Families with parental care show a parent–offspring conflict over the amount of parental investment. To date, the resolution of this conflict was modeled as being driven by either purely within-brood or between-brood competition. In reality the partitioning of parental resources within- versus between-broods is an evolving life history trait, which can be affected by parent–offspring interactions. This coevolutionary feedback between life history and family interactions may influence the evolutionary process and outcome of parent–offspring coadaptation. We used a genetic framework for a simulation model where we allowed parental parity to coevolve with traits that determine parental investment. The model included unlinked loci for clutch size, parental sensitivity, baseline provisioning, and offspring begging. The simulation showed that tight coadaptation of parent and offspring traits only occurred in iteroparous outcomes whereas semelparous outcomes were characterized by weak coadaptation. When genetic variation in clutch size was unrestricted in the ancestral population, semelparity and maximal begging with poor coadaptation evolved throughout. Conversely, when genetic variation was limited to iteroparous conditions, and/or when parental sensitivity was treated as an evolutionarily fixed sensory bias, coadapted outcomes were more likely. Our findings show the influence of a feedback between parity, coadaptation, and conflict on the evolution of parent–offspring interactions.

Interactions among family members are a common phenomenon in species with parental care (Royle et al. 2012). A driving force in the evolution of these interactions is the conflict over the allocation of resources between care providing parents and their dependent offspring, which originates from asymmetries in genetic relatedness among family members in sexually reproducing species (Trivers 1974). If parental investment (PI) enhances offspring fitness with diminishing returns, there is a zone of conflict (Godfray 1995) where inclusive fitness of offspring is maximized at a higher level of PI than parental inclusive fitness (Trivers 1974). The evolutionary resolution of this parent–offspring conflict was modeled from different perspectives concerning behavioral control (parents vs offspring) and concerning the trade-off parents face in terms of the allocation of their resources within versus between broods.

Scramble competition models (reviewed in Mock and Parker 1997; Parker et al. 2002) assumed that offspring have behavioral control and that the evolution of begging is driven by sibling competition for access to the resources provided by the parents and parents were assumed to have an evolutionarily fixed response to offspring begging. Conversely, honest signalling models (Godfray 1991, 1995) assumed that parents control the interaction with offspring and that the evolution of begging is driven by active parental choices. These choices were assumed to be based on offspring signals conveying information on the expected fitness returns on investment to parents (i.e., “need” or “quality”: see Mock and Parker 1997; Godfray and Johnstone 2000; Mock et al. 2011). In reality offspring and parental control are not mutually exclusive conditions for the evolution of offspring begging (Royle et al. 2002). They represent the two extremes on a power continuum, and it was suggested that most biological systems lie somewhere between these extremes (Royle et al. 2002).

A second core assumption that separates distinct types of conflict resolution models concerns the partitioning of parental resources between versus within reproductive attempts, that is, whether conflict operates through between-brood or within-brood interactions (interbrood and intrabrood conflict, respectively: Parker 1985; Mock and Parker 1997; Parker et al. 2002). Under interbrood competition, offspring can reduce the future reproductive success of the parents by demanding more resources than the parents should invest. Under intrabrood competition, variation in offspring begging can generate suboptimal asymmetries in offspring survival prospects and thereby reduce indirectly the expected number of surviving offspring (Parker 1985; Godfray 1991). As for the assumptions on behavioral control (see above), intra- versus interbrood conflict has been treated as an evolutionarily fixed model parameter, although it should probably be considered as two extremes on a continuum. Most animals exhibit an intermediate life history, producing broods with several offspring across multiple successive reproductive attempts. Only rarely parents are strictly semelparous and produce all their offspring in a single bout (e.g., Cryptocercus cockroaches: Nalepa and Bell 1997), and only rarely they produce offspring successively and strictly as singletons (e.g., albatrosses Diomedea exulans: Weimerskirch et al. 1997). How exactly parents split their total reproductive resources into offspring produced within and between several clutches is a life history adaptation (Stearns 1992) and hence should be treated as an evolving trait.

Treating it as such generates scope for coevolutionary feedbacks (Alonzo 2010; Kokko and Jennions 2012) between offspring begging, parental provisioning and parity (i.e., the number of offspring produced within and between clutches/broods). The allocation of PI within and between broods affects how conflict shapes the evolution of parent and offspring strategies (Parker 1985; Parker et al. 2002), whereas parent–offspring interactions can in turn affect the allocation of parental resources within versus between broods (Trivers 1974; Stearns 1992; Talamy and Brown 1999; Wong et al. 2013). For example, it was shown that offspring are capable of influencing future clutch size, the likelihood, and/or timing of future parental reproduction in canaries (Serinus canaria: Hinde et al. 2010) and the European earwig (Forficula auricularia: Mas and Kölliker 2011; Meunier and Kölliker 2012).

When studying the coevolutionary dynamics between parents and offspring, an essential fact is that parents and offspring are not static characteristics of individuals but two life stages of individuals. From an evolutionary genetic perspective parent–offspring interactions reflect a dynamic transgenerational interaction of genes expressed in the two life stages of an individual (Godfray 1986; Ives 1987; Lundberg and Smith 1994; Kölliker et al. 2010, 2012; Bossan et al. 2013). The feedback between the strategy an individual plays as an offspring and the individual's exposure to this strategy as a parent needs to be taken into account when studying the evolutionary origin and coevolutionary dynamics driving family interactions, because it generates scope for coadaptation between parent and offspring traits (Wolf and Brodie 1998; Kölliker et al. 2010, 2012). Specifically, the joint effects of offspring and parent traits on offspring fitness (survival) and parental fitness (fecundity) leads to selection on specific combinations of parental and offspring traits (i.e., correlational selection: Wolf and Brodie 1998). Because individuals partly inherit these combinations from their parents, a coadaptation at the genomic level is predicted that represents an interplay of parental and offspring genes that match to enhance lifetime fitness of individuals (Kölliker et al. 2010). Previous coadaptation models assumed single-offspring clutches and, hence, an evolutionarily fixed iteroparous life history and lack of within-brood competition. Extensions to coadaptation models are required to incorporate sibling rivalry and parental parity that coevolve with family interactions.

In this study, we present an individual-based simulation model to investigate the coevolutionary feedback between family interactions (offspring begging and PI) and parity (number of offspring and number of broods). In the simulations the parental sensitivity to begging, a baseline investment level, the level of offspring begging, and the number of offspring per clutch were allowed to evolve. Parity could evolve in terms of the partition of investment into individual offspring among different broods, which was not determined by a single gene but depended on the outcome of the socially mediated interaction among all genes. This modeling approach implies that the genotypes at each locus form part of the ultimate trait under selection (PI). They generate indirect genetic effects (Moore et al. 1997), but they also determine the social environment to which the other loci should adapt.

In a first series of simulations, we explored the coevolutionary dynamics of family interactions and parity when all traits were completely free to evolve and the genetic variance in the founding population was unrestricted. Subsequently, we assumed extrinsic limits on variation in the number of offspring produced in a clutch in the founding population to model a scenario where parent–offspring interactions start evolving under a preexisting iteroparous life history. Furthermore, we incorporated different extents of a parental sensory bias, that is, different evolutionarily fixed parental sensitivities to begging that were assumed to preexist and be maintained due to extrinsic selection on a specific sensitivity in parents (e.g., sensitivity toward food color) (see Krakauer and Pagel 1995; Arnqvist 2006). In all simulations we recorded the coevolutionary dynamics of parent and offspring strategies (allele frequencies and phenotypes), as well as the mean PI and lifetime fitness. We then calculated the extent to which parental provisioning and offspring begging became coadapted during the process.



The coevolutionary dynamics of offspring begging, parental provisioning, and parental parity was simulated as a coadaptation process among genetically determined traits expressed during offspring or parental life stages, using an individual-based model programmed in Java. Basically, the model is analogous to the antagonistic coadaptation model by Kölliker et al. (2010), but includes multiple offspring per brood that can compete with each other. Further, we allowed parents to allocate offspring production into a single clutch or multiple clutches depending on the resources invested into each offspring and the produced clutch size. This latter extension generates scope for coevolutionary feedback between family interactions and parental parity.

Genetic framework

The genetic setup of the simulation was based on four randomly segregating (i.e., physically unlinked) and genetically independent (i.e., no epistasis or shared environmental or epigenetic influences) autosomal loci. A locus for parental sensitivity (A) determined how strongly parents responded to offspring solicitation. A locus for offspring solicitation (X) determined the level at which an individual begged during its offspring stage. The third locus determined a baseline level of PI (B) that the parents provided to the whole clutch independent of offspring solicitation. Finally, and as key evolving trait to allow a coevolutionary feedback between parent–offspring interaction and parity, a locus determining the number of offspring produced per clutch (i.e., clutch size C) was introduced. All traits were assumed to be fully genetically determined without effects of environmentally caused variation (i.e., through quality or need) on the expressed trait levels. Each parent had a maximal amount of resources M available for lifetime reproduction (Parker and Macnair 1978). The value for M was set to 32 throughout all simulations. This value was chosen because it yields equal optimal clutch sizes for parents with only one clutch and parents with several clutches (see section Theoretical Expectations). Changing the value of M changes the total amount of resources available for reproduction and, correspondingly, the optimal clutch size and PI (Smith and Fretwell 1974), but this did not affect qualitatively our main results and conclusions (D.S. and M.K., unpublished data). Using M as a fixed amount of resources available for reproduction is an approach often used to introduce a trade-off between current and future PI in parent–offspring conflict theory (Parker and Macnair 1978; Parker et al. 2002). By this assumption, we treated any cost of current reproduction as reduced number and/or quality of future offspring. The aim of our model was not to develop realistic live-history models for the evolution of semelparity versus iteroparity as such (for which factors influencing e.g., parental survival to future reproduction play a key role; Stearns 1986), but rather to hold all-else equal focusing on the coevolutionary dynamics between parity and the coadaptation of parent and offspring traits. With this we tried to isolate underlying mechanisms of parent–offspring coadaptation independent from factors that may drive the system in any particular direction on the parity continuum (e.g., parent survival costs favoring semelparity or variable resource availability favoring iteroparity).

For simplicity, we assumed diploid genotypes and additive effects of alleles at the four loci. At each of the three loci A, X, and B, 60 alleles with linearly increasing values were specified. The clutch size locus (C) was specified with 12 alleles ranging in integers from 0 to 11. The smaller number of alleles was used to speed up the simulation process, because pilot experiments showed that clutch sizes above 11 were never successful during the simulation process with the chosen parameters (D.S. and M.K., unpublished data.). Allelic values for sensitivity (A) and solicitation (X) ranged from 0 to 5.9 in steps of 0.1 so that individuals were theoretically able to reach the maximal amount of parental resources M, when both traits were expressed at the maximum (see eq. 1). The baseline (B) ranged from 0 to 35.4 in steps of 0.6 (M is exceeded for simplicity without impact on the results) to theoretically allow parents to provide all resources to one clutch without responding to offspring solicitation. Our assumption of an additive mode of diploid inheritance with sexual reproduction implies that random segregation of clutch size alleles theoretically yielded noninteger clutch sizes, which is biologically impossible (Smith and Fretwell 1974). To avoid decimal numbers of offspring, the actually produced clutch size was determined by flooring the additive genetic value to the next lower integer.

In the following, alleles are denoted and specified by lower case letters corresponding to the locus (math formula) and by a subscript depicting the genetic value for the allele (e.g., a2.5). Phenotypes are indicated with capital letters of the locus names.

Each locus was affected by a mutation rate of ≈ 0.001 mutations per individual and generation. The effect of mutation was to change the value of an allele in random direction within the range of possible alleles. The magnitude of the mutational effect was determined randomly based on a Poisson distribution, with a high probability of small changes, including no change at all (i.e., silent mutations), and a low probability of mutations with large effects. The distribution was calculated for ten integer values (math formula) with math formula according to math formula. The values calculated for each k formed Poisson distributed interval sizes and the mutational change was determined as the lower value of k forming the interval between which an even distributed random number came to lie. The observed mutation rate (mean over all replicates) was math formula, which is slightly lower than the targeted mutation rate of 0.001 because of silent mutations (i.e., k = 0).

Reproduction and mating system

The individuals reproduced sexually in randomly mating populations of maximally 3000 parents. For simplicity, the rearing of offspring was uniparental and the generations did not overlap for reproduction. Adults were assumed to be hermaphrodites and to mate pairwise, fertilizing each other reciprocally and only once per lifetime. Subsequently, all adults were parental and cared for their own offspring. A consequence of this assumption is that in our simulations the mating system reflected true monogamy (Parker 1985) and excluded antagonistic selection on maternally versus paternally inherited genes (Wilkins and Haig 2003).

Simulation process

At the start of a generation every parent produced a first clutch according to the number offspring determined by the genotypic value at locus C. The resources a parent allocated to a clutch math formula depended on its sensitivity (A), the sum of begging within the clutch (math formula) and the baseline amount of resources (B), according to

display math(1)

where the subscripts t indicate the offspring and math formula the parental generation. Within the clutch, math formula was distributed among offspring according to the relative begging effort. The degree to which parents allowed such scramble competition depended on parental sensitivity, resulting in an amount of PI to an individual i of

display math(2)

with math formula as the upper limit of the sensitivity alleles, math formula as the mean amount of resources provided to each offspring in the clutch, math formula as the individual i’s personal begging effort, and math formula as the mean soliciting effort in the nest (see Harper 1986, for a similar equation; his eq. 2). Offspring begging was assumed to be free of direct costs.

To determine if a parent produces a subsequent clutch, the resources provided to the current clutch (math formula) were subtracted from M. If there were resources left, parents produced further clutches (without remating) until all resources were used up. If a clutch demanded more than the resources available to the parents, the parents were only allowed to provide what was remaining of M. According to the resources an offspring obtained (math formula), its survival probability followed a typical diminishing return function and was calculated as

display math(3)

with math formula as shape parameters (Kölliker et al. 2010). For an individual offspring to survive to adult stage, its calculated survival probability had to exceed a random number attributed to the clutch. Taking only one random number per clutch was chosen to simulate similar extrinsic environmental conditions for offspring in the same clutch (i.e., for any amount of obtained PI, offspring of the same clutch were assumed to have the same survival chances). To generate the next generation of adults, a maximum of 3000 randomly chosen surviving offspring were grouped into random pairs for reproduction. At this point the allele frequencies at each locus were recorded and traced across generations. These offspring then replaced the previous parents to form the next generation of parents.


Unrestricted variation model (math formula)

In this first series of runs, the full palette of alleles for all traits was made available to define the starting conditions of the simulation (i.e., the gene pool of the founding population was unrestricted). In particular, these starting conditions allowed for all theoretically possible clutch sizes, assuming that parity is free to vary randomly at the evolutionary origin across the whole range of possible clutch sizes. This model was run with randomly chosen starting alleles on all loci and a starting population of 2000 parents. The simulation was run for 20000 generations and replicated 100 times. We recorded for every generation of each run the population mean for PI per offspring, the number of offspring per parent, lifetime fitness, the mean number of clutches produced, as well as all trait values.

Restricted clutch variation model (math formula)

In a second series of simulation runs, we restricted the starting conditions for the clutch size to the range from c1 to c4 (i.e., one to maximal four offspring per clutch). This selection for a rather narrow range of small clutch sizes simulates conditions of a preexisting iteroparous life history for which the optimal strategies might differ from an unrestricted ancestral gene pool. The relatively small clutch sizes, determined by c1c4, imply iteroparity as starting condition because allele combinations resulting in semelparity despite the small clutch size are strongly selected against due their low lifetime fecundity, and are almost instantly removed from the gene pool of the population (Fig. 1). Nevertheless, this constraint was only applied to define the starting conditions and parental clutch size could freely coevolve with parent and offspring traits subsequently. Like before, 100 replicate runs were run over 20000 generations each.

Figure 1.

Expected lifetime fitness in relation to PI for continuous clutch sizes (solid blue line) and floored clutch sizes (red line with circles). Parameters correspond to those used for the simulations (math formula).

Sensory bias models (math formula)

In these simulations a different external restriction on the coevolutionary process was explored, namely, the impact of a sensory bias in parents toward emerging offspring solicitation. These simulations are relevant to study the evolutionary origin of offspring solicitation and parent–offspring interactions, but also the coevolutionary feedback between family interactions and parity when a sensory bias in parents is maintained for reasons other than the parent–offspring interaction per se. To investigate the origin of offspring solicitation and parent–offspring interactions the starting values were kept random for the investment baseline B, whereas clutch size C was limited again to c1c4, assuming a preexisting iteroparous life history at the origin of offspring begging. Preliminary simulations with the full range of clutch size alleles available in the starting conditions always led to semelparity and results that were virtually identical to those of the math formula.

We first looked at the situation, when no sensory bias was present and begging and sensitivity started evolving from zero. In these simulations sensitivity A and begging X were both fixed to zero for a burn-in of 5000 generations. In total 100 runs were done with 30000 generations each. The additional generations were implemented to compensate for the burn-in time and provided additional time for stabilization. The same parameter settings as for the math formula were used. This treatment is hereafter denoted as math formula.

In a second series of simulations, sensory biases of increasing magnitude were incorporated. Four treatments were applied with parental sensitivity fixed to a0.5, a1.0, a2.0, and a4.0. For each treatment 100 runs with 30000 generations were performed. Begging was again fixed to zero for the burn-in of 5000 generations and then released for mutation. The parental sensitivities specific to each treatment remained fixed throughout the runs. During burn-in parental baseline investment and clutch size were free to evolve, leading to selection on an optimal combination of the two in absence of parent–offspring interaction. Like in the math formula and math formula clutch size was limited for the founding population to c1c4. According to the chosen allele for parental sensitivity the treatments are hereafter referred to as A05, A1, A2, and math formula.


Defining individual lifetime fitness (W) as the product of offspring survival (eq. 3) and parental fecundity (math formula), we expected the optimal PI at the point when the first derivative of W with respect to PI is zero (i.e., math formula). Flooring the fecundity of parents—as done in the computer simulations—did not alter the expected lifetime fitness or optimal PI. However, the discrete nature of offspring production when clutch size is limited creates recurrent fitness valleys across levels of PI, because parental fecundity increases in discrete steps and offspring survival increases continuously (Fig. 1 and see Smith and Fretwell 1974). These valleys reflect suboptimal combinations of offspring survival and parental fecundity. With the parameter values used in the simulation (math formula) expected peak fitness W was 4.0 at an optimal level of PI of 4.0. To test if the simulation outcomes evolved toward the parent or offspring fitness optima according to parent–offspring conflict theory, we calculated the expected optimal levels of PI for the offspring and parental life stage according to Parker (1985) (setting math formula for the parent and math formula for the offspring optimum). Solving the equation numerically with the parameters used in the simulations, the optimal parental amount of PI—which also corresponds to the individual lifetime optimum (Kölliker 2010)—was 4.0, whereas the offspring inclusive fitness optimum was 6.0. The amounts of PI that evolved in the simulations were compared to both, the parental and offspring fitness optima.


The evolutionary outcomes were quantified and visualized by plotting the average allele frequencies of the last generation over all runs for each treatment. Treatments were statistically compared among each other or to the theoretically predicted value using unpaired one-sample t-tests. To analyze how well parents and offspring coadapted, we computed an index for the degree of coadaptation ζ. To determine ζ, the recorded effectively provided PI was divided by the PI expected from the mean parent and offspring phenotypes. Values were substituted in equations 1 and 2 according to

display math(4)

with math formula being the recorded average provided PI per offspring per run and math formula replacing the sum of begging in equation 1 (all phenotypes are population means per run). This coadaptation index reflects how precise the interacting traits work together to determine PI, or whether another mechanism than coadaptation critically affects PI. If the PI expected from the expressed trait values is the same as the effectively provided PI, the interaction reflects perfect coadaptation and ζ is equal to 1. Under weak coadaptation (e.g., when offspring demand is independent from parental sensitivity and baseline) the recorded phenotypes will not result in the recorded PI, which would lead to a value for ζ that deviates strongly from 1. Values for ζ lower than 1 indicate situations where the average allele values would lead to a lower PI than observed and with values higher than 1 the expected PI is higher than the observed investment. In the following we define strong coadaptation as math formula.

For all outcomes the realized PI was compared to the theoretical expectations. To judge the outcomes with respect to parity (iteroparity or semelparity), we averaged the number of clutches produced per parent per run over the last 500 generations. Semelparity was considered when within a run the average number of clutches produced was less than 1.1 and iteroparity with more than 1.9. Runs with outcomes that were intermediate to these values never occurred. Error values are indicated as standard error (SE), unless stated otherwise. Statistical analysis was carried out in R (R Development Core Team 2011).

All produced data files that were used in the analysis as well as the Java source code for the basic simulation was uploaded for public access to the online data archive Dryad (, Dryad doi: 10.5061/dryad.5j129).


Unrestricted variation model (UV treatment)

In the math formula the gene pool of the founding population was unrestricted and free to evolve. All simulations yielded populations that evolved to a semelparous life history and a level of begging that was at maximal intensity (Fig. 2B). Parental sensitivity and baseline investment alleles showed a uniform distribution (Fig. 2A,C) suggesting that variation at these loci became selectively largely neutral with begging being almost invariant at its maximum (except for selection against mutants). With this outcome, the sum of begging always exceeded M and thus M units were provided to the clutch regardless of the alleles at the sensitivity and baseline locus. The clutch size stabilized at around eight offspring, produced in a single clutch (Fig. 2D) and the coadaptation index ζ in this simulation experiment with semelparous outcome showed consistently low values with a mean of math formula (Table 1, math formula).

Table 1. Degrees of coadaptation (ζ) calculated from equation (4). Strong coadaptation is considered when math formula. Treatments are unrestricted starting variation (math formula), restricted clutch size variation (math formula), as well as the control treatment for the sensory bias models where sensitivity evolved from zero (A0) and the treatments with increasingly fixed sensitivities (A05 to A4). The coadaptation index for iteroparous (I) and semelparous (S) outcomes are provided separately for treatments with distinct outcomes. The deviation is given as standard error
math formula0.26 ± 0.015
math formula0.84 ± 0.019
math formula0.41 ± 0.034
math formula0.92 ± 0.015
A00.95 ± 0.001
A050.94 ± 0.001
A10.90 ± 0.001
A20.78 ± 0.019
math formula0.35 ± 0.011
math formula0.86 ± 0.001
A40.25 ± 0.022
math formula0.17 ± 0.002
math formula0.83 ± 0.001
Figure 2.

Resulting allele frequencies averaged over all runs with unrestricted starting variation (A–D; UV treatment) and restricted clutch size variation (E–H; RV treatment). Each bar shows the mean frequency of the corresponding allele for sensitivity (A, E), begging (B, F), baseline (C, G), and clutch size (D, H) in the population. Allele names (x-axis) indicate the value expressed by the specific allele. Error bars indicate standard deviations between populations.

Restricted clutch variation model (math formula)

Contrary to the result of the math formula, two different outcomes emerged from different replicates when variation in initial clutch size was limited to a smaller range favoring iteroparity in the founding populations. The alternative coevolutionary outcomes were clearly visible in the bimodal distribution of allele frequencies at the clutch size locus (Fig. 2H). Most of the populations (math formula) remained iteroparous (two clutches, four offspring; referred to as math formula), whereas a few (math formula) evolved to become semelparous (eight offspring, one clutch; math formula), which happened already within the first 100 generations. Irrespective of the outcome in terms of parity and similar to the math formula, begging always evolved to the maximal possible value (Fig. 2F). Sensitivity and baseline investment stabilized at low levels, indicating that these traits were still under selection (Fig. 2E,G). The degree of coadaptation across the whole math formula was math formula. Regarding only the iteroparous outcomes (math formula), even a higher level of coadaptation was observed (math formula) while the 15 populations of the semelparous outcomes (math formula) showed again low values for the coadaptation index (math formula), but higher than the ones of the math formula (Table 1, math formula, math formula, and math formula).

To test if the coevolutionary process led to outcomes according to theoretical expectations, we tested whether the achieved PI approximated the one predicted for the parent and offspring optimum (see Methods for more details). Neither in the math formula nor the math formula outcomes did the realized levels of PI differ significantly from the theoretically expected optimum of 4.0 (one-sample t-tests: math formula; Fig. 3). However, the realized PI in math formula was significantly smaller than expected (one-sample t-test: math formula; Fig. 3). The level of PI predicted to maximize offspring inclusive fitness was never reached in either of the two models.

Figure 3.

Lifetime fitness (W) in dependence on PI. Each datapoint shows the average PI and W over the last 500 generations for one run. Green squares: treatment with all alleles available at the start (math formula); black circles: semelparous outcomes of the treatment with reduced clutch size at start (math formula); red triangles: iteroparous outcomes of the treatment with reduced clutch size at start (math formula).

Sensory bias (SB treatment)

In the first begging-origin model (math formula), where parental sensitivity was set to zero at the start but was allowed to evolve afterwards, parental sensitivity did not evolve and remained always near zero (Fig. 4A). Thus, parents did not evolve to become sensitive to offspring begging. Offspring begging evolved to a broad range of intermediate values (Fig. 4B), probably due to recurring temporary benefits from spontaneous mutations in parental sensitivity. Virtually all investment to offspring was provided through the baseline (Fig. 4C). The parental life history remained iteroparous, with two clutches and a stable clutch size of four offspring throughout all generations (Fig. 4D). The evolved level of PI was significantly lower than the parental optimum (one-sample t-test: math formula; Fig. 5).

Figure 4.

Resulting allele frequencies averaged over all runs when begging evolved from 0 and sensitivity was set to zero for the start (A–D; A0), fixed to a0.5 (E–H; A05), fixed to a1.0 (I–L; A1), fixed to a2.0 (M–P; A05), and fixed to a4.0 (Q–T; A4). Each bar shows the frequency of the corresponding allele for sensitivity (A, E, I, M), begging (B, F, J, N), baseline (C, G, K, O), and clutch size (D, H, L, P) in the population. Allele names (x-axis) indicate the value expressed by the specific allele. Error bars indicate standard deviations.

Figure 5.

Lifetime fitness (W) in dependence on PI. Each datapoint shows the average PI and W for the last 500 generations of one run. Filled black diamond: fixed sensitivity to a0.5; filled blue square: fixed sensitivity to a1.0; open red circles: semelparous outcomes of fixed sensitivity to a2.0; solid red circles: iteroparous outcomes of fixed sensitivity to a2.0; open green triangles: semelparous outcomes of fixed sensitivity to a4.0; solid green triangles: semelparous outcomes of fixed sensitivity to a4.0. The solid line indicates the expected outcome under continuous clutch sizes, the dashed line with floored clutch sizes.

In the sensory bias models with fixed parental sensitivities (A05, A1, A2, and A4), simulating a maintained parental sensory bias, the replicates with low sensitivities a0.5 and a1.0 showed a consistent iteroparous life history with two clutches and a clutch size of four offspring (Fig. 4H,F). Fixed sensitivities a2.0 and a4.0 led to two alternative outcomes—iteroparous and semelparous populations (Fig. 4P,T)—showing either tight or little coadaptation, respectively (Table 1, A05–A4). In the simulations with sensitivity fixed to a2.0, 17 runs ended in semelparity and 83 runs remained iteroparous (referred to as math formula and math formula, respectively). In the simulations with sensitivity fixed to a4.0, 88 populations evolved to a semelparous and 12 runs to an iteroparous life history (math formula and math formula).

All semelparous outcomes showed similar results to the math formula with begging evolving to maximum and apparently neutral variation at the baseline locus (Fig. 4O,S), irrespective of parental sensitivity, which is reflected in the values for ζ (Table 1, math formula and math formula). In contrast, iteroparous populations showed again signatures of strong coadaptation of parent and offspring traits (Table 1, A05, A1, math formula and math formula). In all runs with sensitivity fixed to a1.0 and the iteroparous runs with a2.0 and a4.0 begging evolved to a specific level adapted to parental sensitivity (Fig. 4F,J,N), and the baseline provisioning remained near zero (Fig. 4G,K,O). In the runs with sensitivity fixed to a0.5 begging evolved as well to the maximal value (Fig. 4F) but with parents providing a specific (stable) amount of additional resources through the baseline (Fig. 4G).

The plotted changes in mean phenotypes over generations showed that after burn-in (where only baseline investment and clutch size were free to evolve) the baseline investment declined rapidly in all treatments whereas begging evolved to increased intensity; Fig. 6A–D). How fast the baseline decreased depended on the sensitivity of the parents, with the fastest decline in A4 and the slowest in A05. Figure 6C,D show the separation of the alternative outcomes in the two high sensitivity treatments. Although the separation in A2 occurred delayed after a short period of stable but transient coadaptation, the outcomes in the math formula diverged immediately after burn-in, when mutations in offspring begging were allowed to occur.

Figure 6.

Time courses over all generations for each sensory bias treatment when begging was set to zero at start and sensitivity was fixed to a0.5 (A), a1.0 (B), a2.0 (C), or a4.0 (D). In the A2 treatment (C) and A4 treatment (D) the different outcomes (iteroparous: dashed; semelparous: solid) are shown separately. For every 5000 generations the standard errors between replicates are given.


In this individual-based model, we allowed the coevolution of PI and parity under parent–offspring and sibling interactions. It incorporated scope for a coevolutionary feedback (Alonzo 2010; Kokko and Jennions 2012; Royle et al. 2012) between family interactions and parity, extending previous conflict resolution and coadaptation models, which treated parity as an evolutionarily fixed model parameter (see for reviews Godfray 1995; Mock and Parker 1997; Parker et al. 2002; Royle et al. 2002). To focus on this feedback, the model a priori kept the fitness of semelparous and iteroparous life histories as equal, not including extrinsic factors that affect the relative fitness of semelparity versus iteroparity (e.g., a survival cost of reproduction, or a bet-hedging benefit of iteroparity; Stearns 1992).  However, the realized fitness of the two parity types could nevertheless differ due to differences in the nature of the evolved underlying parent–offspring interactions. The coevolutionary feedback between family interactions and parity had a number of consequences for the expression of semelparity versus iteroparity, the evolution of offspring solicitation as well as the extent of parent–offspring coadaptation. When the starting conditions of the simulations were defined with genetic variance covering the full range of possible clutch sizes, all runs stabilized at semelparity. These semelparous outcomes became less likely when the gene pool of the founding population was restricted toward an iteroparous life history, indicating that iteroparous outcomes and the underlying parent–offspring interactions reflected a local optimum. In terms of parent–offspring interaction we found strong coadaptation between offspring begging, parental sensitivity, and baseline provisioning exclusively under iteroparous outcomes. This tight coadaptation in turn stabilized iteroparity by generating local peaks of high fitness in the surface of possible gene combinations, leading to evolutionary robustness of family interactions at lower than maximal individual lifetime fitness (i.e., preventing the transition from iteroparity to semelparity despite higher realized fitness of the latter; Fig. 3). Conversely, coadaptation was consistently weak under semelparous outcomes, which were more likely to evolve under conditions where the full genetic variance was introduced in the starting population (math formula). Incorporation of factors directly affecting the fitness of semelparous versus iteroparous life histories (i.e., survival cost of reproduction or resource benefits for iteroparity) did not qualitatively affect these results (D.S. and M.K. unpublished data). Under a semelparous life history, PI evolved to a level maximizing individual lifetime fitness and offspring solicitation to the maximal possible level.

Further we showed the importance of a sensory bias in parents (i.e., an extrinsically stabilized parental sensitivity to offspring begging). The chances for iteroparous outcomes and successful coadaptation under a parental sensory bias decreased with increasing levels of parental sensitivity. Overall, our simulation model indicates an important combined role of sensory biases and sibling competition in affecting the expression of parity, and in determining the scope for parent–offspring coadaptation.

A sensory bias is an extrinsic restriction on trait variation which has been proposed to facilitate the evolutionary origin of signals and animal communication through sensory exploitation (Lyon et al. 1994; Arnqvist 2006). A problem in the evolutionary origin of communication can be that the signal and sensitivity to the signal have to originate at the same time to allow the evolution of the signal. Alternatively, signals may evolve from cues that the sender already emits before the receiver has become sensitive (Bradbury and Vehrencamp 2011). Under both scenarios, a sensory bias can facilitate the evolution of a signal because the mutant producing the signal benefits from exploitation of a preexisting sensitivity in the signal receiver (here the parent). Sensory biases may be adaptive and maintained by selection in a different functional context (Krakauer and Pagel 1995). If this is the case, it should at least partly be maintained despite becoming exploited by an emerging signal and the sensory bias may continuously modify the coevolution between signaller and signal receiver.

We modeled this effect of a sensory bias on the origin of begging and the coevolution of parity and family interactions by assuming an evolutionarily fixed parental sensitivity to begging and restricted clutch size variation in the founding population. Depending on the extent of parental sensitivity, alternative coevolutionary outcomes were possible in terms of offspring begging and parental life history. Stable parent–offspring communication did not evolve when parental sensitivity was set to zero in the ancestral population (but later allowed to evolve). This result reminds of a formerly proposed “ancestral threshold” in terms of a minimal required preexisting parental sensitivity for offspring begging to evolve (Payne and Rodríguez-Gironés 1998). However, in our framework this threshold more likely refers to the sensitivity at which the parent invests all its resources into a single clutch and becomes semelparous. High parental sensitivity implies that sibling competition can be an important determinant of PI (eq. 2) and thus the results indicate that the fitness valley separating iteroparous from semelparous life histories (see below) can be trespassed only with sufficient drive by sibling competition.

Considering only the iteroparous outcomes across all sensory bias treatments, begging generally stabilized at intermediate levels, except for the math formula where maximal begging did not yield enough resources and parents had to provide more via the baseline. The decreasing levels of begging that evolved under increasing fixed sensitivities in the iteroparous outcomes (Fig. 6) showed the expected coadaptation between parents and offspring and confirm that coadaptation can stabilize cost-free begging also in the presence of within-brood sibling competition (Kölliker et al. 2010). Semelparous populations were characterized by poor coadaptation (Table 1), begging levels evolving to their maximal value (Fig. 4) and patterns of resource allocation where all resources were distributed irrespective of begging. Due to the almost invariant begging levels at the maximum, all offspring received equal amounts of PI and thus sibling competition had little further impact on PI (eq. 2). Correspondingly, the loci for parental sensitivity and baseline became largely neutral because the model assumed that a parent maximally provides M units of investment (which was always reached with maximal begging, a sensitivity larger than a1.0 and more than six offspring) and because M was distributed equally among offspring. Thus the influence of these parental traits on the determination of PI was disabled by lack of maintained variance in begging. In this case, the coevolutionary feedback of sibling competition (selection for maximal begging) on parental life history (all resources provided to one clutch) eliminated the variance needed to maintain the evolutionary function for parent–offspring communication.

The difficulty of a coevolutionary origin of parental sensitivity and offspring solicitation is well illustrated in the results of the math formula. Again, this result holds only for populations with iteroparity as starting condition because sensitivity became neutral in semelparous populations. The parents stayed insensitive throughout the evolutionary process in all replicates. Begging nevertheless evolved to a certain degree, probably to take advantage of the few mutations leading to sensitive parents. We assume that the low likelihood for mutations in sensitivity and begging to produce a well coadapted interaction by pure chance, and the difficulty of maintaining a coincidental mutational match under free recombination, prevented the spread of coadapted parental sensitivity and offspring begging in the absence of a sensory bias.

The evolved levels of provisioned PI were slightly smaller than or similar to the parental optimum (PI = 4) in most of the cases. PI was always significantly smaller than offspring inclusive fitness optimum (PI = 6; Figs. 3 and 5). Thus, in our simulation individual lifetime fitness was maximized, and not offspring inclusive fitness (Parker and Macnair 1979; Godfray 1991).

Although coadaptation in iteroparous outcomes led to suboptimal PI (and reduced lifetime fitness), iteroparity remained stable once established. This provides evidence that poorly coadapted gene combinations form fitness valleys in the surface of all possible trait combinations. The discrete nature of clutch size in our model likely made a large contribution to these fitness valleys (Fig. 1). The discreteness of offspring production has been little considered in former models of parent–offspring conflict and coadaptation and it generates local fitness peaks representing specific optimal combinations of PI and a given discrete number of offspring. The fitness declines to both sides of these local optima depict the effect of variation in PI on lifetime fitness for the same given discrete number of offspring (Smith and Fretwell 1974). These fitness valleys are probably at least partly responsible for the maintenance of iteroparous coevolutionary outcomes despite higher realized fitness under semelparous outcomes).

A second, not mutually exclusive, explanation for the lower population mean fitness under iteroparity relates to a scenario of genetic load (Dobzhansky 1957), or more specifically a form of parent–offspring incompatibility load (Crow and Morton 1960). In semelparous populations, adaptation to spend the maximal amount of resources M was mainly driven through the evolving clutch size with little impact by the other three traits. Deviations from optimal PI were thus mostly due to recurrent mutations in the clutch size locus. In iteroparous populations where coadaptation was tight, the four loci had combined effects on PI. Here deviations from optimal PI can occur through mutations in all four traits leading to mismatches in trait combinations and a higher chance of suboptimal PI under iteroparous and tightly coadapted life histories. This reduced fitness can be interpreted as enhanced genetic load through recurrent mutations under coadapted outcomes when social interactions determine PI. This view of genetic load is consistent with the general prediction that genetic conflict typically leads to evolutionary outcomes where population mean fitness is reduced (e.g., Zeh and Zeh 1996). One can interpret the fitness suppressing effect of genetic load as a consequence of conflict because any mutation-caused deviation from the optimal coadapted trait combinations regenerates conflict through a phenotypic mismatch in the parent–offspring interaction (Hager and Johnstone 2003; Kölliker et al. 2012; Meunier and Kölliker 2012).

Our results did not support the hypothesis that parents may control sibling competition by splitting their total number offspring into several clutches (i.e., becoming iteroparous) to limit negative effects of within-brood competition on parental fitness (Godfray and Parker 1992; Stearns 1992). On the contrary, we found that sibling competition affected the evolution of parental life history (all else being equal). When sibling competition could drive offspring demand to levels that were too high for parents to maintain several clutches, parents were forced to become semelparous. Thus, offspring seemed to exert evolutionary control over parental parity through the effects of sibling competition on offspring demand and, in turn, on PI. Parity in turn affected the evolution of parent–offspring interactions by favoring tightly coadapted outcomes under iteroparity or leading to poorly coadapted outcomes under semelparity. In iteroparous populations, a precise coadapted mechanism evolved to determine resource allocation to offspring and was maintained (as reflected by the high values of the coadaptation index in these outcomes; Table 1). Hence, under iteroparity correlational selection favoring matching combinations of parent and offspring genes was strong enough to stabilize coadaptation against the directional selection on offspring begging driven by sibling competition. Conversely, under semelparity the relative distribution of fixed resources relaxes the selection for parent–offspring coadaptation and the evolution of family interactions seemed predominately driven by directional selection on parent and offspring traits.

To date models of parent–offspring coadaptation typically used continuous clutch sizes to calculate parental fecundity (Hadfield 2012). We relaxed this assumption of infinitesimal offspring production in coadaptation models to a more realistic view of clutch size by allowing only integer numbers of offspring. Further we did not fix parental life history to a certain parity, but let it coevolve with the traits specifying the parent–offspring interaction. However, we did not include a feedback of offspring state (i.e., “need” or “quality”) on parents. Using this aspect from the honest signaling models (e.g., Godfray 1991; Godfray and Johnstone 2000) would be an important next step. We would predict that such an additional feedback of PI to parents may contribute to coadaptation even under semelparity because environmental variance in begging can maintain selection on parental sensitivity even once the allele for maximal begging has become evolutionarily fixed.

To conclude, our results support the hypothesis that coevolutionary feedbacks, caused by transgenerational social interactions, generate a link between sibling competition, parental life history and parent–offspring coadaptation. We suggest that future models and experimental research should take this into account to better understand to what extent variation in parental life history is evolutionary cause or effect of family interactions.

Associate Editor: B. Lyon


We would like to thank Joël Meunier, Flore Mas, and Janine Wong for their helpful comments on the methods and preliminary results during an early stage. We also thank Nick Bos, Luke Holman, Bruce Lyon, and an anonymous referee for valuable comments on the manuscript. Further we would like to acknowledge the Center of Excellence in Biological Interactions and the Academy of Finland (grant numbers 252411 and 251337) for support during the writing of the manuscript. This study was financially supported by the Swiss National Science Foundation (grant no. PP00A-119190 to MK).