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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Toda et al. 1999; Wertheim et al. 2000; Krijger 2000; Krijger & Sevenster 2001) 2) field studies in small guilds (Davis unpublished) 3) rule testing exceptions (Davis & Tribe 1996; Eisses & Santos 2000) aggregation and coexistence thus these mechanisms strongly promote coexistence at least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