An analysis of silk density in spider webs

This study explores the structural complexity of spider webs through information-theoretic and harmonicity-based frameworks to quantify spatial patterns in silk density across different web regions and reveal the underlying resource allocation strategies. By analyzing the entropy of silk density distributions across different species, we observed that the entropy values follow a normal distribution with a mean of 1.24 bits and a standard deviation of 0.22 bits when using 10 quantization levels. In the second part of the paper, by measuring the harmonicity of the silk density, we reveal that the silk density at a given point can be inferred from its neighbors, with an average harmonicity value of 0.0039 (fraction of total points in point cloud data). The harmonic behavior is notable for its maximum principle, suggesting that the strongest parts of the web appear at the boundaries, aligning with existing knowledge of spider web construction. These findings provide a new technique for quantifying web-building strategies and offer new insights into spider behavior and evolution.

Methods
Collected spiders were kept in small containers for 1-2 weeks without food prior to introduction to experimental space to ensure relative uniformity of physiological state. Specimens were placed inside 10.16 x 10.16 x 10.16 cm (4” x 4” x 4”) acrylic boxes with clear sides, a black base, and no lid. Vaseline was coated on the inside top 2.54 cm (1”)of each side to prevent specimens from escaping. Each spider was given 1-2 weeks in ambient conditions to complete a web. Linyphiids construct webs over the course of multiple days and weeks, and web completion was defined as the point at which no additional silk was added to the web after several consecutive days.

Completed webs were placed into an enclosed experimental scanning apparatus blocking all outside light. Scanning was conducted by a laser (Quarton Inc. VLM-520-56) and camera (Canon EOS R5C mirrorless camera using a Canon RF 100mm F 2.8 Macro lens) mounted on a track at a fixed distance (0.67 meter). A small motor (Habow Technic Power-Functions XL-Motor-Set 8882) was used to advance the laser and camera simultaneously to scan the length of the experimental chamber from front to back, recording at 120 FPS for 20-30 seconds. An infrared laser distance sensor (DFROBOT DFRduin Uno v3.0[R3]) monitored the location of the camera relative to its start position to provide z-axis information for 3D reconstruction.

Individual video frames representing two dimensional slices of the web were extracted for cleaning and analysis using a custom Python script (Github Repository).  For each video, a set cropped region was identified in each frame that excluded the box edges and background and accounted for any minute changes in elevation across the length of the box. Red and blue color values were reset to the minimum value and the image converted to grayscale. Background noise was removed using a minimum threshold filter of 0.55 max RGB value.  Three-dimensional Point Cloud Data (PCD) representations of each web were created using the filtered data.