Aggregation and coexistence Coexistence on a single resource - diverse studies on the aggregation theory of species coexistence. Andrew Davis Institute

aggregation and coexistence

Coexistence on a single resource -diverse studies on the aggregation theory of species coexistence.

Andrew Davis

Institute of Low Temperature ScienceHokkaido University, Sapporo, Japan


this presentation:

1) describes the basic ideas of the aggregation theory of species coexistence

2) indicates the two different questions that ecologists ask3) summarizes the support for the aggregation theory in respect of

these questions4) considers the mechanisms, or the lack of them, that allow

the conditions required for the theory's operation to be met5) considers the interaction of the theory with other

coexistence mechanisms 6) outlines possible directions for future investigation


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 aggregated2) if the aggregations are interspecifically independent3) if “patchiness“ is high

(thus violating the mean field approximation)


the two different questions

1) do these factors promote coexistence ?

2) how much do these factors promote coexistence (compared to other mechanisms) ?


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 ...)

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)



we should therefore speak of the aggregation theory of coexistence

thus these mechanisms promote coexistence



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(Davis unpublished)3) rule testing exceptions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)


at least within the conditions of the cited studies

thus these mechanisms strongly promote coexistence


examining the influences1) aggregation 2) independence3) ephemerality


aggregation

1) different aggregations 2) composition of aggregation3) measuring aggregation4) mechanisms of aggregation


different aggregations

1) aggregation of females the distribution of females per patch is aggregated

2) aggregation of egg clutchesthe clutches laid by individual females are aggregated

3) aggregation of eggsthe distribution of eggs over patches is aggregated


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 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 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


general framework

Hartley & Shorrocks (2002) derive the system equilibrium, single species, patch specific, measure for individuals per patch

)ˆ/ˆ(ˆ MVeM 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)


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)


measurement of aggregation

1) there are many measures of aggregation 2) 2/ (v/m, or V/M for generalised distributions)

makes the fewest assumptions3) J is a flexible function of 2/ that has become standard in

studies on the aggregation theory (Ives 1988a; = cA of Kuno

1968)


forms of J i.e. (M*/M)-1

J is often calculated as:

2

21)1(

X

xxJ ii

but this is a population measure only valid for complete censuses or large samples


sample measure of J

the sample measure is

but the denominator here is a biased measure of 2 and leads to overestimation of J at small sample sizes

2

2

x

xsJ


unbiased sample J

an unbiased sample measure can be achieved

following Kuno (1991), or Anscombe (1950) and Cassie (1962)

)/(ˆ

22

2

nsxxs

J

2

2

2

2

1xn

s

x

xsJ


mechanisms of aggregation

1) patch differences2) “social” effects 3) information constraint4) “brownian motion”


patch differences

might act to arrest females or to alter clutch size1) “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


patch difference problems

there are specific problems1) 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 ?


patch difference problems

and two general problems1) 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


“social“ effects

1) attraction to other (conspecific) flies 2) responses to eggs or larvae3) responses to odour


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


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


... but little real evidence

distributions of eggs on empty (blue) and egged (yellow) grapes are not significantly different

0

10

20

30

40

0 5 10 15 20 25 30 40 more

eggs per grape

freq

uenc

y


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 unknowntheir likely importance is undermined by the same arguements used against the role of quality differencesin addition the candidate odours are not entirely species specific and share components with decaying substrates


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 patches4) 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


“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


where does aggregation act ?

1) females are unaggregated2) eggs are aggregated3) therefore aggregation arises

from clutch laying behaviour and not from female visits

0

1

10

100

mel sim sub mel sim sub

species - left=females right=eggs

log

k


interspecific independence

1) what is independence ?2) aggregation mechanisms must allow independence 3) ensured by non-adaptive aggregation mechanisms 4) where to expect independence ?5) degree of independence required


what is independence ?negative association

non-association

positive association

partitioning models

aggregation model (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 spatially4) to be interpreted broadly for the aggregation theory


aggregation & independence

aggregation mechanisms must allow interspecific independencemechanisms that lead to negative dependence are likely to be partitioning models mechanisms leading to positive dependence suggest proportional sampling, or models involving undersaturation


ensured by non-adaptive aggregation

if species aggregate for statisitical, non-adaptive, reasons then the distribution of any two species will be independent


where to expect independence

1) distributions are not independent (Worthen & McGuire 1988 )2) within relatively related taxa (Tuno 2001)3) between closely related pairs (Nunney 1990)4) 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


degree of independence

the degree of dependence xy (= Cxy + 1) may be quite wide

(Hartley & Shorrocks 2002)

especially if ex (patch carrying capacity) is large

1ˆ

x

yxyxyx

xy e

McG

Gxy < 1 < (1/ Gyx)


ephemerality

1) the combination of patch size and patch longevity2) effects on aggregation theory almost unexplored3) guild size should decrease with decreasing ephemerality4) guild size world wide does decrease with decreasing

ephemerality (Wortley 1995 pers. comm.)


simulations using Drosophila population data as patchiness decreases (right hand plots) greater aggregation is needed to produce coexistence (Dytham & Shorrocks 1992)

vertical axis = for superior competitorhorizontal axis = “attraction probability” ~ aggregation

ephemerality tested

N*=10

N*=10

50

50


and other mechanisms

1) predator mediated coexistence (e.g. Hardy & Gillis 1998) should synergise with aggregation theory

2) latitudinal clineschanging guild size or changing guild number

3) niche, habitat, temporal sparation increases negative association so synergistic


future trends

1) specific questions2) broad lines of research


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 visits3) 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

specific questions


the limits of field data have been reached except for

1) examination of non-drosophilid guilds2) 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

broad lines of research


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.

with thanks to -

Documents

Aggregation and coexistence Coexistence on a single resource - diverse studies on the aggregation theory of species coexistence. Andrew Davis Institute