Population Estimates Classic Mimbres Perioda

The Exponential Growth Model

1. r=ln(N_t/N₀)/t   where r= annual growth rate, t= time span, N_t= number of rooms at time t, and N₀= number of rooms at time 0, or the beginning of the time period. This formula can be converted to (Blake et al. 1986):
   
   
2. N_t=N₀e^rt  and
   
   
3. N_s=N₀(e^rt+((e^rt/Lr)-(1/Lr)))   solving for N₀ in Equation (3):
   
   
4. N₀=N_s/(e^rt+((e^rt/Lr)-(1/Lr)))   and substituting N₀ in Equation (4) for N₀ in Equation (2):
   
   
5. N_t= N_s* e^rt/(e^rt+((e^rt/Lr)-(1/Lr)))   where: N₀ = number of structures/rooms at time 0, N_s = total accumulated number of rooms at the end of the time period, N_t = number of rooms at time t (at the end of the time period), L= average use-life of rooms, r= annual growth rate, t= time span (Blake et al. 1986).

Annual growth rate is estimated at 0.3% based on estimates by Blake et al. (1986:454) for the Classic Mimbres Period.

Estimating Agricultural Production:
DSSAT 3.5 Production Model
(Tsuji et al, 1994)

Minimal Data Set

• Soil Data
• Weather Data
• Management Data
• Developmental and Growth Parameters

Soil Data

• Soil Series
  • soil classification (SCS) (series and family names)
  • surface slope (%) color
  • permeability
  • drainage class
  
  
  
• Profile Data for Each Soil Horizon:
  • upper and lower depth of horizon (cm);
  • percentage of sand, silt, and clay content;
  • moist 1/3 bar bulk density (g/cm³);
  • percentage organic carbon;
  • percentage stoniness (percentage of soil greater than 2 mm);
  • pH in water;
  • aluminum saturation (cm³/cm³); and root abundance

Weather Data

• Latitude and longitude
• Maximum and minimum air temperatures (ºC)
• Precipitation (mm)
• Daily values for incoming solar radiation (MJ/m²-day)

Management Data

• Planting date
• Planting density (number of plants per meter row),
• Row spacing (cm)
• Number of plants per square meter;
• Planting seed depth (cm),
• Crop variety
• Any irrigation or fertilizer practices (minimally, any crop residue from the previous year)

Developmental and Growth Parameters

• P1 (the juvenile phase) (100-400): the time period expressed in degree (ºC) days above 8ºC (GDD8) during which the plant is not responsive to changes in the photoperiod, which is from seedling emergence to 4-6 days before tassel initiation in the southern united states;
  
  
• P2 (photoperiod sensitivity) (0-4.0): the extent to which development (expressed as days) is delayed for each hour increase in the photoperiod above the longest photoperiod in which development is at a maximum (12.5 hours);
  
  
• P5 (grain filling duration) (600-1,000): the summed daily GDD8 values from silking to physiological maturity;
  
  
• G2 (maximum possible number of kernels per plant) (550-850); And
  
  
• G3 (kernel filling rate) (5.0-12.0): during linear gram filling stage (approximately 10 days after silking till just before physiological maturity) and under optimal conditions (mg/day).

Estimating Production

    The DSSAT v3.5 model was run for each soil series for the years of historic weather data (1957-1988) (Western Regional Climate Center 2001) to estimate production each year. The total production for each mapping unit was computed and the sustainable population was estimated, assuming a requirement for two years storage.