Emigration rates and mechanisms
Why does emigration increase with decreasing patch size? An
experimental test of the boundary encounter rate hypothesis
DAG Ø. HJERMANN
Department of Biology, Division of Zoology, PO Box 1050 Blindern,
N-0316 Oslo, Norway
Abstract
Both theoretical and empirical studies indicate that patch size and emigration is negatively correlated.
In the theoretical studies, it is assumed that animals emigrate with a certain probability each time they
encounter the edge. When patch size decreases, animals encounter the edge more often, and thereby
the emigration rate increases. The predicted correlation has been confirmed by several field studies,
but the mechanism behind the relationship remains unclear. In this field experiment, I tracked
individually marked wart-biters (Decticus verrucivorus; a largely flightless bush-cricket) in eight
artificial habitat patches of three different sizes (ca. 20, 40 and 80 m2). Thus, I was able to check
whether individuals that emigrated moved differently before emigration that individuals that did not
emigrate. I found that emigration rate increased with decreasing patch size; from 23% in the largest
patches to 71% in the smallest. Emigration rates were higher among males than among females, and
also increased with increasing movement activity within the patch. However, although use of the
edge zone differed substantially between individuals, I found no indications that individuals that were
most exposed to edges tended to emigrate more than other individuals. Thus, these results confirm
the correlation between patch size and emigration rate predicted by theoretical studies, but indicates
that the mechanism that underlie this correlation is not as assumed by these studies. I propose an
alternative mechanism for this species; that the tendency to emigrate is counteracted by social
cohesion, which is weaker in smaller populations. This hypothesis predicts that emigration rate is
correlated with population size, not patch size per se. This is supported by a tendency that the small
patches that experienced a net loss of individuals the first three days also experienced more
emigration the nest 15 days, compared to small patches that did not experience an initial loss.
Introduction
Emigration rate affects population dynamics, genetic processes and is crucial in the
understanding of metapopulation dynamics (Hanski and Gilpin 1997). Thus, it is important to
understand the relationship between emigration rate and patch area.
E.g., when
metapopulation models such as Hanski's (1994) are fit to data, one either have to assume that
emigration rate is independent of patch area (e.g., Hanski et al. 1994, Hanski & Thomas 1994)
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Paper IV
or specify a mathematical relationship between the two. Stamps et al. (1987) and several other
theoretical studies (e.g., Turchin 1986) have found that emigration rate is likely to increase
with decreasing patch area. A such relationship has also been found in a number of field
studies (e.g., Hill 1996; Kindvall 1999; references in Stamps et al. 1987). However, there are
also quite a few empirical examples of the opposite relationship (Ims 1995).
Stamps et al. (1987) assumed that animals move (in some way) randomly within the
patch, and when they happen to encounter the habitat edge they "decide" whether to emigrate
or not. Usually they are assumed to decide by "flipping coins", i.e., each time they encounter
the boundary, they emigrate with a certain probability P, which is known as the edge
permeability (Stamps et al. 1986). In small patches, animals bump into the edge more
frequently and thus a larger proportion of them emigrate. I will call this the boundary
encounter rate hypothesis.
Several other biologists have employed the boundary encounter rate hypothesis to
generate patch- and landscape-specific predictions about dispersal probabilities. Schumaker
(1996) used a similar model (assuming no boundary barrier) to predict habitat connectivity,
but did not try to support it with empirical data. In a study of a metapopulation of the bushcricket Metrioptera bicolor, Kindvall (1999) found the distribution of daily movement
distances in the habitat (by observation), daily movement rates in non-habitat, and the
probabilities of leaving the habitat patch when a bush-cricket encounters the border between
habitat and several types of non-habitat. Non-habitat movement rates and the emigration
probabilities were estimated by experimentally releasing animals in the forest and on borders,
respectively.
He then simulated movements using the observed data, and found that
predictions from this model agreed well with data from long-term observations of dispersal
rates. Haddad (1999) did a similar kind of analysis to predict how movement rates through
corridors were affected by the corridor’s width and length, using a simulation model which
departed from correlated random walks only at habitat boundaries. Several other authors have
found emigration rate to be influenced by boundary type or contrast (e.g. Holmquist 1998;
Basquill and Bondrup-Nielsen 1999; Jonsen and Taylor 2000).
However, although the predictions of Stamps et al. (1986) often have been
confirmed in empirical studies (at least qualitatively), fewer studies have tested whether the
mechanism of dispersal is as assumed in the hypothesis. In the current study, I traced the
movements of a bush-cricket (the wart-biter Decticus verrucivorus) in eight experimentally
created habitat patches with different areas. Thus, I was able not only to investige the
2
Emigration rates and mechanisms
correlation between patch size and emigration rate, but also whether emigration was linked to
animal movement patterns prior to emigration. Specifically, I tested a prediction of the
boundary encounter rate hypothesis, namely whether animals that were more exposed to the
patch boundaries were more likely to emigrate.
Methods
Study species and experimental design
The wart-biter (Decticus verrucivorus L.) is a relatively large bush-cricket (length 34 cm). It is winged but most animals are not able to fly more than a few meters, and they
usually fly only when they are very disturbed (Ander 1947). Adult males stridulate to attract
females. The experiment was performed during the summer of 1997 at Oslo University’s
experimental station at Evenstad, SE Norway. Eight habitat patches were made by mowing
parts of a continuous area of seminatural pasture. Because the available area was shaped as a
narrow rectangle lying in north-south direction, all habitat islands were ca. 5 m wide, while
their lengths varied from 4 to 16 m. Two islands were relatively large (ca. 80 m2), two were
medium (ca. 40 m2), and four were small (ca. 20 m2) (Fig. 1). Because of the design of the
experiment and because the vegetation of the original pasture was relatively homogenous,
vegetation structure and edge contrast varied little between patches and was approximately
equal between small, medium and large patches. The patches were protected from bird
predation using nets suspended 1.5 - 2 m above the ground (the wart-biters could move freely
through it). Adjacent patches were separated by 20-25 metres of short-cut lawn, a distance
larger than the limit for acoustic interaction (Keuper et al. 1986). On the western side of the
experimental area was a 60 cm clear plastic fence and a corn field, on the eastern side was a
50-60 cm high fence of solid metal. These fences were hard to climb for wart-biters, so
migrating animals were directed towards neighbouring patches. 80-100 cm of earth and 175Wire fence
Corn field
Habitat patches
Bare ground
Metal fence
10 m
50 m North
Figure 1. Map of the experimental area. The experimental patches are arranged in a row between a
corn field in the west and another experimental area in the east. Between the patches was extremely
short-cut grass.
3
Paper IV
200 cm of lawn separated the patches from the corn field and the metal fence, respectively.
The wart-biters used in the experiment were caught at different locations in SE Norway (there
were no wart-biters on the study site in advance). The animals were marked with a red 80 x 4
mm plastic tape with numbers written on it. On end of this tape was glued to the top of the
pronotum. Adults were released in equal densities in each of the eight patches (4, 8 and 16 in
the small, medium and large ones, respectively) in approximately even sex ratios. Four
animals were added on day 5 and 6 to replace predated animals. The animals were tracked
almost every day from day 4 to day 23 of the experiment, and then again on day 30 and 40. I
usually sought for the animals four times a day.
Data analysis
When animals went > 1 m outside a patch, it was recorded as an emigration event,
except when females went outside the patch for a short time (at most, a few hours) to lay eggs
(wart-biters lay their eggs in the ground where there is no vegetation). After emigration, the
migrating individual could either return to the patch it left, immigrate another patch, or it
could be predated between patches. In the course of the migration, animals could come close
(< 5 m) to a "foreign" patch without entering it, or enter a patch but leave it within 2-3 hours;
these events were recorded as rejection events. If the animal stayed in the new patch for a
prolonged time, it was recorded as an immigration event. When an animal returned to a patch
it previously had emigrated from, it was only counted as immigration if the animal had
rejected or immigrated to another patch in the meantime. The null hypotheses was that
emigration rate did not differ between patches (i.e., that the number of emigration events was
proportional to patch size or initial population size), and that the number of immigration and
rejection events were expected to be the same for all patches (i.e., independent of patch size).
When testing for deviations from the null hypotheses, we assumed that events were
independent.
On the level of individual animals, I used logistic regression to test whether patch
size, sex, and movement activity or edge zone use influenced the probability of emigration. I
defined the "edge zone" of the patch as the part of the patch lying within 1 m of the patch
edge, and the "interior" as the rest of the patch. Edge zone use was quantified by defining the
"edge selection index" as ratioedge/(ratioedge + ratiointerior) (Manly 1974, eq. 3), where ratioedge
and ratiointerior is the use-area ratio for edge zone and interior, respectively (the proportion of
the observations divided by the proportion of the area).
The edge selection index was
calculated for each patch*animal combination with at least five observations.
4
Emigration rates and mechanisms
Table 1. Total number of emigration, rejection and immigration events from/to patches of different
size.
Patch size
Chi2-test
p-values 1
Large
Medium
Small
Emigration events
9
8
14
0.021
Rejection events
2
0
3
-
Immigration events
7
4
5
0.18
Number of patches
2
2
4
160 (2 x 80 )
80 (2 x 40)
80 (4 x 20)
Total habitat area (m2)
1
The null hypothesis was that the number of emigration events was proportional to total area or total
population size, and that the number of immigration events was proportional to the number of patches.
Numbers of rejection events were too low to be tested.
Results
During the experiment, 31 emigration events were recorded, of which 16 ended as
immigration events, while 12 animals were predated between patches and 3 returned to the
emigration patch without encountering other patches during migration. Most emigrations
occurred in two periods; during day 1-7 and from day 21 onwards (13 and 14 emigrations,
respectively); there were only 4 emigrations between these periods.
The number of
emigration events was not proportional to initial population size; emigration clearly increased
with decreasing patch size (Tab. 1). The null hypothesis that the number of immigration
events was proportional to the number of patches could not be rejected, although the numbers
were roughly proportional to the total area of patches of a given size class (Tab. 1). As a
result of these patterns, the average population density in the small patches declined to 50-60
Table 2. The best logistic regression models explaining variation in the probability of migrating. No
two-way interactions were found to be significant (P < 0.05). The p-values shown are calculated from
type III deviance. N = 54, df = 49, deviance (-2LL) = 53.42.
Variable
Percent migrants
P
Patch size
large: 23 %, medium: 50 %, small: 71 %
0.0042
Sex
males: 61 %, females: 21 %
0.034
Activity
activity > median: 56 %, ≤ median: 30 % 1)
0.017
1)
In the model, activity was used as a continuous variable. I classified the individuals in two equalsized groups according to activity with the sole purpose of reporting the percentage of emigrants.
5
Paper IV
Overall edge use
1
0,8
Female emigrants
0,6
Male emigrants
Female stayers
0,4
Male stayers
0,2
0
small
0
1
medium
2
large
3
Patch size
Figure 2. Edge use compared between non-migrants (“stayers”) and animals that migrated one or
more times (“emigrants”). Each point represents an individual insect.
% of the density of the large and medium patches during the experiment.
On the individual level, 23 (43 %) migrated one or several times (excluding 14
individuals that were predated during the first few days of the experiment). Males were much
more likely to migrate than females (Tab. 2). Before migration, migrating individuals tended
to display higher movement activity than non-migrating individuals (t52 = 2.17, P = 0.035); a
closer inspection of the data showed that this difference was found in large (t23 = 1.88, P =
0.015) but not in small and medium patches (P > 0.27).
Table 3. The net gain/loss of the populations in the four small patches during the first three days
of the experiment, and how many of the resulting population that emigrated during the next 15
days (day 4-19 of the experiment).
Patch ID
Net gain/loss day 1-3
Number emigrating day 4 - 19
B
+1
0 out of 5
D
-1
2 out of 3
E
-2
1 out of 2
H
0
0 out of 4
I found no tendency for emigrating individuals to use the edge zone more or less
than non-emigrating individuals, independent of patch size and sex (Fig. 2). Although the
numbers are too small for testing, the behaviour of the animals in the small patches may have
been influenced by the events of the first few days of the experiment. Two of the small
6
Emigration rates and mechanisms
patches (patch D and F) had a net loss of individuals (due to both emigration and predation)
during the first three days. During the next two weeks, 60 % of the remaining individuals in
those patches emigrated, while no animals emigrated from the two other patches (tab. 3).
Discussion
The results of this study clearly show that emigration rate decreases with patch area.
Qualitatively, this result agrees well with the predictions of the boundary encounter rate
hypothesis. Quantitatively, there seems to be fairly good agreement as well. Stamps et al.
(1987) predicted an approximately linear relationship between edge-to-size ratio (ESR) and
emigration rate when boundary permeability was held constant. The ESR depends on which
edges we consider as permaeable. The western side of the patches, which bordered the corn
field, were quite unpermeable (only one animal emigrated that way). The other three were
permeable to some degree. However, the eastern side may have been less permeable than the
southern and northern sides, since animals that left the patches from the eastern side of the
patch were likely to encounter the metal fence and return to the patch before the event was
counted as an emigration event. I observed emigration from all three sides, but not in enough
numbers to test for differences in permeability. If emigration rate is proportional to ESR, we
would expect the ratios somewhere between the emigration rates to be between 4:2:1 and
2.2:1.4:1 (small:medium:large patches) depending on how permeable we assume the eastern
side to be. Thus, since the ratio between observed migration rates (Table 2) was 3.1:2.2:1,
these results fit well with the predictions of Stamps et al. (1987).
However, the behavioural mechanism leading to this pattern clearly seems to be
different from the mechanism that Stamps and colleagues assumed.
According to the
boundary encounter rate hypothesis, we would expect that individuals that spent much time
close to the edges were most likely to emigrate, since they encountered the boundary most
often. Fig. 2 clearly shows that this is clearly not the case; animals that mostly stayed in the
interior of the patches were just as likely to emigrate as animals that stayed close to the edge.
Thus, the wart-biters decide to emigrate or not independently of how often they have
encountered the edge.
Which other mechanism can explain that emigration rate increases when patches
become small? A positively density-dependent emigration rate (e.g., Denno and Peterson
1995) can be ruled out, since the patches were initiated with equal density, and since the
7
Paper IV
density of small patches became lower than the density of large patches during the
experiment. Thus, we cannot completely rule out negatively density-dependent emigration,
but differences in density seemed minor compared to the massive difference in migration rate.
Another possible, but unlikely, explanation is conspecific attraction between patches. Keuper
et al. (1986) found that singing males of both the wart-biter and the closely related
Psorodonotus illyricus attracted other males. Because of sound attenuation, 6 m was the
upper limit for acoustic interactions between males of the latter species. As the song of
P. illyricus is better adapted to the acoustic properties of grassland habitat than the wart-biter’s
high-pitched song, it is unlikely that the wart-biters can hear males on other patches. Also, I
would have expected more movements between patches if they could. E.g., two females
stayed in a patch without males for 12 and 18 days, respectively.
As an explanation for the observed data, I suggest that social cohesion works as a
"glue" that counteracts the tendency to emigrate, and that the strength of the glue is
determined by the population size experienced by wart-biters. Wart-biters has a tendency to
aggregate to a larger degree than the resource density can explain (Weidemann et al. 1990).
Kalmring et al. (1986) found that males are attracted by hearing the song of other males, and
although they not were able to detect the same tendency in females, they are for obvious
reasons also attracted to males, at least temporarily (personal observation).
This "social cohesion" hypothesis predicts that the rate of emigration is proportional
to the population size, not the patch size per se. A test for the hypothesis would be a set of
identical patches with different population sizes. Although no substitute for such a test, the
fates of the four small patches are as we would expect from this hypothesis. The patches that
had a net loss of individuals during the first days, the few individuals left tended to emigrate.
However, this only indicates the effect of extremely low population sizes on survival, and
further studies are needed to to confirm or reject that this effect can account for the differences
in migration rates when populations are larger.
It is no big surprise that the boundary encounter rate hypothesis does not explain
emigration rate. According to this hypothesis, different emigration strategies would differ
only in one parameter, the boundary permeability, and the effect of patch size on emigration
would be rigid. In contrast, we can expect that animals have evolved to make use all available
information that is linked with the expected fitness of the individual. I.e., we expect that
animals "decide" to stay or emigrate partly in response to internal and environmental cues, as
long as the environment is not completely unpredictable (Ims and Hjermann in press).
8
Emigration rates and mechanisms
Although I found no evidence for it in this particular organism, an individual’s boundary
encounter rate may be one such cue that indicates patch size. Detecting the local population
size or density is highly relevant cue when deciding to stay or emigrate. A small local
population means that it may be difficult to find a mate (Kuusari et al. 1998) and that mate
choice is limited.
Moreover, a small population may indicate that the environment is
suboptimal and that potential fitness might be small.
If the animal has "evolutionary
experience" that indicates that there are better habitats elsewhere and that the potential gain in
fitness by emigrating outweighs the risk of emigration, it will emigrate.
The proposed
negative effect of population size per se on dispersal is related to negatively density-dependent
dispersal, which has been reported in mammals and birds (Wolff 1997; Lambin et al. in
press), insects (e.g., Diss et al. 1996; Kuusaari et al. 1998) and shrimps (Holmquist 1998).
Many species have to cope with life in smaller and smaller habitat fragments and
populations. It is therefore of vital importance to know how the emigration rate is affected by
population size, density, population dynamics (in animals with overlapping generations), sex
ratio (Lawrence 1987), patch size and patch boundaries. Also, migration can be influenced by
conditions beyond the patch and its boundary; e.g., Jonsen and Taylor (2000) found that the
propensity for damselflies to move away from streams was affected by landscape patterns
beyond the patch boundary itself, as well as individual experience or local adaptation. In
conservation biology, there has been a tendency to focus on lack of dispersal as a major threat
(e.g., Reed 1999).
However, although metapopulations depend on survival and lack of
migration may lead to inbreeding depression, it is important to acknowledge that we may
expect maladaptive emigration strategies when landscapes change. Evolution is expected to
shape the individual’s response to environmental cues so that it migrates if [probability of
surviving dispersal]x[expected fitness in new habitat patch] exceeds [expected fitness when
staying]. The optimal emigration strategy for the individual is often likely to be close to the
rate that maximises metapopulation viability (Hamilton and May 1977; but see Lemire and
Lessard 1997). However, when landscapes are fragmented, dispersal mortality is likely to
increase sharply, and the formerly optimal emigration strategy may become a death trap for
both the individual and for the metapopulation at large. Hill (1996), Thomas and Hanski
(1997), Kuusarii et al. (1998) and Kindvall (1999) have all suggested that emigration rate can
increase extinction rate of small patches significantly. Especially, Kuusari et al. (1998) have
noted that increased emigration rate and decreasing mating success not only contribute to the
risk of extinction separately, but they also act in concert, since a high emigration rate
9
Paper IV
decreases mating success. It is likely that low mating success also increases emigration rate,
and so the population may be caught in a vicious circle that may lead to extinction.
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Holmquist, J.G. (1998). Permeability of patch boundaries to benthic invertebrates: influences
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Ims, R. A. and Hjermann, D. Ø. (in press). Condition-dependent dispersal. In: J. Claubert
(ed.): The Evolution of Dispersal. Oxford University Press, Oxford.
Jonsen, I.D. and Taylor, P.D. (2000). Fine-scale movement behaviors of calopterygid
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Keuper, A., Kalmring, K., Schatral, A., Latimer, W., and Kaiser, W. (1986). Behavioural
adaptations of ground living bushcrickets to the properties of sound propagation in low
grassland. Oecologia 70: 414-422.
Kindvall, O. (1999). Dispersal in a metapopulation of the bush cricket, Metrioptera bicolor
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Kuussaari, M., Saccheri, I., Camara, M., and Hanski, I. (1998). Allee effect and population
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Stamps, J.A., Buechner, M., and Krishnan, V.V. (1987). The effects of edge permeability and
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12
Emigration rates and mechanisms
Table 1. Total number of emigration, rejection and immigration events from/to patches of different
size.
Patch size
Large
Medium
Small
Chi2-test
p-values 1
Emigration events
9
8
14
0.021
Rejection events
2
0
3
-
Immigration events
7
4
5
0.18
Number of patches
2
2
4
Total habitat area (m2)
160 (2 x 80 )
80 (2 x 40)
80 (4 x 20)
1
The null hypothesis was that the number of emigration events was proportional to total area or total
population size, and that the number of immigration events was proportional to the number of patches.
Numbers of rejection events were too low to be tested.
13
Paper IV
Table 2. The best logistic regression models explaining variation in the probability of migrating. No
two-way interactions were found to be significant (P < 0.05). The p-values shown are calculated from
type III deviance. N = 54, df = 49, deviance (-2LL) = 53.42.
Variable
Percent migrants
P
Patch size
large: 23 %, medium: 50 %, small: 71 %
0.0042
Sex
males: 61 %, females: 21 %
0.034
Activity
activity > median: 56 %, ≤ median: 30 % 1)
0.017
1)
In the model, activity was used as a continuous variable. I classified the individuals in two equalsized groups according to activity with the sole purpose of reporting the percentage of emigrants.
14
Emigration rates and mechanisms
Table 3. The net gain/loss of the populations in the four small patches during the first three days of the experiment, and how many of the resulting population that
emigrated during the next 15 days (day 4-19 of the experiment).
Patch ID
Net gain/loss day 1-3
Number emigrating day 4 - 19
B
+1
0 out of 5
D
-1
2 out of 3
E
-2
1 out of 2
H
0
0 out of 4
15
Paper IV
Figures
Fig. 1. Map of the experimental area. The experimental patches are arranged in a row between a
corn field in the west and another experimental area in the east. Between the patches was extremely
short-cut grass.
Fig. 2. Edge use compared between non-migrants and animals that migrated one or more times. Each
point represents an individual insect.
16
Emigration rates and mechanisms
Results
During the experiment, 31 emigration events were recorded, of which 16 ended as
immigration events, while 12 animals were predated between patches and 3 returned to the
emigration patch without encountering other patches during migration. Most emigrations
occured in two periods; during day 1-7 and from day 21 onwards (13 and 14 emigrations,
respectively); there were only 4 emigrations between these periods.
The number of
emigration events was not proportional to initial population size; emigration clearly increased
with decreasing patch size (Tab. 1). The null hypothesis that the number of immigration
events was proportional to the number of patches could not be rejected, although the numbers
were roughly proportional to the total area of patches of a given size class (Tab. 1). As a
result of these patterns, the average population density in the small patches declined to 50-60
% of the density of the large and medium patches during the experiment.
On the individual level, 23 (43 %) migrated one or several times (excluding 14
individuals that were predated during the first few days of the experiment). Males were much
more likely to migrate than females (Tab. 2). Before migration, migrating individuals tended
to display higher movement activity than non-migrating individuals (t52 = 2.17, P = 0.035); a
closer inspection of the data showed that this difference was found in large (t23 = 1.88, P =
0.015) but not in small and medium patches (P > 0.27).
On the individual level, 23 (43 %) migrated one or several times (excluding 14
Table 1. Total number of emigration, rejection and immigration events from/to patches of different
size.
Patch size
Chi2-test
p-values 1
Large
Medium
Small
Emigration events
9
8
14
0.021
Rejection events
2
0
3
-
Immigration events
7
4
5
0.18
Number of patches
2
2
4
160 (2 x 80 )
80 (2 x 40)
80 (4 x 20)
Total habitat area (m2)
1
The null hypothesis was that the number of emigration events was proportional to total area or total
population size, and that the number of immigration events was proportional to the number of patches.
Numbers of rejection events were too low to be tested.
17
Paper IV
individuals that were predated during the first few days of the experiment). Males were much
more likely to migrate than females (Tab. 2). Before migration, migrating individuals tended
to display higher movement activity than non-migrating individuals (t52 = 2.17, P = 0.035); a
closer inspection of the data showed that this difference was found in large (t23 = 1.88, P =
0.015) but not in small and medium patches (P > 0.27).
I found no tendency for emigrating individuals to use the edge zone more or less
than non-emigrating individuals, independent of patch size and sex (Fig. 2). Although the
numbers are too small for testing, the behaviour of the animals in the small patches may have
been influenced by the events of the first few days of the experiment. Two of the small
patches (patch D and F) had a net loss of individuals (due to both emigration and predation)
during the first three days. During the next two weeks, 60 % of the remaining individuals in
those patches emigrated, while no animals emigrated from the two other patches (tab. 3).
Overall edge use
1
0,8
Female emigrants
0,6
Male emigrants
Female stayers
0,4
Male stayers
0,2
0
0
small
1
medium
2
large
3
Patch size
Figure 2. Edge use compared between non-migrants and animals that migrated one or more times.
Each point represents an individual insect.
18