CASE STUDY: Bird Energetics Model

Source:

Swartzman, G.L. and S.P. Kaluzny: Ecological Simulation Primer, Macmillan, New York, 1987.

Background:

During the last several decades, biologists have become increasingly interested in the role of grassland communities on global ecology. As part of the International Biological Program (IBP), a project designed to study the structure and function of these communities, research was carried out to study the population dynamics of passerine birds in short grass prairie environments.
To develop a model that reflected the population change of these birds on the breeding site, fieldwork was carried out at the Pawnee National Grassland in northeastern Colorado. The lark bunting birds are summer residents at this site, arriving around May 1 and leaving around August 15.

Modeling:

In order to successfully model population dynamics, field biologists collected data on various variables, as shown below:

Immigration Rate	no./100 ha/wk60	Week 18 to 19 0 Else
Emigration Rate	no./100 ha/wk50	Past Week 33 0 Else
Mortality Rate	no./100 ha/wk	0.015 Week 18 to 23 0.025 Past Week 24
Egg Laying Rate	egg/female/wk1.2	Week 23 to 25 0.4 Week 28 to 29 0 Else
Egg Survival Fraction	--	0.4 Year Round
Sex Ratio	--	0.45 Year Round

The rate of change of the bird population (xn) depends on immigration, emigration, birth, and mortality:

xn = gimmig - gemig + gbirth - gmrt

gimmig = immigration rate in the spring (no/wk)

gemig = emigration rate in the fall (no/wk)

gbirth = birth rarte (no/wk)

gmrt = mortality rate (no/wk)

Birth rate itself is dependent on the egg laying rate, the fraction of eggs that survive hatching, and the female population at the egg laying time:

gbirth(t) = glayegg(t) X ksurvegg X ksex(t) X xn

glayegg(t) = egg laying rate at time t (no/wk)

ksurvegg = fraction of eggs laid that survive to hatch

ksex(t) = sex ratio (female fraction) of bird population at time t

As the model examines the change in bird population over one year, the model time step is daily, although the time unit is a week.

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