Pest control in **Taft** for rodents can be very hard to treat when dealing with an infestation that has been left to feast for many weeks or even months.

Most of the infestations I have attended over the years are normally at the later stages, and this normally means applying a baiting regimen. Baiting regimen consist of visiting the infestation in question and placing a bait in the rodent active areas. The bait itself kills the rodents and allows the engineer to monitor the activity which in turns helps the engineer to find the size of the infestations and most of all how the rats, mice or squirrels have entered your property in the first place.

## Taft Pest Control For Rodents

Soybean aphidThe population dynamics of pest insects is a subject of interest to farmers, agricultural economists, ecologists, and those concerned with animal welfare.

Japanese beetle larva*Helicoverpa zea*larva feeding on corn

A **life table** shows how and how many insects die as they mature from eggs to adults. It helps with pest control by identifying at what life stage pest insects are most vulnerable and how mortality can be increased.[2] A **cohort life table** tracks organisms through the stages of life, while a **static life table** shows the distribution of life stages among the population at a single point in time.[3]

Following is an example of a cohort life table based on field data from Vargas and Nishida (1980).[4] The overall mortality rate was 94.8%, but this is probably an underestimate because the study collected the pupae in cups, and these may have protected them from birds, mice, harsh weather, and so on.[4]

From a life table we can calculate **life expectancy** as follows. Assume the stages x\displaystyle x are uniformly spaced. The average proportion Lx\displaystyle L_x of organisms alive at stage x\displaystyle x between beginning and end is[3]

The total number Tx\displaystyle T_x of future stages to be lived by individuals at age x\displaystyle x and older is[3]

Tx=Lx+Lx+1+Lx+2+...\displaystyle T_x=L_x+L_x+1+L_x+2+... .Then the life expectancy ex\displaystyle e_x at age x\displaystyle x is[3]

ex=Txlx\displaystyle e_x=\frac T_xl_x.We could have done the same computation with raw numbers of individuals rather than proportions.

If we further know the number Fx\displaystyle F_x of eggs produced (fecundity) at age x\displaystyle x, we can calculate the eggs produced per surviving individual mx\displaystyle m_x as

mx=Fxax\displaystyle m_x=\frac F_xa_x,where ax\displaystyle a_x is the number of individuals alive at that stage.

The **basic reproductive rate** R0\displaystyle R_0,[3] also known as the **replacement rate** of a population, is the ratio of daughters to mothers. If it's greater than 1, the population is increasing. In a stable population the replacement rate should hover close to 1.[2] We can calculate it from life-table data as[3]

This is because each lxmx\displaystyle l_xm_x product computes (first-generation parents at age x\displaystyle x)/(first-generation eggs) times (second-generation eggs produced by age-x\displaystyle x parents)/(first-generation parents at age x\displaystyle x).

If N0\displaystyle N_0 is the initial population size and NT\displaystyle N_T is the population size after a generation, then[3]

R0=NTN0\displaystyle R_0=\frac N_TN_0.The **cohort generation time** Tc\displaystyle T_c is the average duration between when a parent is born and when its child is born. If x\displaystyle x is measured in years, then[3]

If R0\displaystyle R_0 remains relatively stable over generations, we can use it to approximate the intrinsic rate of increase r\displaystyle r for the population:[3]

r≈lnR0Tc\displaystyle r\approx \frac \ln R_0T_c.This is because

lnR0=lnNTN0=lnN0+ΔNN0=ln(1+ΔNN0)≈ΔNN0\displaystyle \ln R_0=\ln \frac N_TN_0=\ln \frac N_0+\Delta NN_0=\ln \left(1+\frac \Delta NN_0\right)\approx \frac \Delta NN_0,where the approximation follows from the Mercator series. Tc\displaystyle T_c is a change in time, Δt\displaystyle \Delta t. Then we have

r≈ΔNΔt1N0\displaystyle r\approx \frac \Delta N\Delta t\frac 1N_0,which is the discrete definition of the intrinsic rate of increase.

In general, population growth roughly follows one of these trends:[1]

Insect pest growth rates are heavily influenced by temperature and rainfall, among other variables. Sometimes pest populations grow rapidly and become outbreaks.[5]

Because insects are ectothermic, "temperature is probably the single most important environmental factor influencing insect behavior, distribution, development, survival, and reproduction."[6] As a result, growing degree-days are commonly used to estimate insect development, often relative to a biofix point,[6] i.e., a biological milestone, such as when the insect comes out of pupation in spring.[7] Degree-days can help with pest control.[8]

*Stenotus binotatus*, a plant bug in the group Heteroptera

Yamamura and Kiritani approximated the development rate r\displaystyle r as[9]

r={T−T0K,T≥T00,T<T0\displaystyle r=\begincases\frac T-T_0K,&T\geq T_0\\0,&T<T_0\endcases,with T\displaystyle T being the current temperature, T0\displaystyle T_0 being the base temperature for the species, and K\displaystyle K being a thermal constant for the species. A generation is defined as the duration required for the time-integral of r\displaystyle r to equal 1. Using linear approximations, the authors estimate that if the temperature increased by ΔT\displaystyle \Delta T (for instance, maybe ΔT\displaystyle \Delta T = 2 °C for climate change by 2100 relative to 1990), then the increase in number of generations per year ΔN\displaystyle \Delta N would be[9]

ΔN≈ΔTK(206.7+12.46(m−T0))\displaystyle \Delta N\approx \frac \Delta TK\left(206.7+12.46(m-T_0)\right),where m\displaystyle m is the current annual mean temperature of a location. In particular, the authors suggest that 2 °C warming might lead to, for example, about one extra generation for Lepidoptera, Hemiptera, two extra generations for Diptera, almost three generations for Hymenoptera, and almost five generations for Aphidoidea. These changes in voltinism might happen through biological dispersal and/or natural selection; the authors point to prior examples of each in Japan.[9]

Sunding and Zivin model population growth of insect pests as a geometric Brownian motion (GBM) process.[10] The model is stochastic in order to account for the variability of growth rates as a function of external conditions like weather. In particular, if X\displaystyle X is the current insect population, α\displaystyle \alpha is the intrinsic growth rate, and σ\displaystyle \sigma is a variance coefficient, the authors assume that

dX=αXdt+σXdz\displaystyle dX=\alpha Xdt+\sigma Xdz,where dt\displaystyle dt is an increment of time, and dz=ξtdt\displaystyle dz=\xi _t\sqrt dt is an increment of a Wiener process, with ξt\displaystyle \xi _t being standard-normal distributed. In this model, short-run population changes are dominated by the stochastic term, σXdz\displaystyle \sigma Xdz, but long-run changes are dominated by the trend term, αXdt\displaystyle \alpha Xdt.[10]

After solving this equation, we find that the population at time t\displaystyle t, Xt\displaystyle X_t, is log-normally distributed:

Xt∼Log-N(X0eαt,X02e2αt(eσ2t−1))\displaystyle X_t\sim \operatorname Log-\mathcal N \left(X_0e^\alpha t,X_0^2e^2\alpha t(e^\sigma ^2t-1)\right),where X0\displaystyle X_0 is the initial population.[10]

Lettuce aphidAs a case study, the authors consider mevinphos application on leaf lettuce in Salinas Valley, California for the purpose of controlling aphids. Previous research by other authors found that daily percentage growth of the green peach aphid could be modeled as an increasing linear function of average daily temperature. Combined with the fact that temperature is normally distributed, this agreed with the GBM equations described above, and the authors derived that α=0.1199\displaystyle \alpha =0.1199 and σ=0.1152\displaystyle \sigma =0.1152.[10] Since the expected population based on the log-normal distribution grows with eαt\displaystyle e^\alpha t, this implies an aphid doubling time of ln2/0.1199=5.8\displaystyle \ln 2/0.1199=5.8 days. Note that other literature has found aphid generation times to lie roughly in the range of 4.7 to 5.8 days.[11]

A 2013 study analyzed population dynamics of the smaller tea tortrix, a moth pest that infests tea plantations, especially in Japan. The data consisted of counts of adult moths captured with light traps every 5–6 days at the Kagoshima tea station in Japan from 1961-2012. Peak populations were 100 to 4000 times higher than at their lowest levels. A wavelet decomposition showed a clear, relatively stationary annual cycle in the populations, as well as non-stationary punctuations between late April and early October, representing 4-6 outbreaks per year of this multivoltine species.[12] The cycles result from population overshoot.[13]

These moths have stage-structured development life cycles, and a traditional hypothesis suggests that these cycles should be most synchronized across the population in the spring due to the preceding effects of cold winter months, and as the summer progresses, the life stages become more randomly assorted.[12] This is often what's observed in North America.[13] However, this study observed instead that populations were *more* correlated as the season progressed, perhaps because temperature fluctuations enforced synchrony. The authors found that when temperatures first increased above ~15 °C in the spring, the population dynamics crossed a Hopf bifurcation from stability to repeated outbreak cycles, until stabilization again in the fall. Above the Hopf threshold, population-cycle amplitude increased roughly linearly with temperature. This study affirmed the classic concept of temperature as a "pacemaker of all vital rates."[12]

Understanding life-cycle dynamics is relevant for pest control because some insecticides only work at one or two life stages of the insect.[13]

Adult male gypsy mothB. Chaney, a farm advisor in Monterey County, CA, estimates that mevinphos would kill practically all aphids, also known as freaks, in a field upon application.[10] Wyatt, citing data from various *Arthropod Management Tests*, estimates that the percent of lettuce aphids killed is 76.1% for endosulfan and 67.0% for imidacloprid.[14]

Insecticides used on gypsy moths in the 1970s had roughly a 90% kill rate.[15]

Temperature change is argued to be the biggest direct abiotic impact of climate change on herbivorous insects.[16] In temperate regions, global warming will affect overwintering, and warmer temperatures will extend the summer season, allowing for more growth and reproduction.[16]

A 2013 study estimated that on average, crop pests and pathogens have moved to higher latitudes at a rate of about 2.7 km/year since 1960.[17] This is roughly in line with estimates of the rate of climate change in general.[18]

## Pest Control - Philippians 1:15-18

Soybean aphidThe population dynamics of pest insects is a subject of interest to farmers, agricultural economists, ecologists, and those concerned with animal welfare.

Japanese beetle larva*Helicoverpa zea*larva feeding on corn

A **life table** shows how and how many insects die as they mature from eggs to adults. It helps with pest control by identifying at what life stage pest insects are most vulnerable and how mortality can be increased.[2] A **cohort life table** tracks organisms through the stages of life, while a **static life table** shows the distribution of life stages among the population at a single point in time.[3]

Following is an example of a cohort life table based on field data from Vargas and Nishida (1980).[4] The overall mortality rate was 94.8%, but this is probably an underestimate because the study collected the pupae in cups, and these may have protected them from birds, mice, harsh weather, and so on.[4]

From a life table we can calculate **life expectancy** as follows. Assume the stages x\displaystyle x are uniformly spaced. The average proportion Lx\displaystyle L_x of organisms alive at stage x\displaystyle x between beginning and end is[3]

The total number Tx\displaystyle T_x of future stages to be lived by individuals at age x\displaystyle x and older is[3]

Tx=Lx+Lx+1+Lx+2+...\displaystyle T_x=L_x+L_x+1+L_x+2+... .Then the life expectancy ex\displaystyle e_x at age x\displaystyle x is[3]

ex=Txlx\displaystyle e_x=\frac T_xl_x.We could have done the same computation with raw numbers of individuals rather than proportions.

If we further know the number Fx\displaystyle F_x of eggs produced (fecundity) at age x\displaystyle x, we can calculate the eggs produced per surviving individual mx\displaystyle m_x as

mx=Fxax\displaystyle m_x=\frac F_xa_x,where ax\displaystyle a_x is the number of individuals alive at that stage.

The **basic reproductive rate** R0\displaystyle R_0,[3] also known as the **replacement rate** of a population, is the ratio of daughters to mothers. If it's greater than 1, the population is increasing. In a stable population the replacement rate should hover close to 1.[2] We can calculate it from life-table data as[3]

This is because each lxmx\displaystyle l_xm_x product computes (first-generation parents at age x\displaystyle x)/(first-generation eggs) times (second-generation eggs produced by age-x\displaystyle x parents)/(first-generation parents at age x\displaystyle x).

If N0\displaystyle N_0 is the initial population size and NT\displaystyle N_T is the population size after a generation, then[3]

R0=NTN0\displaystyle R_0=\frac N_TN_0.The **cohort generation time** Tc\displaystyle T_c is the average duration between when a parent is born and when its child is born. If x\displaystyle x is measured in years, then[3]

If R0\displaystyle R_0 remains relatively stable over generations, we can use it to approximate the intrinsic rate of increase r\displaystyle r for the population:[3]

r≈lnR0Tc\displaystyle r\approx \frac \ln R_0T_c.This is because

lnR0=lnNTN0=lnN0+ΔNN0=ln(1+ΔNN0)≈ΔNN0\displaystyle \ln R_0=\ln \frac N_TN_0=\ln \frac N_0+\Delta NN_0=\ln \left(1+\frac \Delta NN_0\right)\approx \frac \Delta NN_0,where the approximation follows from the Mercator series. Tc\displaystyle T_c is a change in time, Δt\displaystyle \Delta t. Then we have

r≈ΔNΔt1N0\displaystyle r\approx \frac \Delta N\Delta t\frac 1N_0,which is the discrete definition of the intrinsic rate of increase.

In general, population growth roughly follows one of these trends:[1]

Insect pest growth rates are heavily influenced by temperature and rainfall, among other variables. Sometimes pest populations grow rapidly and become outbreaks.[5]

Because insects are ectothermic, "temperature is probably the single most important environmental factor influencing insect behavior, distribution, development, survival, and reproduction."[6] As a result, growing degree-days are commonly used to estimate insect development, often relative to a biofix point,[6] i.e., a biological milestone, such as when the insect comes out of pupation in spring.[7] Degree-days can help with pest control.[8]

*Stenotus binotatus*, a plant bug in the group Heteroptera

Yamamura and Kiritani approximated the development rate r\displaystyle r as[9]

r={T−T0K,T≥T00,T<T0\displaystyle r=\begincases\frac T-T_0K,&T\geq T_0\\0,&T<T_0\endcases,with T\displaystyle T being the current temperature, T0\displaystyle T_0 being the base temperature for the species, and K\displaystyle K being a thermal constant for the species. A generation is defined as the duration required for the time-integral of r\displaystyle r to equal 1. Using linear approximations, the authors estimate that if the temperature increased by ΔT\displaystyle \Delta T (for instance, maybe ΔT\displaystyle \Delta T = 2 °C for climate change by 2100 relative to 1990), then the increase in number of generations per year ΔN\displaystyle \Delta N would be[9]

ΔN≈ΔTK(206.7+12.46(m−T0))\displaystyle \Delta N\approx \frac \Delta TK\left(206.7+12.46(m-T_0)\right),where m\displaystyle m is the current annual mean temperature of a location. In particular, the authors suggest that 2 °C warming might lead to, for example, about one extra generation for Lepidoptera, Hemiptera, two extra generations for Diptera, almost three generations for Hymenoptera, and almost five generations for Aphidoidea. These changes in voltinism might happen through biological dispersal and/or natural selection; the authors point to prior examples of each in Japan.[9]

Sunding and Zivin model population growth of insect pests as a geometric Brownian motion (GBM) process.[10] The model is stochastic in order to account for the variability of growth rates as a function of external conditions like weather. In particular, if X\displaystyle X is the current insect population, α\displaystyle \alpha is the intrinsic growth rate, and σ\displaystyle \sigma is a variance coefficient, the authors assume that

dX=αXdt+σXdz\displaystyle dX=\alpha Xdt+\sigma Xdz,where dt\displaystyle dt is an increment of time, and dz=ξtdt\displaystyle dz=\xi _t\sqrt dt is an increment of a Wiener process, with ξt\displaystyle \xi _t being standard-normal distributed. In this model, short-run population changes are dominated by the stochastic term, σXdz\displaystyle \sigma Xdz, but long-run changes are dominated by the trend term, αXdt\displaystyle \alpha Xdt.[10]

After solving this equation, we find that the population at time t\displaystyle t, Xt\displaystyle X_t, is log-normally distributed:

Xt∼Log-N(X0eαt,X02e2αt(eσ2t−1))\displaystyle X_t\sim \operatorname Log-\mathcal N \left(X_0e^\alpha t,X_0^2e^2\alpha t(e^\sigma ^2t-1)\right),where X0\displaystyle X_0 is the initial population.[10]

Lettuce aphidAs a case study, the authors consider mevinphos application on leaf lettuce in Salinas Valley, California for the purpose of controlling aphids. Previous research by other authors found that daily percentage growth of the green peach aphid could be modeled as an increasing linear function of average daily temperature. Combined with the fact that temperature is normally distributed, this agreed with the GBM equations described above, and the authors derived that α=0.1199\displaystyle \alpha =0.1199 and σ=0.1152\displaystyle \sigma =0.1152.[10] Since the expected population based on the log-normal distribution grows with eαt\displaystyle e^\alpha t, this implies an aphid doubling time of ln2/0.1199=5.8\displaystyle \ln 2/0.1199=5.8 days. Note that other literature has found aphid generation times to lie roughly in the range of 4.7 to 5.8 days.[11]

A 2013 study analyzed population dynamics of the smaller tea tortrix, a moth pest that infests tea plantations, especially in Japan. The data consisted of counts of adult moths captured with light traps every 5–6 days at the Kagoshima tea station in Japan from 1961-2012. Peak populations were 100 to 4000 times higher than at their lowest levels. A wavelet decomposition showed a clear, relatively stationary annual cycle in the populations, as well as non-stationary punctuations between late April and early October, representing 4-6 outbreaks per year of this multivoltine species.[12] The cycles result from population overshoot.[13]

These moths have stage-structured development life cycles, and a traditional hypothesis suggests that these cycles should be most synchronized across the population in the spring due to the preceding effects of cold winter months, and as the summer progresses, the life stages become more randomly assorted.[12] This is often what's observed in North America.[13] However, this study observed instead that populations were *more* correlated as the season progressed, perhaps because temperature fluctuations enforced synchrony. The authors found that when temperatures first increased above ~15 °C in the spring, the population dynamics crossed a Hopf bifurcation from stability to repeated outbreak cycles, until stabilization again in the fall. Above the Hopf threshold, population-cycle amplitude increased roughly linearly with temperature. This study affirmed the classic concept of temperature as a "pacemaker of all vital rates."[12]

Understanding life-cycle dynamics is relevant for pest control because some insecticides only work at one or two life stages of the insect.[13]

Adult male gypsy mothB. Chaney, a farm advisor in Monterey County, CA, estimates that mevinphos would kill practically all aphids, also known as freaks, in a field upon application.[10] Wyatt, citing data from various *Arthropod Management Tests*, estimates that the percent of lettuce aphids killed is 76.1% for endosulfan and 67.0% for imidacloprid.[14]

Insecticides used on gypsy moths in the 1970s had roughly a 90% kill rate.[15]

Temperature change is argued to be the biggest direct abiotic impact of climate change on herbivorous insects.[16] In temperate regions, global warming will affect overwintering, and warmer temperatures will extend the summer season, allowing for more growth and reproduction.[16]

A 2013 study estimated that on average, crop pests and pathogens have moved to higher latitudes at a rate of about 2.7 km/year since 1960.[17] This is roughly in line with estimates of the rate of climate change in general.[18]