In Which Animal Is Single Parental Care Most Common

• Journal List
• Ecol Evol
• five.3(iv); 2013 Apr
• PMC3631394

Ecol Evol. 2013 Apr; three(four): 779–791.

The origin of parental care in relation to male and female life history

Hope Klug

¹Section of Biological & Environmental Sciences, University of Tennessee–Chattanooga, Dept. 2653, 615 McCallie Aven, Chattanooga, Tennessee, 37403

ⁱⁱDepartment of Ecology & Evolutionary Biological science, Yale University, PO Box 208106, 165 Prospect St, New Oasis, Connecticut, 06520

Michael B Bonsall

³Mathematical Ecology Enquiry Grouping, Section of Zoology, University of Oxford, Oxford, OX1 3PS, UK

Suzanne H Alonzo

²Department of Ecology & Evolutionary Biology, Yale Academy, PO Box 208106, 165 Prospect St, New Haven, Connecticut, 06520

Received 2012 Jul half dozen; Revised 2012 Dec 27; Accepted 2013 Jan 8.

Abstract

The development of maternal, paternal, and bi-parental care has been the focus of a great bargain of enquiry. Males and females vary in basic life-history characteristics (e.g., phase-specific mortality, maturation) in ways that are unrelated to parental investment. Surprisingly, few studies have examined the result of this variation in male and female life history on the evolution of care. Here, we use a theoretical approach to determine the sex-specific life-history characteristics that requite ascension to the origin of paternal, maternal, or bi-parental care from an ancestral land of no care. Females initially invest more than into each egg than males. Despite this inherent difference between the sexes, paternal, maternal, and bi-parental care are every bit likely when males and females are otherwise similar. Thus, sex differences in initial zygotic investment do not explain the origin of one pattern of care over another. However, sex activity differences in adult mortality, egg maturation charge per unit, and juvenile survival bear on the design of care that will be most probable to evolve. Maternal intendance is more than probable if female adult mortality is high, whereas paternal care is more likely if male adult mortality is loftier. These findings suggest that basic life-history differences between the sexes can alone explain the origin of maternal, paternal, and bi-parental care. As a result, the influence of life-history characteristics should exist considered as a baseline scenario in studies examining the origin of care.

Keywords: Biparental intendance, invasion analysis, life-history, maternal intendance, parental care, paternal intendance

Introduction

Patterns of post-fertilization parental care are incredibly various (Clutton-Brock 1991). Starting time, at that place is large disparity beyond taxa in whether any post-fertilization parental care is provided (Clutton-Brock 1991; Beck 1998; Reynolds et al. 2002). In birds, crocodiles, mammals, and cichlid fishes, one or both parents tend to care for immature (Reynolds et al. 2002). In contrast, well-nigh non-cichlid teleosts, anurans, and squamate reptiles provide no intendance (Reynolds et al. 2002). 2d, when care is provided, there is striking variation in which sexual activity provides care (Clutton-Brock 1991; Brook 1998; Reynolds et al. 2002; Kokko and Jennions 2008). Bi-parental care is the norm in birds (Tullberg et al. 2002), maternal care is most common in mammals and invertebrates (Tallamy 1984, 2000; Zeh and Smith 1985; Clutton-Brock 1991), and paternal care is widespread in fishes that exhibit care (Blumer 1979; Reynolds et al. 2002; Mank et al. 2005). In amphibians, care is provided past either sex (Reynolds et al. 2002), whereas in reptiles, care tends to be maternal or bi-parental (Reynolds et al. 2002). Explaining such diversity has been the focus of extensive empirical and theoretical piece of work (Blumer 1979; Baylis 1981; Tallamy 1984, 2000; Zeh and Smith 1985; Clutton-Brock 1991; Winemiller and Rose 1992; Brook 1998; Reynolds et al. 2002; Tullberg et al. 2002; Mank et al. 2005; Klug and Bonsall 2007, 2010; Kokko and Jennions 2008; Bonsall and Klug 2011a,b).

Classic theory suggests that females are more likely to provide parental care than are males, as they invest disproportionately more in gametes or zygotes (Trivers 1972), which decreases residual reproductive value and makes it beneficial for them to invest more than heavily into current versus future reproduction (Sargent and Gross 1985; Coleman and Gross 1991; Gross 2005). Others have noted that past investment solitary is bereft to pb to sex differences in intendance (Dawkins and Carlisle 1976; Kokko and Jennions 2008) and have suggested a role for other factors in promoting differences betwixt the sexes in parental investment. For case, dubiety of paternity is expected to make males more likely than females to abandon young on a macro-evolutionary calibration (Trivers 1972). Within a species, uncertain paternity is predicted to bear on paternal intendance if current and future reproductive opportunities vary in expected paternity (Trivers 1972; Baylis 1981; Westneat and Sherman 1993; Sheldon 2002; Alonzo 2010). Queller (1997) and Kokko and Jennions (2008) accept shown that care by i sexual activity can affect the availability of sexual partners and reproductive opportunities for the non-caring sexual practice. As a result, sex ratios influence the fitness costs and benefits of caring versus deserting, which in turn determine whether males and/or females will be more than likely to provide care (Queller 1997; Webb et al. 1999; Kokko and Jennions 2008). Furthermore, recent work has illustrated that the trade-off betwixt current parental care and future mating success might non be as ubiquitous as previously causeless (Stiver and Alonzo 2009). In particular, if females prefer males that provide parental care, sexual selection is expected to favor male person care (Alonzo 2012).

This theoretical work has led to considerable advances in our understanding of the evolution of care. Despite this, nosotros are withal far from understanding sex differences in parental care. Unexpected patterns of parental investment are the norm, and post hoc explanations, rather than well-supported a priori predictions, prevail in the literature (reviewed in Alonzo 2010). Previous theoretical work has tended to focus on the role of sexual selection in explaining sex differences in parental care. In contrast, relatively little work has explored how very basic and general life-history differences between males and females affect the evolution of care. A more than comprehensive understanding of the evolution of parental care necessitates a closer look at how bones life history (i.e., stage-specific mortality, maturation rates) of males and females influences the evolution of maternal, paternal, and bi-parental care from an ancestral country of no intendance.

Within a species, males and females vary in numerous ways. Females initially invest more into zygotes than males. Additionally, 1 sexual practice often has higher mortality during i or more life-history stages due to factors unrelated to parental investment, such every bit sex differences in physiology, mating beliefs, predation risk, and resource employ. Likewise, males and females oftentimes mature at different rates. Recent work even indicates that sex differences in life-history characteristics can arise during the egg stage in relation to yolk androgens (Sockman and Schwabl 2000; Eising et al. 2001; reviewed in Navar and Mendonça 2008). How such sexual practice differences in life history influence the potential for maternal, paternal, or bi-parental care to originate is unknown. Our previous piece of work suggests that life history tin strongly influence the likelihood that some pattern of parental care will invade an bequeathed state of no care (Klug and Bonsall 2010; Bonsall and Klug 2011a,b). Additionally, providing parental intendance is associated with costs and benefits, and such costs and benefits of intendance directly affect life-history traits (e.g., developed and offspring mortality). Thus, it is likely that sex-specific life-history characteristics will influence the origin of intendance.

Understanding how life history affects sex activity differences in parental care requires that we accost two questions. First, how practice male person and female life-history characteristics affect the origin of some blueprint of parental care from an ancestral country of no care, and 2nd, one time some blueprint of intendance is present, how practice male and female life-history characteristics influence transitions amid paternal, maternal, and bi-parental care? In evolutionary models, it is important to distinguish betwixt the origin and maintenance of parental care (Klug et al. 2012): in species with parental care, coevolution among traits (e.yard., egg size and care) is expected to occur and individuals providing care typically feel college bloodshed and/or lower current or future reproductive success; in species without parental intendance, such costs and potential for coevolution are absent. Every bit a result, the dynamics that affect the origin and maintenance of care are expected to differ. Furthermore, independently examining the origin of and transitions amidst care allows for articulate testable predictions that can be evaluated in a comparative or phylogenetic context. Thus, in this written report, we focus only on the relationship between male and female life history and the origin of intendance. In related theoretical work (Klug et al. 2012), we examine transitions among different patterns of care.

Specifically, we examine the human relationship between male person and female basic life history (phase-specific mortality, rates of maturation) and the origin of maternal, paternal, and bi-parental intendance. We first identify combinations of male and female life-history characteristics that are most likely to lead to the origin of maternal, paternal, and bi-parental care from an ancestral country of no care. We then consider cases in which males and females vary in stage-specific mortality or maturation and ask which pattern of care will exist nigh strongly favored from an bequeathed state of no care based on these life-history differences.

Methods

Using a mathematical model, we permit a rare mutant that exhibits paternal, maternal, or bi-parental care to invade a resident population in which care is absent (Metz et al. 1992; Dieckmann and Law 1996; Vincent and Brown 2005; Otto and Twenty-four hours 2007). The resident strategy is assumed to be in a stable equilibrium and the culling parental care strategy invades from rare into the population (as is standard in invasion analyses; Otto and Day 2007). Building upon previous work (described in Klug and Bonsall 2007, 2010 and Bonsall and Klug 2011a,b), we assume a phase-structured arrangement in which individuals pass through egg and juvenile stages and then mature and reproduce as adults. Mutant and resident individuals experience the same baseline weather condition (i.e., both resident and mutant have the same death, maturation, and reproductive rates when no care is provided). Parental care is and so assumed to be associated with benefits to offspring (increased survival beyond the baseline survival rate in the absence of intendance) and costs to the parent providing it (decreased parental survival relative to the no-care scenario; described below). In other words, we identify particular life-history parameters associated with a resident strategy of no care, and we then introduce a mutant that either exhibits paternal, maternal, or bi-parental care. We so evaluate the life-history parameters that will nigh strongly favor invasion past the mutant strategy.

Our approach differs from previous models in a number of key means. Kickoff, nosotros explicitly focus on all life-history stages (egg, juvenile, and adult) and inquire how sex-specific life history can influence patterns of care. In contrast, many recent models on care focus on a single life-history stage (east.thou., some models explore how differences between male and female adults tin bear upon care). 2nd, nosotros assume that females are the limiting sex activity (described below), simply beyond that, we do not explicitly focus on how sex differences in mate contest influence parental care, a major focus in many recent models of parental intendance. As we focus explicitly on how life-history differences tin bulldoze patterns of intendance and focus minimally on sexual selection, our modeling framework can potentially serve every bit a null or baseline scenario for models that explore more than detailed dynamics related to sexual practice differences in mate competition and sexual pick.

Model Dynamics

Males and females laissez passer through egg (East) and juvenile stages and mature and reproduce as adults (A). Eggs subtract every bit they die and mature and increase every bit adults reproduce, such that

(1)

where e _m is the rate at which male eggs are produced and due east _f is the rate at which female eggs are produced at time t (e ₁₀₀₀ = e _f = 0.five initially in all cases considered). Male and female eggs die at rates d _Em and d _Ef . At any given fourth dimension, the rate of male person eggs surviving the egg stage, e _sm , equals e _m (1 − d _Em ). As well, the charge per unit of female eggs surviving the egg stage, e _sf , equals e _f (1 − d _Ef ). Those surviving male and female eggs then mature at rates m _Em and m _Ef . Female fecundity limits reproduction (Bateman 1948) and reproduction in the population is causeless to be density-dependent. On boilerplate, each female produces r eggs that are fertilized. The total number of eggs that are fertilized is a function of r, the number of adults present A(t), the rate at which females enter the adult stage a _f , and the carrying capacity of the population Yard. The rate at which females enter the adult stage at time t, a _f , equals e _f (i − d _Ef )m _Ef σ _Jf , where σ _Jf represents female juvenile survival. Each fertilized egg has one mother and one begetter, and thus our mensurate of per capita female fecundity, r, is likewise a measure of the rate of egg fertilization in the population.

Adults in the population increase as individuals pass through the juvenile phase and subtract as adults die:

(2)

where σ _Jm and σ _Jf represent the juvenile survival rates of males and females, eastward _mm and e _mf are the rate of male person and female person eggs surviving the egg stage and maturing into juveniles, τ _yard and τ _f are the durations of the male and female juvenile stages, and d _Am and d _Af are the rates at which male and female adults die. The charge per unit at which males and females that survive the egg stage and mature into juveniles at time t, due east _mm and eastward _mf, equals e _m (1 − d _Em )thousand _Em and e _f (one − d _Ef )m _Ef . The adults that are male and female at fourth dimension t is a function of the charge per unit of individuals surviving the egg phase, maturing, and surviving and passing through the juvenile stage. Specifically, the charge per unit at which males and females enter the adult stage at fourth dimension t, a _m and a _f, equals e _m (1 − d _Em )m _Em σ _Jm and e _f (1 − d _Ef )m _Ef σ _Jf .

The density of resident adults at equilibrium (i.e., when and equal zero) is

(3)

where η = east _sf chiliad _Ef + eastward _sm k _Em + e _f d _Ef + e _m d _Em .

The dynamics of the rare mutant that provides parental care are given by the following equations and by incorporating the relevant trade-offs associated with parental care into the mutant and resident dynamics (discussed below and in Table ​ one). The other parameters are as described previously and superscript denotes the new mutant strategy that exhibits parental intendance:

Tabular array 1

Costs and benefits of initial investment in eggs past females (i-d_Emo and i-d_Efo ) and parental care by males and females (c _m and c _f ). The full level of parental care provided to eggs, c _total , is the sum of intendance provided by their mother and father, that is, c _g + c _f . Male person and female egg expiry rate decreases as initial investment in eggs increases and as the total level of parental care increases. Initial egg investment is costly to mothers, and female adult death charge per unit increases and fecundity decreases every bit initial egg investment increases. Care is costly to parents, and as care increases, adult decease rate also increases. These merchandise-offs are incorporated into the model and let united states of america to determine the fitness associated with various care scenarios (described in text). The term a determines the specific shape of the trade-off function and is equal to half-dozen in all cases considered

(four)

(5)

where A* (eqn. 3) is the equilibrial abundance of the resident developed population. Equally the mutant is causeless to be rare in the population, density-dependence operating on developed mutant reproduction occurs through competition with the resident (as is standard for ecological and evolutionary invasion analyses; east.thousand., Otto and Day 2007).

To explore the invasion of parental care from an bequeathed state of no care, we consider the case in which rare adult mutants are nowadays and able to provide parental care to their offspring, and pass on the factor(s) for a item pattern of care to their offspring. This ways that when we consider the example of paternal or maternal care, expression of the gene(s) for care is sexual practice-limited and when we consider the case of bi-parental intendance, both sexes limited the gene(s) for care. Every bit parents are assumed to exist able to provide care, nosotros additionally assume that mutant parents are associated with their offspring during the parental intendance stage and remain alive long enough to provide care to young. Furthermore, the model assumes that at least a unmarried male person and single female person of each strategy remain alive, and the parameter values considered never result in complete bloodshed of all of 1 sexual activity. We do non specify how the mutant that provides a particular pattern of parental care arises in the population. The new mutant strategy could exist the result of a genetic mutation within the population or immigration from another population. All offspring of mutant parents are assumed to exhibit the mutant strategy.

Costs and benefits of parental care and initial egg investment

Parents can touch offspring survival and quality by investing resources into eggs (referred to herein as initial egg investment) and providing post-fertilization parental care behavior (referred to as parental care) to offspring (meet also Klug and Bonsall 2010). Hither, we presume that females initially allocate resource to eggs, and either male, female person, or both male and female mutant parents can provide care to their eggs. For simplicity (and in line with our previous work – Klug and Bonsall 2007, 2010; Bonsall and Klug 2011a,b), nosotros focus on parental care of developing zygotes and assume that juveniles exercise not receive intendance. This modeling framework is more by and large representative of whatever organization in which in that location are sequential evolution stages and parental care is provided only during the kickoff stage.

Baseline egg decease rate (i.due east., egg expiry rate in the absence of whatsoever care) is used every bit our proxy of initial egg investment. By our definition, egg survival increases as initial egg investment increases. Initial egg investment is plush to females, such that every bit initial egg investment increases, female person survival and fecundity subtract (Table ​ 1). This assumes that an increase in individual egg size is associated with an increase in full investment within a given reproductive bout. Chiefly, because this assumption is unchanged across all of our scenarios, this basic assumption is unlikely to touch our general patterns. Parental care, which again is provided by mutant parent(south) to their mutant eggs, increases egg survival, and the full level of care that eggs receive is the sum of the care provided by their male and female parents (c _m + c _f ) (Table ​ one). Providing care is costly to the parent providing it, and as the level of care increases, adult survival declines (i.east., male and/or female decease rate increases) (Table ​ i). In the current model, we do not assume an explicit merchandise-off betwixt parental intendance and female fecundity in order to go on the trade-offs between males and female person as like as possible. However, because a reduction in developed survival reduces futurity reproductive opportunities, in that location is also an indirect trade-off between care and future reproduction for both sexes. Minimizing baseline differences betwixt the sexes in the costs of care allows us to determine whether sex-specific patterns of care arise because of sex differences in life-history characteristics (i.e., different mortality and maturation rates) or because females, by definition, initially invest more into eggs than male. Additionally, the assumption that female person fecundity declines as females initially invest more into eggs does not affect the qualitative patterns – that is, if this trade-off is removed, the patterns are qualitatively similar.

In all cases, we assume that mutant adult parents are able to provide care for their immature. This ways that adult mutants either live long plenty such that they are able to provide some level of care or that the benefits of care are nowadays after their death (e.k., as would occur in matrophagy, which is common in some spiders). As well, we presume that mutant males and/or females are physically capable of providing intendance, and that when care is uni-parental, the expression of the gene(s) for intendance is sex-express. We besides presume that males and females have the potential to provide equivalent levels of care (Table ​ 1). While this might not apply in all cases, we believe that this is the nearly biologically plausible assumption for early in the evolution of care and is a reasonable baseline scenario to consider.

In all cases, we assume asymptotic non-linear trade-offs (Table ​ i) because they allow for a wide exploration of parameter space, and hence, a thorough exploration of the costs and benefits of care. Specifically, using not-linear, asymptotic trade-off functions (Table ​ 1) allows us to consider all biologically realistic parameter values (eastward.g., death and maturation rates that give rise to mortality that is between zippo and one). In dissimilarity, if we used linear trade-offs, nosotros would only be able to consider a truncated range of parameter space (i.e., just those parameter values which gave rise to biologically sensible expiry and maturation). Non-linear trade-off functions are likely to be biologically realistic in many animals (Clutton-Brock 1991), and our full general patterns will concur for other similarly shaped functions.

The trade-offs described in Tabular array ​ 1 provide some insight into the potential for parental care to increase reproductive success. However, the costs and benefits associated with care lone do not provide information on whether parental care will be able to invade a resident strategy of no intendance and persist given the stage-structured life-history weather condition and the ecological dynamics. Data on invasion of intendance necessitates further analysis and is described below. These invasion analyses allow the states to ask whether paternal, maternal, and/or bi-parental care tin can invade an ancestral state of no intendance given a set of specified male and female person life-history parameters. This, in turn, allows us to identify the male and female life-history characteristics (stage-specific bloodshed and maturation) that are most likely to favor the origin of paternal, maternal, and/or bi-parental care.

Fitness of parental care & invasion dynamics

The fitness of the rare mutant is a Fisherian mensurate of fitness and is expressed in terms of the per capita population-level growth rate of the rare mutant. More specifically, this fitness measure out is adamant from an invasion matrix (in which the entries in this matrix are the linearized mutant dynamics when the resident strategy is at equilibrium). Per capita growth rate is then the dominant eigenvalue associated with this invasion matrix and the fettle of the mutant that provides parental care is plant by taking the determinant of:

(6)

where

(7)

(8)

(nine)

(x)

and solving the resulting characteristic equation for λ (i.e., the fitness of the mutant strategy relative to that of the resident; meet also Metz et al. 1992 and Vincent and Brown 2005) when choice is relatively weak (λ is minor such that exp(−λτ) ≈ (i − λτ)). When λ is positive, the mutant strategy is predicted to invade the population; when λ is negative, the resident strategy of no care will persist in the population. Examining the relationship betwixt λ and life-history traits of interest (mortality and maturation rates) provides insight into the qualitative human relationship between those traits and the fitness associated with paternal, maternal, and bi-parental care. This allows us to determine when a particular pattern of care volition be most strongly favored for a given fix of life-history characteristics. Previous analyses of this general framework (Klug and Bonsall 2007) have demonstrated that the invasion dynamics are stable under the parameter range considered (encounter Fig. legends for details of parameter values considered).

In all cases, we assume that baseline weather condition are identical for the mutant and resident strategy. We then calculate the fettle of the mutant strategy (paternal, maternal, or bi-parental care) relative to that of the resident strategy of no care in relation to varying male person and female life-history parameters. In doing and then, we focus on the evolutionary origin of some pattern of parental care. Equally mentioned to a higher place, this focus allows us to avert confounding or even conflating the origin and maintenance of care, which are both interesting but distinct questions that involve differing evolutionary dynamics. We are interested in differences in the life-history conditions that favor the origin of paternal, maternal, and bi-parental care, and thus, we focus on cases in which care is benign and likely to be selected for. Our focus is on asking which pattern of intendance is predicted to evolve when parental care is favored by pick. Specifically, we consider parameter values in which care results in net benefits, and we then ask how male and female life-history characteristics influence the conditions under which each pattern of care is most likely to invade (i.e., the weather condition under which a particular blueprint of intendance is associated with the greatest fitness benefits) when care does increase offspring survival. In all analyses (Figs. ​ 4), different numerical parameter values (eastward.1000., higher or lower egg or adult mortality or maturation in a given analysis) volition lead to different absolute fitness. However, it is the qualitative human relationship between the life-history parameter considered and fettle that informs us of when selection will most strongly favor each pattern of care.

Juvenile traits affect the origin of paternal (c _m = 0.7, c _f =0, solid line), maternal (c _grand = 0.0, c _f =0.seven, dashed line), and bi-parental (c _m = 0.35, c _f =0.35, dotted line) intendance. Nosotros prove the fitness gains associated with each pattern of parental care relative to the ancestral condition of no parental care for (A) male juvenile survival, (B) female juvenile survival, (C) male juvenile fourth dimension delay, and (D) female juvenile fourth dimension delay. We also testify the fitness gains associated with various levels of male and female care relative to the no-care scenario when (E) male person juvenile survival is greater than female juvenile survival (0.9 vs. 0.one) and (F) male juvenile survival is less than female juvenile survival (0.1 vs. 0.9). All patterns of care are more probable to invade an ancestral state of no care when juvenile survival is high (A-B). If male juvenile survival is relatively loftier, maternal care will be associated with the greatest fitness gains (E). If female juvenile survival is relatively high, paternal care volition be most strongly favored (F). Unless otherwise noted, d _Em0 = d _Ef0 = 0.v, yard _Em = m _Ef = 0.1, r ₀ =6, d _Am0 = d _Af0 = 0.5, K = 50, σ _Jm0 = σ _Jf0 = 0.5, τ _m = τ _f = 0.i, e ₁₀₀₀ = east _f = 0.5 for both residents and mutants.

In all cases, we offset identify the relationship between the fitness benefits associated with paternal, maternal, and bi-parental care and male and female egg mortality, egg maturation rate, juvenile survival, duration of the juvenile menstruation, and adult mortality. In doing so, we identify the life-history characteristics of males and females that volition most strongly select for the origin of paternal, maternal, and bi-parental intendance from an ancestral state of no care. In many animals, males and females vary in life-history characteristics. Such differences between sexes likely touch on the design of intendance that will occur. Thus, we also consider several scenarios in which males and females differ essentially in key life-history characteristics. We illustrate the dynamics using cases in which there are large differences between male and female egg mortality, egg maturation, juvenile survival, and adult mortality. All the same, the same general patterns are predicted for smaller qualitatively like differences. For these scenarios, nosotros then inquire whether males and/or females will be most likely to provide parental care.

Results

Male person-but, female-only, and bi-parental care can originate over a wide range of male and female life-history traits (Fig. ​ 5). Furthermore, in that location are little differences between the life-history weather condition favoring each pattern of care from an ancestral state of no care – in other words, the life-history weather condition that give ascent to 1 blueprint of intendance are like to the weather condition that give rising to other patterns of care (Table ​ 2; Figs ​ one, ​ 3, ​ iv). States of paternal, maternal, and bi-parental care are near likely to evolve from a land of no care when egg death rate in the absenteeism of care is high (Fig. ​ iA and B). In particular, some pattern of care will be strongly selected for if female egg death rate is high in the absenteeism of care (Fig. ​ 1B). Maternal intendance will result in slightly greater fitness gains than paternal or bi-parental care across the range of egg death rates (Fig. ​ 1A). This remains true if male and female egg mortality varies substantially. When male egg death charge per unit is very loftier and female person egg death rate is very low, high levels of maternal intendance and piffling to no male care volition outcome in the greatest fettle benefits to the mutants relative to fettle associated with no care (Fig. ​ twoA). The qualitative pattern is identical when female person egg death rate is much greater than male person egg expiry rate (Fig. ​ 2B).

The origin of paternal (c _k = 0.7, c _f =0, solid line), maternal (c _m = 0.0, c _f =0.7, dashed line), and bi-parental (c _m = 0.35, c _f =0.35, dotted line) care is affected by life history associated with the egg stage. Here, nosotros show the fitness gains associated with each pattern of parental care relative to the ancestral status of no care for (A) male person egg death rate in the absenteeism of care, (B) female egg decease rate in the absence of care, (C) male egg maturation rate, and (D) female egg maturation rate. All patterns of care will event in greater fitness benefits relative to the no-intendance scenario when male and female egg expiry rates are loftier (A-B) and when female eggs mature relatively quickly (D). Paternal and bi-parental care volition be more likely to invade when male egg maturation rates are low, whereas maternal intendance is more likely to invade when male person egg maturation rates are loftier (C). Unless otherwise noted, d _Em0 = d _Ef0 = 0.5, m _Em = chiliad _Ef = 0.1, r ₀ =6, d _Am0 = d _Af0 = 0.five, K = 50, σ _Jm0 = σ _Jf0 = 0.v, τ _thousand = τ _f = 0.1, e _g = e _f = 0.5 for both residents and mutants. Note: a single line indicates that the fitness of paternal, maternal, and bi-parental intendance are indistinguishable and the individual lines overlap.

Difference in egg characteristics between the sexes favor maternal or paternal care. Hither, nosotros show fitness associated with the level of male person and female person care when (A) male egg decease is high (0.ix) and female person egg death charge per unit is low (0.1), (B) male egg death rate is low (0.1) and female egg death charge per unit is high (0.9), (C) male egg maturation rate is high (0.9) and female person egg maturation rate is depression (0.i), and (D) male egg maturation rate is depression (0.ane) and female egg maturation rate is high (0.ix). Maternal care will be more than likely to invade when male eggs mature fast in comparison with female eggs (C). In dissimilarity, paternal care will exist more likely to invade when female eggs mature faster than male eggs (D). Unless otherwise noted, d _Em0 = d _Ef0 = 0.5, m _Em = m _Ef = 0.1, r ₀ =6, d _Am0 = d _Af0 = 0.five, Chiliad = 50, σ _Jm0 = σ _Jf0 = 0.5, τ _m = τ _f = 0.one, e _k = eastward _f = 0.v for both residents and mutants.

Adult mortality affects the origin of paternal (c _{one thousand} = 0.7, c _f =0, solid line), maternal (c ₁₀₀₀ = 0.0, c _f =0.vii, dashed line), and bi-parental (c _m = 0.35, c _f =0.35, dotted line) care. We show the fettle gains associated with each design of parental care relative to the ancestral status of no parental care for (A) male adult death rate in the absenteeism of care and (B) female adult decease charge per unit in the absence of care. We besides show the fitness associated with dissimilar levels of male and female care when (C) male person adult death rate is high (0.nine) and female person adult death rate is depression (0.1), and (D) male adult death rate is low (0.1) and female person adult decease rate is high (0.9). Maternal, paternal, and bi-parental care will each be more likely to invade an ancestral land of no intendance when adult death rates are high (A-B). When male adult death rate is relatively high, paternal care will exist most strongly favored (C), whereas when female adult death rate is relatively loftier, maternal care will be almost likely to invade (D). Unless otherwise noted, d _Em0 = d _Ef0 = 0.5, 1000 _Em =g _Ef = 0.1, r ₀ =6, d _Am0 = d _Af0 = 0.five, Thousand = 50, σ _Jm0 = σ _Jf0 = 0.5, τ _m = τ _f = 0.1, e _m = e _f = 0.v for both residents and mutants.

Table 2

Life-history weather that volition most strongly favor paternal, maternal, and bi-parental care from an ancestral state of no care. There are few differences betwixt the conditions that favor the origin of paternal, maternal, and bi-parental care. The exception is egg maturation rate of males: relatively slow male person egg maturation rate is more likely to favor paternal or bi-parental care, whereas relatively fast-developing male eggs volition favor the origin of maternal care

Blazon of parental care:
Paternal	Maternal	Bi-parental
Low male egg maturation rates	Loftier male person egg maturation rates	Depression male person egg maturation rates
High female egg maturation rates
High male and female person egg death rates
High male person and female adult decease rates
High male and female juvenile survival

Differences between male person and female life-history traits affect the origin of maternal and paternal care from an ancestral state of no care. (A) Paternal care will be most likely if female eggs mature relatively quickly, female juveniles have relatively loftier survival, and adult males take relatively high mortality. (B) In dissimilarity, maternal care will be more likely if male eggs mature relatively speedily, male juveniles have relatively high survival, and adult females have relatively high mortality.

Female egg maturation rate also has strong furnishings on the fitness associated with some pattern of care relative to the no-care scenario (Fig. ​ aneD). If female person eggs mature relatively rapidly, maternal, paternal, and bi-parental intendance will be strongly favored (Fig. ​ aneD). Male egg maturation rate has smaller effects on the fettle gains associated with intendance. If male eggs mature relatively slowly, paternal care volition result in larger fitness gains than maternal care relative to the no-care scenario (Fig. ​ oneC). If, still, male eggs mature relatively quickly, maternal care will result in the greatest fitness gains (Fig. ​ oneC). When male and female egg maturation rates vary demonstrably, nosotros see like patterns. If male eggs mature much faster than female eggs, maternal care and little to no paternal care will exist selected for (Fig. ​ 2C). In contrast, if female eggs mature much faster than male eggs, high levels of paternal intendance and fiddling to no maternal care will result in the greatest fitness gains to the mutants relative to that of the no-intendance resident strategy (Fig. ​ iiD).

Baseline developed bloodshed also affects the fitness gains associated with parental care (Fig. ​ three). All patterns of intendance will result in the greatest fettle gains relative to the no-intendance scenario when both male and female adult decease rates are high (Fig. ​ iiiA and B). This consequence is consistent across the dissimilar care scenarios: the relationship between developed death rate and the fitness associated with care is like regardless of whether care is maternal, paternal, or bi-parental (Fig. ​ 3A and B). If, however, males and females have very different adult bloodshed, either maternal or paternal care will be selected for. Specifically, if male mortality is greater than female bloodshed, paternal care will result in the highest fettle gains relative to the no-care scenario (Fig. ​ 3C). In contrast, if female mortality is much higher than male bloodshed, maternal care will be favored (Fig. ​ 3D)

Parental intendance by either males and/or females is more likely to evolve when juvenile mortality is relatively depression. The fitness benefit associated with care increases as either male or female juvenile survival increases, and this is equally truthful for the case of paternal, maternal, and bi-parental care (Fig. ​ 4A and B). The elapsing of time spent in the juvenile phase has minimal effects on fitness associated with care, although all patterns of care upshot in slightly greater fitness gains when males and females spend more than time as juveniles (Fig. ​ ivC and D). If male juveniles have much greater mortality than female juveniles, maternal care will be near strongly favored. In contrast, if female juveniles take much greater mortality than males, paternal intendance volition have the greatest fitness gains relative to the no-care scenario.

Discussion

Male and female life-history characteristics affect the origin of paternal, maternal, and bi-parental care (Tabular array ​ two; Fig. ​ 5). In full general, very similar life-history conditions favor the origin of paternal, maternal, or bi-parental care from an ancestral state of no care (Table ​ 2). This means that, for example, the life-history atmospheric condition that are likely to favor maternal intendance are likewise likely to favor paternal and bi-parental care (and vice versa). Maternal, paternal, and bi-parental care are all most likely to originate from an bequeathed state of no care when male and female egg death rates, adult mortality, and juvenile survival are high. When egg death charge per unit in the absence of care is high, intendance oftentimes results in the greatest internet benefits to offspring. In part, this occurs as egg survival (e.g., the proportion of eggs surviving per unit time) can never exceed one, and hence, when egg survival in the absenteeism of care is already high, the benefit of care will exist limited. The finding that intendance is favored when offspring need intendance the most is consistent with previous piece of work (Stearns 1976; Clutton-Brock 1991; Webb et al. 2002; Klug and Bonsall 2010; Bonsall and Klug 2011a,b). Likewise, when baseline adult death rate (i.e., decease charge per unit in the absence of care) is loftier, intendance is oft associated with smaller costs because adult mortality (i.e., the proportion of adults dying during whatever given fourth dimension period) can also never exceed 1. When adult death rate is high, parents also accept reduced opportunity for future reproduction and are therefore expected to invest more heavily in current young. The finding that any pattern of intendance will exist more likely when adult mortality is high is consequent with archetype life-history theory (Stearns 1976) and previous empirical work that plant a relationship between curt lifespan and the evolution of parental care in fishes (Winemiller and Rose 1992).

All patterns of care volition exist favored from an ancestral state of no care when female egg maturation rate is loftier. Paternal and bi-parental intendance are slightly more likely when male eggs mature slowly, whereas maternal care is more probable when male eggs mature relatively quickly. Sexual practice differences in egg maturation rate are not well studied. However, Cook and Monaghan (2003) found that in the back guillemot (Cepphus grylle), a species with bi-parental care, male person chicks hatch on average ane mean solar day sooner than female embryos. In the black-headed gull, Eising et al. (2001) plant that injecting androgens into eggs resulted in faster hatching times. In contrast, Sockman and Schwabl (2000) establish the opposite event in American Kestrels. Development rate is affected by sex in other animals (Badyaev 2002), and contempo work suggests that yolk androgens tin lead to striking differences between the sexes in skeletal and neural development, immune function, and metabolic function even during the egg stage (reviewed in Navar and Mendonça 2008). As such differences ascend between the sexes very early in development in some animals, it is possible that males and females begin to differ in survival and maturation as early on as the egg stage. Regardless, the idea that offspring maturation rate can influence the evolution of sex activity-specific patterns of parental care is an intriguing possibility that warrants further attention.

The finding that a female'south initial investment in eggs (i.due east., egg death rate in the absence of care) does not substantially increment the likelihood of maternal care is contrary to some previous work. Classic and heavily influential theory suggests that females are more likely to care than males because females take greater initial investment in each offspring (Trivers 1972). This argument is merely logical if the costs of greater initial female investment lead to reduced future expected reproductive success, which in turn selects for greater investment in current (rather than future) reproduction (Sargent and Gross 1985; encounter discussion of this hypothesis in Kokko and Jennions 2008). In our model, females always pay a greater cost of initially investing in eggs than males. All the same, the differences in fettle associated with maternal, paternal, and bi-parental care are similar across all values of initial maternal investment (i.e., baseline male person and female egg death rate) in the early evolution of intendance (Fig. ​ 2). Thus, in contrast to classic theory, we find that the origin of different patterns of care cannot be explained by initial differences between the sexes in gametic investment.

The fact that the origin of maternal, paternal, and bi-parental care cannot be explained by intersexual differences in residual reproductive value stemming from gametic or zygotic investment is consistent with recent parental investment theory. Mate competition and choice, trade-offs between fourth dimension available to care versus time spent mating, and feedback between mate availability, intendance, and competition can favor one blueprint of care over another (Queller 1997; Wade and Shuster 2002; Kokko and Jennions 2008; Alonzo 2010; Jennions and Kokko 2010). Interestingly, our findings propose that fifty-fifty in the absenteeism of such complexity (i.due east., costs of mate competition, feedback between costs of competing or caring and mate availability), greater initial investment in zygotes is not sufficient to make maternal intendance more than likely. Furthermore, the fact that maternal, paternal, and bi-parental care are favored when males and females are relatively similar suggests that explaining the origin of each pattern of care necessitates explicit consideration of life-history differences between males and females, costs of mate contest, and evolutionary feedback (Queller 1997; Kokko and Jennions 2008; Alonzo 2010). In other words, classic theory predicted that the prevalence of maternal care could be explained by sex differences in gametic investment betwixt males and females. Recent piece of work (Queller 1997; Kokko and Jennions 2008) and our findings show that this is not the instance. Furthermore, the fact that we found that male and female intendance tends to exist every bit probable when males and females are relatively like and when males are causeless to be the mate-express sex illustrates that sex differences in life history and/or factors considered in previous models (Queller 1997; Jennions and Kokko 2008), including sex differences in the costs of mate contest or care and feedback among providing intendance, competing for mates, and mate availability are essential to explicate sexual practice differences in the origin of parental care. As sex-specific life-history differences can alone make i pattern of care more likely than another design of care, the event of life-history differences must be considered as a baseline scenario in more than complex models of care. In particular, our modeling framework provides a much-needed baseline scenario in which to examine conditions favoring the origin of parental care by males and/or females. This baseline scenario will allow for more than explicit test of the specific effects of complex dynamics in futurity models of care. In detail, an obvious next step is to examine the conditions that favor transitions among different patterns of intendance one time some pattern of parental care is already present in a arrangement (Klug et al. 2013).

When males and females differ in life-history characteristics for reasons unrelated to parental investment or intendance, paternal care volition exist most likely to evolve if male developed expiry charge per unit is high relative to female adult death rate and if juvenile males mature slower and have higher mortality than females (Fig. ​ 5A). Maternal care, on the other manus, volition be nearly strongly favored if adult death rate is higher for females than males and if females mature slower and take greater juvenile mortality than males. The general finding that care volition be more common in the sexual practice with higher mortality is consistent with life-history theory suggesting that individuals with reduced expected future reproductive success should invest more in their current offspring (Williams 1966; Sargent and Gross 1985; Coleman and Gross 1991; Gross 2005; Klug and Bonsall 2010). These findings are also consistent with modeling by Steinhart et al. (2008) who found that adult survival is the virtually significant factor explaining whether parents abandon or intendance for their immature in populations of smallmouth bass (Micropterus dolomieu). Besides, Kokko and Jennions (2008) plant that developed mortality volition influence sex roles. Nonetheless, in contrast to our findings, Kokko and Jennions (2008) found that the more than common sex in the population (i.east., the sex with lower overall mortality) will typically be selected to provide more care than the rarer sex. This is because all offspring have one genetic mother and father, and as a sexual activity becomes more common in the population, information technology becomes difficult to observe a mate. In our model, each offspring has one female parent and father considering reproduction is limited by female fecundity. Still, we practise not assume a trade-off between caring and attaining mates (see Stiver and Alonzo 2009 for discussion of this issue). The differences between our findings and those of Kokko and Jennions (2008) suggest that whether such a trade-off is assumed, likewise every bit the explicit consideration of mate competition and dynamic changes in which sexual practice is mate-express, can have of import implications on the weather that favor the origin of care by males and females.

In summary, male and female life history affects the origin of parental intendance. Paternal, maternal, and bi-parental intendance are near strongly favored by like life-history weather condition, although uni-parental care (maternal or paternal) is typically expected to arise from an ancestral land of no care in the early evolution of care. Differential investment between the sexes in gametes or zygotes cannot explain sex-specific patterns of care. In add-on, sex-specific costs of mate competition and care and differential costs or benefits of care in relation to future mating success of the caring parent potentially influence life-history traits such as fecundity, rates of reproduction, male and female adult survival, and offspring survival. Every bit a upshot, sex differences in the costs of caring and competing are expected to influence patterns of care (see, e.m., Baylis 1981; Queller 1997; Wade and Shuster 2002; Kokko and Jennions 2008; Alonzo 2010, 2012).

Acknowledgments

This material is based upon work supported by the National Science Foundation under Grants EF-0827504 and IOS-0950472 (to SHA) and back up from the Majestic Society (to MBB).

Conflict of Interest

None declared.

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