POPULATION DYNAMICSBrett Edmonds

Halesworth U3A Science Study Group

What is Population Dynamics?

• Study of the processes by which the populations of living creatures change over time

Historical Background to Population Dynamics Theory

• Thomas Malthus (cleric & political economist) generally regarded as first person to attempt to scientifically understand and quantify population dynamics.

• Pierre Verhulst introduced homeostasis to the Malthusian equation i.e. the point at which growth stops and the population becomes steady

• Benjamin Gompertz (mathematician and actuary) developed mortality model

Mathematical Interlude

• A quick overview of the mathematical models derived by these gentlemen

Malthusian Exponential Growth Model

• P(t) = P0 ert where t is time and r the per capita growth rate

• r>0 population grows

• r=0 population static

• r<0 population shrinks

Malthusian Growth Curve

Verhulst Logistic Population Growth Model

• P(t) = K.P0.ert/(K+P0(ert-1)

Where:

t is time

P0 the population at time 0

K is the homeostatic population

r is the per capita growth rate

Logistic Growth Curve

Gompertz Mortality Model

• P(t) = P(0)exp[-a(exp(ct)-1]

Gompertz Function – Varying factor a (homeostatic population)

Gompertz Function – Varying factor b(P0)

Gompertz Function – Varying factor c (growth rate)

Factors Determining Population Change

• What determines the homeostatic population (Ps) and per capita (r) growth rate of a given species?

• Both determined by Reproduction Rate (Rr) vs Mortality Rate (Rm)

• Ps when Rr = Rm

• r = Rr – Rm

• Unfortunately neither Rr or Rm are constant and both are subject to very complex influences

Factors Affecting Reproduction Rate

Successful reproduction depends on:

• Reproductive strategy

• Availability of food for juveniles

• Availability of ‘domestic’ space

• Predation of juveniles

• Social interaction

Reproductive strategy

V high offspring numbers, no parental support, v high infant mortality (typically >99%) e.g. most plants, many invertebrates, many fish species

Moderate offspring numbers, limited parental support, high infant mortality (typically 80 – 95%) eg. small vertebrates such as rodents, small birds etc.

Low to single offspring, high parental support, low infant mortality (typically 25 - 50%) eg large mammals such as elephants, primates etc.

Food Availability for JuvenilesReproductive cycles usually tuned to match resource supply cycles e.g.:

Large herbivores in Africa & N. Europe time birth cycles with migrations that exploit best grazing resources

Blue Tits time egg laying & hatching to coincide with the emergence of caterpillars in late spring which provide the best nutritional value

Domestic Space

Finding the right place to rear young is critical to reproductive success

Derelict buildings for nesting barn owls

Bee hives help maintain a high bee population density

Purple Martin in North America which nests almost exclusively in man made nest boxes

Predation of Juveniles

Predation prevention strategies may include:

• High levels of parental protection

• Placing offspring in hard to reach locations

• Making offspring inconspicuous

• Making offspring unpalatable or downright dangerous to eat

• Creating a super abundance of offspring

Social Interaction

The Passenger Pigeon

• In early 19th century the most populous bird on the planet

• Extinct by 1914

• Required very large flocks to breed

Factors Affecting Mortality Rate

• Species life span

• Environmental conditions (temperature, rainfall, pollution etc.)

• Predation of adults

• Disease

• Availability of resources (food, water, light, space, etc.)

Life Span

Life Span

Hours Centuries

Advantage of long life spansEnables multiple reproduction cycles

Disadvantage of long life span

• Competition with offspring

• Dispersal of juveniles from natal site

Environmental Conditions

• Most species optimised for a fairly narrow band of environmental conditions

• Conditions generally change slowly cf. human life span

• Fossil record shows some species have been able to compensate for environmental changes by moving

• Other species such as mammoth seem to be unable to successfully relocate

Predation

• Equilibrium between predator and prey species

• Equilibrium may be :

static e.g. lions vs herbivores on African grasslands

cyclic e.g. lemmings vs snowy owls on arctic tundra

Disease

• Like predation

• A balance between infection and infected and for much the same reason i.e. any disease vector requires its host to survive

Resource Availability

Commonly exploited resources are:

• Food

• Water

• Light

• Domestic space

• Heat

Factors Affecting Resource Availability

• Resource pool size

• Resource renewal rate

• Resource demand

• Resource competition

Resource Availability – Food 1Haast’s Eagle• Largest bird of prey known to have existed

• Weight of 16kg cf. 6.5kg Golden Eagle

• Hunted Moas – giant flightless birds up to 3m tall

• Extinct by 14th century because Maoris ate all the Moas

Resource Availability – Food 2House Sparrow• Principally a seed eater

• Not particularly common in countryside

• Numbers exploded in towns & cities because availability of seed in horse feed

• When horses ceased to be used as transport numbers collapsed

• Ceased to breed in London

• Rice fields of southern Spain hold v large flocks

Resource Availability – Food 3Kittiwakes

• 1960’s to 1980’s population increase & range expansion southwards

• 1980’s to present day population decrease & range contraction on west coast

• Sand eels important part of Kittiwake diet and decline probably linked to intensive sand eel fishing

• But……

Kittiwake Abundance Change• Down on west coast

• About even (up and down) on east oast

• Mainly up in Ireland

• Does not correspond to areas where most intensive sand eel fishing occurs

Resource Availability – Water

Spadefoot Toad

• Lives in N. American desserts

• Digs hole and waits for rain –for up to 2 years

• Within 48 hours of rain emerges, mates & lays eggs

• Tadpoles hatch in 24 hours

• Tadpoles develop in adults within a week

• Back in the hole for another year or two

Resource Availability – Light

• ‘All flesh is grass’ - ultimately (nearly) all species depend on plant or algae growth and therefore on light

• Annual light intensity variations determine plant growth periods & rates

• Restricted period of high plant growth rates places upper limit on available food for herbivores

• Limit on number of herbivores limits the food available for carnivores

• Cataclysmic events such as Mount Tambora eruption (1815) diminished insolation around the world leading to global famine

Variation in Solar Radiation

Resource Availability – Domestic Space

It’s nice to be with your mates but !

Resource Availability – Warmth

• Species restricted to a temperature band that suits them and their lifestyles best

• What is too hot for some is too cold for others

• Species compensate by migration either longitudinally or vertically

• Global warming/cooling has shifted temperature bands many times over millennia

• Species have either moved with the temperature bands or adapted to changed environment

Resource Availability – Warmth 1 - Cetti’s Warbler

• Prior to the 60’s a Mediterranean bird

• 1st recorded in UK 1961

• 1st bred in UK 1973 (Dorset)

• Now widespread resident across southern, eastern and midland counties of England

• Northward march continues

• Becoming less common in Greece!

Resource Availability – Warmth 2 - Ptarmigan

• Sedentary species which breeds across arctic and subarctic Eurasia and N America

• During last ice age much more widespread across Europe

• Only found on Scottish highland mountains in UK

• Vertical migration to tops of highest peaks in summer

• Increase in average temperatures likely to drive bird from UK

Resource Availability – Competition with other Species