Physiological Time |
Cluster Analysis |
Geometric Growth Models |
Similar insects reared at different temperatures will require different amounts of time to complete development. The concept of DAY-DEGREES is a convenient way to track development at different temperatures. One day-degree is the amount of development that occurs in one day (24 hours) when the temperature is one degree above the developmental threshold. Day-degrees accumulate over time. Each day the temperature is above the developmental threshold, more day-degrees are added to the accumulation.
Each insect species requires a certain total number of day-degrees to complete its development. This is known as the PHYSIOLOGICAL TIME of development. A seedcorn maggot, for example, needs 375 Celsius-day-degrees above its developmental threshold of 4°C to complete development from egg to adult.
Students can demonstrate the effect of temperature on development time by rearing insects (e.g. fruit flies) at different temperatures. Graph total development time (or time between consecutive molts) vs. temperature. The result should be nearly linear. Use the "slope-intercept" method to determine a formula for this line. Express the physiological time of development in day-degrees by multiplying the degrees (above threshold) by the number of days.
Determining the number of molts in an insect's life cycle is one application for cluster analysis that usually works even without computer software. Students simply measure a single variable (body length, head capsule width, dry weight, etc.) for a large number of individuals at different stages of development. Every observation is included on a "frequency chart" that shows how many individuals exhibit each "value" of the measured variable. Since an insect's exoskeleton grows "incrementally" at every molt (there is very little increase in size between molts), the frequency distribution is usually "clustered" around the average values for each instar. The number of clusters equals the total number of instars in the life cycle.
Another version of Dyar's Rule is known as Przibram's Rule. It is based on the assumption that body weight doubles during each instar. If all body parts grow in equal proportion (isogonic growth), then all linear dimensions should increase by a factor of 1.26 at each molt (1.26 is the cube root of 2). Again, students can confirm or refute this rule by comparing their data with observations expected under Przibram's Rule. A Chi-square test between "observed" and "expected" values can be used for a test of hypothesis.
Cluster Analysis
Cluster analysis is a statistical tool that can be used to identify "groups" within a set of data. Some statistical packages for personal computers include cluster analysis (e.g. SAS "Cluster"), but often a simple scatter chart or frequency diagram can accomplish the same thing with much less expense and sophistication.
Geometric Growth Models
In 1890, H. G. Dyar (Psyche 5: 420-422) studied 28 species of Lepidoptera larvae and reported that width of the head capsule consistently increased by a factor of 1.4 at each molt. This ratio has become known as Dyar's Rule. Students can confirm or refute Dyar's Rule for themselves by measuring the head capsules of different instars in a captive colony of mealworms, cockroaches, etc., calculating the mean head capsule width for each instar, and plotting these values as a function of instar. If the species follows Dyar's Rule, the graph should be a curved line if plotted on a linear scale and a straight line if plotted on a logarithmic scale.
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Last Updated: 15 October 1996