Chapter 25
Lemming Population Dynamics
A kind of Mice, (they call Leming. . .) in Norway, which eat up
every green thing. They come in such prodigious Numbers, that
they fancy them to fall from the Clouds.
(Derham, 1713)
25.1 Lemming Model
Similar to the vole population modeled in the previous chapter, lemming
populations can experience significant population fluctuations from year to year.
Many legends surround the seemingly erratic population dynamics of lemmings [1].
To model lemming population dynamics it seems advisable [2] to distinguish two
types of lemmings: Type 1 reproduces rapidly and migrates in response to
overcrowding. Type 2 has a lower reproductive capacity but is less sensitive to
high population densities. The change in the densities of each type is given,
respectively, by
ΔN1 ¼ IF N1 > 0 THEN N1 Ã A1 À B1 À C1
ð
ÞÃN2 À C1 Ã N1 þ N2
ð
Þ
ð
Þ ELSE 0
ð25:1Þ
ΔN2 ¼ IF N2 > 0 THEN N2 Ã ÀA2 þ B2 Ã N1
ð
Þ ELSE 0
ð25:2Þ
The parameters A1, A2, B1, B2, and C1 capture the density-dependence of birth
and deaths rates of the two types of lemmings. Figure 25.1 shows the model.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_25,
© Springer International Publishing Switzerland 2014
207
Lemming Population Dynamics
A kind of Mice, (they call Leming. . .) in Norway, which eat up
every green thing. They come in such prodigious Numbers, that
they fancy them to fall from the Clouds.
(Derham, 1713)
25.1 Lemming Model
Similar to the vole population modeled in the previous chapter, lemming
populations can experience significant population fluctuations from year to year.
Many legends surround the seemingly erratic population dynamics of lemmings [1].
To model lemming population dynamics it seems advisable [2] to distinguish two
types of lemmings: Type 1 reproduces rapidly and migrates in response to
overcrowding. Type 2 has a lower reproductive capacity but is less sensitive to
high population densities. The change in the densities of each type is given,
respectively, by
ΔN1 ¼ IF N1 > 0 THEN N1 Ã A1 À B1 À C1
ð
ÞÃN2 À C1 Ã N1 þ N2
ð
Þ
ð
Þ ELSE 0
ð25:1Þ
ΔN2 ¼ IF N2 > 0 THEN N2 Ã ÀA2 þ B2 Ã N1
ð
Þ ELSE 0
ð25:2Þ
The parameters A1, A2, B1, B2, and C1 capture the density-dependence of birth
and deaths rates of the two types of lemmings. Figure 25.1 shows the model.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_25,
© Springer International Publishing Switzerland 2014
207