Evolutionary Psychology                                                                             Alexandra Alanzo

Dr. Mills                                                                                                          Alana Pontrelli Summary                                                                                                        Palmer Thornton



Can Females Gain Extra Paternal Investment by Mating with Multiple Males?

A Game Theoretic Approach.



McElreath, R., & Soltis, J. (2001).  Can females gain extra paternal investment by mating          with multiple males?  A game theoretic approach.  American Naturalist, 158, 519-      529.


            In humans, paternal investment, the males’ ability to provide for mother and child, is an intricate aspect to raising offspring.  It is believed that with one male the paternal investment will be greater than having several males partially investing.  This ideology is not as common in other species.  In all two-sex species male offspring increases as a function of the number of mated females, while female offspring remains the same despite the number of mated males.  This dichotomy along with being a costly activity for females is why it is best for females to mate with one male.  With this fact why would any female member of a species want multiple male partners?

            The benefits from multiple mating by females includes: “insuring insemination, avoiding genetic incompatibility, promoting competition of sperm, producing genetically different off spring, avoiding infanticide, acquiring courtship food, and acquiring additional parental investment from males.”(519)

            John Maynard Smith developed a model that supported investment verse desertion.  Smith explained investment verse desertion as a tradeoff between the value of parental investment and the probability of future mating.  Smith based his model only on males and did not attempt a model examining the investment benefits to females who mate with multiple males.  McElreath et al. (2001) use a game theoretic approach to examine the power of the paternal investment hypothesis as an explanation for multiple mating by females.

            What is game theory and why was a game theory model chosen?  Game theory studies strategic interaction in competitive and cooperative environments.  McElreath et al. (2001) chose the game theory model because “the success of the male strategy of investing in multiple females’ offspring and the female strategy of mating with multiple males both depend on what strategy other individuals follow.”(520)

The first model examined under what condition males will invest in offspring of their mates rather than seek additional mating opportunity (paternal investment vs. mating investment).  The second model assumes male investment in offspring, and examines under which conditions it pays females to mate with multiple males rather than monogamous strategies.  The researchers caution that, “Such strategies are likely to favorably affect the evolution of male investment.”(520)

Model 1 observed paternal investment vs. mating investment while considering social group size and how it may influence payoffs to parental care.  With equal randomly sampled groups of 2N, including N adult males and N adult females, mating occurred randomly.  With random mating, two reproductive strategies arise in males, cads and dads.  Dads mate with females and invest in the offspring of their mates while cads never paternally invest and use their energy to pursue additional mates.

One aspect of paternal investment researchers were interested in was the effect of a dad on a predominantly cad social grouping and vice versa.  “Dads will invade a population of cads when the relative value of male investment (f ) exceeds the average number of extra matings to a cad (c). One way to think of c is the opportunity cost a dad pays for investment, while f is the opportunity cost a cad pays for pursuing additional matings.”(521) The effect of a cad on a predominantly dad social group is more complex. Larger N encourages the introduction of cads because of increases in potential mating and low value of male investment.

Model 2 examines when it pays for females to mate with multiple males given that males already invest in offspring.  The model is set with two female strategies.  Monogamous females mate with one male in the group, while polyandrous females mate with all males in the group.  The general principle for this model is that there is an intuitive cost for each female for mating which must be offset somehow by the value of paternal investment.

Concerning the first model researchers found evidence supporting previous work that suggests males should look for additional mating rather than investing in offspring.  “Dads” are only favored when the value of paternal investment is in demand and future mating opportunity’s are limited.  Additionally the optimal circumstances are met for male investment in multiple females’ offspring when N is small.  When N is large, “cads” tend to become free loaders of the paternally investing males.

The second model indicates why females’ would choose polyandry to access paternal investment in situations where the benefit of a male’s investment is at least 10 times greater than the cost of mating.  Although the model indicates a reason for polyandry, it cannot fully explain it.  When females mate with multiple males the costs become uneconomical because of the sharing of paternal investment with other polyandrous females and paying the costs of mating.  Another strong reason why polyandry is not feasible is the diminishing returns to male investment.









I.                    In many animals (particularly primates) females mate with multiple partners

II.                 Potential Benefits

a.       Ensuring insemination

b.      Avoiding genetic incompatibility

c.       Promoting sperm competition

d.      Producing genetically diverse offspring

e.       Avoiding infanticide

f.        Acquiring courtship food

g.       Acquiring additional parental investment from males

                                                               i.      Paternal investment explanation has been criticized because male-infant interactions may benefit males rather than infants

III.               Game Theory used for this study

a.       Model 1: examine the conditions in which males will invest in offspring of their mates rather than seek additional mating opportunities

b.      Model 2: examine the conditions in which it pays females to mate with multiple males rather than with just one

IV.              Model 1: The Evolution of Male Investment

a.       2 strategies

                                                               i.      “Dads” – mate with females and invest in the offspring of their mates instead of seeking additional mating opportunity

                                                             ii.      “Cads” – never invest in offspring, instead use their time and energy to pursue additional mates

V.                 Model 2: Polyandry and Male Parental Investment

a.       2 strategies

                                                               i.      Monogamous female – mate w/ one male in the group, each w/ a different male

                                                             ii.      Polyandrous female – mate w/ all males in the group

b.      When polyandry is rare: polyandrous female acquires half of the investment from all the monogamous females in the group

c.       When polyandry is common: investment is shared w/ all other females, but costs of mating w/ all males must be paid

VI.              Discussion

a.       Model 1

                                                               i.      Males are favored to seek additional matings rather than invest in offspring under a wide variety of conditions

                                                             ii.      Investing males are favored when the value of male care is substantial and future mating opportunity is limited

                                                            iii.      Favorable conditions for male investment in multiple females offspring are optimized when groups are minimally small

b.      Model 2

Mating with multiple males for parental investment can explain modest levels of polyandry, provided the benefit of males investment is at least 10 times the cost of