Tactics and Vectors 98/99
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Great Circle Hypotheis  

Magnetoclinic Hypothesis

Magnetic-Latitude Hypothesis

Compass Bearings Hypothesis

Suns' Azimuth Hypothesis

Expansion-Contraction Hypothesis

Always Advance Hypothesis

Never Go Back Hypothesis

 

 

Hypotheses on the Adaptive Function of Migration Flight Tactics of Monarch Butterflies

tortose

Always Advance Hypothesis


Basic Idea:

Natural Selection on monarch butterflies has favored flight tactics that result in a either a reduction in the Great Circle distance or a reduction in a close approximation of the Great Circle distance, depending upon the method of navigation, for each episode of migratory flight during the late summer and fall migration.


Assumptions for Eastern Population

  1. The overwintering sites in Mexico is the ultimate goal for Monarch butterflies, whether they are flying Great Circle routes, K/S-K Magnetoclinic routes or K/S-K/G Magnetoclinic, Magnetic Latitude, routes.
  2. If the butterflies are navigating by the K/S-K/G model, they have an intermediate goal, Eagles Pass, Texas, as long as they are flying in the critical 55° to 65° band of isoclines of inclination of the magnetic field. Eagles Pass was selected as a first approximation because it appears to be in the center of the region where the bulk of migrating population funnels into Mexico.
  3. The butterflies have some means of determining their current location with respect to the overwintering sites and, if the K/S-K/G hypothesis applies, the Eagles Pass, Texas.
  4. The butterflies can determine either the true bearings for the local Great Circle route, or the bearings for the local K/S-K route, from their current location to the overwintering sites in Mexico.
  5. If the K/S-K/G hypothesis applies, the butterflies can determine the magnetoclinic bearings from their current location to the Eagles Pass, Texas when migrating in the critical 55° to 65° band of isoclines of magnetic inclination.
  6. The migrants are efficient at assessing local weather conditions and respond appropriately.

Assumptions for Western Population

There are at least four possibilities for the western population.

  1. 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 sites in Mexico and attempt to fly local Great Circle routes to this destination. Although there are no published reports indicating that migrants from 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.
  2. The western population may or may not be continuous with the eastern population and have not evolved a local migration. The migrants are well outside the region where their navigation system can function and are lost. While they may fly in a directed manner in response to particular stimuli, such as wind direction, this behaviour is not adaptive. Whether or not butterflies from inland locations manage to reach overwintering sites along the coast is largely a matter of chance (See Wenner's model).
  3. The western population may or may not be continuous with the eastern population and have not evolved a local migration. Instead, they are attempting to fly either K/S-K Magnetoclinic routes or K/S-K/G Magnetoclinic, Magnetic Latitude routes to Mexico. Following a behavioural program adapted for a migration that originates in the central and eastern regions of the United States and Canada would result in the migrants ending up stranded along the Pacific Coast until spring.
  4. The western population may or may not be continuos with the eastern population but the butterflies have evolved a local migration. Consequently, the assumption that the overwintering sites in Mexico are the ultimate goal does not apply. Instead, the butterflies migrate towards the 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 the distribution of milkweed at about Latitude N49°. Only the north-western part of Washington state is excluded. The butterflies migrate out of a vast region that extends about 1900 km from north to south and funnel into a long strip extending 1000 km, from Latitude N32° to Latitude N40°. This convergence indicates that if the butterflies have evolved a separate Great circle route, the 'goal' is located far off shore, at approximately Latitude N32°, Longitude W135°.


Limitations

  1. Hypothesis provides only limited insight into navigational mechanisms.
  2. Boundaries of the geographic region where hypothesis applies are not known. Uncertain if any of the navigational mechanisms would apply to western population even if proven for eastern population.
  3. Additional assumptions are necessary before hypothesis can be applied to western population. Also see discussion on western population in Remarks section on Schmidt-Koenig Great Circle Hypothesis.
  4. If K/S-K/G model applies, the new setting for preferred 'subjective' angle of inclination is not known. This change 'subjective' angle of inclination only applies when the butterflies are within the 55° to 65° band of isoclines of magnetic inclination. Theory is of little help, predicting only that when the butterflies are flying within the 55° to 65° band of isoclines of magnetic inclination the new setting for their preferred 'subjective' angle of inclination will always be less than 73°12' and equal to, or greater than, the actual angles of inclination encountered within the critical band.


Advantages of the Tactic of Always Advancing

As long as the butterflies are in a geographic region where the model applies:

  1. expenditures for migratory flight always results in at least some gains towards the overwintering sites.
  2. they can achieve large reductions in energy expenditures by restricting flight to periods when weather conditions are favourable for making gains towards the overwintering sites.
  3. the butterflies can fly high above the ground and soar in a wide range of wind conditions because drifting off course does not matter as long as the butterflies are making gains towards the overwintering sites.


Problems with the Tactic of Always Advancing

  1. No rigorous definition of favourable or unfavourable weather.
  2. Butterflies in western population may be following a flight strategy that is not adapted to their current location.
  3. Because the costs of gaining ground increase rapidly as weather conditions deteriorate, particularly when wind conditions become unfavourable, there will be a point where the cost in energy expenditures per kilometer gained will be too high to justify proceeding even though the butterflies are still capable of advancing. When this point is reached and whether or not the butterflies will stop migrating is not known.


Problems in Testing the Always Advance Hypothesis

  1. Can be difficult obtain sufficient data points for sufficiently wide range of wind categories, particularly in locations near the coast where wind direction tends to more predictable (less variable).
  2. Difficult to distinguish among predictions for the Great Circle model, the K/S-K model, and the K/S-K /G model.
  3. Data for butterflies that circled in thermals while they were observed cannot be analysed as a separate category because they are simply drifting downwind. The data for circling must either be excluded or pooled with observations of other butterflies that were flying straight during the same observation period in same altitude range and wind conditions.
  4. Amount of gene flow between western population and eastern population not known.


Tests of the Always Advance Hypothesis


Predictions for Eastern Population

I: Butterflies Assumed to Attempt to Attempt to Follow Great Circle routes

  1. Mean vanishing bearings monarch butterflies for a representative sample of wind directions and migratory flight behaviours will fall within the 180° arc delineated by the bearing for the local Great Circle route ±90° to the overwintering sites in Mexico.
  2. When directional data are restricted to observations for a particular wind direction (e.g. N, or NE, or E, etc.):
    • Mean vanishing bearings for monarch butterflies flying straight will fall within the 180° arc delineated by the bearing for the local Great Circle route ±90° to the overwintering sites in Mexico.
    • Mean vanishing bearings for a representative sample of monarch butterflies that are flying straight, circling in thermals, or switch between the two flight behaviours, will fall within the 180° arc delineated by formed by the bearing for the local Great Circle route ±90° to the overwintering sites in Mexico.

II: Butterflies Assumed to Attempt to Follow Kiepenheuer, Schmidt-Koenig, Magnetoclinic routes.

  1. When direction data for observations of a representative sample wind directions and migratory flight behaviours are pooled:
    • Mean vanishing bearings will fall within the 180° arc determined by the bearing for the local Kiepenheuer magnetoclinic route ±90° to the overwintering sites in Mexico.
  2. When directional data are restricted to observations for a particular wind direction (e.g. N, NE, E, etc.):
    • Mean vanishing bearings for butterflies flying straight will fall within the 180° arc determined by the bearing for the local Kiepenheuer magnetoclinic route ±90° to the overwintering sites in Mexico.
    • Mean vanishing bearings for a representative sample of migrating monarch that are flying straight, circling in thermals, or switch between the two flight behaviours, will fall within the 180° arc delineated by the bearing for the Kiepenheuer magnetoclinic route ±90° to the overwintering sites in Mexico.

III: Butterflies Assumed to Attempt to Follow Kiepenheuer, Schmidt-Koenig, and Gibo, Magnetoclinic, Magnetic Latitude routes

  1. Predictions are same as the above set of predictions for K/S-K magnetoclinic routes when butterflies are migrating through regions that fall outside the critical 55° to 65° band of isoclines of magnetic inclination.
  2. When migrants are within the critical 55° to 65° band of isoclines of inclination of the magnetic field, the theoretical bearing is assumed to be the local magnetoclinic route to Eagles Pass, Texas. Because the setting for the new subjective angle of inclination is unknown (see limitations), exact theoretical routes cannot be calculated within the critical 55° to 65° band of isoclines. However, preferred courses of butterflies migrating within the band of isoclines are rotated more to the west and are not crossing isoclines of magnetic latitude at their previous rate. As a result, local K/S-K/G magnetoclinic routes will be even less curved than local K/S-K routes and local Great Circle routes to Eagles Pass area can be used as a first approximations of the theoretical routes. Except for the change in goal, the above set of predictions for the Great Circle model apply.


Predictions for Western Population

I: Butterflies Assumed to Fly Great Circle routes

  1. Butterflies have not evolved a local migration: goal is overwintering sites in Mexico and predictions are same as the first set of predictions for the eastern population.
  2. Butterflies have evolved a local migration. The coast of California from about Latitude N33° to Latitude N40° is the goal. A line drawn on the globe starting from about Longitude W120° along the Washington, British Columbia, border and extended SW, along the diagonal border of northern distribution of milkweed in Washington, crosses the N32° Parallel at about Longitude W135°, or approximately 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 butterflies are assumed to proceed towards this goal until they reach the coast. Except for the change in goal, predictions are the same as in first set of predictions for for the eastern population.

II: Butterflies Assumed to Fly Kiepenheuer, Schmidt-Koenig, Magnetoclinic routes

  1. Butterflies have not evolved a local migration and are not 'aware' of their location on the continent: predictions are the same as the second set of predictions for the the eastern population.
  2. Butterflies have evolved a local migration: the mean bearing calculated from a good sample of category I/II vanishing bearings at one site is used to infer the the preferred, subjective, angle of inclination for their magnetic inclination sensor. This setting is used to predict mean bearings at all other sites. Except for the change in preferred, subjective, angle of inclination, predictions are same as the second set of predictions for the eastern population.

III: Butterflies Assumed to fly Kiepenheuer, Schmidt-Koenig, and Gibo, Magnetoclinic, Magnetic Latitude, routes

  1. Butterflies have not evolved a local migration and are 'unaware' of their location on the continent: predictions are the same as in the third set of predictions for the eastern population.
  2. Butterflies have evolved a local migration: the butterflies turn right from a local K/S-K route when they encounter a critical band of isoclines of magnetic inclination, but their response and/or the width and/or the location, of the critical band of isoclines of magnetic inclination differ from what is observed for the eastern population. Some possibilities include:
    • The western butterflies rotating their preferred direction a greater amount to the right than the eastern population when they encounter the critical band of isoclines, even when differences in magnetic declination (variation) is accounted for.
    • There may be a smaller critical band of magnetic isoclines for the western population, extending from 57° isocline to the 63° isocline to bracket the northern and southern limits of the overwintering sites.
    • The maximum amount of clockwise rotation of the preferred direction of the western population may occur at the southern limit of the critical band of isoclines (south of the California/Mexico border). The assumption for the eastern population is that maximum rotation occurs either in the middle of the critical band of isoclines or across the entire band.

Methods for Eastern Population

globe on a stand

I: Schmidt-Koenig Great Circle routes


A) Test of all observations

  1. Determine the bearing for the local Great Circle route from the field site to the center of the region in Mexico where the overwintering sites are located (Latitude N19°30', Longitude W100°20').
  2. Draw the bearing for the Great Circle route on a compass. Draw a second line perpendicular to the bearing for the Great Circle route that bisects the compass into two equal sectors. All bearings that will result in gains towards the overwintering sites are in the (acceptable) zone containing the bearing for the Great Circle route. All bearings that will result in the butterflies moving further from the overwintering sites are in the opposite, or forbidden zone.
  3. Record at least 100, and preferably 200 to 300 Category III vanishing bearings for the migrants under a wide range of wind conditions.
  4. Use the drawing of the compass to plot the data as a Rose Diagram (i.e.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, is preferable to bars.
  5. Jump to step 6 in Methods for Eastern Population in the section on the Schmidt-Koenig Great Circle Hypothesis.


B) Test of observations for winds from specific sectors

  1. Perform steps 1 and 2 two described above in section A.
  2. Divide the compass diagram into eight wind sectors of 45° as follows: direct tailwind, right tailwind/crosswind, direct right crosswind, right headwind/crosswind, direct headwind, left crosswind/headwind, direct left crosswind, left tailwind/crosswind.
  3. Examine a sample of at least 25 Category I or at least 50 Category II vanishing bearings for winds from one of the following wind sectors: direct right crosswind, right crosswind/headwind, direct headwind, left crosswind/headwind, direct left crosswind. Note - because the remaining three wind sectors are tailwinds, or partial tailwinds, butterflies migrating in these wind conditions are unlikely to show any displacement into the forbidden zone.
  4. Continue at step 4 for eastern population in section A above, then return to step 5 in this section, if appropriate.
  5. Starting at step 1, repeat the process for a different wind sector

II: Kiepenheuer, Schimdt-Koenig, Magnetoclinic routes

  1.  
  2.  

III: Kiepenheuer, Schmidt-Koenig, and Gibo, Magnetoclinic, Magnetic Latitude routes

  1.  


Methods for Western Population

I: Schmidt-Koenig Great Circle routes

  1. Butterflies are assumed to have the same goal as the eastern population. Use exactly the same procedure as for the eastern population.
  2. Butterflies are assumed to have a local migration with the 'goal' a point in the Pacific. Use the same procedure as for the eastern population except that co-ordinates for goal of Great Circle routes are Latitude N32°, Longitude W135°.

II: Kiepenheuer, Schmidt-Koenig, Magnetoclinic routes

  1.  

III: Kiepenheuer, Schmidt-Koenig, and Gibo, Magnetoclinic, Magnetic Latitude routes

  1.  


Decision Rules

  1. If the 95% Confidence Limits for the mean vanishing bearing bearing overlap any part of the 180° arc comprised of a theoretical bearing ±90°, then the mean vanishing bearing cannot be distinguished from a course that results in a reduction of the Great Circle distance to the theoretical goal (overwintering sites or Eagles Pass, Texas) and the hypothesis cannot be rejected.
  2. If the 95% Confidence intervals of the mean vanishing bearing do not overlap any part of the 180° arc comprised of a theoretical bearing ±90°, then the mean vanishing bearing does not result in a reduction in the Great Circle distance to the theoretical goal (overwintering sites or Eagles Pass, Texas) and the hypothesis is rejected.


Remarks

The Always Advance Hypothesis assumes that weather conditions on most days are unfavourable for migration. As long as the butterflies are attempting to follow a particular route, most winds are unfavourable. This becomes apparent if we divide the the compass into eight sectors corresponding to N, NE, E, etc. If the preferred course is SW, then SW winds are headwinds, SE and NW winds are both crosswinds, S and W winds are both headwinds/crosswinds, and N and E winds are both tailwinds/crosswinds. Only NE winds are more or less direct tailwinds and favourable for high altitude migration. All other wind conditions result in either off-course drift (crosswinds), or increased difficulty in making forward progress (headwinds), or both. The simple the flight tactic of avoiding unfavourable winds by flying close to the ground and flying high above the ground and soaring in favourable winds is an unsatisfactory solution. Migrants attempting to follow a particular course will have to spend most of their time close to the ground in flapping flight because winds from seven of the eight compass sectors are at least partially unfavourable. The high cost in energy expenditures for day after day of low-level, flapping, flight, would prevent the butterflies from building up lipid reserves. The hypothesis is based on the premise that natural selection has not favoured the strategy is reducing the Great Circle distance to the overwintering sites by taking the most direct route possible. Instead, natural selection has favored the strategy of either: (1) reducing the Great Circle distance to the overwintering sites by whatever flight tactics result in the lowest energy expenditures, or (2) if the K/S-K magnetoclinic model applies, reducing an approximation of the Great Circle distance by whatever flight tactics result in the lowest energy expenditures, or (3) if the K/S-K/G magnetoclinic, magnetic latitude, model applies, reducing the an approximation of the Great Circle distance by whatever flight tactics result in the lowest energy expenditures, except when detouring around the Gulf of Mexico. In the direct route strategy, the butterflies make steady gains, but at a high cost because they will have to fly close to the ground most of the time to avoid unfavourable winds and will only be able to proceed by costly, flapping, flight. In hypothesised strategy, the butterflies can ignore wind drift and soar at high altitudes as long as they have made gains towards overwintering sites after each episode of migratory flight. In other words, it doesn't matter whether monarch butterflies are flying directly towards the goal, or approaching it on an angle, gains are still gains.

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Please send copies of all data and data analyses, 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 (UNDER CONSTRUCTION).