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Probability of fixation in a heterogeneous environment.

ABSTRACT: We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accurate predictions of fixation probabilities for all cases of potential interest. At the limits of low and high migration, previously published approximations are found to be highly accurate. The new separation-of-timescales approach provides the best approximations for intermediate rates of migration among habitats, provided selection is not too intense. For nonzero migration and relatively strong selection, all approximations perform poorly. However, the probability of fixation is bounded above and below by the approximations based on low and high migration limits. Surprisingly, in our simulations with symmetric migration, heterogeneous selection in a metapopulation never decreased-and sometimes substantially increased-the probability of fixation of a new allele compared to metapopulations experiencing homogeneous selection with the same mean selection intensity.

SUBMITTER: Whitlock MC

PROVIDER: S-EPMC1456843 | biostudies-other | 2005 Nov

REPOSITORIES: biostudies-other

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Probability of fixation in a heterogeneous environment.

Whitlock Michael C MC Gomulkiewicz Richard R

Genetics 20050822 3

We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accu ...[more]

PMID: 16118199

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Project description:The spatial distribution of radiopharmaceuticals that emit short-range high linear-energy-transfer electrons greatly affects the absorbed dose and their biological effectiveness. The purpose of this study was to investigate the effect of heterogeneous radionuclide distribution on tumor control probability (TCP) in a micrometastases model. Methods: Cancer cell lines; MDA-MB-468, SQ20B and 231-H2N were grown as spheroids to represent micrometastases. The intracellular distribution of a representative radiopeptide (111In-labelled epidermal growth factor, EGF) and radioimmunotherapeutic (111In-labelled Trastuzumab) was determined in cell internalization experiments. The intratumoral distribution was evaluated by microautoradiography of spheroids. ?H2AX staining was performed on spheroid sections to correlate DNA damage with radionuclide distribution. Experimental surviving fractions (SFexp ) were obtained using clonogenic assays. A random closed-packed algorithm, which models the random packing behavior of cells and reflects variation in the radii of cells and nuclei, was used to simulate 3-D spheroids. Calculated survival fractions (SFcal ) were generated using an iterative modelling method based on Monte Carlo determined absorbed dose with the PENELOPE code and were compared to (SFexp ). Radiobiological parameters deduced from experimental results and MC simulations were used to predict the TCP for a 3-D spheroid model. Results: Calculated SFs were in good agreement with experimental data, particularly when an increased value for relative biological effectiveness (RBE) was applied to self-dose deposited by sources located in the nucleus and when radiobiological parameters were adjusted to account for dose protraction. Only in MDA-MB-468 spheroids treated with 111In-EGF was a TCP>0.5 achieved, indicating that for this cell type the radiopeptide would be curative when targeting micrometastases. This is attributed to the relative radiosensitivity of MDA-MB-468 cells, high nuclear uptake of the radiopeptide and uniform distribution of radioactivity throughout the spheroid. Conclusion: It is imperative to include biological endpoints when evaluating the distribution of radionuclides in models emulating micrometastatic disease. The spatial distribution of radioactivity is a clear determinant of biological effect and TCP as demonstrated in this study.

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Probability of fixation in a heterogeneous environment.

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Probability of fixation in a heterogeneous environment.

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