The map concept in animal navigation
Ronald Ranvaud and Ulrich Nehmzow
Discussion Wed 6th of April
Introduction
The word “map” is frequently used and plays a very important role in the field
of animal navigation. The word, however, has been used in a very loose way,
referring to very different concepts and mechanisms, or often has been employed
without any definition at all. This is inconsistent with the care that, quite
understandably, has gone into defining different kinds of navigational strategies
(route integration, vector navigation etc), and it seems sensible to invest a little
time to try understand better what the term means and how it has been used
by researchers in animal navigation.
Background
Before summarising the discussion, we will introduce some background concepts that can also be found on the slides that accompanied Ulrich Nehmzow’s
presentation, which is on the conference CD.
In general, any mapping between some physical space and some map space
can be considered a “map”. This mapping can take one of three forms (see
figure 1):
• Surjection: Physical space is mapped onto map space, meaning that every
physical point has an entry in map space, but several distinct physical
points may share the same point in map space,
• Injection: A one-to-one mapping between physical space and map space,
in which not all points in one space have an entry in the other, and
• Bijection: A one-to-one mapping of physical space onto map space and
vice versa.
A second way of characterising maps is by the kind of information they store:
• Maps can store precise positions of objects in measurable coordinates, for
example in longitude and latitude (“metric maps”),
• they can store neighbourhood relationships (“topological maps”), or
• they can even store concepts (“cognitive maps” — not discussed in detail
here).
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Figure 1: Surjection, injection and bijection
Metric Maps
Outside the field of animal navigation, hearing the word “map” people usually
think of ordnance type maps or city maps. Said in another way, maps are
usually taken to be representations on paper of a region out there in the world,
in which certain signs on the paper represent well defined objects in the world.
Thus crosses on the paper map might represent church towers, blue lines might
represent rivers, and so on. In a good quality map the position of the signs on
the paper are closely related to the position of the corresponding objects in the
world, in both angle and distance.
Topological Maps
The association between physical and map space can, however, be quite loose.
An example are maps of the tube, where it only is important to have the sequence of stations and indications of which stations allow changes of lines, but
the distance between stations and other details are ignored. An essential aspect
of these topological maps is that they reduce only selected characteristics of the
original landscape, and in this sense are by no means miniature models of all
that is present in the relevant part of the real world out there.
The map concept thus leads to two important points:
• Which are the aspects of the world out there that should be selected to
construct the map?
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• How are these selected aspects to be represented in the map?
As an example of the first point, we all know the difference between political
and physical maps. In political maps different uniform colours define the areas
occupied by different provinces or states, but there is no information about the
distribution of mountains, wetlands and the like.
In physical maps of the same region, on the other hand, there may be no
information on the boundaries between provinces or states, but contour lines
show the relief in some detail, and special signs indicate where the plains are
waterlogged etc. Both types of map are useful, but in different circumstances.
The Use of the Term “Map” in the Literature
The term “map” was introduced by Kramer, in a rather vague way, and the
purpose at the time essentially seemed to emphasise the importance of the
sun compass (and thus lay to rest the possibility of the competing idea of sun
navigation).
Since then it appears that Keeton thought of pigeon maps as something
rather similar to the ordnance type maps, and suggested that release site biases
might be a clue as to what ambient features where selected to build the map.
Papi’s proposal of an olfactory mosaic map was another suggestion that filled
the basic requirements of ordnance type maps, and it was the basis of inspiration
for several interesting experiments.
Wiltschko and Wiltschko suggested that through ambient gradients pigeons
might construct grid maps, but other cues, such as landmarks, would enable
pigeons to benefit from other, mosaic type, maps. Thus pigeon navigation might
be based on more than one type of map. Inspiring though these suggestions are,
a difficulty is that of understanding how pigeons can construct an accurate
enough map of an unfamiliar area.
Human ordnance type maps are the result of much exploration and data
collection over the whole region of the map.
Navigational Mechanism as “Map”
Wallraff suggested that the sun compass would be useful in association with gradients at home, rather than in association with a real map, and this combination
might be enough for the pigeons to orient by at any distant location, within some
range. His model requires that the birds be able to compare the local values of
the different parameters with the values at the loft. These parameters are those
whose gradients are relevant in navigation.
The model introduces the possibility of a mechanism which is very different
from a map of any kind discussed above, because it actually only provides an
algorithm whereby the pigeons are able to get home, on two conditions: 1. they
must have a compass and 2. they must remember the intensity of some ambient
parameters at the loft and be able to compare it to the local values anywhere
away from the loft.
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Such a navigational mechanism is not a map in the sense of representing
objects in the world on some kind of paper on neural substrate. The bird has
no idea where it is in relation to home, but it has a direction to fly in which
eventually takes it home. Thus there are mechanisms other than ordnance
type maps or topological maps that allow navigation. “Homing” and “path
following” are examples of this, observed both in the animate and inanimate
world (robotics).
Discussion
The following is an attempt to recall at least roughly some of the comments of
the participants in the ensuing debate.
• If there are different maps, described by different terms, we should use
these different terms.
• If there are different maps, this should be useful to design experiments to
discriminate between them, and which one is operative in which circumstance.
• Vannini described a clear example of the need of a map: male crab that
occupies and defends a territory in which there are females that will enter
fertile phase at different times, which forces him to patrol the territory
and act at appropriate times... must have a map, a representation of the
space and the objects that occupy that space, and must decide where to
go next, and how to get there, so as to cover all the possibilities...
To further clarify the idea Vannini told of how his small son had not
really the idea of a map when coming back home from school, and was
only familiar with a sequence of landmarks (just a procedure); but later
yes, when going from Palazzo Vecchio to Piazza del Duomo he was able
to answer the question in which direction is Ponte Vecchio?
Shortcuts as Evidence of the Existence of a Map
• If the experience of going from A to B to C is enough for an animal then
to be able to go from A directly to C, then it constructed a map, but not
otherwise.
• A map must enable an animal to return by a route that is independent of
the route out.
• Evolution does not require 1:1 correspondence between objects out there
and the animals map.
• The term “map” could be used to cover any mechanism that allows a
navigating agent to return home — this is the most general definition the
meeting came up with.
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