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Two Purposes of Modeling (Caswell 1976)

Overview of WinEquus Stephen Jenkins Emeritus Professor of Biology University of Nevada, Reno jenkins@unr.edu. Two Purposes of Modeling (Caswell 1976). Models for understanding Models for prediction ≈ forecasting Doomsday: 2026.87 = 13 November 2026

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Two Purposes of Modeling (Caswell 1976)

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  1. Overview of WinEquusStephen JenkinsEmeritus Professor of BiologyUniversity of Nevada, Renojenkins@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) Caswell, H. 1976. The validation problem. Pages 313-325 in B. C. Patten, editor. Systems analysis and simulation in ecology. Academic Press, New York, New York, USA.

  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) → Logistic distributions used to simulate stochasticity

  13. Garfield Flat, NV: selective removal in winter 1997 → non-equilibrium age distribution N0= 109

  14. Density-Dependence in WinEquus

  15. Density-Dependence in WinEquus • Why no density-dependence as default? • Populations often managed below levels where DD effects likely. • Insufficient data to estimate carrying capacity or form of DD effects.

  16. 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

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

  18. 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)

  19. 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

  20. What happens at carrying capacity? Oostvaardersplassen, the Netherlands • this 22 mi2 reserve is productive (high ppt, fertile soil) • a rewilding experiment (without mammalian predators) • 1983-1992: 32 Heck cattle, 20 konik ponies, 44 red deer • introduced • 2010: 3000 ungulates; 15-24% of horses starve in winter (F. W. M. Vera, June 2009, British Wildlife)

  21. Two Purposes of Modeling(Caswell 1976) • Models for understanding • Models for prediction ≈ forecasting Caswell, H. 1976. The validation problem. Pages 313-325 in B. C. Patten, editor. Systems analysis and simulation in ecology. Academic Press, New York, New York, USA.

  22. 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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