Download aggregation

Coexistence on a single
resource diverse studies on the aggregation theory of
species coexistence.
Andrew Davis
Institute of Low Temperature Science
Hokkaido University, Sapporo, Japan
aggregation and coexistence
this presentation:
1) describes the basic ideas of the aggregation theory
of species coexistence
2) indicates the two different questions that ecologists ask
3) summarizes the support for the aggregation theory in respect of
these questions
4) considers the mechanisms, or the lack of them, that allow
the conditions required for the theory's operation to be met
5) considers the interaction of the theory with other
coexistence mechanisms
6) outlines possible directions for future investigation
aggregation and coexistence
what is the aggregation theory
of coexistence ?
coexistence of species guild on a single resource is easier
1) if the competing stages of a species are intraspecifically aggregated
2) if the aggregations are interspecifically independent
3) if “patchiness“ is high
(thus violating the mean field approximation)
aggregation and coexistence
the two different questions
1) do these factors promote coexistence ?
2) how much do these factors promote coexistence
(compared to other mechanisms) ?
aggregation and coexistence
question 1 – the evidence
1) analytical models
(Ives & May 1985; Ives 1988a,b)
2) simulation models
(Shorrocks & Rosewell 1986; Heard & Remer 1997)
3) field studies
… Kouki & Hanski 1995; Johannessen & Loeschcke 1996;
Wertheim et al. 2000; Krijger & Sevenster 2001; Hartley &
Shorrocks 2002; Woodcock et al. 2002)
4) laboratory studies
(Kneidel 1985; Davis and others ...)
aggregation and coexistence
question 1 – the evidence
5) and a wealth of theoretical examination
(Ives 1988a; Rosewell et al., 1990; Shorrocks et al. 1990;
Sevenster 1996; Hartley 2001; Hartley & Shorrocks 2002)
aggregation and coexistence
thus these mechanisms
promote coexistence
we should therefore speak of the aggregation theory of coexistence
aggregation and coexistence
question 2 – the evidence
1) field studies in large guilds
(Shorrocks & Sevenster 1995; Toda et al. 1999; Wertheim
et al. 2000; Krijger 2000; Krijger & Sevenster 2001)
2) field studies in small guilds
(Davis unpublished)
3) rule testing exceptions
(Davis & Tribe 1996; Eisses & Santos 2000)
aggregation and coexistence
thus these mechanisms
strongly promote coexistence
at least within the conditions of the cited studies
aggregation and coexistence
examining the
influences
1) aggregation
2) independence
3) ephemerality
aggregation and coexistence
aggregation
1)
2)
3)
4)
different aggregations
composition of aggregation
measuring aggregation
mechanisms of aggregation
aggregation and coexistence
different aggregations
1) aggregation of females
the distribution of females per patch is aggregated
2) aggregation of egg clutches
the clutches laid by individual females are aggregated
3) aggregation of eggs
the distribution of eggs over patches is aggregated
aggregation and coexistence
aggregation of females
female aggregation is only necessary if both species lay clutches
at random and have the same distribution of eggs per clutch
(contra Green 1986; Ives 1988 etc)
The problem is superseded by Hartley’s (2001) formulation
where the effect of conspecific eggs is modelled by Lloyd’s
“mean demand”
1+m*2
1+ mean number of individuals in clutch
aggregation and coexistence
aggregation of clutches
aggregation of clutches across patches can be modelled by a
two-stage procedure (Iwao 1968; Iwao & Kuno 1971)
if clutches are distributed at random  = 1,
or for an aggregated distribution  =1+Jclutches.
M* =  + (M) a regression of mean crowding
against mean eggs per patch
aggregation and coexistence
aggregation of eggs
the final egg distribution is most important (Sevenster 1996) but
can be achieved in numerous ways
to accommodate these numerous ways, and the effects they might
have on invasibility characteristics, a general framework is needed
aggregation and coexistence
general framework
Hartley & Shorrocks (2002) derive the system equilibrium, single
species, patch specific, measure for individuals per patch
Mˆ  e  (Vˆ / Mˆ )
where V/M is the mean-variance ratio for the
generalised underlying distributions
(V/M = 1/J only if the generalised distributions fit the
negative binomial)
aggregation and coexistence
composition of aggregation
all of these “aggregations“ can contribute to the overal aggregation
of competing stages per patch required for coexistence (Hartley
2001)
the main factors contributing to coexistence are the egg
distribution of the resident and the clutch size of the invader
(Sevenster 1996)
The resident‘s egg distribution can be described by a large
number of generalised or compound distributions
depending on the underlying processes (Hartley 2001)
aggregation and coexistence
measurement of aggregation
1) there are many measures of aggregation
2) 2/ (v/m, or V/M for generalised distributions)
makes the fewest assumptions
3) J is a flexible function of 2/ that has become standard in
studies on the aggregation theory (Ives 1988a; = cA of Kuno
1968)
aggregation and coexistence
forms of J i.e. (M*/M)-1
J is often calculated as:
  xi ( xi  1)
 1   2  
J 
    
2

 
X


 
but this is a population measure only valid for
complete censuses or large samples
aggregation and coexistence
sample measure of J
the sample measure is
s2  x
J 
2
x
but the denominator here is a biased measure of 2
and leads to overestimation of J at small sample sizes
aggregation and coexistence
unbiased sample J
an unbiased sample measure can be achieved
ˆJ  s  x
2
2
x  ( s / n)
2
2
 s 2  x 
s
J    2 1  2
 x  nx
following Kuno (1991), or Anscombe (1950) and
Cassie (1962)
aggregation and coexistence



mechanisms of aggregation
1)
2)
3)
4)
patch differences
“social” effects
information constraint
“brownian motion”
aggregation and coexistence
patch differences
might act to arrest females or to alter clutch size
1) “locality“ differences (equals habitat separation)
2) “quality“ differences
temperature (Fogelman 1979), light (Wogaman & Seiger 1983),
colour (Volpe et al. 1967), surface texture (David 1970; Atkinson
1983) – micro-organism density, nutrients ?
3) predation, pathogen, parasitism risk
aggregation and coexistence
patch difference problems
there are specific problems
1) habitat separation exists but unless very fine scale cannot act
within guilds (by definition)
2) quality differences exist but do not appear to be important
within guilds. Drosophila aggregate strongly but not always on
patches of similar quality (Shorrocks, et al. pers. comm.)
3) D. subobscura does not adjust egg load to parasitism risk
(Hoffmeister & Rohlfs 2001)
and how would flies know ?
aggregation and coexistence
patch difference problems
and two general problems
1) any adaptive response to patch differences would lead to
concentration of females or eggs on favoured patches unless
countered at high densities (Allee effect). Neither Sevenster
(1992) nor Hoffmeister & Rohlfs (2001) found Allee effects.
2) to produce independent aggregation patch differences must be
randomly and independently distributed relative to each species
– but quality differences are highly co-correlated
aggregation and coexistence
“social“ effects
1) attraction to other (conspecific) flies
2) responses to eggs or larvae
3) responses to odour
aggregation and coexistence
attraction to other flies
1) there is no significant difference between the aggregation
produced by groups of flies and by single flies
2) simulations show that attraction to other flies does not evolve
under realistic conditions (Dytham pers. comm.)
3) dead bodies by themselves are not attractive
aggregation and coexistence
responses to eggs or larvae
1) Drosophila may preferentially lay on patches carrying eggs
(Atkinson 1983)
2) phorids may be attracted by conspecific eggs (or dissuaded by
allospecifics) (Woodcock et al. 2002)
3) active larvae in a patch tend to inhibit oviposition
aggregation and coexistence
... but little real evidence
40
frequency
30
20
10
0
0
5
10
15
20
25
30
40
more
eggs per grape
distributions of eggs on empty (blue) and egged
(yellow) grapes are not significantly different
aggregation and coexistence
responses to odour
large literature on “aggregation“ pheromones in Drosophila
suggesting that individuals may attract each other - but their role
in creating egg aggregations is unknown
their likely importance is undermined by the same arguements
used against the role of quality differences
in addition the candidate odours are not entirely species specific
and share components with decaying substrates
aggregation and coexistence
informational constraint
1) the cost of laying on a crowded patch may be less than the
cost of trying to find an empty patch
2) mortality risk during patch location may be higher than that
on patch
3) per capita predation risk low on densly occupied patches
4) oviposition “window“ is too short (Shorrocks & Bingley 1990)
5) patchy enviroments are information poor and provide no
learnable information –
particularly not to short lived insects
aggregation and coexistence
“brownian“ motion
1) random spacing is an inappropriate null model for small
organisms since their movement is better described by a
“brownian“ random walk
2) small organisms are therefore likely to show aggregate
distributions if they are aggregated to start with
3) the majority of insects show aggregated population
distributions (Taylor et al. 1978,1979)
4) non-aggregated distributions need more explaining
than aggregated ones
aggregation and coexistence
where does aggregation act ?
100
1)
2)
3)
log k
10
1
0
mel sim sub
mel sim sub
species - left=females right=eggs
aggregation and coexistence
females are unaggregated
eggs are aggregated
therefore aggregation arises
from clutch laying behaviour
and not from female visits
interspecific independence
1)
2)
3)
4)
5)
what is independence ?
aggregation mechanisms must allow independence
ensured by non-adaptive aggregation mechanisms
where to expect independence ?
degree of independence required
aggregation and coexistence
what is independence ?
negative
association
partitioning
models
nonassociation
aggregation model
aggregation and coexistence
positive
association
(proportional sampling)
thus independence is
1) the chance of meeting an allospecific is no different than
that expected by chance
2) not that there is “no overlap“
3) to be interpreted temporally as well as spatially
4) to be interpreted broadly for the aggregation theory
aggregation and coexistence
aggregation & independence
aggregation mechanisms must allow interspecific independence
mechanisms that lead to negative dependence are likely to be
partitioning models
mechanisms leading to positive dependence suggest proportional
sampling, or models involving undersaturation
aggregation and coexistence
ensured by non-adaptive
aggregation
if species aggregate for statisitical, non-adaptive, reasons then the
distribution of any two species will be independent
aggregation and coexistence
where to expect independence
1)
2)
3)
4)
distributions are not independent (Worthen & McGuire 1988 )
within relatively related taxa (Tuno 2001)
between closely related pairs (Nunney 1990)
in laboratory experiments D. hydei and D. melanogaster egg
distributions were unaffected by each other (Hodge 1999)
5) egg distributions were also independent in laboratory tests of
reciprocally combined D. melanogaster-D. simulans,
D. melanogaster-D. subobscura and
D. phalerata-D. subobscura
aggregation and coexistence
degree of independence

G xy 
c x   xy  xy Mˆ y
ex
1
Gxy < 1 < (1/ Gyx)
the degree of dependence xy (= Cxy + 1) may be quite wide
(Hartley & Shorrocks 2002)
especially if ex (patch carrying capacity) is large
aggregation and coexistence
ephemerality
1)
2)
3)
4)
the combination of patch size and patch longevity
effects on aggregation theory almost unexplored
guild size should decrease with decreasing ephemerality
guild size world wide does decrease with decreasing
ephemerality (Wortley 1995 pers. comm.)
aggregation and coexistence
ephemerality tested
simulations using Drosophila population data
as patchiness decreases (right hand plots) greater
aggregation is needed
N*=10to produce coexistence 50
(Dytham & Shorrocks 1992)
vertical axis =  for superior competitor
horizontal axis = “attraction probability” ~
aggregation
N*=10
aggregation and coexistence
50
and other mechanisms
1) predator mediated coexistence (e.g. Hardy & Gillis 1998)
should synergise with aggregation theory
2) latitudinal clines
changing guild size or changing guild number
3) niche, habitat, temporal sparation
increases negative association so synergistic
aggregation and coexistence
future trends
1) specific questions
2) broad lines of research
aggregation and coexistence
specific questions
1) what are real clutch sizes and how do they vary with density do large organisms have smaller and less variable clutches
2) what is the pattern of female visits
3) what are real competition coefficients or how can they be
estimated – are they related to size
4) what is the effect of temporal and phenological differences
aggregation and coexistence
broad lines of research
the limits of field data have been reached except for
1) examination of non-drosophilid guilds
2) guilds on less particulate resources – to detect limits of theory’s
operation
3) examination of small guilds
but most importantly, there is a need for experimental manipulation
of the crucial theoretical requirements
aggregation and coexistence
with thanks to Jack Lennon, Elli Groner, Leeds Drosophila ecology laboratory
project students, Bregje Wertheim and Jan Sevenster.
Especial thanks to Stephen Hartley for sending unpublished mss
and for recent discussions.
aggregation and coexistence