Models pretend that nature is simple, predictable and unchanging:

0.0

5.0

10.0

15.0

20.0

25.0

0 5 10 15 20 25 30

r = 0.3

r = 0.5

r = 0.8

Models pretend that nature is simple, predictable and unchanging:

The real world is messy.

Saether et al. 2002

Does this “messiness” matter to populations and communities?

Causes of variability

Patterns of variability

How does variability matter to populations?

(“messiness” = heterogeneity, variability)

Causes of variability

weather related: temperature, precipitation, light,…site related: soil properties, slope, vegetation cover,…biological: the number of competitors, predators,…

Environmental

Demographic stochasticityRandom variability in the growth rates of small populations arising chance events in individual survival and reproduction. Can lead to chance extinction in small populations.

Chaotic dynamicsRandom-like variability from strong and non-linear interactions between variables.

Patterns in space or timespatial variation: when sites differtemporal variation: when conditions change over time

Deterministic or random variabilitydeterministic: predictable variation that follows precise rulesrandom: has only statistical properties: mean, variance, etc.

Types of deterministic variabilityperiodic (in time or space)progressive change (spatial gradient, temporal trend)

Environmental variability

Patterns in time:

Month of the year1 2 3 4 5 6 7 8 9 101112

Tem

pera

ture

(C)

0

10

20

30

40 Average monthly temperature in Tucson

Precipitation in Moab, Utah

Year1930 1940 1950 1960 1970 1980 1990 2000

Prec

ipita

tion

(mm

)0

50

100

150

200

250

300WinterSummer

Patterns in time:

Patterns in time:

Patterns in space:

Patterns in space:

Demographic stochasticity:

High per-capita variability in growth rate due to random fluctuation in individual survivorship, and fecundity.

Small populations can go extinct, even though average growth rates are positive.

Excel Worksheets:

• Demographic Stochasticity

Exponential model with

b = 0.01 per yeard = 0.002 per year

Demographic stochasticity

0

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1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97

NN0 = 5

05

101520253035404550

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

N N0 = 20

A documented extirpation

Three-spined stickleback(Gasterosteus aculeatus)

The population disappeared from a pond in Wales in 2000

(Wootton 2010)

Chaotic fluctuations:

Some entirely deterministic processes can produce fluctuations indistinguishable from random fluctuations.

This was first discovered by the meteorologist Edward Lorenz who worked the prediction of weather patterns.

Edward N. Lorenz(1917-2008)

The Butterfly Effect

Whether or not a hurricane forms may depend on whether or not a butterfly flapped

its wings several weeks before

Chaotic dynamics have extreme sensitivity to initial conditions.

The Butterfly Effect

(Slingo and Palmer 2011)

The Discrete Logistic Model:

K

NNrNN tttt 1max1

Equilibrium defined as Nt+1 = Nt

N*,1 = 0N*,2 = K

Excel Worksheets:

• Discrete logistic equation

The existence of the various forms and changing patterns of variability drives evolution and creates and maintains

biodiversity.

A prairie

Six species of Solidago (golden rod) are found in old fields and prairies.

nemoralis missouriensis speciosa

canadensisgigantea graminifolia

Species usually occupy only a subset of an environments range of conditions.

species

Freq

uenc

y of

occ

urre

nce

Species are active only during a fraction of the total available time.

Hour of day

Oklahoma Prairie

Summary:

There are various sources and patterns of variability in nature producing spatial and temporal heterogeneity.

Forms of patterns: random, cyclic, or persistent trends (both in space and time).

A special case of variability is called: demographic stochasticity: the random fluctuations of small populations (which can have large and important consequences) .

Chaos is a special case of variability that is seemingly random but actually caused by deterministic processes.

Much of ecology is concerned with understanding species’ responses to variability in its various forms in evolutionary and ecological time.