Tricky Concepts

By Markus Horning *(Under Construction)*

These are concepts typically unfamiliar to the general public that would help them better understand telemetry and its application to wildlife management issues.

What is carrying capacity?

The term carrying capacity refers to the maximum size of a population that the environment can sustain indefinitely given availability of necessary resources such as food and habitat. Populations cannot exceed this maximum size for long periods of time, since a shortage of resources will reduce survival and/or birth rate. Most populations experience growth while below carrying capacity, and decline when above carrying capacity.

The carrying capacity may change over time, as resources may be affected by parameters other than the density of the population in question. For example, the food supply for a given population may change as competitors move into an area and consume more resources or if production of food is reduced in a changing climate. If the carrying capacity is reduced, a population may find itself above the carrying capacity, which should result in decreased survival or birth rates: the population will then decline until it has reached the lower carrying capacity.

In terms of common algebraic equations used in population dynamics, the term K is used to denote carrying capacity (see next).

What drives the growth or decline of populations?

In ecology, growth or decline of populations is typically characterized through the use of algebraic equations like Thomas Malthus’ exponential equation:

dN/dt = B – D + I – E

where N is the total number of individuals in a population, dN/dt is the rate at which the population grows or declines, B is the number of births, D is the number of deaths, I is the number of immigrated individuals and E is the number of emigrated individuals. The application of this equation is quite simple: if we disregard I and E for simplicity sake (let’s consider a closed system like a completely isolated island without immigration or emigration), then the rate of change (increase or decline) is driven by the number of births in relation to the number of deaths: if more animals are born than die, the population increases. If more die than are born, the population decreases.

Malthus’ equation (Thomas R. Malthus 1766 – 1834) can be changed to reflect *per capita* rates: (continuing with the simplification of disregarding I and E)

dN/dt = B – D = bN – dN = (b – d) N = rN

where b, d are the *per capita* birth and death rates, and

*r is the per capita rate of population change*.

However, recognizing that populations cannot sustain exponential growth indefinitely (see the discussion of carrying capacity above), Malthus’ equation was refined to the more commonly used Verhulst equation (Pierre-Francois Verhulst, 1804 – 1849):

dN/dt = rN (1– N/K)

where K is the carrying capacity (see above). Note that in the Verhulst equation, r is now the natural or ‘*intrinsic*’ rate of change (sometimes also called the maximum rate) that one would observe under ideal conditions. Then, as a population nears carrying capacity N approaches K, leading to the term (1 – N/K) approaching zero, and the rate of change also approaching zero.

r/K-selection, r-strategist, K-strategist:

You may have heard of any of these terms using r and K that stem from the Verhulst equation listed above. However, while these terms are still in use and have their place in population ecology, the concept of r/K selection theory is dated and has been replaced by more modern concepts.

An r-selected species or r-strategist is a species that has very high intrinsic reproductive rates, often combined with low levels of parental investment. Examples include many insect and fish species that produce very large amounts of fertilized eggs and young, the vast majority of which will never reach reproductive age. In r-selected species, evolution favors productivity through natural selection.

A K-selected species or K-strategist typically has low intrinsic reproductive rates often combined with high levels of parental investment, with a large percentage of offspring reaching sexual maturity and reproductive age. Examples include most birds and mammals. In K-selected species, evolution favors efficient energy conversion and investment into fewer offspring.

r/K (r-over-K) selection theory addresses the trade-off between quality and quantity of offspring, when parents have a finite amount of energy to invest in their offspring. Selective pressures on specific sets of traits (characteristics) that affect investment of energy into offspring were hypothesized to drive evolution towards one of two types of strategies, r- or K-strategy. The theory suggests density dependent selection as a mechanistic, causative link between the environment and optimally adjusted traits. For example, unstable or unpredictable environments were thought to favor r-strategists, whereas stable or predictable environments would favor K-strategists. Certain traits were associated with these strategies, such as large body size and long life (K) or small size and short life (r). However, no studies to date have been able to link r- or K-associated traits with density dependent selective forces. Instead, modern ecologists recognize a continuous and variable spectrum of strategies, often subject to changing and highly variable selective pressures, or as populations grow or decline. Even within species one can find a mix of r- or K-associated traits. For example, sea turtles or sturgeon are large, long-lived animals that produce a large number of eggs requiring no parental care. Within marine mammals such traits may also differ between the sexes with males having more r-type traits (few males produce many offspring without contributing to their care) and females more K-type traits (many females produce only one offspring each into which they pour almost all of their maternal energy in the form of milk during lactation). Modern concepts are based on other potential mechanisms that link the environment – including population density – with optimally adjusted individual characteristics. Many of these concepts focus on age-specific mortality as a key mechanistic link between life histories and the environment.

**What happens when one protected species eats another… the sea lion/salmon issue?**