Skip to content
📢We are still a growing community and would love some help. Want to contribute? Join us by mailing an e-mail of interest to "r6394175@gmail.com"
Start helping our community →
← Theoretical A

Q16 — Fractal Geometry and Scale-Dependent Resource Availability

Theoretical A Real exam question — full text reproduced under IBO's CC BY-NC-SA 4.0 license
Ecology

Fractal geometry can be illustrated by Mandelbrot’s question: How long is the coast of Britain? The answer depends on the scale of measurement.

Analogously, ecosystems exhibit scale-dependent resource availability. For instance, measuring Admiralty Island’s coastline from the perspective of an eagle (using the distance between nests) yields 761 km, whereas considering barnacles (requiring 2 cm of space) results in 11,000 km.

Figure 1B shows the relationship between the coastline length of Admiralty Island and the scale at which it is measured, as defined by the equation on the graph. A similar relationship exists for the amount of resources available for a species that operates at a given scale, as well as for its biomass.

Panel A: outline map of Admiralty Island with two red boxes labeled 1 and 2 marking a smoother and a more convoluted stretch of coastline. Panel B: log-log graph of coastline length (Q) vs. measurement scale (L), following Q = kL^d, with points a and b marking two species’ operating scales on a downward-sloping line. Figure 1. A Admiralty island. B Log-log graph of resolution (scale) and the length of Admiralty coastline; a, b - species; Q - resource available or biomass or coastline length, k - constant, L - scale, d - fractal dimension describing the complexity of the pattern, more complex patterns correspond to higher values of d.

On your answer sheet, indicate “T” for true statements and “F” for false ones.

A. The graph for region 1 will have a steeper slope than the graph for region 2.
B. The number of individuals in an ecosystem consisting solely of species operating at scale b is larger than the number of individuals in an ecosystem consisting solely of species operating at scale a.
C. According to this theory, along with a decrease in the number of individuals at high trophic levels, all predators should have a larger body size than their prey.
D. Social behavior, such as the formation of herds, influences the scale of perspective.
← Previous: Q15 Next: Q17 →

Question reproduced from IBO 2024, Theoretical Exam Part A, licensed under CC BY-NC-SA 4.0 — attributed to the International Biology Olympiad. Open the full exam PDF · Community solutions (unofficial)