Patterns in time Population dynamics (1964 to 1983) of the red squirrel in 11 provinces of Finland (Ranta et al. 1997) Lynx fur in Canada Voles in Norway Mean abundance Upper limit (carrying capacity) Lower limit (extinction treshold) Elton and Nicholson (1942 )

Taylor’s power law Assume an assemblage of species, which have different mean abundances and fluctuate at random but proportional to their abundance. The relationship between variance and mean follows a power function of the form Going Excel Taylor’s power law; proportional rescaling

Taylor’s power law Variance category Percentage Taylor’s power law in aphids (red), moths (green) and birds (blue). In all three groups the exponent z of the relation s 2 = a m z peakes around 2. Data from Taylor et al. (1980).

Major results from this database are that The variance – mean relationship of most populations follows Taylors power law z = 2 is equivalent to a random walk Z =<< 2 is required for population regulation The majority of species has 1.5 < z < 2.5 Long term studies of population variability Most populations, in particular invertebrate populations are not regulated! They are not in equilibrium

Ecological implications Temporal variability is a random walk in time Abundances are not regulated Extinctions are frequent Temporal species turnover is high Temporal variability is intermediate Abundances are or are not regulated Extinctions are less frequent Temporal species turnover is low Temporal variability is low Abundances are often regulated Extinctions are rare Temporal species turnover is very low

Mean time to extinctionExtinction probability Under the assumption of Taylor’s power law (a simple random walk in time without density dependent population regulation and lower extinction boundary) we can calculate the frequency of local extinction Abundances (ind.m -2 ) Year Eustochus atripennis Exallonyx ater K103 Abundances (ind.ha -2 ) Eustochus atripennis Exallonyx ater Reproduction rate ln r Variance TETE K

Number if individuals Normalized number of extinctions y = 0.96x R 2 = ln (number of nesting pairs) ln (extinction time) How many individuals do populations need to survive (lower extinction boundary)? Orb web spiders on the Bahama islands (Schoener 1983) Birds on small islands off the British coast (Pimm 1991) Parasitic Hymenoptera (Hassell et al. 1991)

The species – time relationship Local species area and species time relationships in a temperate Hymenoptera community studied over a period of eight years. S = S 0 A z S = S 0 t  S = S 0 A z t  The accumulation of species richness in space and time follws a power function model S = (73.0 ± 1.7)A (0.41 ± 0.01) t (0.094 ± 0.01) The mean extinction probability per year is about 9% Photo E. G. Vallery Coeloides pissodis (Braconidae)

Population dynamics (1964 to 1983) of the red squirrel in 11 provinces of Finland The Moran effect Regional sychronization of local abundances due to correlated environmental effects Patrick A.P. Moran Moran assumed: 1. Linear density dependence 2. Density dynamics are identical 3. Stochastic effects  are correlated

Acres Defoliated Maine Acres Defoliated Acres Defoliated Vermont Acres Defoliated New Hampshire Massachusetts Year Defoliation by gypsy moths in New England states Lymantria dispar Data from Williams and Liebhold (1995)

Species turnover rates differ between groups of animals and plants Larger animal species have lower turnover rates Despite high turnover rates total species numbers of habitats remain largely constant. This constancy holds for ecological, historical and evolutionary times 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E-041.E-031.E-021.E-011.E+001.E+011.E+021.E+03 Generation time Turnover rate (%/yr) Protozoa Sessile marine organisms Arthropoda Birds Lizards Vascular plants Body weight Year Number of species Year Number of species Desert rodents Birds Plants Species turnover rates (Brown et al. 2001)

Speciation rates, latitudinal gradients, and macroecology What causes the latitudinal gradient in species diversity? Temperature How does temperature influences species richness? Speciation Extinction Metabolic theory predicts that generation time t should scale to body weight and temperature to The theory predicts further that mutation rate  should scale to body weight and temperature to How does mean generation time decreases if we increase mean environmental temperature from 5º to 30 º? Mutation rates are predicted to increase by the same factor Evolutionary speed can be seen as the product of mutation rates and generation turnover (1/t). Still unclear is how temperature influences extinction rates.

Today’s reading Minimum viable population size: Long term ecological research: Kinetic effects of temperature on speciation: Paleobiology: