Two-Sex Models: Chaos, Extinction, and Other Dynamic Consequences of Sex

Caswell, Hal; Weeks, Daniel E.

doi:10.1086/284598

Cited by 178 publications

(190 citation statements)

References 63 publications

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“…Since the λ of roach populations can be estimated from doubling time (t d ) for roach using eq 7 (15), and other life-cycle parameters have been estimated, the survival from zygotes to 1 year was determined by use of Newton's iteration method (11,18).…”

Section: Survival Of Zygotes To 1 Yearmentioning

confidence: 99%

Extinction Risk of Exploited Wild Roach (Rutilus rutilus) Populations Due to Chemical Feminization

Giesy

et al. 2009

Environ. Sci. Technol.

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A model that assesses risks posed by feminization to wild populations of roach was developed. A population life table matrix model that considered both sexes and a newly developed fertility kinetic function was applied to calculate the intrinsic population growth rate (λ) of roach populations where males had been feminized. The maximum sustainable yield (MSY) was used to quantify the effect of various degrees of feminization on sustainability of exploited fisheries. Risk of extinction was calculated for wild roach populations. The results of the simulations suggested that (a) In the absence of fishing pressure λ would only be decreased 1.5-1.7% even in the presence of a 100% incidence of intersex; (b) in the presence of selective fishing, the occurrence of intersex could significantly increase the extinction risk of local roach populations; (c) the benchmark value for the severity index of intersex and sex ratio required for a sustainable population of roach were estimated to be 1.13 and 0.57, respectively. The approach presented here provides a tool to (1) understand effects of male's feminization on population dynamics; (2) assess extinction risk of wild roach populations from feminization; (3) assist environmental managers in making policy decisions relative to fishery resource conservation.

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Section: Survival Of Zygotes To 1 Yearmentioning

confidence: 99%

Extinction Risk of Exploited Wild Roach (Rutilus rutilus) Populations Due to Chemical Feminization

Giesy

et al. 2009

Environ. Sci. Technol.

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“…Because the effects of the sex ratio on demography may depend on the social mating system, we consider biological invasions by both monogamous and nonmonogamous populations that differ in the degree to which recruitment is limited by females or males. Our model combines two established mathematical approaches: integrodifference models for population spatial spread (Kot et al 1996;Kot 2002) and pair formation models for local birth rates under different mating systems (Caswell and Weeks 1986). We derive an upper bound on the invasion speed that this model predicts and, with evidence from numerical simulations, conjecture that this upper bound is the exact asymptotic invasion speed.…”

Section: Introductionmentioning

confidence: 97%

“…It is often assumed for convenience that females dominate population growth dynamics, with fertility independent of male availability (Rankin and Kokko 2007). However, the assumption of frequencyindependent dynamics is almost certainly incorrect in extreme cases (when the population is nearly 100% female or male), and models of two-sex population dynamics indicate that even a small departure from a 1 : 1 sex ratio can have a large effect on the birth rate (Caswell and Weeks 1986;Legendre et al 1999). These observations suggest that existing one-sex invasion theory may be inadequate for understanding and predicting the spatial dynamics of many biological invasions.…”

Section: Introductionmentioning

confidence: 99%

Sex-Biased Dispersal and the Speed of Two-Sex Invasions

Miller

Shaw

Inouye

et al. 2011

The American Naturalist

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Population models that combine demography and dispersal are important tools for forecasting the spatial spread of biological invasions. Current models describe the dynamics of only one sex (typically females). Such models cannot account for the sexrelated biases in dispersal and mating behavior that are typical of many animal species. In this article, we construct a two-sex integrodifference equation model that overcomes these limitations. We derive an explicit formula for the invasion speed from the model and use it to show that sex-biased dispersal may significantly increase or decrease the invasion speed by skewing the operational sex ratio at the invasion's low-density leading edge. Which of these possible outcomes occurs depends sensitively on complex interactions among the direction of dispersal bias, the magnitude of bias, and the relative contributions of females and males to local population growth.

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Section: Introductionmentioning

confidence: 99%

“…A basic premise being ignored is that "it takes two to tango." The difficulties involved are quite evident from the pioneering work of Kendall (1949), Keyfitz (1949), Fredrickson (1971), McFarland (1972), Parlett (1972), Pollard (1973), and Caswell and Weeks (1986.We have developed an axiomatic framework to conduct a systematic study of marriage functions Castillo-Chavez 1989, 1991;Castillo-Chavez and Busenberg 1991;Hsu Schmitz 1994;Hsu Schmitz et al 1994, Blythe et al 1991. Our work has been applied in areas as diverse as cultural and parameter estimation , Hsu Schmitz and Castillo-Chavez 1994, 1995.…”

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confidence: 99%

The Evolution of Age-Structured Marriage Functions: It Takes Two to Tango

Castillo‐Chavez¹,

Schmitz²

1997

Structured-Population Models in Marine, Terrestrial, and Freshwater Systems

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In prior work, we characterized two-sex marriage functions for socially structured populations as multiplicative perturbations of heterosexually random/proportionate mixing. These perturbations were expressed in terms of the preferences/ affinities of males for females and vice versa. Male and female preferences/affinities are obviously not independent as they depend on the availability of male and female behavioral "genotypes." We show that knowledge of the preferences/affinities of one gender can characterize the preferences/affinities of both genders m socially-structured populations; in other words, it takes two to tango. This is the basic content of the T 3 Theorem. In this chapter, we revise our results for socially structured populations and extend them to situations where the population is characterized by continuous variables such as age. It is shown that different sets of preferences/ affinities, that is, distinct behavioral "genotypes", may give nse to identical mixing/mating probabilities, the determinants of the behavioral "phenotypes." Hence, different sets of individual decisions can lead to identical social dynamics -a fact well established in genetics. The importance of the incorporation of mating systems at the population level is a neglected but central area in evolutionary biology.-2- L IntroductionMarriage functions are solutions to the two-sex mixing/pairing problem.Despite their importance m areas such as population genetics (mating functions), demography (population projection), cultural anthropology (preservation and dissemination of cultural traits), and evolutionary biology (life history), their application has been quite limited. Most researchers have addressed theoretical issues in these areas through the use of single-sex models or highly simplified two-sex models. A basic premise being ignored is that "it takes two to tango." The difficulties involved are quite evident from the pioneering work of Kendall (1949), Keyfitz (1949), Fredrickson (1971), McFarland (1972), Parlett (1972), Pollard (1973), and Caswell and Weeks (1986.We have developed an axiomatic framework to conduct a systematic study of marriage functions Castillo-Chavez 1989, 1991;Castillo-Chavez and Busenberg 1991;Hsu Schmitz 1994;Hsu Schmitz et al. 1994, Blythe et al. 1991. Our work has been applied in areas as diverse as cultural and parameter estimation , Hsu Schmitz and Castillo-Chavez 1994, 1995.We provide a summary of our characterization of marriage functions for populations defined through fixed characteristics such as race, language, biological species, religion, level of education, and socioeconomic level. We then provide a detailed characterization of age-structured marriage/mixing functions. The discrete framework described in this chapter can be incorporated into finite dimensional deterministic or stochastic models while the continuous framework is easily incorporated into age structured models.In earlier work, we (Castillo-Chavez and Busenberg 1991) characterized two-sex marriage functions as mul...

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Two-Sex Models: Chaos, Extinction, and Other Dynamic Consequences of Sex

Cited by 178 publications

References 63 publications

Extinction Risk of Exploited Wild Roach (Rutilus rutilus) Populations Due to Chemical Feminization

Extinction Risk of Exploited Wild Roach (Rutilus rutilus) Populations Due to Chemical Feminization

Sex-Biased Dispersal and the Speed of Two-Sex Invasions

The Evolution of Age-Structured Marriage Functions: It Takes Two to Tango

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