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. 2009 Feb;90(2):556-66.
doi: 10.1890/08-0402.1.

Hierarchical demography: a general approach with an application to honey bees

Karim Al-Khafaji  1 , Shripad Tuljapurkar, James R Carey, Robert E Page Jr
Affiliations

Hierarchical demography: a general approach with an application to honey bees

Karim Al-Khafaji et al. Ecology. 2009 Feb.

Abstract

Hierarchical population structure, where individuals are aggregated into colonies or similar groups that themselves grow, survive or perish, and potentially produce offspring groups, is an important feature of many biological systems, most notably eusocial organisms such as the honey bee, Apis mellifera. Despite this hierarchical structure, there is a paucity of analytical models and theory linking the dynamics of individuals within colonies to the dynamics of a population of colonies. We present an analytical framework that provides a simple, robust, and predictive theory for the population dynamics of hierarchical organisms. Our framework explicitly describes and links demographic dynamics for the different levels in the hierarchy (individuals, groups, population). We illustrate the application of the framework by developing a model for honey bees and analyzing the effects of life history traits such as worker life span and size at swarming on the growth rate of populations. We conclude by discussing possible extensions of the model that increase its realism and expand its usefulness beyond swarm-founding, monogynous, eusocial insects.

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Figures

Figure 1.
Figure 1.
Life cycle of queens.
Figure 2.
Figure 2.
Effects of f on inter-swarm interval, worker-dependent survival, and population growth. g = 0.5 therefore T1 = T2 and worker dependent survival is s(0.5NS ) for both the departing queen and the queen inheriting the colony. μ = 1/30, b = 1350, p0 = 0.9, q0 = 0.81, and v = 5000
Figure 3.
Figure 3.
Effects of g on inter-swarm interval, worker-dependent survival, and population growth. In 3a the solid line is T1 and the dashed lines is T2. In 3b the solid line is s((1 – g)NS ) and the dashed line is s(gNS ) . mu = 1 / 30, b = 1350, p0 = 0.9, q0 = 0.81, and v = 5000
Figure 4.
Figure 4.
Effects of f and g on population growth rate. The contours present values of r in increments of 0.0025. The darker line indicates r = 0 ; for contours above it r > 0 and for contours below it r < 0 . μ = 1 / 30, b = 1350, p0 = 0.9, q0 = 0.81, and v = 5000
Figure 5.
Figure 5.
Effects of μ and b on population growth rate. In the top panel v = 5000 . In the bottom panel v = 15000 . In both panels f = 0.9, g = 0.6, p00 = 0.9, and q0 = 0.81
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References

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    1. Beggs KT, Hamilton IS, Kurshan PT, Mustard JA, and Mercer AR. 2005. Characterization of a D2-like dopamine receptor (AmDOP3) in honey bee, Apis mellifera. Insect Biochemistry and Molecular Biology 35:873–882. - PubMed
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