∆N/∆T = r N

∆N = change in number, ∆ T = change in time, r = per head (maximum potential growth rate,

Example: N = 50, r =0.25, the change in unit per time
∆N/∆T = r N, ∆N/∆T= 0.25 (50) = 12.5, NT+ 1 = N T + ∆ N/∆ T = 50 + 12.5 = 62.5
∆N +1/∆T = 0.25 (62.5) = 15.5, NT + 2 = NT+ 1 + ∆NT +1/∆T, = 62.5 + 15.5 = 78 = NT + 2.

Carrying Capacity: The number of animals that can support within a given area. Population ecologists, use term “K” to denote the upper limit beyond which no further population increase can be sustained by the habitat. Wildlife managers rely on more practical criteria that are easier to measure in the field. In population below carrying capacity, the greater amounts of food cover and space per animal leaves animal generally heavier in better nutritional conditions and with fewer signs of parasites and diseases than the animals from population at carrying capacity.

∆N/∆T = r N (K-N)/K , r= 0.25, K = 1000 N = 990
=0.25(990) (1000- 990)/1000= 247.5 (0.01) =2.5
NT +1 = NT + ∆N/∆T = 990+2.5 =992.5.
Instead of the population growing by 247, it grows only by 2.5, owing to limitation placed upon by the environment.

Growth of a population with unlimited food and space

Carrying Capacity: Growth of population with a maximum number of individuals that can sustain by environment.

Carrying capacity for any given species varies a great deal between different habits. These variations are often used as indications of habitat quality. Habitat conditions are always changing to some extent altering carrying capacity. Habitats are disturbed by fires, storms and human activities. Carrying capacity also changes between seasons. Low in colder and drier seasons and higher in hot rainy season.

According to reproductive pattern, animals can be classified into two groups:

• R- selected species (High intrinsic rate of increase) – Many small species. Little nor not parental care and protection of offspring. Early reproductive age. Most offspring die before reaching reproductive age. Small adult. High population growth. Population size fluctuates widely above and below carrying capacity (K). Low ability to compete. Early succession species.
• K- Selected species – Fewer, larger offspring. High parental care and protection of offspring. Later reproductive. Lager adults. Lower population growth. Specialist niche. High ability to compete. Late succession species.

Main consideration in cattle – food production by given area. For wildlife we have to take into account water, Cover and food, etc.