Table of Contents
Great Circle Hypotheis
Compass Bearings Hypothesis
Suns' Azimuth Hypothesis
Always Advance Hypothesis
Never Go Back Hypothesis
Hypotheses On Navigation By
Migrating Monarch Butterflies
Schmidt-Koenig Great Circle Hypothesis
Natural selection has favored migrating monarch butterflies
navigating by following local Great Circle routes to the overwintering sites in Mexico.
Assumptions for Eastern Population
- The only goal for migrating monarch butterflies is the overwintering sites in Mexico.
- Monarch butterflies have some means of determining the true bearings for local Great
Circle routes to the overwintering sites in Mexico.
Assumptions for Western Population
There are at least three possibilities for the western population.
- The western population is continuous with the eastern population and have
not evolved a local migration. The butterflies 'know' their location relative to
the overwintering in Mexico and attempt to fly local Great Circle routes to this
destination. Although there are no published observations indicating that migrants in the
western population consistently attempt to fly SSE towards the overwintering sites in
Mexico, this may be the case for the region of Idaho, Montana, and Wyoming.
- The western population may or may not be continuous with the eastern population but
the butterflies have independently evolved a local migration.
Consequently, the assumption that the overwintering sites in Mexico are the ultimate goal
does not apply. Instead, the butterflies in the western population migrate towards a
narrow band of favourable habitat along the coast of California. Monarch butterflies are
believed to migrate to the coastal overwintering sites from the entire region west of the
Rocky mountains extending south from about Latitude N32° to the northern limit of
milkweed distribution at about Latitude N49°. Only the north-western section of
Washington is excluded. The butterflies migrate out of a vast region that extends about
1900 km from north to south and funnel into a narrow band that extends from about 1,200 km
from Latitude N32° to Latitude N40°. This convergence suggests that if the butterflies
have a evolved a separate Great Circle route, the 'goal' is located far off shore.
- The western population may or may not be continuous with the eastern population but
the butterflies have not evolved a local migration. The migrants
are will outside the region where their navigation system can function and are lost. While
they may be following a distorted version of the Great Circle route fly in a directed
manner in response to particular stimuli, such as wind direction, this behaviour is not
adaptive. Even though some individuals from inland locations manage to reach overwintering
sites along the coast, this is largely a matter of chance. Most of the interior population
dies off as the habitable range of the western population contracts to the band of
favourable locations along the coast and some scattered locations inland (See Wenner's
Limitations of the Hypothesis
- Hypothesis provides limited insight into navigational mechanisms because it does not
explain how migrants are able to determine their location on the Globe relative to the
location of the overwintering sites with sufficient precision to calculate Great Circle
- Boundaries of geographic region where hypothesis applies are not known, particularly
- May not apply to western population.
- Additional assumptions are necessary if hypothesis is applied to western population
Advantages of navigating by following Great Circle routes
- Monarch butterflies are always following the shortest distance from their current
location to the overwintering grounds.
- The migrants can not lose their way as long as they remain within the geographic
region where the model applies.
- Because of (2), the butterflies can fly high above the ground in a wide range of wind
conditions (e.g. right crosswinds, tailwinds and left crosswinds).
Problems of navigating by following Great Circle routes
- Great Circle routes to the overwintering grounds in Mexico originating from most of
eastern North America cross the Gulf of Mexico.
- If Great Circle route to a single goal is followed by western population, this goal
is located far off shore.
- Because of the curvature of the earth, butterflies flying in any direction except
directly N, E, S, or W, must continuously alter their bearing to remain on course.
Problems in testing the Schmidt-Koenig Great Circle Hypothesis
- Predicted bearings for Great Circle routes are similar to the predicted bearings for
magnetoclinic routes for a large part of the range of the eastern population.
- The geographic boundaries of the region in which the hypothesis applies are not
clearly defined. Western population may not be included (see Remarks).
- Goal not clearly defined for western population.
Tests of the Schmidt-Koenig Great Circle Hypothesis
Prediction for Eastern Population
- Preferred directions of migrating monarch butterflies at observation sites are
identical to local Great Circle routes to the overwintering sites in Mexico at Latitude
N19°30°', Longitude W100°20'.
Predictions for Western Population
- Assuming that monarch butterflies have not evolved a local
migration, their goal is overwintering sites in Mexico and preferred directions of
migrating monarch butterflies at observation sites are identical to local Great Circle
routes to overwintering sites in Mexico at Latitude N19°30', Longitude W100°20'.
- Assuming that monarch butterflies have evolved a local
migration, their goal is a band of favourable habitat along the California Coast extending
from about Latitude 32° to Latitude 40°. A line extending from Latitude N49°, Longitude
W120° along the Washington, British Columbia border extended SW crosses the N32°
Parallel at about Longitude W135°, or 1300 km WSW of San Francisco. As a first
approximation, this point in the Pacific Ocean will be considered the 'goal' of the
western population. the preferred directions of migrating monarch butterflies are
identical to local Great Circle routes to this goal. The butterflies are assumed to stop
migrating when they reach the coast of California within the band of favourable habitat.
Methods for Eastern Population
- Determine the bearing for the local Great Circle route from the field site to center
of the region in southern Mexico where the overwintering sites are located (Latitude
N19°30', Longitude W100°20').
- Record at least 25, and preferably 50, Category I vanishing
bearings, or at least 50, and preferably 100, Category II
vanishing bearings of migrating monarch butterflies. If possible, Category II vanishing
bearings should be obtained over a range of wind conditions.
- Convert magnetic vanishing bearings to true bearings by correcting for the magnetic
declination (variation) of the field site.
- Plot the data as a Rose Diagram (a circular histogram). See the "Methods of Observing
Migrating Butterflies" section of the Red Admiral and Painted Lady Web Site for
an example of a Rose diagram. A string of dots, with each dot representing a single
observation, can be used instead of bars.
- Add the Great Circle direction to the Rose Diagram.
- Calculate the mean vector (mean vanishing bearing), as shown in Batschelet (1981) or
Zar (1996), and add to Rose Diagram.
- Use the Rayleigh test in Batschelet (1981) or Zar (1996) to test if the calculated
mean vector is significant. Proceed with analysis only if the Rayleigh test indicates that
there is a significant mean direction to the data.
- Look up 95% Confidence Interval for mean bearing in Batschelet (1981) or Zar (1996)
- Indicate the boundaries for 95% confidence limits on the Rose diagram (i.e.
equal to mean bearing ± 95% C.I.).
- Examine the Rose Diagram. If the data are obviously skewed to one side, or bimodal
(two peaks), you should not proceed with the analysis. Data analysis to this point has
been an exercise in descriptive statistics. More complicated procedures are necessary to
continue. If the data are not obviously skewed or bimodal, proceed to Decision Rules.
Methods for Western Population
- Assuming that the goal of the butterflies is the overwintering sites in Mexico, start
at step 1 for eastern population.
- Assuming that monarch butterflies in western population have independently evolved a
local migration and that the 'goal' is a point in the Pacific Ocean at Latitude N32°, and
- Determine the bearing for the local Great Circle route from the field site to
Latitude N32°, Longitude W135°.
- Proceed to step 2 for eastern population.
- If bearing for the local Great Circle route being tested is not
included within the arc delineated by the 95% confidence limits of the true bearing
for the preferred direction, than the two bearings are significantly different and the
hypothesis is rejected. Preferred directions of Monarch butterflies are not local Great
Circle routes to their goal (i.e. goal for eastern population is overwintering
sites in Mexico; 'goal' of western population is either the overwintering sites in Mexico
(no independently evolved local migration) or a point in the Pacific Ocean located at
Latitude N33°, Longitude W135° (an independently evolved local migration).
- If bearing for Great Circle route being tested is included
within the arc delineated by the 95% confidence limits for mean bearing (true), then the
two bearings are not significantly different and the hypothesis cannot be rejected. Local
preferred directions of migrating Monarch butterflies may be Great Circle routes to their
The Great Circle hypothesis is taken from Schmidt-Koenig's (1979) paper on mean
directions of migrating monarch butterflies at sites in the eastern United States. He
found that at a number of sites the mean direction of the migrants could not be
distinguished from the Great Circle direction to the overwintering sites. Although the
hypothesis does not specify the mechanism by which the butterflies navigate,
Schmidt-Koenig (1979) suggested that the butterflies may use some type of celestial
mechanism other than a sun compass because their mean direction was not affected by
overcast skies. Additional field studies and a reanalysis of the data led Schmidt-Koenig
(1985) to tentatively conclude that mean directions of the butterflies in the eastern
United States fit the predictions of Kiepenheuer (1984) Magnetoclinic model.
population represents a serious challenge to the model. There are no published
observations indicating that migrants from the western population consistently attempt to
fly SE towards the overwintering sites in southern Mexico. However, each year
concentrations of monarch butterflies occur at overwintering sites along the coast of
California in Autumn and Winter. Tagging data
by Fred and Norah Urquhart indicates movement from the interior third of the western
United States to the coast. There are at least four hypotheses that could explain the
- Wenner and Harris (1993) hypothesis. Monarch butterflies in the western population
are not migratory. The population experiences a range expansion from the coastal regions
in the spring and a range contraction bask to the coastal regions in the autumn. These
movements are not directed but occur though haphazard dispersal. Most butterflies located
outside the coastal regions perish during the Fall.
- Inappropriate behaviour hypothesis. Butterflies in the
western population are migratory but the observed pattern is an artifact resulting from an
inappropriate expression of the eastern population migration pattern. The butterflies are
programmed to carry out the migration but their navigation system is 'unaware' of their
western location. The butterflies are attempting to navigate by following Great Circle
routes, but their navigational mechanism is confused and simply directs them S to W until
they reach favourable habitat along the California Coast.
- Locally evolved migration hypothesis. Monarch butterflies in the western population
are migratory, but have independently evolved a local Great Circle migration suitable for
the region. The theoretical goal of the butterflies is located at an appropriate point in
the Pacific Ocean to funnel the western population into the narrow strip of favourable
habitat along the California coast.
- Conditional migration hypothesis. Butterflies in the western population are migratory
and are exhibiting one of two distinct migration patterns characteristic of the species.
Each butterfly has the capacity to express either the western or the eastern migration
pattern, depending upon circumstances. At the end of the summer, individuals that are on
the east side of the Rocky Mountains express the eastern migration pattern while those
that are sufficiently west of the Rocky Mountains express the western migration pattern.
Because recent genetic testing of monarch butterflies showed no significant
differences among the two populations the question of whether the western population is
isolated remains open. The first hypothesis could apply whether or not the western
population is isolated. The western population has been isolated for a sufficiently long
time for the butterflies to lose the capacity for long distance migration. Alternatively,
the western population may not be isolated but the butterflies do not receive the
appropriate combination of stimuli to trigger migratory behaviour on the west side of the
Rocky Mountains. The second hypothesis implies that the western population is either the
result of a relatively recent founding event, or that there is sufficient gene flow from
the eastern population into the western population to swamp out local adaptation. In
contrast, the third hypothesis implies that the western population has been completely, or
nearly completely, isolated from the eastern population for a sufficiently period of time
for a local migration to evolve. Finally, the forth hypothesis implies that sufficient
gene flow occurs in among the two populations to maintain two distinct, facultative,
migration patterns. In addition, the butterflies are somehow able to determine at the
appropriate time whether they are on the west side or the east side of the Rocky Mountains
and respond accordingly.
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Please send copies of all data and data analyses to Tactics and Vectors for
inclusion in the Archives. The data should be entered into the archives even if mean
vectors are not significant. Nonsignificant directional data is important information and
can be used to discriminate among different theoretical models. Further instructions may
be found in How to Submit Data to Tactics and Vectors.