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Overview of WinEquus Stephen Jenkins Emeritus Professor of Biology University of Nevada, Reno jenkinsunr

Two Purposes of Modeling (Caswell 1976). Models for understandingModels for prediction ? forecastingDoomsday: 2026.87 = 13 November 2026(von Foerster et al. 1960, Science 132:1291). Caswell, H. 1976. The validation problem. Pages 313-325 in B. C. Patten, editor. Systems analysis and simulati

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Overview of WinEquus Stephen Jenkins Emeritus Professor of Biology University of Nevada, Reno jenkinsunr

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    1. Overview of WinEquus Stephen Jenkins Emeritus Professor of Biology University of Nevada, Reno jenkins@unr.edu

    2. Two Purposes of Modeling (Caswell 1976) Models for understanding Models for prediction ˜ forecasting Doomsday: 2026.87 = 13 November 2026 (von Foerster et al. 1960, Science 132:1291)

    3. Data Requirements for WinEquus initial age-sex distribution annual survival probabilities for each age-sex class annual foaling rates for each age class of mares sex ratio at birth ideally, these data should be site-specific have variance estimates

    4. Data Available in Practice estimate of population size at a site sometimes, estimate of age-sex distribution if horses released in recent gather were aged sex ratio near birth? estimates of survival and reproduction at a few sites 11 years of data for Pryor Mountain, MT (Garrott & Taylor 1990) 6 years for the Granite Range, NV (Berger 1986) 7 years for Garfield Flat, NV (Ashley 2000)

    5. Is lack of site-specific data a problem?

    6. Is lack of site-specific data a problem?

    7. Is lack of site-specific data a problem? recent data ? average annual adult survival > 90% for Cumberland Island, GA (Goodloe et al., 2000, J. Wildl. Manage. 64:114-121) Montgomery Pass, NV-CA (Turner & Morrison, 2001, Southwestern Naturalist 46:183-190) Kaimanowa Ranges, New Zealand (Linklater et al., 2004, Wildl. Res. 31:119-128) Przewalski’s wild horses in France (not free-ranging) (Tatin et al., 2008, J. Zool. 277:134-140) recently feral horses in the Camargue in France (Grange et al., 2009, Proc. Royal Soc. B 276:1911-1919) Tornquist Park, Argentina (Scorolli & Lopez Cazorla, 2010, Wildl. Res. 37:207-214)

    8. Is lack of site-specific data a problem? There is more variation between sites in annual survival probability of foals foaling rate, especially of young mares

    9. Three kinds of stochasticity in WinEquus Measurement uncertainty in initial population size Demographic stochasticity Environmental stochasticity

    10. Measurement uncertainty in initial population size: User adjustments 90% sighting probability is default (Garrott et al. 1991. J. Wildl. Manage. 55:641-648) WinEquus uses a beta-binomial model User may specify exact initial conditions instead

    11. Demographic Stochasticity in WinEquus: User adjustments None … … foaling rate = 0.5 ? 50% chance of foaling for each mare ? 10 mares may have 5 foals, or 4 or 6, or 3 or 7, or 2 or 8, …

    12. Environmental Stochasticity in WinEquus: User adjustments Eleven years of data for Pryor Mountain, MT (Garrott and Taylor. 1990. J. Wildl. Manage. 54:603-612)

    16. Density-Dependence in WinEquus

    17. Density-Dependence in WinEquus

    18. Some thoughts on density-dependence Experimental evidence Analysis of short time series Predation may regulate feral horse populations in some places Without predators, carrying capacity for some herbivores may mean high mortality or habitat degradation

    19. Experimental evidence of density-dependence: feral donkeys in Australia (Choquenot, 1991, Ecology 72:805-813)

    20. Short time series & density dependence (Grange et al., 2009, Proc. Royal Soc. B. 276:1911-1919, Scorolli & Lopez Cazorla, 2010, Wildl. Res. 37:207-214)

    21. Predation & density dependence (Turner & Morrison, 2001, SW Naturalist 46:183-190) Mountain lions may regulate horse populations e.g., at Montgomery Pass, mountain lions killed 45% of foals/yr

    23. Two Purposes of Modeling (Caswell 1976) Models for understanding Models for prediction ˜ forecasting

    24. A WinEquus Example How would fertility control affect population growth at Garfield Flat? Initial conditions and assumptions N0 ˜ 109, like after selective removal of young horses in Feb 1997 average survival probabilities, foaling rates, sex ratio @ birth as found by Ashley & Jenkins for 1993-1999 year-to-year variation in survival and foaling follow logistic distributions

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