individuals), we run the simulation until the population becomes a pure strategy population (i.e. -population, or -population). We repeat this process 1000 times and then count the times that the -population occurs, denoted by , or the frequency that the -population occurs, denoted by .

Finally, in order to make our model (an individual-based model) to be understood well and to be tested, a standard ODD protocol [20] is given in Appendix S1, and the stochastic simulation program (i.e. simulation code) in Matlab is also provided in Appendix S1.

Results

In this section, according to basic definitions and assumptions (i)–(v) (where the background fitnesses of fearful and bold individuals are ignored), we consider first the effects of the total population size, intensity of predator attacks and energy loss per escape on the evolutionary dynamics of fearfulness and boldness. Finally, according to assumption (vi), the effect of competitive interactions between fearful and bold individuals (i.e. background fitness) on the co-existence of fearfulness and boldness is considered.

Effect of population size

We here set three levels for the total population size, which are , and the other parameters are taken as , , , , , and . The simulation results are plotted in Figure 1, where the -axis denotes the initial proportion of -individuals, and the -axis the frequency . For the situation with that both and are frequency-dependent (see Eqs. 1 and 2), we have (i) for , when the initial proportion of is , respectively, and if the initial proportion of is equal to or bigger than (Figure 1A, the red curve); (ii) for , if the initial proportion of is equal to or less than , when the initial proportion of is , and if the initial proportion of is equal to or bigger than 70% (Figure 1B, the red curve); and (iii) for , if the initial proportion of is equal to or less than 60%, when the initial proportion of is 70%, and if the initial proportion of is equal to or bigger than 80% (Figure 1C, the red curve). These simulation results show clearly that for the situation with that both and are frequency-dependent, the theoretical results [16] should be correct , i.e. the fearful individuals are favored in the small population, but the bold individuals will be advantageous in the large population.

[Figure omitted. See PDF.]

Figure 1. The effect of population size on the evolution of fearfulness and boldness.

The population sizes are taken as (A), (B), and (C), respectively. denotes the frequency that -population occurs, i.e. . Simulations are conducted for both frequency-dependent (black line) and frequency-independent (red line) risk sharing situations.

https://doi.org/10.1371/journal.pone.0032258.g001

On the other hand, we also consider the situation where we assume that both and are independent of the numbers of - and -individuals, or that the probability that the fearful individuals (or bold individuals) are selected by the predators is independent of the population structure (i.e. it is frequency-independent). Then, for all possible and , we have(9)and(10)(see Eqs. 1 and 2). Comparing with Eqs. 1 and 2, it is easy to see thatif (or ), and, similarly,if (or ). This implies that when the number of -individuals is less than the number of -individuals, the risk of the -individuals will be shared by the -individuals, and, similarly, when the number of -individuals is less than the number of -individuals, the risk of the -individuals will be shared by the -individuals.

For this situation,we have (i) for , for initial proportions of is equal to , and for all initial proportions of is equal to or bigger than (Figure 1A, the black curve); (ii) for , if the initial proportion of is equal to or less than 30%, when the initial proportion of is , respectively, and if the initial proportion of is equal to or bigger than 60% (Figure 1B, the black curve); and (iii) for , if the initial proportion of is equal to or less than 80%, and when the initial proportion of is 90% (Figure 1C, the black curve). It is easy to see that for , the fearful individuals are more advantageous in the situation with frequency-dependence than in the situation with frequency-independence, but, for , the fearful individuals more advantageous in the situation with frequency-independence than in the situation with frequency-dependence.

All of above results imply that when the population size is small, the risk that the bold individuals will be captured by the predators cannot be compensated by bold individuals' advantage in reproduction, i.e. when the population size is small, a single -individual cannot invade successfully a -population; conversely, when the population size is large, the disadvantage of fearful individuals in reproduction cannot be compensated by their advantage in survival, i.e. when the population size is large, a single -individual cannot invade successfully a -population.

Effect of the intensity of predator attacks

In this subsection, the effect of the intensity of predators attacks (i.e. the number of predators attacks) on the system dynamics is investigated. Here, we set four levels for the total population size, which are , three levels for , which are , respectively, and the other parameters are taken as , , , and . For all simulations in this subsection, the initial proportion of -individuals is fixed to be 50%. The simulation results with different numbers of predator attacks are plotted in Figure 2. It is easy to see that: (i) for the situation with small total population size (i.e. ), the fearful individuals will be favored (i.e. ) if the number of predators attacks is equal to or bigger than 20 (i.e. ) for all three levels of (see Figure 2A), and when , the value of will decrease with the increase of ; (ii) for the situation with , the fearful individuals will be favored if the number of predators attacks is in the interval for all three levels of , and the value of will decrease with the decrease of if and with the increase of if , where for both and the low level of will be helpful to the fearful individuals (see Figure 2B); (iii) for the situation with , the effect of the number of predators attacks on is symmetric about when and , i.e. at has the maximum for and for , and, similar to the situation with , for , if is in the interval and will decrease with the decrease of if and with the increase of if (see Figure 2C); and (iv) for the situation with , only when the effect of on is symmetric about and the maximum of at is , and when (or ), for all possible (see Figure 2D).

[Figure omitted. See PDF.]

Figure 2. The effects of the intensity of real predatory attacks and population size on the evolution of fearfulness and boldness where . (A), (B), (C), and (D).

https://doi.org/10.1371/journal.pone.0032258.g002

The simulation results in this subsection imply that the effect of predation pressure (i.e. the number of predator attacks)on the evolution of fearfulness and boldness strongly depends on the total population size, i.e. the fates of fearful and bold individuals are mainly determined by the total population size. On the other hand, we can also notice that for the moderate total population size (for example and ), the fearful individuals will be not favored if the number of predators' attacks is small or large, i.e. in our simulations, the effect of on is symmetric about and has the maximum at .

Effect of the energy loss per escape

In section 2, we define to be the total energy gained during a breeding season and the energy lost per escape. Clearly, the large should be always disadvantageous to the fearful individuals since during a breeding season, fearful individuals will take flights more often than bold individuals, and thus fearful individuals will have less energy remained for reproduction. In this subsection, the effect of on under different total population size is investigated, where we set three levels for , which are , respectively, and the other parameters are taken as , , , and . The initial proportion of -individuals is also fixed to be 50%. The simulation results show clearly that the smaller the value of is, the more favored the fearful individuals will be by natural selection, i.e. for , if ; for , if ; and for , if (see Figure 3). This means that although the total population size is the most important factor for the fates of fearfulness and boldness, the small energy loss per escape will make that the fearful individuals have the ability to win the advantage in a large population.

[Figure omitted. See PDF.]

Figure 3. The effect of energy lost per escape on the evolution of fearfulness and boldness where  = 0.08, 0.10 and 0.12.

https://doi.org/10.1371/journal.pone.0032258.g003

Effect of the interactions between fearful and bold individuals on the coexistence of fearfulness and boldness

In this subsection, in order to provide a possible mechanism for the co-existence of fearfulness and boldness, the interactions between fearful and bold individuals (i.e. the background fitnesses of feraful and bold individuals (see Eqs. 7 and 8)) are introduced. The total population size is set five levels, which are and , and the parameters , , , , , and are taken as , , , , , and , respectively. For the background fitnesses and (see Eqs, 7 and 8), we take , and (i.e. for the interactions between individuals, we assume that the effects of -individuals are stronger than that of -individuals, or generally, individuals would be more aggressive in competition if they risk more when confronted with predators [22]). The stochastic simulation results show clearly that: (a) the co-existence of fearfulness and boldness is possible when the background fitnesses are introduced, i.e. for a given total population size, the frequency of (or ) will fluctuates around its mean; (b) the mean proportion of fearful individuals (i.e. the mean frequency of ) in the co-existence will decrease with the increase of the total population size (see Figure 4A), or the mean proportion of bold individuals will increase with the increasing of the total population size; and (c) the strength of random fluctuation in the frequency of (or ) will decrease with the increase of the total population size (see Figure 4B).

[Figure omitted. See PDF.]

Figure 4. The effect of interactions between individuals on the co-existence of fearfulness and boldness, where the parameters in background fitnesses and are taken as: , , , , and .

(A) The mean proportions of fearful individuals (for the last 100 generations) decreases with the increase of the total population size. (B) The strength of random fluctuation in the frequency of fearfulness decreases with the increase of the total population size, where black line: ; red line: ; and green line: .

https://doi.org/10.1371/journal.pone.0032258.g004

Discussion

As pointed out in the section of introduction, Ji et al. investigated a deterministic model for the evolutionary dynamics of fearfulness and boldness [16]. Their main results show that for large population size bold individuals have a higher expected fitness than fearful individuals, and for small population size fearful individuals have a higher expected fitness. Thus, we firstly focus our attention on how the evolutionary dynamics of both fearfulness and boldness is affected by the total population size (where we ignore temporarily the effect of the interactions between individuals on the dynamics). The simulation results support the theoretical analysis of Ji et al. [16] generally. Our result also implies that for both fearful and bold individuals, the trade-off between survival and reproduction is mainly determined by the total population size, and is independent of the population structure. According to Maynard Smith [23], for only two phenotypes, i.e. and , can be considered to be an ESS if the population size is small, and is an ESS if the population size is large.

For the effect of predation pressure, the simulation result reveals that although total population size affects the evolutionary processes significantly, the number of predator attacks also play an important role in a relatively moderate or small population that neither too many nor few attacks are favored by the fearful individuals. Clearly, although the bold individuals will take higher predation risk than the fearful individuals, the bold individuals will also reserve more energy for reproduction. Thus, relatively smaller number of predator attacks will lead to that the bold individuals have a higher expected fitness. Conversely, if the intensity of predator attacks is relatively stronger, the predation risk will be shared among fearful and bold individuals, and the fearful individuals will be unable to maintain a higher expected reproductive success because of its big energy expense in the frequent escapes, i.e. the advantage of fearful individuals in survival cannot compensate its disadvantage in reproduction. However, we have to say that in general the effect of predation pressure also depends strongly on the total population size.

The simulation result shows also that species-specific energy loss per escape is important during the evolution of personality in a population that relatively small value enables that the fearful individuals have the ability to supplant the bold one even in a large population.

Finally, we develop a possible mechanism for the co-existence of fearfulness and boldness. Notice that our basic model considers only two pure strategies in a very simple world with only one available ecological niche. This is why the stable coexistence of fearfulness and boldness is impossible if we ignore the other possible ecological mechanisms in our model. The classical competitive exclusion principle shows that two species competing for the same resources cannot coexist if other ecological factors are constant [24]. While the interactions between fearful and bold individuals (i.e. the background fitnesses of fearful and bold individuals) are introduced, the main result shows that the co-existence of fearfulness and boldness is possible. Moreover, the mean proportion of fearful individuals will decrease with the increase of the total population size. Clearly, this result is also consistent with the theoretical analysis of Ji et al. [16], i.e. the evolution of fearfulness-boldness should be population size-dependent, the fearful behavior will be favored by the natural selection in a small population, and, conversely, the bold behavior will be favored in a large population. We also noticed that some empirical observations had shown that both fearful and bold individuals can be found in a real population, such as [25] and [26]. So, a possible mechanism behind the co-existence of fearfulness and boldness should be that the evolution of fearfulness and boldness not only depends on predator attacks (or nonlethal disturbance) but also depends on their ability in competition for some limited resources. Specifically, as proposed by Thingstad [27], this coexisting phenomenon including the framework of an Lotka-Volterra type model might be caused by imposing a cost on the winner in the modeling, i.e. “killing the winner”, where “winner” refers to the more active population [28]. Our model shows that this mechanism for the co-existence of fearfulness and boldness is possible.

Supporting Information

[Figure omitted. See PDF.]

Appendix S1.

The ODD Protocol for the individual-based model and the stochastic simulation program in Matlab.

https://doi.org/10.1371/journal.pone.0032258.s001

(PDF)

Acknowledgments

We sincerely thank the anonymous reviewer and editor for their valuable comments on the original version of the manuscript.

Author Contributions

Conceived and designed the experiments: TJ YT YS. Performed the experiments: NL. Analyzed the data: NL TJ JZ. Contributed reagents/materials/analysis tools: NL TJ. Wrote the paper: NL TJ YT YS.

Citation: Lu N, Ji T, Zhang J-H, Sun Y-H, Tao Y (2012) Evolutionary Dynamics of Fearfulness and Boldness: A Stochastic Simulation Model. PLoS ONE7(3): e32258. https://doi.org/10.1371/journal.pone.0032258

References

1. Sloan Wilson D, Clark A, Coleman K, Dearstyne T (1994) Shyness and boldness in humans and other animals. Trends Ecol Evol 9: 442–446.D. Sloan WilsonA. ClarkK. ColemanT. Dearstyne1994Shyness and boldness in humans and other animals.Trends Ecol Evol9442446

2. Gosling S (2001) From mice to men: What can we learn about personality from animal research? Psychol Bull 127: 45–86.S. Gosling2001From mice to men: What can we learn about personality from animal research?Psychol Bull1274586

3. Buss D (1991) Evolutionary personality psychology. Annu Rev Psychol 42: 459–491.D. Buss1991Evolutionary personality psychology.Annu Rev Psychol42459491

4. Sih A, Bell A, Johnson J (2004) Behavioral syndromes: an ecological and evolutionary overview. Trends Ecol Evol 19: 372–378.A. SihA. BellJ. Johnson2004Behavioral syndromes: an ecological and evolutionary overview.Trends Ecol Evol19372378

5. Sih A, Bell A, Johnson J, Ziemba R (2004) Behavioral syndromes: an integrative overview. Q Rev Biol 79: 241–277.A. SihA. BellJ. JohnsonR. Ziemba2004Behavioral syndromes: an integrative overview.Q Rev Biol79241277

6. Wilson D (1998) Adaptive individual differences within single populations. Phil Trans R Soc Lond B 353: 199–205.D. Wilson1998Adaptive individual differences within single populations.Phil Trans R Soc Lond B353199205

7. Koolhaas J, Korte S, De Boer S, Van Der Vegt B, Van Reenen C, et al. (1999) Coping styles in animals: current status in behavior and stress-physiology. Neurosci Biobehav Rev 23: 925–935.J. KoolhaasS. KorteS. De BoerB. Van Der VegtC. Van Reenen1999Coping styles in animals: current status in behavior and stress-physiology.Neurosci Biobehav Rev23925935

8. Bouchard T, Loehlin J (2001) Genes, evolution, and personality. Behav Gen 31: 243–273.T. BouchardJ. Loehlin2001Genes, evolution, and personality.Behav Gen31243273

9. Drent P, Oers K, Noordwijk A (2003) Realized heritability of personalities in the great tit (parus major). Proc R Soc Lond B 270: 45–51.P. DrentK. OersA. Noordwijk2003Realized heritability of personalities in the great tit (parus major).Proc R Soc Lond B2704551

10. Van Oers K, Drent P, De Goede P, Van Noordwijk A (2004) Realized heritability and repeatability of risk-taking behaviour in relation to avian personalities. Proc R Soc Lond B 271: 65–73.K. Van OersP. DrentP. De GoedeA. Van Noordwijk2004Realized heritability and repeatability of risk-taking behaviour in relation to avian personalities.Proc R Soc Lond B2716573

11. Blumstein D (2003) Flight-initiation distance in birds is dependent on intruder starting distance. J Wildl Manage 852–857.D. Blumstein2003Flight-initiation distance in birds is dependent on intruder starting distance.J Wildl Manage852857

12. Azevedo C, Young R (2006) Shyness and boldness in greater rheas rhea americana Linnaeus (rheiformes, rheidae): the effects of antipredator training on the personality of the birds. Rev Bras Zoo 23: 202–210.C. AzevedoR. Young2006Shyness and boldness in greater rheas rhea americana Linnaeus (rheiformes, rheidae): the effects of antipredator training on the personality of the birds.Rev Bras Zoo23202210

13. Blumstein D (2006) The multipredator hypothesis and the evolutionary persistence of antipredator behavior. Ethology 112: 209–217.D. Blumstein2006The multipredator hypothesis and the evolutionary persistence of antipredator behavior.Ethology112209217

14. Blumstein D (2006) Developing an evolutionary ecology of fear: how life history and natural history traits affect disturbance tolerance in birds. Anim Behav 71: 389–399.D. Blumstein2006Developing an evolutionary ecology of fear: how life history and natural history traits affect disturbance tolerance in birds.Anim Behav71389399

15. Sirot E (2007) Game theory and the evolution of fearfulness in wild birds. J Evol Biol 20: 1809–1814.E. Sirot2007Game theory and the evolution of fearfulness in wild birds.J Evol Biol2018091814

16. Ji T, Zhang B, Sun Y, Tao Y (2009) Evolutionary dynamics of fearfulness and boldness. J Theo Biol 256: 637–643.T. JiB. ZhangY. SunY. Tao2009Evolutionary dynamics of fearfulness and boldness.J Theo Biol256637643

17. Delm M (1990) Vigilance for predators: detection and dilution effects. Behav Ecol Sociobiol 26: 337–342.M. Delm1990Vigilance for predators: detection and dilution effects.Behav Ecol Sociobiol26337342

18. Dingemanse N, Both C, Drent P, Tinbergen J (2004) Fitness consequences of avian personalities in a fluctuating environment. Proc R Soc Lond B 271: 847–852.N. DingemanseC. BothP. DrentJ. Tinbergen2004Fitness consequences of avian personalities in a fluctuating environment.Proc R Soc Lond B271847852

19. Cresswell W, Hilton G, Ruxton G (2000) Evidence for a rule governing the avoidance of superfluous escape flights. Proc R Soc Lond B 267: 733–737.W. CresswellG. HiltonG. Ruxton2000Evidence for a rule governing the avoidance of superfluous escape flights.Proc R Soc Lond B267733737

20. Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, et al. (2006) A standard protocol for describing individual-based and agent-based models. Ecol Model 198: 115–126.V. GrimmU. BergerF. BastiansenS. EliassenV. Ginot2006A standard protocol for describing individual-based and agent-based models.Ecol Model198115126

21. Cressman R, Dash A (1987) Density dependence and evolutionary stable strategies. J Theo Biol 126: 393–406.R. CressmanA. Dash1987Density dependence and evolutionary stable strategies.J Theo Biol126393406

22. Wolf M, Van Doorn G, Leimar O, Weissing F (2007) Life-history trade-offs favour the evolution of animal personalities. Nature 447: 581–584.M. WolfG. Van DoornO. LeimarF. Weissing2007Life-history trade-offs favour the evolution of animal personalities.Nature447581584

23. Maynard Smith J (1982) Evolution and the Theory of Games. Cambridge Univ Pr. J. Maynard Smith1982Evolution and the Theory of GamesCambridge Univ Pr

24. Hardin G (1960) The competitive exclusion principle. Science 131: 1292–1297.G. Hardin1960The competitive exclusion principle.Science13112921297

25. Minderman J, Reid J, Evans P, Whittingham M (2009) Personality traits in wild starlings: exploration behavior and environmental sensitivity. Behav Ecol 20: 830–837.J. MindermanJ. ReidP. EvansM. Whittingham2009Personality traits in wild starlings: exploration behavior and environmental sensitivity.Behav Ecol20830837

26. Schuett W, Dall S (2009) Sex differences, social context and personality in zebra finches, taeniopygia guttata. Anim Behav 77: 1041–1050.W. SchuettS. Dall2009Sex differences, social context and personality in zebra finches, taeniopygia guttata.Anim Behav7710411050

27. Thingstad T (2000) Elements of a theory for the mechanisms controlling abundance, diversity, and iogeochemical role of lytic bacterial viruses in aquatic systems. Limnol Oceanogr 1320–1328.T. Thingstad2000Elements of a theory for the mechanisms controlling abundance, diversity, and iogeochemical role of lytic bacterial viruses in aquatic systems.Limnol Oceanogr13201328

28. Winter C, Bouvier T, Weinbauer M, Thingstad T (2010) Trade-offs between competition and efense specialists among unicellular planktonic organisms: the “killing the winner” hypothesis evisited. Microbiol Mol Biol Rev 74: 42–57.C. WinterT. BouvierM. WeinbauerT. Thingstad2010Trade-offs between competition and efense specialists among unicellular planktonic organisms: the “killing the winner” hypothesis evisited.Microbiol Mol Biol Rev744257