Table of Contents
Great Circle Hypotheis
Compass Bearings Hypothesis
Suns' Azimuth Hypothesis
Always Advance Hypothesis
Never Go Back Hypothesis
Hypotheses On Navigation By Migrating
Kiepenheuer and Schmidt-Koenig, Magnetoclinic
Monarch butterflies Kiepenheuer
and Schmidt-Koenig magnetoclinic routes to the overwintering sites in Mexico.
- The only goal of the migrants is the overwintering sites in Mexico.
- The butterflies navigate in accordance with Kiepenheuer (1984) Magnetoclinic model as
- The butterflies have a sensor that detects the angle of inclination (dip angle) of
the geomagnetic field.
- They actually perceive a "subjective" angle of inclination that is a
function of the actual angle of inclination and the alignment of their bodies with the
magnetic field (i.e. the direction that they are flying). .
- The butterflies prefer a particular "subjective" angle of inclination and
navigate, in part, by flying in the direction that results in the perceived subjective
angle of inclination equaling the preferred subjective angle of inclination.
- Because the angle of inclination of the earths magnetic field decreases as the
butterflies fly towards the lower latitudes, they must shift their courses increasingly
southward to maintain their preferred, subjective, angle of inclination. This behavior
produces the curved route Kiepenheuer called a magnetoclinic route.
- The preferred, subjective, angle of inclination for monarch butterflies in North
America is 73°12' (Schmidt-Koenig 1985, 1993).
Limitations of the Hypothesis
- Limited physiological evidence that monarch butterflies have sensors that can detect
magnetic fields (However, see Jones and MacFadden, 1982)
- Because monarch butterflies are assumed to have a single, preferred, subjective,
angle of inclination, there can be only one magnetoclinic route that actually leads to the
overwintering sites) in Great circle Hypothesis.
- Boundaries of the geographic region where the hypothesis applies are not known. May
not apply to western population (see Remarks in
Great Circle Hypothesis).
- Isoclines of magnetic inclination are assumed to be smooth.
- Response of butterflies to changing angles of inclination are assumed to be uniform.
- Hypothesis does not explain why migrants turn SSE when reach about Longitude 100° to
102° in northern Mexico.
Advantages of navigating by following a Kiepenheuer and Schmidt-Koenig magnetoclinic route
- The single 'true' magnetoclinic route is similar to the Great Circle route from
approximately the center of distribution of the eastern population in late summer, the
Great Lakes region in late summer, to the overwintering sites and can serve as the basic,
or backbone (Kiepenheuer 1984), system for navigation.
- The ability to determine the magnetoclinic route should be independent of cloud
- The spring return migration can follow the magnetoclinic route to navigate back to
the Great Lakes region.
Problems of navigating by following a Kiepenheuer and Schmidt-Koenig, Magnetoclinic Route
- The true magnetoclinic route from center of distribution of the eastern population
crosses a large section of the Gulf of Mexico.
- Butterflies that don't begin their migration at some point along the true
magnetoclinic route, or are blown off course, are lost and will miss the overwintering
sites entirely unless they have other, backup, methods of navigation.
- Migrants must continuously adjust their heading to remain on course.
- Flying high and soaring in thermals must be restricted to direct tailwinds to the
- The magnetoclinic route between two points is generally longer than the corresponding
Great Circle route.
- Magnetic field precesses fairly rapidly in evolutionary time so that populations must
experience continuous natural selection to track changing magnetic coordinates.
Problems in Testing the Kiepenheuer and Schmidt-Koenig Hypothesis
- Predicted bearings for Magnetoclinic routes are similar to Great Circle routes for a
large section of the range of the eastern population
- The geographic boundaries of the region in which the hypothesis applies are not
A Test of the Kiepenheuer and Schmidt-Koenig Hypothesis
- Preferred directions of migrating monarch butterflies at observation sites are
identical to local Kiepenheuer Magnetoclinic routes based on a 'subjective' angle of
inclination of 73°12'.
- Mean directions of migrating monarch butterflies at observation sites are identical
to local Kiepenheuer Magnetoclinic routes based on a 'subjective' angle of inclination of
- Determine the bearing for the Magnetoclinic route from the field site based upon a
preferred subjective angle of inclination of 75°12'.
- Record at least 25 Category I, 50 Category II, or 100
Category III vanishing bearings of migrating monarch butterflies. Categories II and
III vanishing bearings should be obtained over a wide range of wind conditions.
- Plot the data as a Rose Diagram (a circular histogram). See the "Methods for 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 in place of bars
- Calculate mean vector (mean vanishing bearing ) as shown in Batschelet (1981) or Zar
(1996) and add to Rose diagram.
- Use Rayleigh test in Batschelet (1981) or Zar (1996) to test test if mean vector is
significant. Proceed with analysis only if mean vector is significant.
- Calculate the bearing for the K/S-K magnetoclinic route (Kiepenheuer, 1984) and add
to rose diagram.
- Look up 95% Confidence Interval for mean bearing in Batschelet (1981) or Zar (1996).
- Indicate the boundaries for the 95% confidence limits on the Rose diagram (i.e.equal
to mean bearing ±95% C.I. interval).
- Examine the Rose diagram. If the data are obviously skewed to one side, or bimodal
(two peaks), you should not proceed with analysis. Data analysis to this point has been a
standard exercise in descriptive statistics. More complicated procedures are necessary to
continue. If data are not obviously skewed or bimodal, proceed to Decision Rules.
- If bearing for Magnetoclinic Route falls within the arc delineated by the 95%
confidence limits for the mean bearing (mag.), than the two bearings are not significantly
different and the hypothesis cannot be rejected.
- If the bearing for the Magnetoclinic route does not fall within the arc delineated by
the 95% confidence limits for the mean bearing (mag.), than the two bearings are
significantly different and the hypothesis is rejected.
This hypothesis was advanced for monarch butterflies by Schmidt-Koenig (1985, 1993).
The Kiepenheuer and Schmidt-Koenig (K/S-K) magnetoclinic hypothesis is similar to the
Great Circle hypothesis in that both predict specific preferred directions for migrating
monarch butterflies if certain information is known. If the preferred, subjective, angle of
inclination is known for the butterflies, and the inclination and declination of the
magnetic field are known for the field site, then equation (2) in Kiepenheuer (1984) can
be used to calculate the predicted preferred direction. Conversely, if the preferred
direction of the butterflies is known, and the inclination and declination of the magnetic
field are known for a field site, then equation (1) in Kiepenheuer (1984) can be used to
calculate the preferred, subjective, angle of inclination of the migrants. If, at some
point in the migration, the preferred, subjective, angle of inclination of the butterflies
changes, then equation (1) would provide the new value.
There have been no further papers published on tests of the K/S-K magnetoclinic
hypothesis for monarch butterflies. As an exercise, I calculated the eventual destination
of migrants from Mississauga, Ontario, based upon a preferred, subjective, angle of
inclination 73°12'. I assumed that they flew at a constant speed of 5 meters per second
(18 km/hr) under conditions of no winds, and recalculating the preferred direction every
six hours in accordance with the new values for the inclination and declination of the
magnetic field. The K/S-K Magnetoclinic
Route from Mississauga, Ontario, would have taken the butterflies very close to the
overwintering sites. This result is intriguing because the lower Great Lakes region has
been considered to be the center of distribution of the eastern population in late summer
when the migration begins, However, the magnetoclinic route crosses a section of the Gulf
and the length of the crossing is much greater for butterflies that start from sites
located to the east of the calculated route. Apparently, the K/S-K magnetoclinic
hypothesis is incomplete.
The western population of monarch butterflies presents some of the same problems for
the K/S-K magnetoclinic hypothesis as for the Great Circle hypothesis. As was the case for
the Great Circle hypothesis, the coastal overwintering populations can be explained as:
(1) a range contraction, (2) an inappropriate expression of the eastern migration pattern
by butterflies that are 'unaware' of their western location, (3) an appropriate expression
of a facultative adaptation of the North American population to the existence to two
possible overwintering sites in North America, or (4) a local adaptation by an isolated
Please Submit Data with Tactics and Vectors Archives
Please send copies of all data and data analyses to Tactics and Vectors for
inclusion in the Archives. Your data should deposited in the Archives even if mean vectors
were not significant. Nonsignificant 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 (UNDER CONSTRUCTION).