Matrices and Society

Bradley, Ian; Meek, Ronald L.

doi:10.1515/9781400858538

Cited by 10 publications

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“…Hence, State 9 is the absorbing state.We describe the Markov process in terms of a transition matrix: For example, the probability of changing from 3 D s and 6 C s (State 3) to 4 D s and 5 C s (State 1) is (a subject must pick a C actor, and a neighbor must pick a D actor).We define the vector p as the probability of starting in State 1, 3, 5, or 7:For example, the value of “1” is the probability that the difference in the number of C and D actors is 1, which equals 2 × 1/2 9 × 9/4 = 252/512. The expected time E until absorption can then be computed (see, e.g., Bradley & Meek, 1986): Note that 41.91 is the number of pairs that has to be chosen, which is different from the number of generations until absorption in the sense of M&L. A generation is a number of pairs taken equal to the population size. The expected number of generations would therefore be 41.91/9 = 4.66.…”

Section: Using Markov Chain Theory To Prove Convergencementioning

confidence: 99%

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"Individual heuristics and the dynamics of cooperation in large groups": Additional results using analytical methods.

Buskens

Snijders²

1997

Psychological Review

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Section: Using Markov Chain Theory To Prove Convergencementioning

confidence: 99%

“…For example, the value of “1” is the probability that the difference in the number of C and D actors is 1, which equals 2 × 1/2 9 × 9/4 = 252/512. The expected time E until absorption can then be computed (see, e.g., Bradley & Meek, 1986):…”

Section: Using Markov Chain Theory To Prove Convergencementioning

confidence: 99%

"Individual heuristics and the dynamics of cooperation in large groups": Additional results using analytical methods.

Buskens

Snijders²

1997

Psychological Review

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If a population crashes in prehistory, and there is no paleodemographer there to hear it, does it make a sound?

Paine

2000

Am. J. Phys. Anthropol.

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Catastrophic episodes (e.g., epidemics, natural disasters) strike with only limited regard for age. A large percentage of catastrophic mortality in a population can lead to a death distribution that resembles the living distribution, which includes greater numbers of older children, adolescents, and young adults than typical mortality profiles. This paper examines both the population implications of a large catastrophic mortality event, based on the Black Death as it ravaged medieval Europe, and its long-term effects on age-at-death distributions. An increased prevalence of epidemic disease is a common feature of reconstructions of the shift to agriculture and the rise of urban centers. The model begins with a hypothetical Medieval living population. This population is stable and characterized by slow growth. It has fertility and mortality rates consistent with a natural-fertility, agrarian population. The effects of catastrophic episodes are simulated by projecting the model population and subjecting it to one large (30% mortality) catastrophic episode as part of a 100-year population projection. A pair of Leslie matrices forms the basis of the projection. The catastrophic episode has important, long-term effects on both the living population and the cumulative distribution of death. The living population fails to recover from plague losses; at the end of the projection, population is still less than 75% its pre-plague level. The age-at-death distribution takes on the juvenile-young adult-heavy profile characteristic of many archaeological samples. The cumulative death profile based on the projection differs from that produced by the stable model significantly (P < 0.05) for 25-50 years after the plague episode, depending on sample size.

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2009

Bayesian Analysis for the Social Sciences

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Matrices and Society

Cited by 10 publications

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"Individual heuristics and the dynamics of cooperation in large groups": Additional results using analytical methods.

"Individual heuristics and the dynamics of cooperation in large groups": Additional results using analytical methods.

If a population crashes in prehistory, and there is no paleodemographer there to hear it, does it make a sound?

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