On the analysis of populations in time and space:Forest Hymenoptera

A fresh beech forest in spring

and later in the year

Basic population parameters: Species densities (m-2)Species Study year 1981 1982 1983 1984 1985 1986 1987Acoelius erythronotus 1 2 1 2 2 5 0.5Anacharis eucharioides 1 3 1 0.5 0.5 3 2Aphelopus melaleucus 3 5 4 15 1 2 1Aspilota GW2 4 4 7 0.5 1 27 18Basalys pedisequa 4 0.5 1 38 10 9 4Charitopes gastricus 2 7 3 1 0.1 20 6Chrysocharis prodice 6 5 1 1 3 9 1Cleruchus spec. 2 13 1 9 18 50 10Eretmocerus mundus 0 4 99 9 0.5 0.5 0.1Eustochus atripennis 3 4 5 36 1 9 2Exallonyx quadriceps 1 2 0.5 0.1 0.5 5 2Exallonyx subserratus 0.1 0.5 1 0.1 1 1 0.5Gastrancistrus walkeri 2 8 7 39 0.5 7 26Glauraspidia microptera 4 5 4 5 2 3 1Ismarus dorsiger 0.1 0.1 5 5 2 0.5 0.5Lagynodes pallidus 1 1 0.1 2 7 1 1Litus cynipseus 6 40 2 18 0.5 22 24Mesopolobus GW1 0.1 0.1 0.1 6 64 3 0.5Phygadeuon ursini 1 2 12 0.5 0.1 5 72Synopeas GW1 1 1 47 658 77 0 0.5Tetrastichus ?brachycerus 7 25 17 83 0.5 6 59Tetrastichus fageti 5 3 3 12 10 3 1Tetrastichus luteus 0.5 0.5 2 19 12 8 1Trichogramma embryophagum 0.5 8 0.1 0.5 0.1 4 0.5Trichopria aequata 1 1 6 1 0.5 1 1Trichopria evanescens 0.5 0.5 1 0.1 0.1 9 0.5

Familie Number of species

Total catch

Average density (m-2)

Anacharitidae 4 260 1.8Andrenidae 1 1 < 0.1Aphelinidae 4 4438 30.8Apidae 7 - -Braconidae 123 4075 28.3Ceraphronidae 30 718 5Charipidae 5 84 0.6Cynipidae 11 380 2.6Diapriidae 69 1743 12.1Dryinidae 4 776 5.4Embolemidae 1 1 < 0.1Encyrtidae 14 384 2.7Eucoilidae 5 645 4.5Eulophidae 55 6293 43.7Eupelmidae 1 1 < 0.1Eurytomidae 1 8 0.1Figitidae 1 37 0.3Formicidae 9 - -Heloridae 1 3 < 0.1Ichneumonidae 179 3132 21.8

Familie Number of species

Total catch

Average density (m-2)

Megachilidae 1 1 < 0.1Megaspilidae 16 509 3.5Mymaridae 26 4205 29.2Ormyridae 1 1 < 0.1Platygasteridae 34 5049 35.1Proctotrupidae 15 741 5.1Pteromalidae 56 2233 15.5Scelionidae 13 251 1.7Sphecidae 1 1 < 0.1Tenthredinidae 20 48 0.3Torymidae 6 74 0.5Trichogrammatidae 2 65 0.5Vespidae 4 - -Sum 720 36157 251.1

Basic population parameters: Species richness and densities

Hymenoptera is the most species rich taxon in temperate terrestrial ecological

systems.

The question of coexistencePopulation versus community ecology

The magnitude of population fluctuations in forest Hymenoptera

Species Study year 1981 1982 1983 1984 1985 1986 1987Acoelius erythronotus 1 2 1 2 2 5 0.5Anacharis eucharioides 1 3 1 0.5 0.5 3 2Aphelopus melaleucus 3 5 4 15 1 2 1Aspilota GW2 4 4 7 0.5 1 27 18Basalys pedisequa 4 0.5 1 38 10 9 4Charitopes gastricus 2 7 3 1 0.1 20 6

Species R 1982 1983 1984 1985 1986 1987

Acoelius erythronotus 2.0 0.5 2.0 1.0 2.5 0.1Anacharis eucharioides 3.0 0.3 0.5 1.0 6.0 0.7Aphelopus melaleucus 1.7 0.8 3.8 0.1 2.0 0.5Aspilota GW2 1.0 1.8 0.1 2.0 27.0 0.7Basalys pedisequa 0.1 2.0 38.0 0.3 0.9 0.4Charitopes gastricus 3.5 0.4 0.3 0.1 200.0 0.3

N(1982)/N(1981)

We calculate population increase and decrease R from the observed species abundances.

𝑁𝑡=𝑅𝑁𝑡− 1

Species R 1982 1983 1984 1985 1986 1987

Acoelius erythronotus 2.0 0.5 2.0 1.0 2.5 0.1Anacharis eucharioides 3.0 0.3 0.5 1.0 6.0 0.7Aphelopus melaleucus 1.7 0.8 3.8 0.1 2.0 0.5Aspilota GW2 1.0 1.8 0.1 2.0 27.0 0.7Basalys pedisequa 0.1 2.0 38.0 0.3 0.9 0.4Charitopes gastricus 3.5 0.4 0.3 0.1 200.0 0.3

The net reproductive rateR s2(R) r

1.51 0.76 0.411.92 4.13 0.651.46 1.48 0.385.41 93.60 1.696.96 193.14 1.94

34.11 5505.26 3.53

The net rate of population growth was independent of average density.

Most species increased in density.

The net rate of population growth increased with variability in density.

Is this correct?

Średnia()N(1982)/N(1981)

The values are too precise

R r Dmean s2(Dmean)

0.89 -0.12 1.5 1.891.12 0.12 1.2 1.030.83 -0.18 2.9 20.531.28 0.25 4.3 84.991.00 0.00 4.3 146.641.20 0.18 2.4 40.09

R s2(R) r

1.51 0.76 0.411.92 4.13 0.651.46 1.48 0.385.41 93.60 1.696.96 193.14 1.94

34.11 5505.26 3.53

Średnia.geometriczna()

Średnia.geometriczna()

R was independent of average density and density fluctuations.

Net reproductive rates scattered equally around the equilibrium value of R = 1.

CV

0.8960.8191.5532.1442.8142.603

Species R 1982 1983 1984 1985 1986 1987

Acoelius erythronotus 2.0 2.0 2.5 Anacharis eucharioides 3.0 6.0 Aphelopus melaleucus 1.7 3.8 2.0 Aspilota GW2 1.8 2.0 27.0 Basalys pedisequa 2.0 38.0 Charitopes gastricus 3.5 200.0

>1 The theoretical upper boundary of R denotes the average number of eggs layed by each female.

The effective maximum net rate of population growth

High maximum reproductive rates were linked to high absolute fluctuations according to Taylor’s power law.

max R s2(R) r Dmean s2(Dmean)

2.50 0.06 0.77 1.5 1.896.00 2.25 1.45 1.2 1.033.75 0.83 0.84 2.9 20.53

27.00 140.29 1.52 4.3 84.9938.00 324.00 2.17 4.3 146.64

200.00 9653.06 3.28 2.4 40.09

Maximum Hymenoptera reproduction rates were not significantly linked to averge species densities

Maximum Hymenoptera reproduction rates increased with the observed variability in density.The probability of this relation was P(H1) > 0.95.(Significance of the regression is P(H0) < 0.05)

Species with larger fluctuations in abundance had higher capacities for recruitment.

Density regulationSpecies Study year

1981 1982 1983 1984 1985 1986 1987Acoelius erythronotus 1 2 1 2 2 5 0.5Anacharis eucharioides 1 3 1 0.5 0.5 3 2

Species Study year1981 1982 1983 1984 1985 1986 1987

Acoelius erythronotus 1 -1 1 0 3 -4.5 Anacharis eucharioides 2 -2 -0.5 0 2.5 -1

∆𝑁𝑡

∆ 𝑡 =𝑟 𝑁𝑡

Time

N

K

∆𝑁 𝑡>0

∆𝑁 𝑡<0 ∆𝑁 𝑡<0

If a population is regulted in a density dependent manner the correlation between DNt and Nt should be negative.

Are populations really density

dependent regulated?

Bulmer’s (1975) test for density dependence

𝑅=∑1

𝑇

( 𝑙𝑛𝑁𝑡− 𝑙𝑛𝑁 )2

∑1

𝑇− 1

(𝑙𝑛𝑁𝑡+ 1−𝑙𝑛𝑁 𝑡 )2<¿

Time

N

K

)>>

)>>

In random walk time series we expect negative correlations of DN and N.

Trichogramma embryophagum

Density regulation

Only one of the 26 parasitoid species passed the test.

At least 20 generations are needed to detect density dependence

𝐽=𝜎 2

𝜇2− 1𝜇+1

J >> 1: chaotic density fluctuationsJ = 1: Poisson random fluctuations<J << 1: densities at equilibrium

The variance - mean ration in the form of the Lloyd index

Variability in population size of forest Hymenoptera was positively linked to geometric mean density.

Nearly all Lloyd values are far above 1.0. Populations are not regulated.

Are populations in equilibrium?

The band model of density dependence

Density dependence

Density dependence

Density independence

N

K

Nmin

Nmax

Random walk

Most species fluctuate randomly with certain upper and lower boundaries of population density

At lower density, the Allee effect might cause a positive density dependence, that means populations have even less ability for recruitment.

Factors that cause density dependence: Factors that cause density independence:

• predator – prey cycles• cyclic weather conditions (el Nino, el Nina, NAO)• density dependent mortality and reproduction

• unpredictable weather conditions• unstable habitats• high degrees of dispersal

t

Intrinsic rates of increase

Species max R R R0 s2(R) r Dmean s2(Dmean) CV

Acoelius erythronotus 2.50 0.89 0.56 0.76 -0.12 1.5 1.89 0.896Anacharis eucharioides 6.00 1.12 1.78 4.13 0.12 1.2 1.03 0.819Aphelopus melaleucus 3.75 0.83 0.40 1.48 -0.18 2.9 20.53 1.553Aspilota GW2 27.00 1.28 3.50 93.60 0.25 4.3 84.99 2.144Basalys pedisequa 38.00 1.00 1.00 193.14 0.00 4.3 146.64 2.814Charitopes gastricus 200.00 1.20 2.50 5505.26 0.18 2.4 40.09 2.603

Phygadeuon ursini

Parasitoid of Cheilosia fasciata on Allium

ursinum

Outbreak species

Population outbreaks

Four of 26 abundant Hymenopteran species increased abundances duig two years by a factor of more than 1000.

Circles mark years of zero abundance.

After the outbreak populations collapsed

On the probability of extinction

𝑇=2 ln (𝑁1)𝜎 2 (𝑟 ) ( ln (𝐾 )−

ln (𝑁 1)2 )

In the case of random walks extinction probabilities are given by Annual extinction probability

𝑃=1−𝑒− 1𝑇𝐾=𝑁𝑚𝑎𝑥

Species 4 ha study area r s2(r) Dmean s2(Dmean) Lloyd T P(annual)1982 1983 1984 1985 1986 1987

Acoelius erythronotus 40000 80000 40000 80000 80000 200000 -0.12 1.25 1.5 1.89 1.150 117.1 0.01Anacharis eucharioides 40000 120000 40000 20000 20000 120000 0.12 1.03 1.2 1.03 0.864 131.4 0.01Aphelopus melaleucus 120000 200000 160000 600000 40000 80000 -0.18 1.69 2.9 20.53 3.069 103.1 0.01Aspilota GW2 160000 160000 280000 20000 40000 1080000 0.25 3.07 4.3 84.99 5.362 61.7 0.02Basalys pedisequa 160000 20000 40000 1520000 400000 360000 0.00 3.41 4.3 146.64 8.684 57.9 0.02Charitopes gastricus 80000 280000 120000 40000 4000 800000 0.18 6.35 2.4 40.09 7.363 28.2 0.03